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Galaxies - Glittering Lights - Marco Lorenzi
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Spiral Galaxy NGC 300
Spiral Galaxy NGC 300
NGC 300 is so interesting because it is so normal. An Sc-type spiral galaxy in the nearby Sculptor group of galaxies, NGC 300 shows typical flowing blue spiral arms, an expected compact nucleus, and the requisite amount of stars, star clusters, and nebulae. Therefore, studying NGC 300 should indicate how, exactly, a normal spiral galaxy works. NGC 300 lies only 7 million light years away, spans nearly the same amount of sky as the full moon, and is visible with a small telescope toward the constellation of Sculptor (text adapted from APOD).
Apo TEC140 (140/f7.2) - FLI Proline 16803 - Ha (200m) L (440m) R (80m) G (80m) B (80m) - Warrumbungle Observatory, Coonabarabran, NSW, Australia
SpiralGalaxyNGC300
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Review
, 82 (2), 291-5
Oxidative Stress: Oxidants and Antioxidants
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Oxidative Stress: Oxidants and Antioxidants
H Sies. Exp Physiol.
Abstract
An imbalance between oxidants and antioxidants in favour of the oxidants, potentially leading to damage, is termed 'oxidative stress'. Oxidants are formed as a normal product of aerobic metabolism but can be produced at elevated rates under pathophysiological conditions. Antioxidant defense involves several strategies, both enzymatic and non-enzymatic. In the lipid phase, tocopherols and carotenes as well as oxy-carotenoids are of interest, as are vitamin A and ubiquinols. In the aqueous phase, there are ascorbate, glutathione and other compounds. In addition to the cytosol, the nuclear and mitochondrial matrices and extracellular fluids are protected. Overall, these low molecular mass antioxidant molecules add significantly to the defense provided by the enzymes superoxide dismutase, catalase and glutathione peroxidases.
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Prime-Composite number : This section explains you around Prime-Composite numbers.Prime numbers: The numbers whose determinants are 1 and also the number chin is called Prime numbers.Example : 2,3,5,7,11,13,…2 is the smallest even prime number and also 3 is the smallest odd prime number.The element numbers as much as 100 room :2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,73, 79, 83, 89, 97Composite Number : The number which has at least one variable other 보다 1 and the number itself.Example : 4,6,8,9,12,…Note : 1 is no prime no one composite.Co-prime Numbers : 2 numbers that carry out not have actually a usual factor various other than 1.The first 100 composite numbers are4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33,34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58,60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85,86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108,110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,126, 128, 129.Example : 35 and 3935 = 7 x 5 x 139 = 3 x 13 x 1Both 35 and also 39 space composite numbers,the only element common between them is 1.∴ 35 and 39 space co-prime numbers.Some more examples are : 1) 2,3 ; 2) 3,4 3) 5,6 4) 8,13, and also so on.Twin Primes : two prime number are known as twin primes of over there is only one composite number in between them.The pair primes in between 1 come 100 are3-5, 5-7, 11-13, 17-19, 29-31, 41-43, 59-61, 71-73Factors and also Multiples• Prime-Composite numbers• Divisibility rules• element Factorization• H.C.F or G.C.F• L.C.M• applications on LCMPrime and composite numbers to Factors and MultiplesNumber SystemHome Page
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Mathematics LibreTexts
5.2: Vector Fields
• Page ID
119738
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Learning Objectives
• Recognize a vector field in a plane or in space.
• Sketch a vector field from a given equation.
• Identify a conservative field and its associated potential function.
• Explain how to find a potential function for a conservative vector field.
• Explain how to test a vector field to determine whether it is conservative.
Vector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. They are also useful for dealing with large-scale behavior such as atmospheric storms or deep-sea ocean currents. In this section, we examine the basic definitions and graphs of vector fields so we can study them in more detail in the rest of this chapter.
Examples of Vector Fields
How can we model the gravitational force exerted by multiple astronomical objects? How can we model the velocity of water particles on the surface of a river? Figure \(\PageIndex{1}\) gives visual representations of such phenomena.
Two images, labeled A and B. Image A shows the gravitational field exerted by two astronomical bodies on a small object. The earth is on the left, and the moon is on the right. The earth is surrounded by long arrows pointing towards its center arranged in concentric circles. There is a break in the circle on the right, across from the moon. The moon is surrounded by smaller arrows that curve out and to the right. Image B shows the vector velocity field of water on the surface of a river with a large rock in the middle. The arrows tend to point at the same angle as the riverbank. Where the river meets the rock, the arrows point around the rock. After the rock, the some arrows point forward, and others turn back to the rock. The water flows fastest towards the middle of the river and around the rock and slowest along the riverbank.
Figure \(\PageIndex{1}\) (a) The gravitational field exerted by two astronomical bodies on a small object. (b) The vector velocity field of water on the surface of a river shows the varied speeds of water. Red indicates that the magnitude of the vector is greater, so the water flows more quickly; blue indicates a lesser magnitude and a slower speed of water flow.
Figure \(\PageIndex{1a}\) shows a gravitational field exerted by two astronomical objects, such as a star and a planet or a planet and a moon. At any point in the figure, the vector associated with a point gives the net gravitational force exerted by the two objects on an object of unit mass. The vectors of largest magnitude in the figure are the vectors closest to the larger object. The larger object has greater mass, so it exerts a gravitational force of greater magnitude than the smaller object.
Figure \(\PageIndex{1b}\) shows the velocity of a river at points on its surface. The vector associated with a given point on the river’s surface gives the velocity of the water at that point. Since the vectors to the left of the figure are small in magnitude, the water is flowing slowly on that part of the surface. As the water moves from left to right, it encounters some rapids around a rock. The speed of the water increases, and a whirlpool occurs in part of the rapids.
Each figure illustrates an example of a vector field. Intuitively, a vector field is a map of vectors. In this section, we study vector fields in \(ℝ^2\) and \(ℝ^3\).
DEFINITION: vector field
• A vector field \(\vecs{F}\) in \(ℝ^2\) is an assignment of a two-dimensional vector \(\vecs{F}(x,y)\) to each point \((x,y)\) of a subset \(D\) of \(ℝ^2\). The subset \(D\) is the domain of the vector field.
• A vector field \(\vecs{F}\) in \(ℝ^3\) is an assignment of a three-dimensional vector \(\vecs{F}(x,y,z)\) to each point \((x,y,z)\) of a subset \(D\) of \(ℝ^3\). The subset \(D\) is the domain of the vector field.
Vector Fields in \(ℝ^2\)
A vector field in \(ℝ^2\) can be represented in either of two equivalent ways. The first way is to use a vector with components that are two-variable functions:
\[\vecs{F}(x,y)=⟨P(x,y),Q(x,y)⟩\]
The second way is to use the standard unit vectors:
\[\vecs{F}(x,y)=P(x,y) \,\hat{\mathbf i}+Q(x,y) \,\hat{\mathbf j}.\]
A vector field is said to be continuous if its component functions are continuous.
Example \(\PageIndex{1}\): Finding a Vector Associated with a Given Point
Let \(\vecs{F} (x,y)=(2y^2+x−4)\,\hat{\mathbf i}+\cos(x)\,\hat{\mathbf j}\) be a vector field in \(ℝ^2\). Note that this is an example of a continuous vector field since both component functions are continuous. What vector is associated with point \((0,−1)\)?
Solution
Substitute the point values for \(x\) and \(y\):
\[\begin{align*} \vecs{F} (0,-1) &=(2{(−1)}^2+0−4) \,\hat{\mathbf i}+\cos(0) \,\hat{\mathbf j} \\[4pt] &=−2 \,\hat{\mathbf i} + \hat{\mathbf j}. \end{align*}\]
Exercise \(\PageIndex{1}\)
Let \(\vecs{G}(x,y)=x^2y\,\hat{\mathbf i}−(x+y)\,\hat{\mathbf j}\) be a vector field in \(ℝ^2\). What vector is associated with the point \((−2,3)\)?
Hint
Substitute the point values into the vector function.
Answer
\(\vecs{G}(−2,3)=12\hat{\mathbf i}−\hat{\mathbf j}\)
Drawing a Vector Field
We can now represent a vector field in terms of its components of functions or unit vectors, but representing it visually by sketching it is more complex because the domain of a vector field is in \(ℝ^2\), as is the range. Therefore the “graph” of a vector field in \(ℝ^2\) lives in four-dimensional space. Since we cannot represent four-dimensional space visually, we instead draw vector fields in \(ℝ^2\) in a plane itself. To do this, draw the vector associated with a given point at the point in a plane. For example, suppose the vector associated with point \((4,−1)\) is \(⟨3,1⟩\). Then, we would draw vector \(⟨3,1⟩\) at point \((4,−1)\).
We should plot enough vectors to see the general shape, but not so many that the sketch becomes a jumbled mess. If we were to plot the image vector at each point in the region, it would fill the region completely and is useless. Instead, we can choose points at the intersections of grid lines and plot a sample of several vectors from each quadrant of a rectangular coordinate system in \(ℝ^2\).
There are two types of vector fields in \(ℝ^2\) on which this chapter focuses: radial fields and rotational fields. Radial fields model certain gravitational fields and energy source fields, and rotational fields model the movement of a fluid in a vortex. In a radial field, all vectors either point directly toward or directly away from the origin. Furthermore, the magnitude of any vector depends only on its distance from the origin. In a radial field, the vector located at point \((x,y)\) is perpendicular to the circle centered at the origin that contains point \((x,y)\), and all other vectors on this circle have the same magnitude.
Example \(\PageIndex{2}\): Drawing a Radial Vector Field
Sketch the vector field \(\vecs{F} (x,y)=\dfrac{x}{2}\hat{\mathbf i}+\dfrac{y}{2}\hat{\mathbf j}\).
Solution
To sketch this vector field, choose a sample of points from each quadrant and compute the corresponding vector. The following table gives a representative sample of points in a plane and the corresponding vectors.
Table \(\PageIndex{1}\)
\((x,y)\) \(\vecs{F}(x,y)\) \((x,y)\) \(\vecs{F}(x,y)\) \((x,y)\) \(\vecs{F}(x,y)\)
\((1,0)\) \(⟨\dfrac{1}{2},0⟩\) \((2,0)\) \(⟨1,0⟩\) \((1,1)\) \(⟨\dfrac{1}{2},\dfrac{1}{2}⟩\)
\((0,1)\) \(⟨0,\dfrac{1}{2}⟩\) \((0,2)\) \(⟨0,1⟩\) \((−1,1)\) \(⟨−\dfrac{1}{2},\dfrac{1}{2}⟩\)
\((−1,0)\) \(⟨−\dfrac{1}{2},0⟩\) \((−2,0)\) \(⟨−1,0⟩\) \((−1,−1)\) \(⟨−\dfrac{1}{2},−\dfrac{1}{2}⟩\)
\((0,−1)\) \(⟨0,−\dfrac{1}{2}⟩\) \((0,−2)\) \(⟨0,−1⟩\) \((1,−1)\) \(⟨\dfrac{1}{2},−\dfrac{1}{2}⟩\)
Figure \(\PageIndex{2a}\) shows the vector field. To see that each vector is perpendicular to the corresponding circle, Figure \(\PageIndex{2b}\) shows circles overlain on the vector field.
A visual representation of the given vector field in a coordinate plane with two additional diagrams with notation. The first representation shows the vector field. The arrows are circling the origin in a clockwise motion. The second representation shows concentric circles, highlighting the radial pattern. The The third representation shows the concentric circles. It also shows arrows for the radial vector <a,b> for all points (a,b). Each is perpendicular to the arrows in the given vector field.
Figure \(\PageIndex{2}\): (a) A visual representation of the radial vector field \(\vecs{F}(x,y)=\dfrac{x}{2}\hat{\mathbf i}+\dfrac{y}{2} \hat{\mathbf j}\). (b) The radial vector field \(\vec{F}(x,y)=\dfrac{x}{2}\hat{\mathbf i}+\dfrac{y}{2} \hat{\mathbf j}\) with overlaid circles. Notice that each vector is perpendicular to the circle on which it is located.
Exercise \(\PageIndex{2}\)
Draw the radial field \(\vecs{F} (x,y)=−\dfrac{x}{3}\hat{\mathbf i}−\dfrac{y}{3}\hat{\mathbf j}\).
Hint
Sketch enough vectors to get an idea of the shape.
Answer
A visual representation of the given radial field in a coordinate plane. The magnitudes increase further from the origin. The arrow seem to be stretching away from the origin in a rectangular shape.
In contrast to radial fields, in a rotational field, the vector at point \((x,y)\) is tangent (not perpendicular) to a circle with radius \(r=\sqrt{x^2+y^2}\). In a standard rotational field, all vectors point either in a clockwise direction or in a counterclockwise direction, and the magnitude of a vector depends only on its distance from the origin. Both of the following examples are clockwise rotational fields, and we see from their visual representations that the vectors appear to rotate around the origin.
Example \(\PageIndex{3}\): Drawing a Rotational Vector Field
Sketch the vector field \(\vecs{F} (x,y)=⟨y,\,−x⟩\).
Solution
Create a table (see the one that follows) using a representative sample of points in a plane and their corresponding vectors. Figure \(\PageIndex{3}\) shows the resulting vector field.
Table \(\PageIndex{2}\)
\((x,y)\) \(\vecs{F}(x,y)\) \((x,y)\) \(\vecs{F}(x,y)\) \((x,y)\) \(\vecs{F}(x,y)\)
\((1,0)\) \(⟨0,−1⟩\) \((2,0)\) \(⟨0,−2⟩\) \((1,1)\) \(⟨1,−1⟩\)
\((0,1)\) \(⟨1,0⟩\) \((0,2)\) \(⟨2,0⟩\) \((−1,1)\) \(⟨1,1⟩\)
\((−1,0)\) \(⟨0,1⟩\) \((−2,0)\) \(⟨0,2⟩\) \((−1,−1)\) \(⟨−1,1⟩\)
\((0,−1)\) \(⟨−1,0⟩\) \((0,−2)\) \(⟨−2,0⟩\) \((1,−1)\) \(⟨−1,−1⟩\)
clipboard_eefd79a8783ad793483370902770aaa4f.png
Figure \(\PageIndex{3}\): (a) A visual representation of vector field \(\vecs{F}(x,y)=⟨y,−x⟩\). (b) Vector field \(\vecs{F}(x,y)=⟨y,−x⟩\) with circles centered at the origin. (c) Vector \(\vecs{F}(a,b)\) is perpendicular to radial vector \(⟨a,b⟩\) at point \((a,b)\).
Analysis
Note that vector \(\vecs{F}(a,b)=⟨b,−a⟩\) points clockwise and is perpendicular to radial vector \(⟨a,b⟩\). (We can verify this assertion by computing the dot product of the two vectors: \(⟨a,b⟩·⟨−b,a⟩=−ab+ab=0\).) Furthermore, vector \(⟨b,−a⟩\) has length \(r=\sqrt{a^2+b^2}\). Thus, we have a complete description of this rotational vector field: the vector associated with point \((a,b)\) is the vector with length r tangent to the circle with radius r, and it points in the clockwise direction.
Sketches such as that in Figure \(\PageIndex{3}\) are often used to analyze major storm systems, including hurricanes and cyclones. In the northern hemisphere, storms rotate counterclockwise; in the southern hemisphere, storms rotate clockwise. (This is an effect caused by Earth’s rotation about its axis and is called the Coriolis Effect.)
A photgraph of a hurricane, showing the rotation around its eye.
Figure \(\PageIndex{4}\): (credit: modification of work by NASA)
Example \(\PageIndex{4}\): Sketching a Vector Field
Sketch vector field \(\vecs{F}(x,y)=\dfrac{y}{x^2+y^2}\hat{\mathbf i}, -\dfrac{x}{x^2+y^2}\hat{\mathbf j}\).
Solution
To visualize this vector field, first note that the dot product \(\vecs{F}(a,b)·(a \,\hat{\mathbf i}+b \,\hat{\mathbf j})\) is zero for any point \((a,b)\). Therefore, each vector is tangent to the circle on which it is located. Also, as \((a,b)\rightarrow(0,0)\), the magnitude of \(\vecs{F}(a,b)\) goes to infinity. To see this, note that
\(||\vecs{F}(a,b)||=\sqrt{\dfrac{a^2+b^2}{ {(a^2+b^2)}^2 }} =\sqrt{\dfrac{1}{a^2+b^2}}\).
Since \(\dfrac{1}{a^2+b^2}\rightarrow \infty\) as \((a,b)\rightarrow (0,0)\), then \(||\vecs F(a,b)||\rightarrow \infty\) as \((a,b)\rightarrow (0,0)\). This vector field looks similar to the vector field in Example \(\PageIndex{3}\), but in this case the magnitudes of the vectors close to the origin are large. Table \(\PageIndex{3}\) shows a sample of points and the corresponding vectors, and Figure \(\PageIndex{5}\) shows the vector field. Note that this vector field models the whirlpool motion of the river in Figure \(\PageIndex{5}\)(b). The domain of this vector field is all of \(ℝ^2\) except for point \((0,0)\).
Table \(\PageIndex{3}\)
\((x,y)\) \(\vecs{F}(x,y)\) \((x,y)\) \(\vecs{F}(x,y)\) \((x,y)\) \(\vecs{F}(x,y)\)
\((1,0)\) \(⟨0,−1⟩\) \((2,0)\) \(⟨0,−\dfrac{1}{2}⟩\) \((1,1)\) \(⟨\dfrac{1}{2},−\dfrac{1}{2}⟩\)
\((0,1)\) \(⟨1,0⟩\) \((0,2)\) \(⟨\dfrac{1}{2},0⟩\) \((−1,1)\) \(⟨\dfrac{1}{2},\dfrac{1}{2}⟩\)
\((−1,0)\) \(⟨0,1⟩\) \((−2,0)\) \(⟨0,\dfrac{1}{2}⟩\) \((−1,−1)\) \(⟨−\dfrac{1}{2},\dfrac{1}{2}⟩\)
\((0,−1)\) \(⟨−1,0⟩\) \((0,−2)\) \(⟨−\dfrac{1}{2},0⟩\) \((1,−1)\) \(⟨−\dfrac{1}{2},−\dfrac{1}{2}⟩\)
A visual representation of the given vector field in a coordinate plane. The magnitude is larger closer to the origin. The arrows are rotating the origin clockwise. It could be use to model whirlpool motion of a fluid.
Figure \(\PageIndex{5}\): A visual representation of vector field \(\vecs{F}(x,y)=\dfrac{y}{x^2+y^2}\hat{\mathbf i}−\dfrac{x}{x^2+y^2}\hat{\mathbf j}\). This vector field could be used to model whirlpool motion of a fluid.
Exercise \(\PageIndex{4}\)
Sketch vector field \(\vecs{F}(x,y)=⟨−2y,\,2x⟩\). Is the vector field radial, rotational, or neither?
Hint
Substitute enough points into \(\vecs{F}\) to get an idea of the shape.
Answer
Rotational
A visual representation of a rotational vector field in a coordinate plane. The arrows circle the origin in a counterclockwise manner.
Example \(\PageIndex{5}\): Velocity Field of a Fluid
Suppose that \(\vecs{v} (x,y)=−\dfrac{2y}{x^2+y^2}\hat{\mathbf i}+\dfrac{2x}{x^2+y^2}\hat{\mathbf j}\) is the velocity field of a fluid. How fast is the fluid moving at point \((1,−1)\)? (Assume the units of speed are meters per second.)
Solution
To find the velocity of the fluid at point \((1,−1)\), substitute the point into \(\vecs{v} \):
\(\vecs{v}(1,−1)=\dfrac{−2(−1)}{1+1}\hat{\mathbf i}+\dfrac{2(1)}{1+1}\hat{\mathbf j}=\hat{\mathbf i}+\hat{\mathbf j}\).
The speed of the fluid at \((1,−1)\) is the magnitude of this vector. Therefore, the speed is \(||\hat{\mathbf i}+\hat{\mathbf j}||=\sqrt{2}\) m/sec.
Exercise \(\PageIndex{5}\)
Vector field \(\vecs{v} (x,y)=⟨4|x|,\,1⟩\) models the velocity of water on the surface of a river. What is the speed of the water at point \((2,3)\)? Use meters per second as the units.
Hint
Remember, speed is the magnitude of velocity.
Answer
\(\sqrt{65}\) m/sec
We have examined vector fields that contain vectors of various magnitudes, but just as we have unit vectors, we can also have a unit vector field. A vector field \(\vecs{F}\) is a unit vector field if the magnitude of each vector in the field is 1. In a unit vector field, the only relevant information is the direction of each vector.
Example \(\PageIndex{6}\): A Unit Vector Field
Show that vector field \(\vecs{F} (x,y)=\left\langle\dfrac{y}{\sqrt{x^2+y^2}},−\dfrac{x}{\sqrt{x^2+y^2}}\right\rangle\) is a unit vector field.
Solution
To show that \(\vecs{F}\) is a unit field, we must show that the magnitude of each vector is \(1\). Note that
\[\begin{align*} \sqrt{ \left(\dfrac{y}{\sqrt{x^2+y^2}}\right)^2+\left(−\dfrac{x}{\sqrt{x^2+y^2}}\right)^2} &=\sqrt{ \dfrac{y^2}{x^2+y^2}+\dfrac{x^2}{x^2+y^2}} \\[4pt] &=\sqrt{\dfrac{x^2+y^2}{x^2+y^2}} \\[4pt] &=1 \end{align*}\]
Therefore, \(\vecs{F} \) is a unit vector field.
Exercise \(\PageIndex{6}\)
Is vector field \(\vecs{F} (x,y)=⟨−y,\,x⟩\) a unit vector field?
Hint
Calculate the magnitude of \(\vecs{F} \) at an arbitrary point \((x,y)\).
Answer
No.
Why are unit vector fields important? Suppose we are studying the flow of a fluid, and we care only about the direction in which the fluid is flowing at a given point. In this case, the speed of the fluid (which is the magnitude of the corresponding velocity vector) is irrelevant, because all we care about is the direction of each vector. Therefore, the unit vector field associated with velocity is the field we would study.
If \(\vecs{F} =⟨P,Q,R⟩\) is a vector field, then the corresponding unit vector field is \(\big\langle\tfrac{P}{||\vecs F||},\tfrac{Q}{||\vecs F||},\tfrac{R}{||\vecs F||}\big\rangle\). Notice that if \(\vecs{F}(x,y)=⟨y,\,−x⟩\) is the vector field from Example \(\PageIndex{6}\), then the magnitude of \(\vecs{F} \) is \(\sqrt{x^2+y^2}\), and therefore the corresponding unit vector field is the field \(\vecs{G} \) from the previous example.
If \(\vecs{F} \) is a vector field, then the process of dividing \(\vecs{F} \) by its magnitude to form unit vector field \(\vecs{F}/||\vecs{F}||\) is called normalizing the field \(\vecs{F} \).
Vector Fields in \(ℝ^3\)
We have seen several examples of vector fields in \(ℝ^2\); let’s now turn our attention to vector fields in \(ℝ^3\). These vector fields can be used to model gravitational or electromagnetic fields, and they can also be used to model fluid flow or heat flow in three dimensions. A two-dimensional vector field can really only model the movement of water on a two-dimensional slice of a river (such as the river’s surface). Since a river flows through three spatial dimensions, to model the flow of the entire depth of the river, we need a vector field in three dimensions.
The extra dimension of a three-dimensional field can make vector fields in \(ℝ^3\) more difficult to visualize, but the idea is the same. To visualize a vector field in \(ℝ^3\), plot enough vectors to show the overall shape. We can use a similar method to visualizing a vector field in \(ℝ^2\) by choosing points in each octant.
Just as with vector fields in \(ℝ^2\), we can represent vector fields in \(ℝ^3\) with component functions. We simply need an extra component function for the extra dimension. We write either
\[\vecs{F}(x,y,z)=⟨P(x,y,z),Q(x,y,z),R(x,y,z)⟩\]
or
\[\vecs{F}(x,y,z)=P(x,y,z)\hat{\mathbf i}+Q(x,y,z)\hat{\mathbf j}+R(x,y,z)\hat{\mathbf k}.\]
Example \(\PageIndex{7}\): Sketching a Vector Field in Three Dimensions
Describe vector field \(\vecs{F}(x,y,z)=⟨1,\,1,\,z⟩\).
Solution
For this vector field, the \(x\)- and \(y\)-components are constant, so every point in \(ℝ^3\) has an associated vector with \(x\)- and \(y\)-components equal to one. To visualize \(\vecs{F}\), we first consider what the field looks like in the \(xy\)-plane. In the \(xy\)-plane, \(z=0\). Hence, each point of the form \((a,b,0)\) has vector \(⟨1,1,0⟩\) associated with it. For points not in the \(xy\)-plane but slightly above it, the associated vector has a small but positive \(z\)-component, and therefore the associated vector points slightly upward. For points that are far above the \(xy\)-plane, the \(z\)-component is large, so the vector is almost vertical. Figure \(\PageIndex{6}\) shows this vector field.
Figure \(\PageIndex{6}\): A visual representation of vector field \(\vecs{F}(x,y,z)=⟨1,1,z⟩\).
Exercise \(\PageIndex{7}\)
Sketch vector field \(\vecs{G}(x,y,z)=⟨2,\,\dfrac{z}{2},\,1⟩\).
Hint
Substitute enough points into the vector field to get an idea of the general shape.
Answer
In the next example, we explore one of the classic cases of a three-dimensional vector field: a gravitational field.
Example \(\PageIndex{8}\): Describing a Gravitational Vector Field
Newton’s law of gravitation states that \(\vecs{F}=−G\dfrac{m_1m_2}{r^2}\hat{\mathbf r}\), where G is the universal gravitational constant. It describes the gravitational field exerted by an object (object 1) of mass \(m_1\) located at the origin on another object (object 2) of mass \(m_2\) located at point \((x,y,z)\). Field \(\vecs{F}\) denotes the gravitational force that object 1 exerts on object 2, \(r\) is the distance between the two objects, and \(\hat{\mathbf r}\) indicates the unit vector from the first object to the second. The minus sign shows that the gravitational force attracts toward the origin; that is, the force of object 1 is attractive. Sketch the vector field associated with this equation.
Solution
Since object 1 is located at the origin, the distance between the objects is given by \(r=\sqrt{x^2+y^2+z^2}\). The unit vector from object 1 to object 2 is \(\hat{\mathbf r}=\dfrac{⟨x,y,z⟩}{||⟨x,y,z⟩||}\), and hence \(\hat{\mathbf r}=\big\langle\dfrac{x}{r},\dfrac{y}{r},\dfrac{z}{r}\big\rangle\). Therefore, gravitational vector field \(\vecs{F}\) exerted by object 1 on object 2 is
\[ \vecs{F}=−Gm_1m_2\big\langle\dfrac{x}{r^3},\dfrac{y}{r^3},\dfrac{z}{r^3}\big\rangle. \nonumber\]
This is an example of a radial vector field in \(ℝ^3\).
Figure \(\PageIndex{7}\) shows what this gravitational field looks like for a large mass at the origin. Note that the magnitudes of the vectors increase as the vectors get closer to the origin.
A visual representation of the given gravitational vector field in three dimensions. The magnitudes of the vectors increase as the vectors get closer to the origin. The arrows point in, towards the mass at the origin.
Figure \(\PageIndex{7}\): A visual representation of gravitational vector field \(\vecs{F}=−Gm_1m_2⟨\dfrac{x}{r^3},\dfrac{y}{r^3},\dfrac{z}{r^3}⟩\) for a large mass at the origin.
Exercise \(\PageIndex{8}\)
The mass of asteroid 1 is 750,000 kg and the mass of asteroid 2 is 130,000 kg. Assume asteroid 1 is located at the origin, and asteroid 2 is located at \((15,−5,10)\), measured in units of 10 to the eighth power kilometers. Given that the universal gravitational constant is \(G=6.67384×10^{−11}m^3{kg}^{−1}s^{−2}\), find the gravitational force vector that asteroid 1 exerts on asteroid 2.
Hint
Follow Example \(\PageIndex{8}\) and first compute the distance between the asteroids.
Answer
\(1.49063×{10}^{−18}\), \(4.96876×{10}^{−19}\), \(9.93752×{10}^{−19}\) N
Gradient Fields (Conservative Fields)
In this section, we study a special kind of vector field called a gradient field or a conservative field. These vector fields are extremely important in physics because they can be used to model physical systems in which energy is conserved. Gravitational fields and electric fields associated with a static charge are examples of gradient fields.
Recall that if \(f\) is a (scalar) function of \(x\) and \(y\), then the gradient of \(f\) is
\[ \text{grad}\, f =\vecs \nabla f(x,y) =f_x(x,y) \hat{\mathbf i} +f_y(x,y) \hat{\mathbf j}. \]
We can see from the form in which the gradient is written that \(\vecs \nabla f\) is a vector field in \(ℝ^2\). Similarly, if \(f\) is a function of \(x\), \(y\), and \(z\), then the gradient of \(f\) is
\[ \text{grad}\, f =\vecs \nabla f(x,y,z) = f_x(x,y,z) \hat{\mathbf i}+f_y(x,y,z) \hat{\mathbf j}+f_z(x,y,z)\hat{\mathbf k}. \]
The gradient of a three-variable function is a vector field in \(ℝ^3\). A gradient field is a vector field that can be written as the gradient of a function, and we have the following definition.
DEFINITION: Gradient Field
A vector field \(\vecs{F}\) in \(ℝ^2\) or in \(ℝ^3\) is a gradient field if there exists a scalar function \(f\) such that \(\vecs \nabla f=\vecs{F}\).
Example \(\PageIndex{9}\): Sketching a Gradient Vector Field
Use technology to plot the gradient vector field of \(f(x,y)=x^2y^2\).
Solution
The gradient of \(f\) is \(\vecs \nabla f(x,y)=⟨2xy^2,\,2x^2y⟩\). To sketch the vector field, use a computer algebra system such as Mathematica. Figure \(\PageIndex{8}\) shows \(\vecs \nabla f\).
A visual representation of the given gradient vector field in two dimensions. The arrows point up above the x axis and down below the x axis, and they point left on the left side of the y axis and to the right on the right side of the y axis. The further the arrows are from zero, the more vertical they are, and the closer the arrows are to zero, the more horizontal they are.
Figure \(\PageIndex{8}\): The gradient vector field is \(\vecs \nabla f\), where \(f(x,y)=x^2y^2\).
Exercise \(\PageIndex{9}\)
Use technology to plot the gradient vector field of \(f(x,y)=\sin x\cos y\).
Hint
Find the gradient of \(f\).
Answer
A visual representation of the given given vector in two dimensions. The arrows seem to be forming several ovals. The first is around the origin, where the arrows curve to the right above and below the x axis. The closer the arrows are to the x axis, the flatter they are. There appear to be six other ovals, three on either side of the central one. The vectors get longer as they get farther from the origin, and then they start to get shorter again.
Consider the function \(f(x,y)=x^2y^2\) from Example \(\PageIndex{9}\). Figure \(\PageIndex{9}\) shows the level curves of this function overlaid on the function’s gradient vector field. The gradient vectors are perpendicular to the level curves, and the magnitudes of the vectors get larger as the level curves get closer together, because closely grouped level curves indicate the graph is steep, and the magnitude of the gradient vector is the largest value of the directional derivative. Therefore, you can see the local steepness of a graph by investigating the corresponding function’s gradient field.
A visual representation of the given gradient field. The arrows are flatter the closer they are to the x axis and more vertical the further they are from the x axis. The arrows point left to the left of the y axis, and they point to the right to the right of the y axis. They point up above the x axis and down below the x axis. Severl level curves are drawn, each asymptotically approaching the axes. As the level curves get closer together, the magnitude of the gradient vactors increases.
Figure \(\PageIndex{9}\): The gradient field of \(f(x,y)=x^2y^2\) and several level curves of \(f\). Notice that as the level curves get closer together, the magnitude of the gradient vectors increases.
As we learned earlier, a vector field \(\vecs{F}\) is a conservative vector field, or a gradient field if there exists a scalar function \(f\) such that \(\vecs \nabla f=\vecs{F}\). In this situation, \(f\) is called a potential function for \(\vecs{F}\). Conservative vector fields arise in many applications, particularly in physics. The reason such fields are called conservative is that they model forces of physical systems in which energy is conserved. We study conservative vector fields in more detail later in this chapter.
You might notice that, in some applications, a potential function \(f\) for \(\vecs{F}\) is defined instead as a function such that \(−\vecs \nabla f=\vecs{F}\). This is the case for certain contexts in physics, for example.
Example \(\PageIndex{10}\): Verifying a Potential Function
Is \(f(x,y,z)=x^2yz−\sin(xy)\) a potential function for vector field
\(\vecs{F}(x,y,z)=⟨2xyz−y\cos(xy),x^2z−x\cos(xy),x^2y⟩\)?
Solution
We need to confirm whether \(\vecs \nabla f=\vecs{F}\). We have
\[ \begin{align*} f_x(x,y) =2xyz−y\cos(xy) \\[4pt] f_y(x,y) =x^2z−x\cos(xy) \\[4pt] f_z(x,y) =x^2y \end{align*}.\]
Therefore, \(\vecs \nabla f=\vecs{F}\) and \(f\) is a potential function for \(\vecs{F}\).
Exercise \(\PageIndex{10}\)
Is \(f(x,y,z)=x^2\cos(yz)+y^2z^2\) a potential function for \(\vecs{F}(x,y,z)=⟨2x\cos(yz),−x^2z \sin(yz)+2yz^2,y^2⟩\)?
Hint
Compute the gradient of \(f\).
Answer
No
Example \(\PageIndex{11}\): Verifying a Potential Function
The velocity of a fluid is modeled by field \(\vecs v(x,y)=⟨xy,\tfrac{x^2}{2}−y⟩\). Verify that \(f(x,y)=\dfrac{x^2y}{2}−\dfrac{y^2}{2}\) is a potential function for \(\vecs{v}\).
Solution
To show that \(f\) is a potential function, we must show that \(\vecs \nabla f=\vecs v\). Note that \(f_x(x,y)=xy\) and \(f_y(x,y)=\dfrac{x^2}{2}−y\). Therefore, \(\vecs \nabla f(x,y)=⟨xy,\tfrac{x^2}{2}−y⟩\) and \(f\) is a potential function for \(\vecs{v}\) (Figure \(\PageIndex{10}\)).
A visual representation of the given directional field in two dimensions. The arrows in quadrant 1point to the right. Closer to the y axis, they point down, but they quickly cuve and soon point up at at roughly 90-degree angle. The closer the arrows are to the x axis, the more vertical they are. Quadrant 2 is a reflection of quadrant 1. In quadrant 3, the arrows are more vertical the closer they are to the x and y axes. They point up and to the right. The further they are from the axes, the closer the arrows are to a 90-degree angle. Quadrant 4 is a reflection of quadrant 3.
Figure \(\PageIndex{10}\): Velocity field \(\vecs{v}(x,y)\) has a potential function and is a conservative field.
Exercise \(\PageIndex{11}\)
Verify that \(f(x,y)=x^2y^2+x\) is a potential function for velocity field \(\vecs{v}(x,y)=⟨3x^2y^2+1,2x^3y⟩\).
Hint
Calculate the gradient.
Answer
\(\vecs \nabla f(x,y)=\vecs{v}(x,y)\)
If \(\vecs{F}\) is a conservative vector field, then there is at least one potential function \(f\) such that \(\vecs \nabla f=\vecs{F}\). But, could there be more than one potential function? If so, is there any relationship between two potential functions for the same vector field? Before answering these questions, let’s recall some facts from single-variable calculus to guide our intuition. Recall that if \(k(x)\) is an integrable function, then \(k\) has infinitely many antiderivatives. Furthermore, if \(\vecs{F}\) and \(\vecs{G}\) are both antiderivatives of \(k\), then \(\vecs{F}\) and \(\vecs{G}\) differ only by a constant. That is, there is some number \(C\) such that \(\vecs{F}(x)=\vecs{G}(x)+C\).
Now let \(\vecs{F}\) be a conservative vector field and let \(f\) and \(g\) be potential functions for \(\vecs{F}\). Since the gradient is like a derivative, \(\vecs{F}\) being conservative means that \(\vecs{F}\) is “integrable” with “antiderivatives” \(f\) and \(g\). Therefore, if the analogy with single-variable calculus is valid, we expect there is some constant \(C\) such that \(f(x)=g(x)+C\). The next theorem says that this is indeed the case.
To state the next theorem with precision, we need to assume the domain of the vector field is connected and open. To be connected means if \(P_1\) and \(P_2\) are any two points in the domain, then you can walk from \(P_1\) to \(P_2\) along a path that stays entirely inside the domain.
UNIQUENESS OF POTENTIAL FUNCTIONS
Let \(\vecs{F}\) be a conservative vector field on an open and connected domain and let \(f\) and \(g\) be functions such that \(\vecs \nabla f=\vecs{F}\) and \(\vecs \nabla g=\vecs{F}\). Then, there is a constant \(C\) such that \(f=g+C\).
Proof
Since \(f\) and \(g\) are both potential functions for \(\vecs{F}\), then \(\vecs \nabla (f−g)=\vecs \nabla f−\vecs \nabla g=\vecs{F}−\vecs{F}=\vecs 0\). Let \(h=f−g\), then we have \(\vecs \nabla h=\vecs 0\).We would like to show that \(h\) is a constant function.
Assume \(h\) is a function of \(x\) and \(y\) (the logic of this proof extends to any number of independent variables). Since \(\vecs \nabla h=\vecs 0\), we have \(h_x(x,y)=0\) and \(h_y(x,y)=0\). The expression \(h_x(x,y)=0\) implies that \(h\) is a constant function with respect to \(x\)—that is, \(h(x,y)=k_1(y)\) for some function \(k_1\). Similarly, \(h_y(x,y)=0\) implies \(h(x,y)=k_2(x)\) for some function \(k_2\). Therefore, function \(h\) depends only on \(y\) and also depends only on \(x\). Thus, \(h(x,y)=C\) for some constant \(C\) on the connected domain of \(\vecs{F}\). Note that we really do need connectedness at this point; if the domain of \(\vecs{F}\) came in two separate pieces, then \(k\) could be a constant \(C_1\) on one piece but could be a different constant \(C_2\) on the other piece. Since \(f−g=h=C\), we have that \(f=g+C\), as desired.
\(\square\)
Conservative Vector Fields and Potential Functions
As we have learned, the Fundamental Theorem for Line Integrals says that if \(\vecs{F}\) is conservative, then calculating \(\int_C \vecs F·d\vecs r\) has two steps: first, find a potential function \(f\) for \(\vecs{F}\) and, second, calculate \(f(P_1)−f(P_0)\), where \(P_1\) is the endpoint of \(C\) and \(P_0\) is the starting point. To use this theorem for a conservative field \(\vecs{F}\), we must be able to find a potential function \(f\) for \(\vecs{F}\). Therefore, we must answer the following question: Given a conservative vector field \(\vecs{F}\), how do we find a function \(f\) such that \(\vecs \nabla f=\vecs{F}\)? Before giving a general method for finding a potential function, let’s motivate the method with an example.
Example \(\PageIndex{5}\): Finding a Potential Function
Find a potential function for \(\vecs F(x,y)=⟨2xy^3,3x^2y^2+\cos(y)⟩\), thereby showing that \(\vecs{F}\) is conservative.
Solution
Suppose that \(f(x,y)\) is a potential function for \(\vecs{F}\). Then, \(\vecs \nabla f=\vecs F\), and therefore
\[f_x(x,y)=2xy^3 \; \; \text{and} \;\; f_y(x,y)=3x^2y^2+\cos y. \nonumber\]
Integrating the equation \(f_x(x,y)=2xy^3\) with respect to \(x\) yields the equation
\[f(x,y)=x^2y^3+h(y). \nonumber\]
Notice that since we are integrating a two-variable function with respect to \(x\), we must add a constant of integration that is a constant with respect to \(x\), but may still be a function of \(y\). The equation \(f(x,y)=x^2y^3+h(y)\) can be confirmed by taking the partial derivative with respect to \(x\):
\[\dfrac{∂f}{∂x}=\dfrac{∂}{∂x}(x^2y^3)+\dfrac{∂}{∂x}(h(y))=2xy^3+0=2xy^3. \nonumber\]
Since \(f\) is a potential function for \(\vecs{F}\),
\[f_y(x,y)=3x^2y^2+\cos(y), \nonumber\]
and therefore
\[3x^2y^2+g′(y)=3x^2y^2+\cos(y). \nonumber\]
This implies that \(h′(y)=\cos y\), so \(h(y)=\sin y+C\). Therefore, any function of the form \(f(x,y)=x^2y^3+\sin(y)+C\) is a potential function. Taking, in particular, \(C=0\) gives the potential function \(f(x,y)=x^2y^3+\sin(y)\).
To verify that \(f\) is a potential function, note that \(\vecs \nabla f(x,y)=⟨2xy^3,3x^2y^2+\cos y⟩=\vecs F\).
Exercise \(\PageIndex{5}\)
Find a potential function for \(\vecs{F}(x,y)=⟨e^xy^3+y,3e^xy^2+x⟩\).
Hint
Follow the steps in Example \(\PageIndex{5}\).
Answer
\(f(x,y)=e^xy^3+xy\)
The logic of the previous example extends to finding the potential function for any conservative vector field in \(ℝ^2\). Thus, we have the following problem-solving strategy for finding potential functions:
PROBLEM-SOLVING STRATEGY: FINDING A POTENTIAL FUNCTION FOR A CONSERVATIVE VECTOR FIELD \(\vecs{F}(x,y)=⟨P(x,y),Q(x,y)⟩\)
1. Integrate \(P\) with respect to \(x\). This results in a function of the form \(g(x,y)+h(y)\), where \(h(y)\) is unknown.
2. Take the partial derivative of \(g(x,y)+h(y)\) with respect to \(y\), which results in the function \(gy(x,y)+h′(y)\).
3. Use the equation \(gy(x,y)+h′(y)=Q(x,y)\) to find \(h′(y)\).
4. Integrate \(h′(y)\) to find \(h(y)\).
5. Any function of the form \(f(x,y)=g(x,y)+h(y)+C\), where \(C\) is a constant, is a potential function for \(\vecs{F}\).
We can adapt this strategy to find potential functions for vector fields in \(ℝ^3\), as shown in the next example.
Example \(\PageIndex{6}\): Finding a Potential Function in \(ℝ^3\)
Find a potential function for \(F(x,y,z)=⟨2xy,x^2+2yz^3,3y^2z^2+2z⟩\), thereby showing that \(\vecs{F}\) is conservative.
Solution
Suppose that \(f\) is a potential function. Then, \(\vecs \nabla f= \vecs{F}\) and therefore \(f_x(x,y,z)=2xy\). Integrating this equation with respect to \(x\) yields the equation \(f(x,y,z)=x^2y+g(y,z)\) for some function \(g\). Notice that, in this case, the constant of integration with respect to \(x\) is a function of \(y\) and \(z\).
Since \(f\) is a potential function,
\[x^2+2yz^3=f_y(x,y,z)=x^2+g_y(y,z). \nonumber\]
Therefore,
\[g_y(y,z)=2yz^3. \nonumber\]
Integrating this function with respect to \(y\) yields
\[g(y,z)=y^2z^3+h(z) \nonumber\]
for some function \(h(z)\) of \(z\) alone. (Notice that, because we know that \(g\) is a function of only \(y\) and \(z\), we do not need to write \(g(y,z)=y^2z^3+h(x,z)\).) Therefore,
\[f(x,y,z)=x^2y+g(y,z)=x^2y+y^2z^3+h(z). \nonumber\]
To find \(f\), we now must only find \(h\). Since \(f\) is a potential function,
\[3y^2z^2+2z=g_z(y,z)=3y^2z^2+h′(z). \nonumber\]
This implies that \(h′(z)=2z\), so \(h(z)=z^2+C\). Letting \(C=0\) gives the potential function
\[f(x,y,z)=x^2y+y^2z^3+z^2. \nonumber\]
To verify that \(f\) is a potential function, note that \(\vecs \nabla f(x,y,z)=⟨2xy,x^2+2yz^3,3y^2z^2+2z⟩=\vecs F(x,y,z)\).
Exercise \(\PageIndex{6}\)
Find a potential function for \(\vecs{F}(x,y,z)=⟨12x^2,\cos y\cos z,1−\sin y\sin z⟩\).
Hint
Following Example \(\PageIndex{6}\), begin by integrating with respect to \(x\).
Answer
\(f(x,y,z)=4x^3+\sin y\cos z+z\)
We can apply the process of finding a potential function to a gravitational force. Recall that, if an object has unit mass and is located at the origin, then the gravitational force in \(ℝ^2\) that the object exerts on another object of unit mass at the point \((x,y)\) is given by vector field
\(\vecs F(x,y)=−G\left\langle\dfrac{x}{ {(x^2+y^2)}^{3/2} },\dfrac{y}{ {(x^2+y^2)}^{3/2} }\right\rangle\),
where \(G\) is the universal gravitational constant. In the next example, we build a potential function for \(\vecs{F}\), thus confirming what we already know: that gravity is conservative.
Example \(\PageIndex{7}\): Finding a Potential Function
Find a potential function \(f\) for \(\vecs{F}(x,y)=−G\left\langle\dfrac{x}{ {(x^2+y^2)}^{3/2} },\dfrac{y}{ {(x^2+y^2)}^{3/2} }\right\rangle\).
Solution
Suppose that \(f\) is a potential function. Then, \(\vecs \nabla f= \vecs{F}\) and therefore
\[f_x(x,y)=\dfrac{−Gx}{ {(x^2+y^2)}^{3/2} }.\nonumber\]
To integrate this function with respect to \(x\), we can use \(u\)-substitution. If \(u=x^2+y^2\), then \(\dfrac{du}{2}=x\,dx\), so
\[\begin{align*} \int \dfrac{−Gx}{ {(x^2+y^2)}^{3/2} }\,dx &=\int \dfrac{−G}{2u^{3/2}} \,du \\[4pt] &=\dfrac{G}{\sqrt{u}}+h(y) \\[4pt] &=\dfrac{G}{\sqrt{x^2+y^2}}+h(y) \end{align*}\]
for some function \(h(y)\). Therefore,
\[f(x,y)=\dfrac{G}{ \sqrt{x^2+y^2}}+h(y).\nonumber\]
Since \(f\) is a potential function for \(\vecs{F}\),
\[f_y(x,y)=\dfrac{−Gy}{ {(x^2+y^2)}^{3/2} }\nonumber\].
Since \(f(x,y)=\dfrac{G}{ \sqrt{x^2+y^2}}+h(y)\), \(f_y(x,y)\) also equals \(\dfrac{−Gy}{ {(x^2+y^2)}^{3/2} }+h′(y)\).
Therefore,
\[\dfrac{−Gy}{ {(x^2+y^2)}^{3/2} }+h′(y)=\dfrac{−Gy}{ {(x^2+y^2)}^{3/2} }, \nonumber\]
which implies that \(h′(y)=0\). Thus, we can take \(h(y)\) to be any constant; in particular, we can let \(h(y)=0\). The function
\[f(x,y)=\dfrac{G}{ \sqrt{x^2+y^2} } \nonumber\]
is a potential function for the gravitational field \(\vecs{F}\). To confirm that \(f\) is a potential function, note that
\[\begin{align*} \vecs\nabla f(x,y) &=⟨−\dfrac{1}{2} \dfrac{G}{ {(x^2+y^2)}^{3/2} } (2x),−\dfrac{1}{2} \dfrac{G}{ {(x^2+y^2)}^{3/2} }(2y)⟩ \\[4pt] &=⟨\dfrac{−Gx}{ {(x^2+y^2)}^{3/2} },\dfrac{−Gy}{ {(x^2+y^2)}^{3/2} }⟩\\[4pt] &=\vecs F(x,y). \end{align*}\]
Exercise \(\PageIndex{7}\)
Find a potential function \(f\) for the three-dimensional gravitational force \(\vecs{F}(x,y,z)=\left\langle\dfrac{−Gx}{ {(x^2+y^2+z^2)}^{3/2} },\dfrac{−Gy}{ {(x^2+y^2+z^2)}^{3/2} },\dfrac{−Gz}{ {(x^2+y^2+z^2)}^{3/2} }\right\rangle\).
Hint
Follow the Problem-Solving Strategy.
Answer
\(f(x,y,z)=\dfrac{G}{\sqrt{x^2+y^2+z^2}}\)
Testing a Vector Field
Until now, we have worked with vector fields that we know are conservative, but if we are not told that a vector field is conservative, we need to be able to test whether it is conservative. Recall that, if \(\vecs{F}\) is conservative, then \(\vecs{F}\) has the cross-partial property (see The Cross-Partial Property of Conservative Vector Fields). That is, if \(\vecs F=⟨P,Q,R⟩\) is conservative, then \(P_y=Q_x\), \(P_z=R_x\), and \(Q_z=R_y\). So, if \(\vecs{F}\) has the cross-partial property, then is \(\vecs{F}\) conservative? If the domain of \(\vecs{F}\) is open and simply connected, then the answer is yes.
Theorem: THE CROSS-PARTIAL TEST FOR CONSERVATIVE FIELDS
If \(\vecs{F}=⟨P,Q,R⟩\) is a vector field on an open, simply connected region \(D\) and \(P_y=Q_x\), \(P_z=R_x\), and \(Q_z=R_y\) throughout \(D\), then \(\vecs{F}\) is conservative.
Although a proof of this theorem is beyond the scope of the text, we can discover its power with some examples. Later, we see why it is necessary for the region to be simply connected.
Combining this theorem with the cross-partial property, we can determine whether a given vector field is conservative:
Theorem: CROSS-PARTIAL PROPERTY OF CONSERVATIVE FIELDS
Let \(\vecs{F}=⟨P,Q,R⟩\) be a vector field on an open, simply connected region \(D\). Then \(P_y=Q_x\), \(P_z=R_x\), and \(Q_z=R_y\) throughout \(D\) if and only if \(\vecs{F}\) is conservative.
The version of this theorem in \(ℝ^2\) is also true. If \(\vecs F(x,y)=⟨P,Q⟩\) is a vector field on an open, simply connected domain in \(ℝ^2\), then \(\vecs F\) is conservative if and only if \(P_y=Q_x\).
Example \(\PageIndex{8}\): Determining Whether a Vector Field Is Conservative
Determine whether vector field \(\vecs F(x,y,z)=⟨xy^2z,x^2yz,z^2⟩\) is conservative.
Solution
Note that the domain of \(\vecs{F}\) is all of \(ℝ^2\) and \(ℝ^3\) is simply connected. Therefore, we can use The Cross-Partial Property of Conservative Vector Fields to determine whether \(\vecs{F}\) is conservative. Let
\[P(x,y,z)=xy^2z \nonumber\]
\[Q(x,y,z)=x^2yz \nonumber\]
and
\[R(x,y,z)=z^2.\nonumber\]
Since \(Q_z(x,y,z)=x^2y\) and \(R_y(x,y,z)=0\), the vector field is not conservative.
Example \(\PageIndex{9}\): Determining Whether a Vector Field Is Conservative
Determine vector field \(\vecs{F}(x,y)=⟨x\ln (y), \,\dfrac{x^2}{2y}⟩\) is conservative.
Solution
Note that the domain of \(\vecs{F}\) is the part of \(ℝ^2\) in which \(y>0\). Thus, the domain of \(\vecs{F}\) is part of a plane above the \(x\)-axis, and this domain is simply connected (there are no holes in this region and this region is connected). Therefore, we can use The Cross-Partial Property of Conservative Vector Fields to determine whether \(\vecs{F}\) is conservative. Let
\[P(x,y)=x\ln (y) \;\; \text{and} \;\;\ Q(x,y)=\dfrac{x^2}{2y}. \nonumber\]
Then \(P_y(x,y)=\dfrac{x}{y}=Q_x(x,y)\) and thus \(\vecs{F}\) is conservative.
Exercise \(\PageIndex{8}\)
Determine whether \(\vecs{F}(x,y)=⟨\sin x\cos y,\,\cos x\sin y⟩\) is conservative.
Hint
Use The Cross-Partial Property of Conservative Vector Fields from the previous section.
Answer
It is conservative.
When using The Cross-Partial Property of Conservative Vector Fields, it is important to remember that a theorem is a tool, and like any tool, it can be applied only under the right conditions. In the case of The Cross-Partial Property of Conservative Vector Fields, the theorem can be applied only if the domain of the vector field is simply connected.
To see what can go wrong when misapplying the theorem, consider the vector field from Example \(\PageIndex{4}\):
\[\vecs F(x,y)=\dfrac{y}{x^2+y^2}\,\hat{\mathbf i}+\dfrac{−x}{x^2+y^2}\,\hat{\mathbf j}.\]
This vector field satisfies the cross-partial property, since
\[\dfrac{∂}{∂y}\left(\dfrac{y}{x^2+y^2}\right)=\dfrac{(x^2+y^2)−y(2y)}{ {(x^2+y^2)}^2}=\dfrac{x^2−y^2}{ {(x^2+y^2)}^2}\]
and
\[\dfrac{∂}{∂x}\left(\dfrac{−x}{x^2+y^2}\right)=\dfrac{−(x^2+y^2)+x(2x)}{ {(x^2+y^2)}^2}=\dfrac{x^2−y^2}{ {(x^2+y^2)}^2}.\]
Since \(\vecs{F}\) satisfies the cross-partial property, we might be tempted to conclude that \(\vecs{F}\) is conservative. However, \(\vecs{F}\) is not conservative. To see this, let
\[\vecs r(t)=⟨\cos t,\sin t⟩,\;\; 0≤t≤\pi\]
be a parameterization of the upper half of a unit circle oriented counterclockwise (denote this \(C_1\)) and let
\[\vecs s(t)=⟨\cos t,−\sin t⟩,\;\; 0≤t≤\pi\]
be a parameterization of the lower half of a unit circle oriented clockwise (denote this \(C_2\)). Notice that \(C_1\) and \(C_2\) have the same starting point and endpoint. Since \({\sin}^2 t+{\cos}^2 t=1\),
\[\vecs F(\vecs r(t)) \cdot \vecs r′(t)=⟨\sin(t),−\cos(t)⟩ \cdot ⟨−\sin(t), \cos(t)⟩=−1\]
and
\[\vecs F(\vecs s(t))·\vecs s′(t)=⟨−\sin t,−\cos t⟩·⟨−\sin t,−\cos t⟩={\sin}^2 t+{\cos}^2t=1.\]
Therefore,
\[\int_{C_1} \vecs F·d\vecs r=\int_0^{\pi}−1\,dt=−\pi\]
and
\[\int_{C_2}\vecs F·d\vecs r=\int_0^{\pi} 1\,dt=\pi.\]
Thus, \(C_1\) and \(C_2\) have the same starting point and endpoint, but \(\int_{C_1} \vecs F·d\vecs r≠\int_{C_2} \vecs F·d\vecs r\). Therefore, \(\vecs{F}\) is not independent of path and \(\vecs{F}\) is not conservative.
To summarize: \(\vecs{F}\) satisfies the cross-partial property and yet \(\vecs{F}\) is not conservative. What went wrong? Does this contradict The Cross-Partial Property of Conservative Vector Fields? The issue is that the domain of \(\vecs{F}\) is all of \(ℝ^2\) except for the origin. In other words, the domain of \(\vecs{F}\) has a hole at the origin, and therefore the domain is not simply connected. Since the domain is not simply connected, The Cross-Partial Property of Conservative Vector Fields does not apply to \(\vecs{F}\).
Key Concepts
• A vector field assigns a vector \(\vecs{F}(x,y)\) to each point \((x,y)\) in a subset \(D\) of \(ℝ^2\) or \(ℝ^3\). \(\vecs{F}(x,y,z)\) to each point \((x,y,z)\) in a subset \(D\) of \(ℝ^3\).
• Vector fields can describe the distribution of vector quantities such as forces or velocities over a region of the plane or of space. They are in common use in such areas as physics, engineering, meteorology, oceanography.
• We can sketch a vector field by examining its defining equation to determine relative magnitudes in various locations and then drawing enough vectors to determine a pattern.
• A vector field \(\vecs{F}\) is called conservative if there exists a scalar function \(f\) such that \(\vecs \nabla f=\vecs{F}\).
Key Equations
• Vector field in \(ℝ^2\)
\(\vecs{F}(x,y)=⟨P(x,y),\,Q(x,y)⟩\)
or
\(\vecs{F}(x,y)=P(x,y) \,\hat{\mathbf i}+Q(x,y) \,\hat{\mathbf j}\)
• Vector field in \(ℝ^3\)
\(\vecs{F}(x,y,z)=⟨P(x,y,z),\,Q(x,y,z),\,R(x,y,z)⟩\)
or
\(\vecs{F}(x,y,z)=P(x,y,z) \,\hat{\mathbf i} +Q(x,y,z) \,\hat{\mathbf j}+R(x,y,z) \,\hat{\mathbf k}\)
Glossary
conservative field
a vector field for which there exists a scalar function \(f\) such that \(\vecs ∇f=\vecs{F}\)
gradient field
a vector field \(\vecs{F}\) for which there exists a scalar function \(f\) such that \(\vecs ∇f=\vecs{F}\); in other words, a vector field that is the gradient of a function; such vector fields are also called conservative
potential function
a scalar function \(f\) such that \(\vecs ∇f=\vecs{F}\)
radial field
a vector field in which all vectors either point directly toward or directly away from the origin; the magnitude of any vector depends only on its distance from the origin
rotational field
a vector field in which the vector at point \((x,y)\) is tangent to a circle with radius \(r=\sqrt{x^2+y^2}\); in a rotational field, all vectors flow either clockwise or counterclockwise, and the magnitude of a vector depends only on its distance from the origin
unit vector field
a vector field in which the magnitude of every vector is 1
vector field
measured in \(ℝ^2\), an assignment of a vector \(\vecs{F}(x,y)\) to each point \((x,y)\) of a subset \(D\) of \(ℝ^2\); in \(ℝ^3\), an assignment of a vector \(\vecs{F}(x,y,z)\) to each point \((x,y,z)\) of a subset \(D\) of \(ℝ^3\)
Contributors and Attributions
• Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download for free at http://cnx.org.
This page titled 5.2: Vector Fields is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.
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How to create User Controls in ASP.NET MVC?
First of all, User Control is a concept in ASP.NET web form. While MVC only has three components, namely model, view, and control, asking how to create user control in MVC without defining which component user control belongs to is invalid. The following are instead the valid questions pertinent to user control.
How to create User Controls in Model?
How to create User Controls in View?
nested layout (master view, child view)
tag helper
Razor Declarative Helpers
– Inline Razor helpers
– Convert declarative helpers to tag helpers[1]Jon Galloway. Comparing MVC 3 Helpers: Using Extension Methods and Declarative Razor @helper Syntax. . 2011-03-23 [2018-01-28].
editor template, display template
How to create User Controls in Controller?
Render action, return partial view. A child request
References
[CiteBook author=”Dino Esposito” title=”ASP.NET MVC 5编程实战” edition=”第三版” publisher=”清华大学出版社” isbn=”978-7-302-39480-8″]
[ + ]
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技術 || 如何快速開發“高速、精準”的高速點膠機
專欄：行業動態
發布日期：2018-08-09
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技術 || 如何快速開發“高速、精準”的高速點膠機一. 應用背景傳統點膠機 又稱涂膠機、滴膠機、打膠機、灌膠機。是專門對流體進行控制，并將流體點滴、涂覆于產品表面或產品內部的自動化機器。但通常點膠以接觸式為主，易產生拉尖、膠量不均、刮傷元器件等問題，適合稍粗、厚的物體點膠。點膠軌跡多采用教導盒加人眼示教方式，編程復雜，精度不高，無法滿足要求越來越精準、效率越來越高的應用場合。而全自動化高速點膠機利...
技術 || 如何快速開發“高速、精準”的高速點膠機
一. 應用背景
傳統點膠機 又稱涂膠機、滴膠機、打膠機、灌膠機。是專門對流體進行控制，并將流體點滴、涂覆于產品表面或產品內部的自動化機器。但通常點膠以接觸式為主，易產生拉尖、膠量不均、刮傷元器件等問題，適合稍粗、厚的物體點膠。點膠軌跡多采用教導盒加人眼示教方式，編程復雜，精度不高，無法滿足要求越來越精準、效率越來越高的應用場合。
而全自動化高速點膠機利用無接觸式點膠技術，對流體進行精確控制，高速且準確地噴射于預先設定好的位置，借由膠點的疏密及軌跡的控制，形成點、線和各式圖形，滿足輕薄化、短小化產品點膠需求。
但是國內高速點膠機除少數廠家外普遍存在精度不高、打膠不夠穩定或系統偶發卡頓等問題，因此國內很多廠商有志于開發高速點膠機，但往往花費大量的時間與精力，卻達不到合格的速度與精度的設備，更達不到國外大廠的水平。
二. 高速點膠機常見痛點
1.膠距不準、膠直徑不一致
對于噴射式膠閥，通過對膠閥的精確開關觸發，控制從而精確控制膠量（重）、膠直徑以及間距。而常見問題是膠點與膠點間距不準，沒有做到精確觸發膠閥，工件不平問題，導致膠直徑一致性差。
圖1：等間距點膠不準示意圖
2.拐角堆膠
加減速段/轉角處，機構的移動勢必需要降速來完成拐角過彎的動作， 當高速的 直線運動于轉角進行降速時，速度的快慢會與影響膠的間距，會有溢膠的問題產生
圖2：拐角溢膠圖
而常規的解決方案是采用增加空跑軌跡避開加減速段噴射點膠，以點一個等間距矩形軌跡為例，一般采用井字形點膠方法來解決拐角堆膠問題。但此方法雖然可解決問題，但以犧牲部分效率為代價。
圖3：傳統井字型點膠做法示意圖
3.機構問題導致的精度不夠
執行機構精度達不到，則再調整控制系統也沒有辦法提升精度。機構的設計、安裝水平限制了整機設備的性能，導致設備達不到高速點膠機的定義指標，設備沒有競爭力。
4.點膠速度不達標
由于機構設計與控制系統設計的原因，導致加工速度達不到指標要求，使得產品設計達不到市場要求或低于客戶要求。
5. 軟件擴展及維護困難
由于衍生設備眾多, 往往整體均用C++等高級語言開發的高速點膠機應用軟件擴充功能費時費力且非常不易維護。
三. 研華方案針對痛點見招拆招
1.膠距不準、膠直徑不一致拆招方案
針對噴射點膠間距、膠直徑、任意軌跡離散點的精確點膠，研華SoftMotion運動控制實時核心，準確的速度控制、雙軸任意高速位置比較觸發功能，保證了控制的位置精準性。而方案可選配激光測高模塊開啟功能，保證了不平整工件點膠恒高度，同時精準控制開發時間長短，確保了膠直徑的一致性。
圖4：合格點膠效果圖
圖5：激光測高Z軸自動補償
2.拐角堆膠拆招方案
研華方案運動控制上采用拐角降速與動態PWM輸出控制膠閥 ，根據軌跡速度大小實時調整PWM信號，從而實現拐角不堆膠的矩形等距高速點膠 。
圖6：直接90度拐角取代井字軌跡
3.機構問題導致的精度不夠拆招方案
研華與具有十幾年的點膠類行業設備設計、開發、調試經驗的系統集成商合作，聯合推出的此控制系統方案，不但可解決控制系統問題，還可向客戶提供設計出合格的高速高精度設備的服務，甚至可提供機架，其豐富的設備調試經驗，可最大程度的確保設計的高速點膠機能達到性能要求，幫助用戶快速推出合格設備，把握市場商機。
4.點膠速度不達標拆招方案
研華控制系統的運動控制算法、系統集成商機構設計經驗、調試經驗的指導，可確保用戶設備點膠在保證精度的前提下，點膠速度達到合格以上。目前典型的測試數據為：
在3mm間距點，平均點膠速度為45000點/小時，高峰為48000點/小時。
5. 軟件擴展及維護困難拆招方案
研華的方案基于研華設備自動化控制器（MAS）開發，其二次快速開發平臺Motion Studio改變了以往高速點膠機控制部分均用C++/C#等高級語言開發帶來的一些維護不易、費時費力問題，可快速響應客戶定制需求。硬件可彈性擴充，保留設備升級擴軸、擴I/O、擴視覺彈性。
四. 研華高速點膠機完整解決方案
研華提供的高速點膠機控制系統解決方案，以嵌入式無風扇MAS-4285 PC-based控制器為核心， 集運動控制、機器視覺、膠閥控制、通信于一體，搭載針對高速點膠機設備的應用軟件，采用非接觸噴射式定量點膠控制，實現更小的點膠直徑，同時提高點膠的可靠性、一致性。方案中的點膠軌跡采用視覺精密示教、AutoCAD DXF文件導入等多種方式，配合視覺自動定位糾偏，保證了實際點膠的精確性。
圖7：高速點膠機實機圖
高速點膠機動力單元主要由3軸松下伺服+2軸步進電機組成（進料和調寬軸）
圖8: 研華方案架構圖
五、研華解決方案軟+硬優勢
1. 硬件優勢：一體式無風扇運動控制器
圖9：點膠控制器硬件圖
2. 軟件優勢：高速點膠機行業軟件
圖10：高速點膠機應用軟件圖
完備的行業專用軟件
功能齊全：打點、線、弧、飛點、連續線、連續弧。提前開關膠，手動操作，視覺示教，校準等。
界面友好：柔和的界面顏色，直觀的顯示系統狀態、數據、加工點和軌跡。
操作人性化：支持各功能的獨立測試，支持視覺圖像上示教與各軸點動。
PCB視覺定位＆視覺點位示教
圖11：視覺抓Mark點糾偏及視覺示教
功能預留接口，滿足不同用戶的不同要求
圖12：激光測高補償功能
圖13：可選擇配置的稱重功能
實際打膠效果
圖13：實際點膠效果
視覺定位、示教
點膠軌跡預覽
六. 選擇研華整體解決方案的四大理由
1. 軟+硬解決方案
同時可提供二次開發，方便根據不同的需求做簡單的修改
2. 一體式控制器
小體積，無風扇，抗震，固態硬盤，控制器配線比舊機器簡單
3. 速度與精度
透過PWM+拐角降速與2D位置比較觸發、打點/打線/飛點不卡頓，速移動下能精準開/關膠
4. 降低成本
一個控制器整合運動控制和視覺定位
七. 研華高速點膠機控制系統清單
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Nutrient Agar vs. Blood Agar
Scientists have a variety of methods at their disposal when they need to cultivate microorganisms such as bacteria. Two of those methods involve growing the bacteria in special plates called Petri dishes. Scientists fill these Petri dishes with a special kind of food that the bacteria need to live and to multiply. The two types of special food used are nutrient agar and blood agar.
In this post, we are going to define agar, go over the two types of agar most commonly used in science, and go into detail about the differences between the two.
Let's Define Agar
In and of itself, agar provides no nutrient support for bacteria. We define agar as a complex polysaccharide that scientists derive from marine algae. It possesses several unique properties that make it valuable to microbiologists.
First, few microbes can degrade agar, so it remains solid. Second, it will not liquefy until it reaches a temperature of 100° Celsius, and once liquefied, it will remain so until brought down to 40° Celsius. Its ability to remain solid at high temperatures makes it an ideal medium for growing thermophilic (heat-loving) bacteria.
Read more about the types of agar plates.
Nutrient Agar
Since agar is only a solidifying agent, it carries no value for the bacteria grown on it. Bacteria need nutrients to live and reproduce. One solution to this issue involves the mixing of agar with a nutrient broth, containing peptone and beef extract, to create nutrient agar.
Carbohydrates, vitamins, salts, and trace amounts of organic nitrogen make up the beef extract. The principle source of organic nitrogen, amino acids, and long-chained peptides is the peptone. This provides all of the nutrients needed for bacteria to grow on the agar.
Nutrient Agar Is a Complex Media
For practical purposes, nutrient agar works well for growing most types of non-fastidious heterotrophic bacteria. "Fastidious" means selective, and "heterotrophic" means the bacteria cannot make their own food. Non-fastidious heterotrophic bacteria, therefore, need their food supplied to them, and they are not fussy about from where it comes.
Since many pathogenic (disease-causing) bacteria fall into the non-fastidious heterotrophic category, a complex media consisting of various nutrients such as peptones and beef extracts is the ideal choice for bacterial growth and cultivation.
Scientists are also able to manipulate the nutrients in the nutrient agar in order to isolate genetically modified bacteria during cloning, sequencing, and other genetic experiments.
Read more about how to make nutrient agar at home.
Blood Agar
Blood agar is almost identical to nutrient agar except that it contains five to ten percent sheep, rabbit, or horse blood. Blood agar consists of:
• Beef extract, for nitrogen
• Blood, for nitrogen, amino acids, and carbon
• Sodium chloride, for maintaining osmotic balance
• Agar, for the solidifying agent
Microbiologists use blood agar to identify fastidious pathogenic bacteria by studying the hemolytic (blood cell destroying) reactions they cause.
Blood Agar Is a Differential Media
Microbiologist use differential media to identify and isolate specific bacteria. An example of this is the bacteria Streptococcus pyogenes, which is the pathogen that causes strep throat. You can grow these bacteria on a complex media such as nutrient agar, but if other bacteria are also growing on that agar, it is very difficult to distinguish one bacterial colony from another without the use of microscopic examination and special staining techniques.
If you grow it on blood agar, though, it will destroy the red blood cells in a process called beta-hemolysis, and other cells will not cause this reaction, which makes identifying Streptococcus pyogenes much easier.
So while both nutrient and blood agar are used to cultivate bacteria and other microorganisms, blood agar serves a more particular and specific purpose during lab work.
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__label__pos
| 0.738979 |
Background
The relative reinforcing value (RRV) of food, or how rewarding one finds eating compared to alternative activities, predicts obesity in children and adults. The promotion of alternative reinforcers, or rewarding activities that could take the place of eating, could help to promote healthy weight outcomes. The overall objective of this pilot study was to promote positive parent-child interactions in the context of interactive reading, hypothesizing that these could function as a novel alternative reinforcer, decreasing the RRV of food.
Methods
Twelve 4-to-5-year-old children (M=4.75+0.53 years; 66.7% female) with at least one overweight parent participated, completing a 7-day home-based intervention promoting positive parenting during reading and baseline and follow-up RRV assessments in the laboratory. RRV of food was calculated as the maximum schedule reached when working for access to food divided by the maximum schedule for food plus the maximum schedule for reading with a parent. Intervention compliance was assessed via daily photographs of parent/child reading. Intervention acceptability was parent reported.
Results
Children’s RRV of food decreased from baseline (Mdn=0.83) to follow-up (Mdn=0.50). This change corresponds to a medium-to-large effect (d=0.64). Changes in maximum schedules reached for food and reading were not significant, but magnitudes were consistent with both a decrease in food reinforcement (from Mdn=96.0 to 48.0) and an increase in reinforcement of reading with a parent (from Mdn=4.0 to 32.0). Eleven families (92%) submitted 7 photographs of parent/child reading. Parent perspectives supported intervention feasibility.
Conclusions
Findings provide initial support for this intervention and highlight areas for further investigation.
|
__label__pos
| 0.766965 |
Learn
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How do Drugs Work?
Proteins are tiny molecular machines that perform most of the tasks needed to keep cells alive. These machines are far too small to see, so you might imagine that it is impossible to affect their action. However, drugs can be used to turn proteins on or off.
Drugs are small molecules that bind to one specific protein and modify its action. Some very powerful drugs, such as antibiotics or anticancer drugs, are used to completely disable a critical molecular machine. These drugs can kill a bacterial or cancer cell. Other molecules, such as aspirin, gently block less-critical proteins for a few hours. With the use of these drugs, we can make changes inside our own cells, such as the blocking of pain signals. Many structures of drugs that bind to proteins have been determined by scientists. These atomic structures allow us to see how drugs work, and perhaps how to modify them to improve their action. A few examples are shown here. Some of these drugs, like penicillin, were discovered in nature. Other drugs, such as HIV protease inhibitors, were created by using the target protein structure to design new drug molecules. These structures of proteins and drugs, along with many others, can be explored at RCSB PDB.
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Related Resources
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__label__pos
| 0.945486 |
Programming-Idioms
This language bar is your friend. Select your favorite languages!
Idiom #110 Check if string is blank
Set boolean blank to true if string s is empty, or null, or contains only whitespace ; false otherwise.
blank = s == nil || String.length(String.trim s) == 0
with Ada.Strings.Fixed;
use Ada.Strings.Fixed;
Blank := Index_Non_Blank (Str) = 0;
(require '[clojure.string :refer [blank?]])
(blank? s)
IDENTIFICATION DIVISION.
PROGRAM-ID. blank string.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 BOOLEAN-BLANK PIC X.
88 BLANK VALUE "T".
88 NOT-BLANK VALUE "F".
PROCEDURE DIVISION.
IF s = ' '
SET BLANK TO TRUE
ELSE
SET NOT-BLANK TO TRUE
END-IF
STOP RUN.
#include <algorithm>
#include <cctype>
#include <string>
bool blank = false;
if (s.empty() || std::all_of(s.begin(), s.end(), [](char c){return std::isspace(c);})) {
blank = true;
}
System;
bool blank = string.IsNullOrWhiteSpace(s);
bool blank = string.IsNullOrWhiteSpace(s);
import std.algorithm;
import std.uni;
bool blank = s.all!isSpace;
final blank = s == null || s.trim() == '';
Blank = string:is_empty(string:trim(S)).
blank = s == ''
import "strings"
blank := strings.TrimSpace(s) == ""
import Data.Char (isSpace)
b = null (dropWhile isSpace s)
import Data.Char (isSpace)
blank :: Bool
blank = all isSpace s
const blank = s == null || s.trim() === ''
boolean blank = s.trim().isEmpty();
import org.apache.commons.lang.StringUtils;
boolean blank = StringUtils.isBlank(s);
val blank = s.isNullOrBlank()
(setf blank (not (find #\space s :test-not #'eql)))
blank = s ~= nil and s:match("%S") ~= nil
$blank = !trim($s);
$blank = (empty(trim($s));
blank := trim(s) = '';
$blank = !$s || $s=~/^\s*$/;
blank = s.strip() == ''
blank = s.strip.empty?
let blank = s.trim().is_empty();
val blank = s.trim().isEmpty()
Dim myString As String = "abcdefg"
If String.IsNullOrEmpty(myString) Then
'''
End If
Do you know the best way to do this in your language ?
New implementation...
Idiom created by
programming-idioms.org
|
__label__pos
| 0.956975 |
About
Essent pertinax dissentias te vel, an saepe propriae quo. Esse fabellas tractatos an sed, eripuit vituperata nec no, animal virtute nonummy quo ex. Mea lorem nostro nusquam ut, simul prodesset similique id per. Exerci nostrum platonem has ne, vis ei dicat alienum corpora, no reque possim neglegentur duo. Cu vocibus quaerendum per, ei error fierent detraxit vix.
Veritus oportere suavitate duo at, et sale probo quaerendum qui. Eum et elit constituto sententiae. Eius utinam concludaturque eu eum, fuisset convenire reprimique quo ut, no quo salutandi omittantur philosophia. Has et erant dictas verterem, ius labore aeterno phaedrum in, et vim putant iuvaret. Ad dico falli principes has, posse populo constituam te sed.
Globals Profiler (996.34 ms) SQL (128 queries in 34.35 ms) Errors (1, 1!) Toggle Close
$_GET = array (
);
$_POST = array (
);
$_COOKIE = array (
);
$_SESSION = array (
);
$_SERVER = array (
'SERVER_SOFTWARE' => 'Apache',
'REQUEST_URI' => '/about/',
'TZ' => 'Australia/Melbourne',
'REDIRECT_REDIRECT_UNIQUE_ID' => 'ZuKLM2IVNwb-oBebc2pnTgAAAAA',
'REDIRECT_REDIRECT_SCRIPT_URL' => '/about/',
'REDIRECT_REDIRECT_SCRIPT_URI' => 'https://demo.wp-cinema.com/about/',
'REDIRECT_REDIRECT_WPR_SSL' => '-https',
'REDIRECT_REDIRECT_WPR_ENC' => '_gzip',
'REDIRECT_REDIRECT_HTTP_AUTHORIZATION' => '',
'REDIRECT_REDIRECT_HTTPS' => 'on',
'REDIRECT_REDIRECT_SSL_TLS_SNI' => 'demo.wp-cinema.com',
'REDIRECT_REDIRECT_STATUS' => '200',
'REDIRECT_UNIQUE_ID' => 'ZuKLM2IVNwb-oBebc2pnTgAAAAA',
'REDIRECT_SCRIPT_URL' => '/about/',
'REDIRECT_SCRIPT_URI' => 'https://demo.wp-cinema.com/about/',
'REDIRECT_WPR_SSL' => '-https',
'REDIRECT_WPR_ENC' => '_gzip',
'REDIRECT_HTTP_AUTHORIZATION' => '',
'REDIRECT_HTTPS' => 'on',
'REDIRECT_SSL_TLS_SNI' => 'demo.wp-cinema.com',
'REDIRECT_HANDLER' => 'application/x-httpd-ea-php74',
'REDIRECT_STATUS' => '200',
'UNIQUE_ID' => 'ZuKLM2IVNwb-oBebc2pnTgAAAAA',
'SCRIPT_URL' => '/about/',
'SCRIPT_URI' => 'https://demo.wp-cinema.com/about/',
'HTTPS' => 'on',
'SSL_TLS_SNI' => 'demo.wp-cinema.com',
'HTTP_USER_AGENT' => 'CCBot/2.0 (https://commoncrawl.org/faq/)',
'HTTP_ACCEPT' => 'text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8',
'HTTP_ACCEPT_LANGUAGE' => 'en-US,en;q=0.5',
'HTTP_IF_MODIFIED_SINCE' => 'Wed, 29 May 2024 03:11:23 GMT',
'HTTP_ACCEPT_ENCODING' => 'br,gzip',
'HTTP_HOST' => 'demo.wp-cinema.com',
'HTTP_CONNECTION' => 'Keep-Alive',
'HTTP_X_HTTPS' => '1',
'PATH' => '/usr/local/jdk/bin:/usr/kerberos/sbin:/usr/kerberos/bin:/usr/local/sbin:/usr/local/bin:/sbin:/bin:/usr/sbin:/usr/bin:/usr/X11R6/bin:/usr/local/bin:/usr/X11R6/bin:/root/bin:/opt/bin',
'SERVER_SIGNATURE' => '',
'SERVER_NAME' => 'demo.wp-cinema.com',
'SERVER_ADDR' => '45.76.117.172',
'SERVER_PORT' => '443',
'REMOTE_ADDR' => '3.235.226.14',
'DOCUMENT_ROOT' => '/home/demwpcn/public_html',
'REQUEST_SCHEME' => 'https',
'CONTEXT_PREFIX' => '/cgi-sys',
'CONTEXT_DOCUMENT_ROOT' => '/usr/local/cpanel/cgi-sys/',
'SERVER_ADMIN' => '[email protected]',
'SCRIPT_FILENAME' => '/home/demwpcn/public_html/index.php',
'REMOTE_PORT' => '36834',
'REDIRECT_URL' => '/index.php',
'GATEWAY_INTERFACE' => 'CGI/1.1',
'SERVER_PROTOCOL' => 'HTTP/1.1',
'REQUEST_METHOD' => 'GET',
'QUERY_STRING' => '',
'SCRIPT_NAME' => '/index.php',
'ORIG_SCRIPT_FILENAME' => '/usr/local/cpanel/cgi-sys/ea-php74',
'ORIG_PATH_INFO' => '/index.php',
'ORIG_PATH_TRANSLATED' => '/home/demwpcn/public_html/index.php',
'ORIG_SCRIPT_NAME' => '/cgi-sys/ea-php74',
'PHP_SELF' => '/index.php',
'REQUEST_TIME_FLOAT' => 1726122803.54104900360107421875,
'REQUEST_TIME' => 1726122803,
'argv' =>
array (
),
'argc' => 0,
);
Profiler Initiaded 0.0000 ms 29035 kB
Profiler Noise 0.0069 ms 29035 kB
Profiler Stopped 996.3439 ms 125170 kB
4.0660 [ms]
SELECT option_name, option_value FROM w3qwdjwsqp_options WHERE autoload = 'yes';
0.4089 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'uninstall_plugins' LIMIT 1;
0.5040 [ms]
SHOW TABLES LIKE 'sib_model_users';
0.2849 [ms]
SHOW TABLES LIKE 'sib_model_forms';
0.2630 [ms]
SHOW TABLES LIKE 'sib_model_forms';
0.3400 [ms]
CREATE TABLE IF NOT EXISTS w3qwdjwsqp_sib_model_forms (
`id` int(20) NOT NULL AUTO_INCREMENT,
`title` varchar(120) CHARACTER SET utf8 COLLATE utf8_unicode_ci,
`html` longtext CHARACTER SET utf8 COLLATE utf8_unicode_ci,
`css` longtext,
`dependTheme` int(1) NOT NULL DEFAULT 1,
`listID` longtext,
`templateID` int(20) NOT NULL DEFAULT -1,
`confirmID` int(20) NOT NULL DEFAULT -1,
`isDopt` int(1) NOT NULL DEFAULT 0,
`isOpt` int(1) NOT NULL DEFAULT 0,
`redirectInEmail` varchar(255),
`redirectInForm` varchar(255),
`successMsg` varchar(255) CHARACTER SET utf8 COLLATE utf8_unicode_ci,
`errorMsg` varchar(255) CHARACTER SET utf8 COLLATE utf8_unicode_ci,
`existMsg` varchar(255) CHARACTER SET utf8 COLLATE utf8_unicode_ci,
`invalidMsg` varchar(255) CHARACTER SET utf8 COLLATE utf8_unicode_ci,
`requiredMsg` varchar(255) CHARACTER SET utf8 COLLATE utf8_unicode_ci,
`attributes` TEXT CHARACTER SET utf8 COLLATE utf8_unicode_ci,
`date` DATE NOT NULL,
`isDefault` int(1) NOT NULL DEFAULT 0,
`gCaptcha` int(1) NOT NULL DEFAULT 0,
`gCaptcha_secret` varchar(255) CHARACTER SET utf8 COLLATE utf8_unicode_ci,
`gCaptcha_site` varchar(255) CHARACTER SET utf8 COLLATE utf8_unicode_ci,
`termAccept` int(1) NOT NULL DEFAULT 0,
`termsURL` varchar(255) CHARACTER SET utf8 COLLATE utf8_unicode_ci,
PRIMARY KEY (`id`)
);;
0.3090 [ms]
SELECT * FROM w3qwdjwsqp_sib_model_forms;
0.1001 [ms]
CREATE TABLE IF NOT EXISTS w3qwdjwsqp_sib_model_users (
`id` int(20) NOT NULL AUTO_INCREMENT,
`email` varchar(255),
`code` varchar(100),
`listIDs` longtext,
`redirectUrl` varchar(255),
`info` TEXT CHARACTER SET utf8 COLLATE utf8_unicode_ci,
`frmid` int(2),
`user_added_date` DATETIME NOT NULL,
PRIMARY KEY (`id`)
);;
0.5651 [ms]
SHOW COLUMNS FROM `w3qwdjwsqp_sib_model_forms` LIKE 'gCaptcha' ;
0.3521 [ms]
SHOW COLUMNS FROM `w3qwdjwsqp_sib_model_forms` LIKE 'termAccept';;
0.3541 [ms]
SHOW COLUMNS FROM `w3qwdjwsqp_sib_model_forms` LIKE 'confirmID';;
0.3490 [ms]
SHOW COLUMNS FROM `w3qwdjwsqp_sib_model_forms` LIKE 'requiredMsg';;
0.3350 [ms]
SHOW COLUMNS FROM w3qwdjwsqp_sib_model_users LIKE 'user_added_date' ;
0.3750 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'updraft_restore_in_progress' LIMIT 1;
0.3841 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'wordfence_case' LIMIT 1;
0.9198 [ms]
SELECT name, val FROM w3qwdjwsqp_wfConfig WHERE autoload = 'yes';
0.2520 [ms]
SELECT `name`, `value` FROM `w3qwdjwsqp_wfls_settings` WHERE `autoload` = 'yes';
0.2139 [ms]
SELECT name, val, autoload FROM w3qwdjwsqp_wfConfig WHERE name = 'detectProxyRecommendation';
0.2091 [ms]
SELECT * FROM `w3qwdjwsqp_wfBlocks7` WHERE `IP` = X'00000000000000000000ffff03ebe20e' AND `type` = 7 AND (`expiration` = 0 OR `expiration` >
UNIX_TIMESTAMP());
0.1690 [ms]
SELECT name, val, autoload FROM w3qwdjwsqp_wfConfig WHERE name = 'scansEnabled_geoipSupport';
0.1099 [ms]
SELECT name, val, autoload FROM w3qwdjwsqp_wfConfig WHERE name = 'wordfenceCentralConnected';
0.3872 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'active_sitewide_plugins' LIMIT 1;
0.1481 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'ic-buddypress-settings' LIMIT 1;
0.1330 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'as_has_wp_comment_logs' LIMIT 1;
0.1540 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'rsssl_encryption_keys_set' LIMIT 1;
0.2010 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'medium_crop' LIMIT 1;
0.0982 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'medium_large_crop' LIMIT 1;
0.0970 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'large_crop' LIMIT 1;
0.2320 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'eum_unproven_updates_post_install' LIMIT 1;
0.2561 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'updraft_migrator_localkeys' LIMIT 1;
0.1731 [ms]
SELECT name, val, autoload FROM w3qwdjwsqp_wfConfig WHERE name = 'needsGeoIPSync';
0.1440 [ms]
SELECT name, val, autoload FROM w3qwdjwsqp_wfConfig WHERE name = 'detectProxyRecommendation';
0.1469 [ms]
SELECT MAX(attackLogTime) FROM w3qwdjwsqp_wfHits;
0.1352 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'wordfence_lastSyncAttackData' LIMIT 1;
0.2701 [ms]
SELECT *, CASE
WHEN `type` = 3 THEN 0
WHEN `type` = 4 THEN 1
WHEN `type` = 7 THEN 2
WHEN `type` = 6 THEN 3
WHEN `type` = 5 THEN 4
WHEN `type` = 9 THEN 5
WHEN `type` = 8 THEN 6
WHEN `type` = 2 THEN 7
WHEN `type` = 1 THEN 8
ELSE 9999
END AS `typeSort`, CASE
WHEN `type` = 3 THEN `parameters`
WHEN `type` = 4 THEN `parameters`
WHEN `type` = 1 THEN `IP`
WHEN `type` = 9 THEN `IP`
WHEN `type` = 5 THEN `IP`
WHEN `type` = 6 THEN `IP`
WHEN `type` = 7 THEN `IP`
WHEN `type` = 2 THEN `IP`
WHEN `type` = 8 THEN `IP`
ELSE 9999
END AS `detailSort`
FROM `w3qwdjwsqp_wfBlocks7` WHERE `type` IN (4) AND (`expiration` = 0 OR `expiration` > UNIX_TIMESTAMP()) ORDER BY `typeSort` ASC, `id` DESC;
0.1740 [ms]
SELECT *, CASE
WHEN `type` = 3 THEN 0
WHEN `type` = 4 THEN 1
WHEN `type` = 7 THEN 2
WHEN `type` = 6 THEN 3
WHEN `type` = 5 THEN 4
WHEN `type` = 9 THEN 5
WHEN `type` = 8 THEN 6
WHEN `type` = 2 THEN 7
WHEN `type` = 1 THEN 8
ELSE 9999
END AS `typeSort`, CASE
WHEN `type` = 3 THEN `parameters`
WHEN `type` = 4 THEN `parameters`
WHEN `type` = 1 THEN `IP`
WHEN `type` = 9 THEN `IP`
WHEN `type` = 5 THEN `IP`
WHEN `type` = 6 THEN `IP`
WHEN `type` = 7 THEN `IP`
WHEN `type` = 2 THEN `IP`
WHEN `type` = 8 THEN `IP`
ELSE 9999
END AS `detailSort`
FROM `w3qwdjwsqp_wfBlocks7` WHERE `type` IN (3) AND (`expiration` = 0 OR `expiration` > UNIX_TIMESTAMP()) ORDER BY `typeSort` ASC, `id` DESC;
0.1569 [ms]
SELECT * FROM `w3qwdjwsqp_wfBlocks7` WHERE `type` IN (1, 8, 9, 2, 5, 6) AND `IP` = X'00000000000000000000ffff03ebe20e' AND (`expiration` = 0 OR
`expiration` > UNIX_TIMESTAMP()) ORDER BY `blockedTime` DESC LIMIT 1;
0.3140 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = '_transient_timeout_wp_rocket_pricing' LIMIT 1;
0.1471 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = '_transient_wp_rocket_pricing' LIMIT 1;
0.1280 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = '_transient_timeout_wp_rocket_customer_data' LIMIT 1;
0.1211 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = '_transient_wp_rocket_customer_data' LIMIT 1;
0.3510 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'rsssl_le_certificate_generated_by_rsssl' LIMIT 1;
0.2060 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'rsssl_ssl_activation_active' LIMIT 1;
0.1471 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'wp_mail_smtp' LIMIT 1;
0.1140 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'limit_login_client_type' LIMIT 1;
0.1140 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'limit_login_allowed_retries' LIMIT 1;
0.1020 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'limit_login_lockout_duration' LIMIT 1;
0.1061 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'limit_login_valid_duration' LIMIT 1;
0.1309 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'limit_login_cookies' LIMIT 1;
0.0789 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'limit_login_lockout_notify' LIMIT 1;
0.0761 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'limit_login_allowed_lockouts' LIMIT 1;
0.0932 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'limit_login_long_duration' LIMIT 1;
0.0770 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'limit_login_notify_email_after' LIMIT 1;
0.1800 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = '_transient_timeout_et_core_path' LIMIT 1;
0.1080 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = '_transient_et_core_path' LIMIT 1;
0.1099 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = '_transient_timeout_et_core_version' LIMIT 1;
0.1030 [ms]
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0.1080 [ms]
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0.1299 [ms]
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0.1051 [ms]
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0.1030 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'et_core_page_resource_remove_all' LIMIT 1;
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0.2918 [ms]
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0.4611 [ms]
SELECT t.term_id
FROM w3qwdjwsqp_terms AS t INNER JOIN w3qwdjwsqp_term_taxonomy AS tt ON t.term_id = tt.term_id
WHERE tt.taxonomy IN ('wp_theme') AND t.name IN ('Divi')
LIMIT 1
;
0.1941 [ms]
SELECT w3qwdjwsqp_posts.*
FROM w3qwdjwsqp_posts
WHERE 1=1 AND (
0 = 1
) AND w3qwdjwsqp_posts.post_type = 'wp_template_part' AND ((w3qwdjwsqp_posts.post_status = 'publish'))
GROUP BY w3qwdjwsqp_posts.ID
ORDER BY w3qwdjwsqp_posts.post_date DESC
;
0.3791 [ms]
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0.1130 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = '_transient_imagify_activation' LIMIT 1;
0.1230 [ms]
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0.1059 [ms]
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0.1760 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'et_support_options' LIMIT 1;
0.2081 [ms]
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0.1149 [ms]
SELECT option_value FROM w3qwdjwsqp_options WHERE option_name = 'https_migration_required' LIMIT 1;
0.6490 [ms]
SHOW FULL COLUMNS FROM `w3qwdjwsqp_wfLiveTrafficHuman`;
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AND expiration >= UNIX_TIMESTAMP();
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@wfcurrenthits := 1) ON DUPLICATE KEY UPDATE hits = IF(@wfcurrenthits := hits + 1, hits + 1, hits + 1);
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|
__label__pos
| 0.929971 |
base (version 3.6.2)
print: Print Values
Description
print prints its argument and returns it invisibly (via invisible(x)). It is a generic function which means that new printing methods can be easily added for new classes.
Usage
print(x, …)
# S3 method for factor print(x, quote = FALSE, max.levels = NULL, width = getOption("width"), …)
# S3 method for table print(x, digits = getOption("digits"), quote = FALSE, na.print = "", zero.print = "0", right = is.numeric(x) || is.complex(x), justify = "none", …)
# S3 method for function print(x, useSource = TRUE, …)
Arguments
x
an object used to select a method.
further arguments passed to or from other methods.
quote
logical, indicating whether or not strings should be printed with surrounding quotes.
max.levels
integer, indicating how many levels should be printed for a factor; if 0, no extra "Levels" line will be printed. The default, NULL, entails choosing max.levels such that the levels print on one line of width width.
width
only used when max.levels is NULL, see above.
digits
minimal number of significant digits, see print.default.
na.print
character string (or NULL) indicating NA values in printed output, see print.default.
zero.print
character specifying how zeros (0) should be printed; for sparse tables, using "." can produce more readable results, similar to printing sparse matrices in Matrix.
right
logical, indicating whether or not strings should be right aligned.
justify
character indicating if strings should left- or right-justified or left alone, passed to format.
useSource
logical indicating if internally stored source should be used for printing when present, e.g., if options(keep.source = TRUE) has been in use.
Details
The default method, print.default has its own help page. Use methods("print") to get all the methods for the print generic.
print.factor allows some customization and is used for printing ordered factors as well.
print.table for printing tables allows other customization. As of R 3.0.0, it only prints a description in case of a table with 0-extents (this can happen if a classifier has no valid data).
See noquote as an example of a class whose main purpose is a specific print method.
References
Chambers, J. M. and Hastie, T. J. (1992) Statistical Models in S. Wadsworth & Brooks/Cole.
See Also
The default method print.default, and help for the methods above; further options, noquote.
For more customizable (but cumbersome) printing, see cat, format or also write. For a simple prototypical print method, see .print.via.format in package tools.
Examples
# NOT RUN {
require(stats)
ts(1:20) #-- print is the "Default function" --> print.ts(.) is called
for(i in 1:3) print(1:i)
## Printing of factors
attenu$station ## 117 levels -> 'max.levels' depending on width
## ordered factors: levels "l1 < l2 < .."
esoph$agegp[1:12]
esoph$alcgp[1:12]
## Printing of sparse (contingency) tables
set.seed(521)
t1 <- round(abs(rt(200, df = 1.8)))
t2 <- round(abs(rt(200, df = 1.4)))
table(t1, t2) # simple
print(table(t1, t2), zero.print = ".") # nicer to read
## same for non-integer "table":
T <- table(t2,t1)
T <- T * (1+round(rlnorm(length(T)))/4)
print(T, zero.print = ".") # quite nicer,
print.table(T[,2:8] * 1e9, digits=3, zero.print = ".")
## still slightly inferior to Matrix::Matrix(T) for larger T
## Corner cases with empty extents:
table(1, NA) # < table of extent 1 x 0 >
# }
|
__label__pos
| 0.964404 |
What Does A Spoiler Do On A Car
[ad_1]
What Does A Spoiler Do On A Car?
When it comes to automotive design, there are numerous features that serve both functional and aesthetic purposes. One such feature is a spoiler, a common addition to many modern cars. But what does a spoiler actually do? In this article, we will explore the purpose of a car spoiler, its different types, and its impact on vehicle performance. Additionally, we will provide answers to some commonly asked questions about spoilers. So, buckle up and let’s dive into the world of car spoilers.
1. Improved Aerodynamics: The primary function of a spoiler is to improve a car’s aerodynamics. By altering the airflow around the vehicle, spoilers reduce drag and turbulence, resulting in better overall performance.
2. Increased Stability: Spoilers generate downforce, which helps to keep the car stable at higher speeds. By pressing the car down onto the road surface, spoilers enhance traction and reduce the risk of losing control.
3. Enhanced Fuel Efficiency: By reducing drag, spoilers can also contribute to improved fuel efficiency. When a car encounters less resistance while moving, it requires less power to maintain its speed, ultimately leading to better mileage.
4. Aesthetic Appeal: While spoilers serve a practical purpose, they also enhance the visual appeal of a car. Available in various shapes, sizes, and materials, spoilers can give a vehicle a sportier and more aggressive appearance.
5. Different Types of Spoilers: There are several types of spoilers, each designed for specific purposes. Lip spoilers, for instance, are small and attach to the edge of the trunk or roof, providing minimal aerodynamic benefits. Wing spoilers, on the other hand, are larger and generate more downforce, improving stability at high speeds.
6. Racing Influence: Spoilers have their roots in motorsports, particularly in racing cars. Originally developed to increase performance on the track, spoilers have now become a common feature in production cars, allowing everyday drivers to benefit from their advantages.
7. Technological Innovations: With advancements in automotive technology, spoilers have evolved too. In the year 2024, we can expect to see spoilers equipped with active aerodynamics. These spoilers will automatically adjust their position based on the car’s speed and driving conditions, optimizing performance in real-time.
Now, let’s address some common questions about car spoilers:
1. Do all cars come with spoilers?
No, not all cars come with spoilers as standard equipment. Spoilers are often optional or found on high-performance models.
2. Can I install a spoiler on any car?
In most cases, yes. Spoilers can be installed on almost any car, provided there is enough space and proper mounting points.
3. Do spoilers only serve a cosmetic purpose?
No, spoilers have functional benefits beyond aesthetics. They improve aerodynamics, stability, and fuel efficiency.
4. Are spoilers only suitable for sports cars?
While spoilers are commonly found on sports cars, they can be installed on various types of vehicles, including sedans and hatchbacks.
5. How much does a spoiler affect fuel economy?
The impact on fuel economy varies depending on the design and size of the spoiler. Generally, spoilers contribute to minor improvements in mileage.
6. Can spoilers be customized?
Yes, spoilers come in different styles, materials, and colors. Customizing your spoiler can add a personal touch to your vehicle.
7. Are spoilers legal?
Spoilers are legal as long as they comply with local laws and regulations. It’s important to ensure the spoiler you choose meets legal requirements.
8. Do spoilers hinder rear visibility?
Spoilers are designed to not obstruct the rear view. However, depending on the size and position of the spoiler, it may slightly affect visibility.
9. Can spoilers be functional on front bumpers?
Spoilers are typically installed on the rear of a car to generate downforce. However, some high-performance vehicles may have small spoilers on the front to optimize aerodynamics.
10. Can spoilers be removed easily?
Yes, spoilers can be easily removed if desired. However, it’s crucial to consult a professional to ensure proper removal without causing damage.
11. Do spoilers make a significant difference in top speed?
Spoilers can improve stability at high speeds, which indirectly affects top speed. However, their impact on reaching a higher speed is minimal.
12. Are there any downsides to having a spoiler?
Spoilers can increase wind noise and may require additional care during car washes. Additionally, some people may find certain spoiler designs visually unappealing.
13. Can spoilers be added to electric cars?
Yes, spoilers can be added to electric cars just like any other vehicle. The benefits of improved aerodynamics and stability apply to electric cars as well.
14. Are spoilers worth the investment?
If you prioritize improved performance, enhanced stability, and a more aggressive look, then spoilers can be a worthwhile investment. However, the impact may be more noticeable on high-performance vehicles.
In conclusion, car spoilers serve a dual purpose of enhancing vehicle performance and aesthetics. By improving aerodynamics, stability, and fuel efficiency, spoilers have become a popular feature in the automotive industry. Whether you’re a racing enthusiast or simply looking for a stylish addition to your car, spoilers can provide a significant impact. So, consider investing in a spoiler to experience the benefits firsthand in the year 2024 and beyond.
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|
__label__pos
| 0.97622 |
0
WEBの記事を参考に、JSONを作成しようとしています。
クラス定義の直下に以下のように記述すると、エラーになってしまいます。
var jsonDic = Dictionary<String, Any>()
jsonDic["id"] = 1
1行目ではエラーが出ないのですが、2行目でエラーになります。
エラー内容は以下の通りです。
Consecutive declarations on a line must be separated by ';'
Insert ';'
Expected '(' in argument list of function declaration
Expected '{' in body of function declaration
Expected 'func' keyword in instance method declaration
Insert 'func '
Expected declaration
Invalid redeclaration of 'jsonDic()'
2行目はviewDidLoad内部などに書けば良いのでしょうか？
なぜこのようなエラーが出てしまうのでしょうか？
どうしたらエラーを直せますか？
0
2
「クラス定義の直下」ということは、多分こんな風に書いていませんか？
class Hoge {
var jsonDic = Dictionary<String, Any>()
jsonDic["id"] = 1
}
これですと、var jsonDic = Dictionary<String, Any>()の部分はメンバ変数宣言となりますが、jsonDic["id"] = 1の方は実行文（Swiftでの用語は違うかもしれませんが）なので、func fuga() { }などの中に書く必要があります。（初期化処理ならfuncなしのinit() { }など）
「viewDidLoad内部などに書けば良いのでしょうか？」という質問が出る時点で、まずSwiftの最低限の言語仕様の把握や、実際にどう書けばいいかの基礎が飛ばされているようなので、まずは何か入門書を読むなどして基礎部分を勉強した方が良さそうです。
回答
“回答を投稿”をクリックすることで利用規約プライバシーポリシー、及びクッキーポリシーに同意したものとみなされます。
求めていた回答ではありませんか？ のタグが付いた他の質問を参照するか、自分で質問をする
|
__label__pos
| 0.82707 |
Next Article in Journal
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Article Menu
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Nanomaterials 2011, 1(1), 3-19; doi:10.3390/nano1010003
Article
Films, Buckypapers and Fibers from Clay, Chitosan and Carbon Nanotubes
Thomas M. Higgins, Holly Warren and Marc in het Panhuis *
Soft Materials Group, School of Chemistry, University of Wollongong, Northfields Avenue, Wollongong, NSW 2522, Australia
*
Author to whom correspondence should be addressed; Tel.: +61-24221-3155; Fax: +61-24221-4287.
Received: 10 February 2011; in revised form: 17 March 2011 / Accepted: 23 March 2011 / Published: 6 April 2011
Abstract
:
The mechanical and electrical characteristics of films, buckypapers and fiber materials from combinations of clay, carbon nanotubes (CNTs) and chitosan are described. The rheological time-dependent characteristics of clay are maintained in clay–carbon nanotube–chitosan composite dispersions. It is demonstrated that the addition of chitosan improves their mechanical characteristics, but decreases electrical conductivity by three-orders of magnitude compared to clay–CNT materials. We show that the electrical response upon exposure to humid atmosphere is influenced by clay-chitosan interactions, i.e., the resistance of clay–CNT materials decreases, whereas that of clay–CNT–chitosan increases.
Keywords:
chitosan; clay; carbon nanotubes; electrical; mechanical
1. Introduction
Clays are excellent stabilizing and rheological agents due to their colloidal structure in water [1]. Each smectite particle is composed of thousands of platelets (thickness = 1 nm, width > 100 nm) stacked in a sandwich fashion. Hydration of the clay promotes delamination of this sandwich structure until the platelets are completely separated. This allows the weakly positive platelet edges to interact with the negatively charged platelet faces resulting in the formation of a three dimensional colloidal structure, commonly referred to as the “house of cards” [2]. The building of this structure also gives the clay time-dependent (thixotropic) rheological properties [2]. Initially, the building of the colloidal structure is rapid, leading to a sharp increase in viscosity. This increase slows down as the remaining free platelets take a longer time to find an available site in the structure. Applying a shear results in the opposite behavior, as most of the structure is disrupted leading to a decrease in viscosity [2].
The colloidal structure of clays has an ability to trap and segregate solids in suspensions, oils in emulsions, and gases in foams or mousses as well as drug delivery [1,35]. Recently, clays have also been used to assist with the well-known disperse-ability issue surrounding conducting fillers such as carbon nanotubes (CNTs) and carbon black (CB) in common solvents [612]. These studies focused on the preparation of composite materials with enhanced mechanical and/or electrical properties. For example, Tang et al. reported that chitosan can be reinforced through addition of clay and functionalized multi-walled carbon nanotubes (FMWNT) [7,9]. The clay–FMWNT–chitosan composite materials exhibited increased Young's modulus (125%), tensile strength (165%) and storage modulus (55%) compared to chitosan materials [7,9]. The increase in mechanical characteristics was attributed to a synergistic effect of anionic clay and anionic FMWNT on cationic chitosan through electrostatic interactions and hydrogen bonding formation. The use of electrostatic interaction in the formation of composites from oppositely charged materials is well known and generally referred to as ionic self-assembly or polyelectrolyte complexation [13].
Studies by Grunlan et al. investigated the electrical and mechanical characteristics of clay-epoxy composite materials with either CNTs or CB as conducting fillers [8,12]. For CNT containing composites they observed improvements in the electrical conductivity (from 0.25 mS/cm to 2 mS/cm) and lowering of percolation threshold (5-fold reduction) upon addition of clay. But the improvement in mechanical characteristics (storage modulus) was due to addition of nanotubes and not clay [8]. However, they did report synergistic effects between CB and clay resulting in improved electrical and mechanical characteristics of clay–CB–epoxy composites [12]. In contrast, they observed that clay adversely affected the mechanical and electrical behavior of clay–CB–latex materials [11]. Other research by Sue et al. has shown that clay–FMWNT–epoxy composite materials exhibited increased Young's modulus (40%) and tensile strength (55%) compared to epoxy materials.
In this paper, we report the mechanical and electrical characteristics of films, buckypapers and fibers prepared from combinations of clay, carbon nanotubes and chitosan. To our knowledge, these buckypapers and fibers are novel materials, which have not been reported in the literature. We show that the brittleness of clay–CNT materials can be improved through addition of chitosan, allowing the assessment of their mechanical properties. Addition of chitosan was found to decrease the electrical conductivity by up to three orders of magnitude. We also demonstrate that the addition of chitosan affects the electrical response upon hydration, providing new insights into their behavior. In addition, we show that clay–CNT–chitosan fibers can be prepared by a wet-spinning approach. The resulting fibers display higher Young's modulus, but lower conductivity values compared to the corresponding film materials.
2. Results and Discussion
2.1. Dispersing CNTs
Our initial attempts to hydrate clays involving simultaneous heating (80 °C), stirring and sonicating for up to two days were unsuccessful. The resulting clay suspension was unstable and it was not possible to obtain a stable CNT dispersion. This suggested that this treatment does not fully delaminate the clay's platelet layers. Full delamination is only achieved through vigorous application of mechanical force or with the assistance of surfactants, as shown previously [14]. Therefore, all our clay suspensions were hydrated using a homogenizer. Light microscopy images (Figure 1a and b) show that the presence of aggregates is significantly reduced after hydration.
Single-walled carbon nanotubes (SWNT) were easily dispersed in these properly hydrated clay suspensions (1.12% w/v, pH = 7.9), and were stable for months (Figure 1c). Typical UV-visible spectra (Figure 1d) show broad CNT absorption features due to the presence of nanotube aggregates. The absorbance of the dispersions at 747 nm was plotted as a function of concentration (inset in Figure 1d). This particular wavelength was selected as it corresponds to the maxima of an absorption band arising from the van Hove singularities for SWNT [15,16]. Figure 1d shows that the absorption intensity increases linearly with increasing carbon nanotube concentration, indicating an excellent degree of disperse-ability (in the concentration range studied). This allowed us to determine the extinction coefficient (ε) of CNTs in the clay suspension, yielding ε= 0.864 mL mg−1cm−1.
2.2. Rheological Studies
Rheological studies were undertaken to examine the flow and time-dependent behavior of the clay-CNT dispersions as well as the effect of incorporating chitosan. Both types of dispersions and the chitosan solution display shear thinning behavior, i.e., viscosity (η) decreases with increasing shear rate (data not shown). Combining chitosan with clay–CNT into a clay–CNT–chitosan dispersion results in a two and three orders of magnitude decrease in the apparent viscosity compared to that of the chitosan solution and clay-CNT dispersion, respectively. For example, at a shear rate of 0.01 s−1 the viscosity values of typical chitosan solutions, and clay–CNT (1000 mg/L) and clay–CNT–chitosan dispersions are 15.4 Pa.s, 370 Pa.s, and 0.266 Pa.s, respectively. The apparent viscosity of the ternary dispersion is lower than the oppositely charged solutions used to form the dispersion, i.e., the anionic clay–CNT dispersion and the cationic chitosan solution. Figure 2a shows that the clay-CNT dispersion exhibits a yield point, i.e., the sample starts to flow only when a certain amount of force is applied. This point can be determined using the Bingham model [17],
τ = τ B + η B s
where τB and τB indicate the Bingham yield point and Bingham flow coefficient, respectively. Although, the values obtained using the Bingham model are dependent on the shear rate range it provides a good approximation for the determination of yield points. The model shows that the yield point of clay–CNT dispersion decreases by 2-orders of magnitude upon addition of chitosan (Table 1). Similar differences are observed for the Bingham flow coefficient.
These results indicate that the electrostatic interaction between the negatively charged clay and positively charged chitosan decreases the resistance against flow. Similar observations have been reported previously for the addition of other types of clay (montmorillonite) to chitosan [18]. This study showed that a decrease in the electrostatic potential of chitosan upon addition of clay was coupled with a decrease in flow resistance [18].
Thixotropic behavior testing (Figure 2b) revealed that clay–CNT materials exhibit the expected time-dependent rheology characteristics consistent with a “house of cards” structure [2]. As evident from the 20% decrease in viscosity during the reference and high-shear intervals applying a constant shear, results in disruption of this structure. During the regeneration interval, clay–CNT dispersions exhibit a rapid increase in viscosity, which is indicative of the re-building of the colloidal structure. Eventually, the viscosity will start to decrease again due to effect of applying a constant shear rate (Table 1). In contrast, chitosan does not show any of these characteristics, i.e., the viscosity does not exhibit any significant time-dependent behavior in any of the three intervals. Whereas, combining chitosan with clay–CNT results in a dispersion which has retained the time-dependent characteristics of clay–CNT dispersions. The difference in the magnitude of these viscosity effects is evident from the inset in Figure 2b, i.e., a binary dispersion can be easily inverted without flowing, whereas the ternary composite will still flow.
Oscillatory amplitude sweeps confirmed that the ternary (clay–CNT–chitosan) dispersion has more in common with the binary (clay–CNT) dispersion than the chitosan solution (Figure 2c–d). Both dispersions display distinctive linear viscoelastic (LVE) regions, although the length of LVE region and maximum shear stress is lower for the ternary dispersion due to the presence of chitosan (Table 1). The magnitude of the storage (G′) and loss (G″) moduli of the ternary dispersion (in the LVE region) is lower than those of the binary dispersion. This difference is also reflected in the shear modulus obtained using G* = ((G′)2 + (G″)2)1/2, resulting in values of 80.6 ± 1.9 Pa and 1.40 ± 0.23 Pa for the binary and ternary dispersions, respectively. The corresponding value for chitosan is 4.81 ± 0.08 Pa. The value for the clay-CNT dispersion is similar to that of typical dispersions such as lotions and creams, whereas that of chitosan and clay–CNT–chitosan is comparable to that of salad dressings [19].
Figure 2c–d shows that for the dispersions, the storage modulus (G′) is larger than the loss modulus (G″) in the LVE region, indicating that the elastic behavior dominates over the viscous behavior. In contrast, chitosan solutions exhibit the opposite trend, i.e., viscous behavior is dominating (G′ < G″). Above the maximum shear strain, a cross-over from elastic to viscous behavior (tan δ > 1, Figure 2d) takes place for both dispersions indicates a disruption of the “house-of-card” structure. Furthermore, the strain at which the cross-over takes place is larger in the binary dispersion than that in the ternary dispersion. These results clearly indicate lower resistance to flow behavior due to addition of chitosan.
2.3. Clay–CNT Films
Free-standing clay–CNT films (Figure 1a) were prepared by evaporative casting of clay–CNT dispersions. The current–voltage (IV) characteristics were investigated under controlled ambient conditions (21 °C, 45% relative humidity, RH). All films exhibited linear IV characteristics, which indicate Ohmic behavior. The conductivity (σ) can then be evaluated by making resistance measurements as a function of sample length (l) [20]. The total resistance was found to scale linearly according to:
R T = 1 σ A C l + R C
where Ac is the film's cross-sectional area. The straight line fit for a typical film with nanotube mass fraction 0.067 is shown in Figure 3b. The slope is used to calculate the so-called two-probe dc conductivity, yielding 0.14 ± 0.04 S/cm under controlled ambient conditions.
Previously, we have demonstrated that (dried) CNT composite materials prepared using water soluble dispersants change their electrical behavior upon hydration. For example, exposure to a humid atmosphere resulted in an increase in electrical resistance for water soluble polyaniline and polypeptide-CNT composite materials [21,22], while gellan gum–CNT composite materials decrease their resistance [20,23,24]. It was demonstrated that resistance decreased due to an increased cation mobility upon exposure to humid atmosphere [20].
Figure 3c shows that exposing our clay–CNT film to humid atmosphere for 15 hours results in a decrease in the current compared to that observed under ambient conditions. This decrease in current corresponds to an increase in electrical resistance, from 9.7 ± 2.0 kΩ (RB, before exposure) to 36 ± 4 kΩ(RA, after exposure). Exposure to the humid atmosphere results in hydration of the clay–CNT film, i.e., osmotic forces drive water in between the smectite platelet galleries. This leads to a swelling-induced disruption of conductive pathways resulting in an increase in resistance.
Figure 3d shows that the current response to a square wave potential is different before and after exposure to humid conditions. Under ambient conditions (before exposure) the magnitude of the current response to a square wave potential is linear, while after exposure to humid atmosphere the current displays non-linear behavior.
This behavior can be explained through the mobility and charge collection of the counter-ions. Under an applied positive potential the counter-ion (cations) will migrate towards the negative electrode (1) leading to a buildup of positive charge. Upon reversal of the potential, the cations will be repelled from the now positive electrode 1 causing a non-linear current flow due to migration of the ionic charge carriers (indicated in the circled area in Figure 3d). The cations migrate towards the negative electrode (2) leading to a charge collection at this electrode. This effect manifests itself as the non-linear current response, until all mobile ions have migrated and the current becomes linear again.
Thus, the resistance of our composite material consists of an electrical contribution from electron transport through the carbon nanotube network and an ionic contribution due to the cations. The latter is small or negligible under ambient conditions. Under humid conditions we would expect a decrease in resistance due to an increased ionic contribution, similar to that observed in our previous work on composites consisting of the anionic polysaccharide gellan gum and SWNT [20,24]. However, the swelling-induced disruption of conductive pathways results in a more significant reduction in the electrical contribution (−70%, estimated from Figure 3d). As such the resistance of a hydrated film is higher compared to that of a dry film.
Clay–CNT dispersions were used to fabricate buckypapers via vacuum filtration. The two-probe dc conductivity of a typical buckypaper yielded 0.9 ± 0.2 S/cm under controlled ambient conditions (Figure 3b). As expected, the buckypaper conductivity is higher compared to the conductivity (0.14 ± 0.04 S/cm) of the evaporative cast film. Exposure of buckypapers to humid atmosphere resulted in a swelling-induced decrease in the current (increase in resistance), but we did not observe any non-linear current behavior in response to a square wave potential. This indicates that most of the counter-ions were removed during the washing procedure in the buckypaper preparation method.
2.4. Clay–CNT–Chitosan Films
The clay–CNT films produced by evaporative casting and vacuum filtration were too brittle to allow a detailed analysis of their mechanical properties, i.e., the films could not be subjected to any significant strain without breaking. Polyelectrolyte complexation of the negatively charged, hydrated clay platelets with the positively charged biopolymer chitosan was utilized to improve the mechanical robustness of these materials, i.e., the materials could be subjected to strain.
Free-standing ternary clay–CNT–chitosan composite films (Figure 4a) were prepared by evaporative casting of clay–CNT–chitosan dispersions with CNT mass fraction of 0.028. The resulting materials were more mechanically robust compared to clay–CNT films, allowing for an assessment of their mechanical properties (see Figure 4b). Combining clay–CNT with chitosan results in an improvement in Young's modulus (E), coupled with a decrease in tensile strength and strain at break values compared to chitosan (Table 2). More significant increases in E as well as an increase in TS have been observed for composites prepared using functionalized multi-walled carbon nanotubes (FMWNT, see also Table 2) [7,9]. This larger increase can be attributed to the presence of carboxy and hydroxyl functional groups on the nanotube surface, which facilitates an improved interfacial adhesion between clay and chitosan through electrostatic interactions and hydrogen bonding, compared to the non-functionalized SWNT used in our composites. Larger increases in modulus were also observed for composites prepared using other matrix materials (epoxy and latex) in combination with carbon black and FMWNT (Table 2) [8,1012].
The increased robustness of the ternary (clay–CNT–chitosan) composite materials is coupled with a decrease in conductivity by 3-orders of magnitude (from 0.14 S/cm to 1.0 × 10−4 S/cm) compared to the binary (clay–CNT) composites, see Table 2. These observations suggest that chitosan may act as “glue” or “binder” between the clay–CNT domains thereby improving the mechanical properties, as suggested previously [25]. However, the significant reduction in conductivity suggests that the number of electrical (CNT–CNT) pathways has decreased and the number of ionic-electrical pathways has increased compared to clay-SWNT films, i.e., pathways dominated by chitosan and clay–chitosan. This is evident from the difference in surface morphology between the two types of films. The CNT pathways are clearly visible in the clay–CNT film (Figure 3a), but almost entirely covered by the biopolymer in the clay–CNT–chitosan film (Figure 4a). We were unable to compare our conductivity values with that of the other clay–CNT–chitosan materials shown in Table 2, due to lack of available data (at least to our knowledge). However, our conductivity value is in the same order of magnitude as clay–CNT–epoxy materials, with higher values (8.6 mS/cm) reported for carbon black (CB) containing materials (Table 2).
Under ambient conditions (in the absence of water vapor), chitosan and clay act as tunneling barriers in these junctions thereby blocking transport. We have already seen that exposure to humid atmosphere of clay–CNT materials results in an additional contribution to the current. As chitosan is a cationic polyelectrolyte, exposure to humid atmosphere increases the counter-ion mobility allowing these anionic charge carriers to transport the current along the polymer component of the chitosan-dominated junctions. This may enable transport through these pathways leading to an additional contribution to the current.
Despite the increase in current (as a result of increased ion-mobility), the resistance of the clay–CNT films increased upon exposure to humid atmosphere due to a swelling effect. Figure 4c shows that the clay–CNT–chitosan films exhibit different behavior. The current magnitude increases with increasing time of exposure to humid atmosphere. After 140 min of exposure the resistance has decreased by one order of magnitude from RB = 2.8 ± 0.6 MΩ to RA = 0.27 ± 0.08 MΩ (see also Table 2). It is likely that interactions between the oppositely charged clay and chitosan materials limits expansion (swelling) of the clay. As such swelling-induced disruption of conductive pathways (resulting in an increase in resistance) is not significant in these composites. The decrease in resistance can then be attributed to enhanced ion-mobility of the clay and chitosan counter-ions.
These ternary composite materials showed another interesting and somewhat unexpected response to humidity. Exposing one face of the film to a higher humidity than the other face, results in rapid curling (Figure 4c). This response was found to be reversible, i.e., the film uncurled upon removal of the humidity gradient. This may suggests that water is adsorbed into the inter-layer spacing on only one side of the film; expansion of that side relative to the other (dryer) side results in the curling actuator response. The actuator response (the level of reversible curling) was better for dry films compared to hydrated films. The latter do not exhibit the same degree of actuation as transport of water in and out of the film becomes more uniform and with it, the amount of expansion.
2.5. Clay–CNT–Chitosan Fibers
In our previous work we prepared fibers by facilitating polyelectrolyte complexation through injection of a SWNT-biopolymer dispersion into a coagulation bath containing a biopolymer of opposite charge [23]. Initial attempts to produce fibers via this approach, i.e., injection of a clay–CNT dispersion into a chitosan coagulation bath, were unsuccessful. The resulting fibers were not mechanically robust enough to be recovered after passing through the coagulation bath. We suspect that this may be a result of the high yield strength (5.87 Pa) and apparent viscosity (370 Pa.s at 0.01 s−1) of the clay–CNT dispersion which may inhibit the diffusion of chitosan and subsequent coagulation of chitosan with the clay platelets. In other words, during the continuous spinning approach the clay–CNT dispersion is passed too quickly through the chitosan coagulation bath to facility polyelectrolyte complexation.
We devised an alternative spinning method whereby the chitosan coagulation bath is replaced by a long coagulation channel into which a stream of a clay–CNT dispersion is injected, which remains in the channel for three hours. This is followed by removing the fiber from the channel to a supporting frame and drying under controlled ambient conditions. We refer to this modification of the continuous spinning approach as “stop-and-go wet spinning”. During the “stop stage”, the additional three hours in the coagulation channel, chitosan diffuses into the clay thereby facilitating the polyelectrolyte complexation. The gradual inclusion of the chitosan between the smectite platelets, causes a reduction in the thickness of the charged double layer responsible for face-face electrostatic repulsion of adjacent clays platelets. The observed shrinkage of the fibers is in support of this suggestion.
The stop-and-go spinning method allowed us to easily spin clay–CNT–chitosan fibers (Figure 5a). These fibers (diameter 210 ± 40 μm) showed an interesting surface morphology as evident from the scanning electron microscopy micrographs (Figures 5b and 5c). These ternary composite materials appear to be composed of numerous smaller fibers (diameter 23 ± 9 μm), producing a yarn like appearance. Similar surface features have been reported for other types of polyelectrolyte complexed fibers using gellan gum and chitosan solutions [26].
Figure 4b and Table 2 clearly show that a typical ternary composite fiber exhibits significantly higher E, similar TS and lower strain at break values compared to a typical ternary composite film. The electrical resistance of typical dry fibers (RB = 300 ± 14 MΩ) is two order of magnitude higher compared to typical dry films of similar length, but due to the difference in the cross-sectional area of fiber and film samples the difference in conductivity is only 1 order of magnitude (Table 2).
The fiber's electrical response to humid atmosphere is similar to that observed for clay–CNT–chitosan films. After 250 min of exposure the resistance has decreased by almost one order of magnitude from RB = 300 ± 14 MΩ to RA = 68 ± 4 MΩ. Swelling of the fiber in response to exposure to humid atmosphere was apparent through elongation of the fiber (+20%) within its constrained position in the environmental chamber. This swelling behavior was found to be reversible. Similar to the ternary film composites we do not consider the swelling-induced disruption of conductive pathways (resulting in an increase in resistance) to be significant in the fibers. As such the decrease in resistance is attributed to enhanced ion-mobility of the clay and chitosan counter-ions.
3. Experimental Section
3.1. Materials
Purified SWNTs produced by the HiPco process by catalytic chemical vapor deposition were obtained from Unidym (Lot P0341). Sodium smectite clay (cationic exchange capacity 80–100 meq/100 g, lot 6D-904) was a gift from R.T. Vanderbilt. Chitosan (high molecular weight, 75.6% degree of deacetylation, product number 419419, lot number 10305DD) was obtained from Sigma Aldrich. All materials were used as received. Clay dispersions (2.0% w/v) were prepared by slowly adding 12 g of as-received clay powder to 600 mL Milli-Q water (∼80 °C), and homogenized at ∼10,000 rpm (Tokushu Kika Homo Mixer) for 40 min at 80 °C. The clay dispersions were centrifuged (Heraeus Labofuge 300) for 5 min at 2,000 rpm prior to usage resulting in a clay concentration of 1.12% w/v. Homogeneous SWNT dispersions were prepared by the probe sonication process in a water bath (Digital Branson Sonifier) utilizing a power output of 120 W for 24 min and 40 W for 3 min in pulse mode (0.5 s on/off), respectively. Different amounts of SWNT (0.040% w/v, 0.060% w/v, 0.080% w/v, 0.10% w/v) were dispersed in a clay dispersion. Chitosan solutions (1.0% w/v) were prepared by dissolving chitosan powder in acetic acid (2.0% w/v) under continuous stirring at 40 °C. Clay–SWNT–chitosan dispersions were prepared by combining equivalent amounts of clay–SWNT dispersions (SWNT concentration = 0.060% w/v) with chitosan solutions, followed by sonication at 40W for 3 min in pulse mode (0.5 s on/off).
3.2. Film Preparation
Free-standing films were prepared by evaporative casting of clay-CNT, and clay-CNT-chitosan composite dispersions onto plastic substrates. Five mL of dispersion was injected into the base of a cylindrical plastic container (diameter ∼5.5 cm) and dried under controlled ambient conditions, 21 °C, 45% relative humidity (RH) for ∼36 hours. The films were then peeled off the substrate to yield uniform free-standing films. Buckypapers were prepared by vacuum filtration of clay–CNT dispersions. The clay–CNT dispersion was prepared by diluting 30 mL of a dispersion (0.10% w/v SWNT, 1.12% w/v clay) with 70 mL Milli-Q water and subsequently suction filtered at 30–50 mbar. Once the dispersion had been filtered, the resulting buckypaper was washed with 250 mL Milli-Q water followed by methanol (99.8%) whilst still in the filtration unit.
3.3. Fiber Spinning
Fibers were prepared using a custom-made fiber preparation system, consisting of a coagulation channel containing coagulant solution (1.0% w/v chitosan) confined to linear motion by a channel path guide, a syringe pump for injecting spinning solution into the coagulation channel, and a constant velocity motor-driven spool assembly to pull the coagulation channel through the path guide, away from the syringe. A 5 mL syringe with a detachable needle (diameter = 0.60 mm) controlled by a syringe pump (KDS Scientific-100) was used to deliver the clay–CNT spinning dispersion (CNT concentration = 0.060% w/v) at 249 mL/min to the coagulation channel, while simultaneously pulling the coagulation channel away from the needle at 2 cm/s. The freshly formed fiber was allowed to remain in the coagulation channel for 3 hours. The resulting composite fibers were washed and dried in air under tension.
3.4. Characterization
The absorption behavior of clay-CNT dispersions was obtained using a Cary 500 UV-Vis-NIR and quartz cuvette (1 cm pathlength). Rheological testing was conducted using an Anton Paar–Physica MCR 301 parallel plate rheometer working with a 50 mm head at 21 °C. CNT dispersions and chitosan solutions were analyzed using flow curves (viscosity and shear stress vs. shear rate), thixotropy tests and oscillatory amplitude sweeps. The thixotropy behavior was carried out using a shear rate profile with three intervals as a step function, i.e., shear rate = 0.01 s−1 for 40 s, shear rate = 1000 s−1 for 30 s and shear rate = 0.01 s−1, for 180 s. These three intervals are hereafter referred to as: “reference interval”, “high-shear interval”, and “regeneration interval”, respectively. Oscillatory amplitude experiments were obtained at constant oscillation frequency of 1.6 Hz.
For conductivity measurements, films (cut into strips of 0.5 cm × 3.0 cm) and fibers (cut to 3.0 cm in length) were contacted with conducting silver paint. Current (I)–voltage (V) characteristics were obtained by measuring current using a digital multimeter (Agilent 34410A) under a cycling potential applied by a waveform generator (Agilent 33220A). IV measurements were conducted under controlled ambient conditions in air (21 °C, 45% RH) as a function of film length, by repeatedly cutting the end off the strip, contacting with silver and re-measuring the IV characteristics. Film thicknesses and fiber diameters (dfiber) were determined using a Mitutoyo digital micrometer and a Leica macroscope (Z16 APO), respectively.
The electrical responses of film and fiber samples to a humid environment were determined using an in-house designed sealed environmental chamber. IV characteristics were conducted under controlled ambient conditions (21 °C, 45% RH) as well as during and after exposure to a humid atmosphere (21 °C, 90% RH for ∼15 hours) through measurement of the current response to applied sawtooth and square wave potentials, cycling at 5 mHz. The exposure area of films and fibers is 2.0 cm2 and πdfiber × 1 cm2, respectively.
The mechanical properties were determined using a Instron 5566 at a strain rate of 0.1 mm min−1. Film samples were cut into strips of 5 × 30 mm2 and their thicknesses were measured using the digital micrometer. Fiber samples were mounted on aperture cards (1 cm length window) with commercial superglue and allowed to air dry. Stress is calculated from the load (in Newtons) per cross-sectional area. The cross-sectional area A of fibers is estimated using A = ¼π(dfiber)2. Strain is obtained from the ratio of the increase in sample length (Δl) and the initial sample length (l0 = 1.0 cm) during a tensile test. Young's modulus and tensile strength values are calculated from the slope of the linear part of the stress-strain curve and the maximum stress, respectively.
Scanning electron microscopy (SEM) was carried out on a Hitachi S-900 field emission SEM through the Australian Microscopy and Microanalysis Research Facilities at the University of New South Wales (Sydney, Australia).
4. Conclusions
In this paper, the production of conducting films, buckypapers and fibers from combinations of clay, SWNT and chitosan is reported. Rheological studies showed that although interactions between clay and chitosan decrease the magnitude of apparent viscosity, the clay's time-dependent characteristics are maintained. The conductivity of films and buckypapers prepared from clay–SWNT dispersion is 0.14 ± 0.04 S/cm and 0.9 ± 0.2 S/cm, respectively. Hydration through exposure to humid atmosphere resulted in enhanced ion mobility (decrease in resistance) as well as swelling (increase in resistance). The increased resistance indicated that the effect of swelling (resulting in disruption of conducting pathway) was larger than the ion contribution. Clay–SWNT materials were found to be too brittle to allow assessment of their mechanical properties. The addition of chitosan increased their mechanical robustness, but resulted in a decrease of more than 3-orders of magnitude in conductivity (from 140 mS/cm to 0.8 mS/cm) compared to clay–SWNT materials. In contrast, the resistance of clay–SWNT–chitosan films decreases by an order of magnitude upon exposure to a humid atmosphere for two hours. This indicated that due to the presence of chitosan the effect of swelling on the resistance is not significant in these composites. Rather, the decrease in resistance can be attributed to ion mobility.
We also prepared clay–SWNT–chitosan fibers using a wet-spinning approach. Polyelectrolyte complexation was facilitated by injecting an anionic clay–SWNT dispersion into a coagulation bath containing the cationic biopolymer chitosan. The fiber materials exhibited higher Young's modulus (2.3 GPa), but lower tensile strength (23 MPa), strain at break (1.2%) and conductivity (0.10 mS/cm) values compared to corresponding clay-SWNT-chitosan films. The fibers displayed similar electrical response upon hydration compared to film materials, i.e., an order of magnitude decrease in electrical resistance. This work contributes to the development of clay-based film and fiber materials.
Figure 1. Optical microscopy images of a clay suspension: (a) before and (b) after hydration; Inset: photograph of the clay suspension after hydration; (c) Optical microscopy image of 800 mg/L single-walled carbon nanotubes (SWNT) dispersed in a 1.12% w/v clay suspension; Inset: photograph of the SWNT dispersion; (d) UV-visible absorption spectra of 400 mg/L (line 1), 600 mg/L (line 2), 800 mg/L (line 3) and 1,000 mg/L (line 4) SWNT dispersed in a 1.12% w/v clay suspension; Inset: UV-vis absorbance at 747 nm as a function of SWNT concentration in the clay suspension.
Figure 1. Optical microscopy images of a clay suspension: (a) before and (b) after hydration; Inset: photograph of the clay suspension after hydration; (c) Optical microscopy image of 800 mg/L single-walled carbon nanotubes (SWNT) dispersed in a 1.12% w/v clay suspension; Inset: photograph of the SWNT dispersion; (d) UV-visible absorption spectra of 400 mg/L (line 1), 600 mg/L (line 2), 800 mg/L (line 3) and 1,000 mg/L (line 4) SWNT dispersed in a 1.12% w/v clay suspension; Inset: UV-vis absorbance at 747 nm as a function of SWNT concentration in the clay suspension.
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Figure 2. Rheological studies: (a) Shear stress as a function of shear rate for clay–carbon nanotube (CNT) (diamonds), clay–CNT–chitosan (triangles) and chitosan (squares); (b) thixotropic behavior test, viscosity as a function of time for clay–CNT (blue line), clay–CNT–chitosan (green line) and chitosan (red line). Shear rates in intervals 1, 2 and 3 are 0.01 s−1, 1000 s−1 and 0.01 s−1, respectively; Inset: photographs of clay–CNT suspension (1) and clay–CNT–chitosan (2) after being left undisturbed for one day; (c) Oscillatory amplitude sweep for clay–CNT (diamonds), clay–CNT–chitosan (triangles) and chitosan (squares). Filled and open symbols indicate storage (G′) and loss (G″) modulus, respectively; (d) Loss factor (tan δ = G″/G′) as a function of strain for clay–CNT (diamonds), clay–CNT–chitosan (triangles) and chitosan (squares).
Figure 2. Rheological studies: (a) Shear stress as a function of shear rate for clay–carbon nanotube (CNT) (diamonds), clay–CNT–chitosan (triangles) and chitosan (squares); (b) thixotropic behavior test, viscosity as a function of time for clay–CNT (blue line), clay–CNT–chitosan (green line) and chitosan (red line). Shear rates in intervals 1, 2 and 3 are 0.01 s−1, 1000 s−1 and 0.01 s−1, respectively; Inset: photographs of clay–CNT suspension (1) and clay–CNT–chitosan (2) after being left undisturbed for one day; (c) Oscillatory amplitude sweep for clay–CNT (diamonds), clay–CNT–chitosan (triangles) and chitosan (squares). Filled and open symbols indicate storage (G′) and loss (G″) modulus, respectively; (d) Loss factor (tan δ = G″/G′) as a function of strain for clay–CNT (diamonds), clay–CNT–chitosan (triangles) and chitosan (squares).
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Figure 3. (a) Photograph of a typical free standing film (nanotube mass fraction = 0.067) prepared by evaporative casting of a clay–CNT composite dispersion; Inset: scanning electron microscopy image; (b) Resistance versus sample length for films prepared by evaporative casting (squares) and vacuum filtration (buckypaper, circles) under controlled ambient conditions (21 °C, 45% RH). The straight lines are fits to Equation (2); (c) IV characteristics of a typical film prepared by evaporative casting before, and after exposure to humid atmosphere (21 °C, 90% RH) for 15 hours; (d) Current response to a square wave potential (±1 V) of a typical film prepared by evaporative casting before and after exposure to humid atmosphere (21 °C, 90% RH) for 15 hours. The circled areas highlight the non-linear behavior of the current response of the film after exposure to humid atmosphere.
Figure 3. (a) Photograph of a typical free standing film (nanotube mass fraction = 0.067) prepared by evaporative casting of a clay–CNT composite dispersion; Inset: scanning electron microscopy image; (b) Resistance versus sample length for films prepared by evaporative casting (squares) and vacuum filtration (buckypaper, circles) under controlled ambient conditions (21 °C, 45% RH). The straight lines are fits to Equation (2); (c) IV characteristics of a typical film prepared by evaporative casting before, and after exposure to humid atmosphere (21 °C, 90% RH) for 15 hours; (d) Current response to a square wave potential (±1 V) of a typical film prepared by evaporative casting before and after exposure to humid atmosphere (21 °C, 90% RH) for 15 hours. The circled areas highlight the non-linear behavior of the current response of the film after exposure to humid atmosphere.
Nanomaterials 01 00003f3
Figure 4. (a) Photograph of a typical free standing film (nanotube mass fraction = 0.028) prepared by evaporative casting of a clay-CNT-chitosan composite dispersion; Inset: scanning electron microscopy image; (b) Stress–strain curves for typical clay–CNT–chitosan fibers and typical free standing film (nanotube mass fraction = 0.028) prepared by evaporative casting of a clay–CNT–chitosan composite dispersion; (c) Typical film resistance as a function of time during exposure to humid atmosphere (21 °C, 90% RH) for 150 minutes; Inset: current response of the film to a triangular wave potential of during exposure to humid atmosphere; (d) Video images showing the actuatory response of a typical film when exposed to water vapor. Numbers indicate the time lapsed with respect to the first image.
Figure 4. (a) Photograph of a typical free standing film (nanotube mass fraction = 0.028) prepared by evaporative casting of a clay-CNT-chitosan composite dispersion; Inset: scanning electron microscopy image; (b) Stress–strain curves for typical clay–CNT–chitosan fibers and typical free standing film (nanotube mass fraction = 0.028) prepared by evaporative casting of a clay–CNT–chitosan composite dispersion; (c) Typical film resistance as a function of time during exposure to humid atmosphere (21 °C, 90% RH) for 150 minutes; Inset: current response of the film to a triangular wave potential of during exposure to humid atmosphere; (d) Video images showing the actuatory response of a typical film when exposed to water vapor. Numbers indicate the time lapsed with respect to the first image.
Nanomaterials 01 00003f4
Figure 5. (a) Photograph of a typical clay–CNT–chitosan fiber; (b, c) Scanning electron microscopy images of the fiber's surface morphology; (d) Typical fiber resistance as a function of time during exposure to humid atmosphere (21 °C, 90% RH) for 270 minutes.
Figure 5. (a) Photograph of a typical clay–CNT–chitosan fiber; (b, c) Scanning electron microscopy images of the fiber's surface morphology; (d) Typical fiber resistance as a function of time during exposure to humid atmosphere (21 °C, 90% RH) for 270 minutes.
Nanomaterials 01 00003f5
Table 1. Summary of rheology analysis of typical clay–CNT dispersion, clay–CNT–chitosan dispersion and chitosan solution. Bingham yield point (τB) and Bingham flow coefficient (ηB) values were obtained using the Bingham model, over shear rate range 1–100 s−1 (Figure 2a). ηref and ηhigh are the apparent viscosity values at the end of the reference interval (shear rate = 0.01 s−1) and high-shear (shear rate = 1000 s−1) intervals during the thixotropic behavior test (Figure 2b). η30, η60, η120, and η180 indicate the apparent viscosity during the regeneration interval (shear rate = 0.01 s−1) at 30, 60, 120 and 180 s, respectively. Values in square brackets indicate percentage values. τmax and γmax, refer to the maximum shear stress and shear strain of the linear viscoelastic region observed in the amplitude sweep profiles (Figure 2c).
Table 1. Summary of rheology analysis of typical clay–CNT dispersion, clay–CNT–chitosan dispersion and chitosan solution. Bingham yield point (τB) and Bingham flow coefficient (ηB) values were obtained using the Bingham model, over shear rate range 1–100 s−1 (Figure 2a). ηref and ηhigh are the apparent viscosity values at the end of the reference interval (shear rate = 0.01 s−1) and high-shear (shear rate = 1000 s−1) intervals during the thixotropic behavior test (Figure 2b). η30, η60, η120, and η180 indicate the apparent viscosity during the regeneration interval (shear rate = 0.01 s−1) at 30, 60, 120 and 180 s, respectively. Values in square brackets indicate percentage values. τmax and γmax, refer to the maximum shear stress and shear strain of the linear viscoelastic region observed in the amplitude sweep profiles (Figure 2c).
SampleτB (Pa)ηB (Pa.s)ηref (Pa.s)ηhigh (Pa.s)η30 (Pa.s)η60 (Pa.s)η120 (Pa.s)η180 (Pa.s)τmax (Pa)γmax (%)
Clay–CNT5.87 ± 0.020.0153 ± 0.0003287 ± 340.0142 ± 0.0001433 ± 24601 ± 5405 ± 7297 ± 52.0 ± 0.54.0 ± 1.1
Clay–CNT–Chitosan0.017 ± 0.0010.00429 ± 0.000010.265 ± 0.0080.0040 ± 0.00020.596 ± 0.0060.53 ± 0.030.384 ± 0.0080.23 ± 0.03(1.3 ± 0.5) × 10−30.10 ± 0.02
Chitosan1.19 ± 0.140.458 ± 0.00215.4 ± 0.10.24 ± 0.111.1 ± 0.110.7 ± 0.110.0 ± 0.110.1 ± 0.2n.a.n.a.
Table 2. Summary of Young's/storage modulus (Modulus), tensile strength (TS), strain at break (γ), electrical conductivity (σ), ratio of resistance after (RA) and before (RB) exposure to humid atmosphere for the different materials prepared by combining sample 1 with sample 2. For example, a combination of clay-SWNT and chitosan indicates a clay–SWNT–chitosan material. Differences between the sample materials are indicated by numbers, e.g., clay1 is montmorillonite clay, while clay2 is a model clay consisting of ZrP platelets. FMWMT1–2, chitosan1–2 and CB indicate different types of chitosan, different types of functionalized multi-walled carbon nanotubes and carbon black, respectively, see tabulated references for complete details. Storage modulus values indicated by * (errors not stated in source).
Table 2. Summary of Young's/storage modulus (Modulus), tensile strength (TS), strain at break (γ), electrical conductivity (σ), ratio of resistance after (RA) and before (RB) exposure to humid atmosphere for the different materials prepared by combining sample 1 with sample 2. For example, a combination of clay-SWNT and chitosan indicates a clay–SWNT–chitosan material. Differences between the sample materials are indicated by numbers, e.g., clay1 is montmorillonite clay, while clay2 is a model clay consisting of ZrP platelets. FMWMT1–2, chitosan1–2 and CB indicate different types of chitosan, different types of functionalized multi-walled carbon nanotubes and carbon black, respectively, see tabulated references for complete details. Storage modulus values indicated by * (errors not stated in source).
Sample 1Sample 2Modulus (GPa)TS (MPa)γ (%)σ (mS/cm)RA/RBSource
Chitosan-1.2 ± 0.239 ± 510 ± 20-This work-film
Clay–SWNT----140 ± 403.7 ± 1.2This work-film
Clay–SWNTChitosan1.4 ± 0.225 ± 65.8 ± 1.30.80 ± 0.200.10 ± 0.05This work-film
Clay–SWNTChitosan2.3 ± 0.223 ± 41.2 ± 0.20.10 ± 0.010.23 ± 0.02This work-fiber
Chitosan1-1.40 ± 0.0543 ± 212 ± 3--7-film
Chitosan1–Clay1FMWNT13.14 ± 0.03114 ± 57 ± 2--7-film
Chitosan2-3.771 *----9-film
Chitosan2–Clay1FMWNT25.889 *----9-film
Epoxy1-3.06 *--0-8-film
Clay1–SWNTEpoxy13.73 *--2-8-film
Clay1–CBEpoxy14.31 *--0.016 ± 0.002-12-film
Latex-2.3 *--0-11-film
Latex–CBClay12.54 *--8.6-11-film
Epoxy2-3.04 ± 0.0475 ± 43.7 ± 0.1--10-film
Clay2-FMWNT2Epoxy24.27 ± 0.07116 ± 64.3 ± 0.4--10-film
Acknowledgments
This work was funded by the University of Wollongong (URC Grant) and Australian Research Council Future Fellowship (M. in het Panhuis). We wish to thank J. Lamont and K. Chapman (Nowra Chemical Manufacturers Pty. Ltd.) for use of equipment, and S. Ralph, A. Granero, L. Sweetman, and J. Boge (all University of Wollongong) for assistance with fiber spinning and electron microscopy.
References
1. Bergaya, F.; Theng, B.K.G.; Lagaly, G. Handbook of Clay Science; Elsevier: Amsterdam, The Netherlands, 2006; Volume 1. [Google Scholar]
2. Martin, C.; Pignon, F.; Piau, J.M.; Magnin, A.; Lindner, P.; Cabane, B. Dissociation of thixotropic clay gels. Phys. Rev. E 2002, 66, 021401:1–021401:11. [Google Scholar]
3. Kelessidis, V.C.; Christidis, G.; Makri, P.; Hadjistamou, V.; Tsamantaki, C.; Mihalakis, A.; Papanicolaou, C.; Foscolos, A. Gelation of water-bentonite suspensions at high temperatures and rheological control with lignite addition. Appl. Clay Sci. 2007, 36, 221–231. [Google Scholar]
4. Jung, H.; Kim, H.-M.; Choy, Y.B.; Hwang, S.-J.; Choy, J.-H. Itraconazole–laponite: Kinetics and mechanism of drug release. Appl. Clay Sci. 2008, 40, 99–107. [Google Scholar]
5. Lin, F.H.; Lee, Y.H.; Jian, C.H.; Wong, J.-M.; Shieh, M.-J.; Wang, C.-Y. A study of purified montmorillonite intercalated with 5-fluorouracil as drug carrier. Biomaterials 2002, 23, 1981–1987. [Google Scholar]
6. In het Panhuis, M. Carbon nanotubes: Enhancing the polymer building blocks for intelligent materials. J. Mater. Chem. 2006, 16, 3598–3605. [Google Scholar]
7. Tang, C.; Xiang, L.; Su, J.; Wang, K.; Yang, C.; Zhang, Q.; Fu, Q. Largely improved tensile properties of chitosan film via unique synergistic reinforcing effect of carbon nanotube and clay. J. Phys. Chem. B 2008, 112, 3876–3881. [Google Scholar]
8. Liu, L.; Grunlan, J.C. Clay assisted dispersion of carbon nanotubes in conductive epoxy nanocomposites. Adv. Funct. Mater. 2007, 17, 2343–2348. [Google Scholar]
9. Tang, C.; Chen, N.; Zhang, Q.; Wang, K.; Fu, Q.; Zhang, X. Preparation and properties of chitosan nanocomposites with nanofillers of different dimensions. Polym. Degrad. Stab. 2009, 94, 124–131. [Google Scholar]
10. Sun, D.; Chu, C.C.; Sue, H.J. Simple approach for preparation of epoxy hybrid nanocomposites based on carbon nanotubes and a model clay. Chem. Mater. 2010, 22, 3773–3778. [Google Scholar]
11. Miriyala, S.M.; Kim, Y.S.; Liu, L.; Grunlan, J.C. segregated networks of carbon black in poly(vinyl acetate) latex: Influence of clay on the electrical and mechanical behavior. Macromol. Chem. Phys. 2008, 209, 2399–2409. [Google Scholar]
12. Etika, K.C.; Liu, L.; Hess, L.A.; Grunlan, J.C. The influence of synergistic stabilization of carbon black and clay on the electrical and mechanical properties of epoxy composites. Carbon 2009, 47, 3128–3136. [Google Scholar]
13. Yamamoto, H.; Nakazawa, A.; Hayakawa, T.; Nishi, N. Induced optical-activity in the complex of chitosan with azo dyes. J. Polym. Sci. Lett. Ed. 1984, 22, 255–260. [Google Scholar]
14. Patil, A.J.; Muthusamy, E.; Mann, S. Fabrication of functional protein-organoclay lamellar nanocomposites by biomolecule-induced assembly of exfoliated aminopropyl-functionalized magnesium phyllosilicates. J. Mater. Chem. 2005, 15, 3838–3843. [Google Scholar]
15. Ryabenko, A.; Dorofeeva, T.; Zvereva, G. UV-VIS-NIR spectroscopy study of sensitivity of single-wall carbon nanotubes to chemical processing and van-der-Waals SWCNT/SWCNT interaction. Verification of the SWCNT content measurements by absorption spectroscopy. Carbon 2004, 42, 1523–1535. [Google Scholar]
16. Attal, S.; Thiruvengadathan, R.; Regev, O. Determination of the concentration of single-walled carbon nanotubes in aqueous dispersions using UV-visible absorption spectroscopy. Anal. Chem. 2006, 78, 8098–8104. [Google Scholar]
17. Barnes, H.A.; Hutton, J.F.; Walters, K. An Introduction to Rheology; Elsevier: Amsterdam, The Netherlands, 1989. [Google Scholar]
18. Gunister, E.; Pestreli, D.; Unlu, C.H.; Atici, O.; Gungor, N. Synthesis and characterization of chitosan-MMT biocomposite systems. Carbohyd. Polym. 2007, 67, 358–365. [Google Scholar]
19. Mezger, T.G. The Rheology Handbook, 2nd ed.; Vincentz Network: Hannover, Germany, 2006. [Google Scholar]
20. Ferris, C.J.; In het Panhuis, M. Gel-carbon nanotube composites: The effect of carbon nanotubes on gelation and conductivity behaviour. Soft Matter 2009, 5, 1466–1473. [Google Scholar]
21. In het Panhuis, M.; Gowrisanker, S.; Vanesko, D.J.; Mire, C.A.; Jia, H.; Xie, H.; Baughman, R.H.; Musselman, I.H.; Gnade, B.E.; Dieckmann, G.R.; Draper, R.K. Nanotube network transistors from peptide-wrapped single-walled carbon nanotubes. Small 2005, 1, 820–823. [Google Scholar]
22. Small, W.R.; In het Panhuis, M. Inkjet printing of transparent, electrically conducting single-wall carbon nanotube composites. Small 2007, 3, 1500–1503. [Google Scholar]
23. Granero, A.J.; Razal, J.M.; Wallace, G.G.; In het Panhuis, M. Spinning carbon nanotube-gel fibers using polyelectrolyte complexation. Adv. Funct. Mater. 2008, 18, 3759–3764. [Google Scholar]
24. In het Panhuis, M.; Heurtematte, A.; Small, W.R.; Paunov, V.N. Inkjet printed water sensitive transparent films from natural gum—Carbon nanotube composites. Soft Matter 2007, 3, 840–843. [Google Scholar]
25. Boge, J.; Sweetman, L.J.; In het Panhuis, M.; Ralph, S.F. The effect of preparation conditions and biopolymer dispersants on the properties of SWNT buckypapers. J. Mater. Chem. 2009, 19, 9131–9140. [Google Scholar]
26. Yamamoto, H.; Senoo, Y. Polyion complex fiber and capsule formed by self-assembly of chitosan and gellan at solution interfaces. Macromol. Chem. Phys. 2000, 201, 84–92. [Google Scholar]
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Build new shapes with Shaper and Shape Builder tools
1. Illustrator User Guide
2. Get to know Illustrator
1. Introduction to Illustrator
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1. Overview
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1. Illustrator on the iPad overview
2. Illustrator on the iPad FAQs
3. System requirements | Illustrator on the iPad
4. What you can or cannot do on Illustrator on the iPad
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1. Work with Illustrator cloud documents
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4. Illustrator cloud documents | Common questions
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1. Troubleshoot create or save issues for Illustrator cloud documents
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2. Edit paths
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4. Draw with the Pen, Curvature, or Pencil tool
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11. Design a flower in 5 easy steps
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1. About 3D effects in Illustrator
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4. Adjust colors
5. Use the Adobe Color Themes panel
6. Color groups (harmonies)
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8. Recolor your artwork
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1. About painting
2. Paint with fills and strokes
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4. Gradients
5. Brushes
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11. Work with Live Corners
12. Enhanced reshape workflows with touch support
13. Edit clipping masks
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16. Global editing
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1. Add text and work with type objects
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About the Shaper Tool
The Shaper tool helps you create complex and beautiful designs by drawing, stacking, and placing shapes together, and then simply combining, merging, deleting, or moving them. Use simple, visually-intuitive gestures to perform operations that previously may have taken multiple actions to achieve.
Use the Shaper tool to turn natural gestures into vector shapes. Use a mouse or the ease of a touch device to create polygons, rectangles, or circles. The shapes drawn are live shapes. This feature is enabled in the traditional workspaces, the specialized Touch workspace, and on your mobile with Adobe Fresco.
Using the Shaper tool (drawing shapes)
1. In Illustrator, from the Toolbox, click the Shaper tool (Shift+N).
2. In the document, draw a shape. For example, draw a rough representation of a rectangle, circle, ellipse, or triangle or other polygon.
3. The shape you draw is converted into a crisp geometric shape. The shape created is Live, and is fully editable like any Live shape.
Convert free-hand gestures into crisp vector shapes
Convert free-hand gestures into crisp vector shapes
Using the Shaper tool (creating shapes)
1. Do one of the following:
• Select a few overlapping shapes in your document
• Use a tool to draw shapes that are overlapping
• Use the Shaper tool (Shift + N) to quickly draw rectangles, circles, or polygons
2. If not already selected, select the Shaper tool (Shift + N).
3. Using your mouse (on a non-touch device) or your finger scribble on an area that you would either like to merge, delete, or punch out.
The following rules determine how portions of the shapes are punched out or merged, and what the color of a merged shape is:
• If the scribble is within one shape, the area is punched out.
• If the scribble is across intersecting areas of two or more shapes, the intersecting areas are punched out
• If scribble originates from the shape in the front:
• From a non-overlapping area to an overlapping area, the shape in the front is punched out
• From an overlapping area to a non-overlapping area, the shapes are merged, with the color of the merged area being that of the scribble origin point.
• If the scribble originates from the shape in the back:
• From a non-overlapping area to an overlapping area, the shapes are merged, with the color of the merged area being that of the scribble origin point.
Examples of the scribble action with the Shaper tool
(Left) Scribble action, and (Right) Resulting Shaper Groups
Selecting shapes in a Shaper Group
All shapes in a Shaper Group stay editable, even after portions of shapes may have been punched out or merged. The following actions allow you to select individual shapes or the group:
Face Selection mode
1. Select the Shaper Tool.
2. Tap or click on a Shaper Group. The Shaper Group is selected, and a bounding box appears with the Arrow widget .
3. Tap the shape again (or an individual shape, if individual shapes exist). You are now in Face Selection mode.
4. If the Shaper Group contains merged shapes, the face of the shape appears matted. You can change the Fill color of shapes.
Face Selection mode
Face Selection mode
Construction Mode
1. With a Shaper Group selected, do one of the following:
• Tap or click the Arrow widget so that it appears pointing upwards .
• Double-click a shape.
• Single-click a shape's stroke.
2. With a single underlying object selected, you can modify any property or appearance of the object.
Construction mode in Illustrator
Construction mode
Removing a shape from a Shaper Group
1. Perform the steps required to get into Construction mode.
2. Drag and drop a shape out of the bounding box.
About the Shape Builder Tool
The Shape Builder tool is an interactive tool for creating complex shapes by merging and erasing simpler shapes. It works on simple and compound paths.
It intuitively highlights edges and regions of the selected art, which can be merged to form new shapes. An edge is defined as the section of a path, which does not intersect any other path of the selected objects. A region is a closed area bounded by edges.
By default, the tool is in merge mode where it allows you to combine paths or regions. You can also switch to the erase mode to delete any unwanted edges or regions by pressing Alt (Windows) or Option (Mac).
Setting the Shape Builder tool options
You can set up and customize various options such as gap detection, coloring source, and highlighting to get the required merging capability and better visual feedback.
Double-click the Shape Builder Tool icon in the Tools panel to set these options in the Shape Builder Tool Options dialog box.
Shape Builder Tool Options dialog box
Shape Builder Tool Options dialog box
Gap Detection
Set the gap length using the Gap Length drop-down list. The values available are Small (3 points), Medium (6 points), and Large (12 points).
Select the Custom check box if you want to provide an exact gap length.
When you select the gap length, Illustrator finds the gaps only close to the specified gap length value. Make sure that the gap length value is close (approximately) to the actual gap length of the art. You can check if the gaps are being detected by providing different gap length values until the gaps in the art are detected.
For example, if you set the gap length to 12 points, whereas the shape that you need to merge contains gaps at 3 points, Illustrator may not detect the gaps.
Gap Detection
The highlighted area shows that the gap is detected and is considered as a region
Consider Open Filled Paths as Closed
If this option is selected, an invisible edge is created for an open path to make a region. When you click inside the region, a shape is created.
In Merge Mode, Clicking the Stroke Splits the Path
Select the check box, In Merge Mode, Clicking Stroke Splits the Path. This option allows you to split the parent path into two. The first path is created from the edge on which you click and second path is the remaining portion of the parent path excluding the first path. If this option is selected, the pointer changes to , while splitting the path.
Pick Color From
You can choose to color objects using the color swatches or the colors used in existing artwork. Use the Pick Color From drop-down list to select the Color Swatches or Artwork option.
If you select the Color Swatches option, you get the Cursor Swatch Preview option. You can select the Cursor Swatch Preview check box to preview and select colors. A Live Paint style cursor swatch is provided when you select this option. It allows iteration (using the arrow keys) and selecting colors from the swatches panel.
note: You can iterate using the arrow keys even if the Cursor Swatch Preview is disabled.
To change the color of the stroke, move the pointer over object edges to highlight and change the color of the stroke. This option works only if the option, In Merge Mode, Clicking Stroke Splits the Path is selected.
You can select the fill color of a region by pointing anywhere on the document.
note: The Cursor Swatch Preview is not displayed while merging, to ensure that the shapes are clearly visible.
If you select the Artwork option, Illustrator uses the same rules that are used for other art styles on merged objects. For more information, see step 6 in Creating shapes using Shape Builder Tool.
Fill
The Fill check box is selected by default. If this option is selected, the path or region that you can merge, is highlighted in gray, when you mouse over the selected path. If this option is not selected, the selected region or path appears as normal.
Highlight Stroke When Editable
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| 0.975556 |
Plant Adaptations
What's the strangest place you've ever seen a plant growing? It sometimes seems as though plants can grow everywhere. You see them growing in your house, in your yard, and even in the cracks of highways and rocks. Some grow in swamps or oceans. Some grow in the dry desert. Some plants thrive under the snow, and others live in forests. Plants grow on every continent on Earth. Even Antarctica has several species of lichens and mosses growing there.
Because they stay in one place, plants must be able to get what they need from their environment. Think of all the different types of environments where plants live. Some plants have adaptations that help them survive. Plants in the far north or high on mountains grow close to the ground as protection from the wind. Desert plants grow far apart so that they can get water and nutrients from a larger area. The sharp spines of a cactus keep animals from eating it.
Plants have adapted to many different environments on Earth. Desert plants look very different from plants that live near the ocean or in the mountains. The leaves, stems, roots, and reproductive parts of plants can be very different depending on where the plant lives.
Mosses are soft cushiony plants that live in damp places. Mosses have few or no stems. They are non-vascular plants. They grow close to the ground. They hold soil in a forest and prevent it from being washed away by heavy rains. These plants have no roots so most of them grow close to the ground to keep from drying up. Some mosses, known as sphagnum peat mosses, absorb water like sponges and hold the water in their stems. The mosses often form wet, spongy quilts between the trees in damp forests.
It takes a very special sort of plant to cope with the boiling hot days, freezing nights, and the dry soils of a desert. Desert plants have special features such as spines, huge root systems, and deadly poisons that help them survive. The creosote plant produces a poison in its roots that prevents any other plant from growing near it. That way, it gets to keep all the available water near it for itself. Desert plants may have smaller leaves to minimize moisture loss. Leaves may have a waxy coating for the same reason. Hair-like structures on the plant help to slow evaporation and reflect sunlight.
. . . Print Entire Reading Comprehension with Questions
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Irritated Eyelids (Blepharitis)
Blepharitis is a common inflammatory condition that causes burning, itching and irritation of the eyelids. In severe cases, it may also cause styes and irritation or inflammation of the cornea (keratitis) or conjunctiva (conjunctivitis). Blepharitis is characterized by sandy, itchy eyes, red or swollen eyelids, and crusty or flaky skin on the eyelids.
Blepharitis is usually a chronic problem that can be controlled with extra attention to lid hygiene. Begin by soaking a clean washcloth in warm tap water. Place the compress on closed eyelids for five minutes and then repeat. Next, gently scrub the eyelids with a washcloth or cotton swab soaked in a mixture of equal parts of baby shampoo and water. Finally, rinse the eyelids thoroughly with warm water. Repeat the treatment two to three times daily for two weeks and then reduce to once daily. In some cases, anti-inflammatory and antibiotic drops or ointments may be necessary for flare-ups and more severe cases.
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Stochastic Quantum Zeno by Large Deviation Theory
27 Sep 2015 · Gherardini Stefano, Gupta Shamik, Cataliotti Francesco Saverio, Smerzi Augusto, Caruso Filippo, Ruffo Stefano ·
Quantum measurements are crucial to observe the properties of a quantum system, which however unavoidably perturb its state and dynamics in an irreversible way. Here we study the dynamics of a quantum system while being subject to a sequence of projective measurements applied at random times... In the case of independent and identically distributed intervals of time between consecutive measurements, we analytically demonstrate that the survival probability of the system to remain in the projected state assumes a large-deviation (exponentially decaying) form in the limit of an infinite number of measurements. This allows us to estimate the typical value of the survival probability, which can therefore be tuned by controlling the probability distribution of the random time intervals. Our analytical results are numerically tested for Zeno-protected entangled states, which also demonstrates that the presence of disorder in the measurement sequence further enhances the survival probability when the Zeno limit is not reached (as it happens in experiments). Our studies provide a new tool for protecting and controlling the amount of quantum coherence in open complex quantum systems by means of tunable stochastic measurements. read more
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Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics
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__label__pos
| 0.704418 |
Journal cover Journal topic
Climate of the Past An interactive open-access journal of the European Geosciences Union
doi:10.5194/cp-2016-42
© Author(s) 2016. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
06 Apr 2016
Review status
This discussion paper has been under review for the journal Climate of the Past (CP). The manuscript was not accepted for further review after discussion.
Chemical composition of soluble and insoluble particles around the last termination preserved in the Dome C ice core, inland Antarctica
Ikumi Oyabu1,2, Yoshinori Iizuka1, Eric Wolff3, and Margareta Hansson4 1Institute of Low Temperature Science, Hokkaido Unive rsity, Sapporo 060-0819, Japan
2National Institute of Polar Research, Tokyo 190-8518, Japan
3Department of Earth Sciences, University of Cambridge, Cambridge CB2 3EQ, UK
4Department of Physical Geography, Stockholm University, Stockholm 106 91, Sweden
Abstract. Knowing the chemical composition of particles preserved in polar ice sheets is useful for understanding past atmospheric chemistry. Recently, several studies have examined the chemical compositions of soluble salt particles preserved in ice cores from inland and peripheral regions in both Antarctica (Dome Fuji and Talos Dome) and Greenland (NEEM). On the other hand, there is no study that compares salt compositions between different sites in inland Antarctica. This study examines the chemical compositions of soluble salt particles around the last termination in the Dome C ice core, and compares them to those from Dome Fuji. Particles larger than 0.45 μm are obtained from the ice core by an ice sublimation method, and their chemical compositions are analyzed using scanning electron microscopy and energy dispersive X-ray spectroscopy. The major soluble salt particles are CaSO4, Na2SO4, and NaCl, which is the same as that from the Dome Fuji ice core. Time-series changes in the composition of these salts are similar to those for the Dome Fuji ice core. Specifically, from 25 to 18 ka, the ratio of NaCl to Na2SO4 is variable, but generally the CaSO4 and NaCl fractions are high and the Na2SO4 fraction is low. Between 18 and 17 ka, the CaSO4 and NaCl fractions decrease and the Na2SO4 fraction increases. Between 16 and 6.8 ka, the CaSO4 and NaCl fractions are low and Na2SO4 fraction is high. However, the sulfatization rate of NaCl at Dome C is higher than that at Dome Fuji. We argue that this higher rate arises because at Dome C more SO42− is available for NaCl to form Na2SO4 due to a lower concentration of Ca2+.
Citation: Oyabu, I., Iizuka, Y., Wolff, E., and Hansson, M.: Chemical composition of soluble and insoluble particles around the last termination preserved in the Dome C ice core, inland Antarctica, Clim. Past Discuss., doi:10.5194/cp-2016-42, 2016.
Ikumi Oyabu et al.
Ikumi Oyabu et al.
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Short summary
This study presented the chemical compositions of non-volatile particles around the last termination in the Dome C ice core by using the sublimation-EDS method. The major soluble salt particles are CaSO4, Na2SO4, and NaCl, and time-series changes in the composition of these salts are similar to those for the Dome Fuji ice core. However, some differences occurred. The sulfatization rate of NaCl at Dome C is higher than that at Dome Fuji.
This study presented the chemical compositions of non-volatile particles around the last...
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| 0.882497 |
Introducing Collective Communication Primitive APIs in Ray
By Hao Zhang and Richard Liaw
In Ray 1.2.0, we’ve added a library for “collective communication primitives” to Ray. These primitives can be used in your Ray program to simplify the exchange of information across many distributed processes at the same time, speeding up certain distributed operations by an order of magnitude.
What Is Collective Communication?
In many distributed computing applications, processes need to communicate with other processes in order to exchange information or synchronize progress. This type of communication usually relies upon “send” and “receive” operations -- a sender process sends a message to a receiver process, such as the image above shows.
This communication pattern is known as point-to-point communication -- which should be quite familiar to Ray users -- and can be realized using Ray’s “ray.remote()” and “ray.get()” APIs.
However, there are many cases where a sending process may want to communicate with multiple receivers at once. A typical example is in data-parallel distributed deep learning: a training process has to broadcast its gradients to all other peer processes in order to perform a coordinated update of model parameters.
Theoretically, one can use multiple send and receive operations (e.g., in Ray, many “ray.put()” and “ray.get()” among different actors/tasks), such as Figure 2 (left) shows. However, this ends up being programmatically cumbersome and might end up with suboptimal communication performance.
fig 2 Collective Communication
Figure 2: A process needs to send a message to a set of other process: (Left) a sender process performs point-to-point communication to every receiver process; (Right) Processes are put in the same collective group and they perform a collective broadcast communication to achieve the goal
Collective communication primitives allow programs to express such communication patterns between many processes (a “group”). The key advantages of providing specialized APIs and implementations for these communication primitives are:
• The ability to implement a collective communication backend at a low level in order to make the best use of the network hardware (Ethernet, InfiniBand, etc.), and provide the greatest communication performance.
• The ability to optimize for different types of computing devices, such as GPUs, and avoid many unnecessary overheads.
Example: AllReduce Explained
In this section, we’ll walk through a high-level example of a collective communication primitive. Among the many collective communication primitives, allreduce is the most adopted one in many distributed ML training systems, including Horovod and distributed TensorFlow.
The image below from the NCCL documentation illustrates the AllReduce procedures.
fig3 NCCL Collective Communication
Figure 3: The procedures of the collective AllReduce operation.
Specifically, it starts with independent arrays (notated with four different colors) “in0”, “in1”, “in2”, “in3” on each of the 4 processes of a collective group. Each process in the group is assigned with a unique integer ID, called “rank”. It then performs communications and reductions on data (e.g. sum) across all ranks and ends with identical arrays “out”, where out[i] = sum(in0[i], in1[i], in2[i], in3[i]) for each rank k.
fig4
Figure 4: All-reducing gradients in data-parallel distributed ML training.
This maps perfectly with the gradient synchronization procedure in data-parallel distributed deep learning, as shown in Figure 4: in each training iteration, on each training worker, the gradient is calculated during the backpropagation pass, and synchronized via an “allreduce” operation across all training processes. After this, all processes will have the aggregated gradients from all other processes and can safely apply the gradients to update their local parameters -- keeping all processes synchronized!
There are a variety of different ways that “allreduce” can be implemented, and each implementation can have different performance characteristics -- if you are interested in learning more, you can check out this survey paper.
Walkthrough
This blogpost introduces a set of native Ray collective communication primitives for distributed CPUs or GPUs. Let’s walk through the usage of these collective communication APIs.
Importing
Before starting, make sure you have installed the latest ray>=1.2.0 wheel. You can import the collective API using the code below:
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import ray.util.collective as col
Under the namespace col, we have provided a series of collective primitives that can be used in Ray task and actor implementations to specify collective communication. Next, let’s walk through an example.
Example
Suppose we want to launch a distributed ML training task on 16 GPUs spread across a 16-node cluster, each with one GPU. The ray actor API allows you to define a GPU actor in the following way:
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import ray
import cupy
@ray.remote(num_gpus=1)
class GPUWorker:
def __init__(self):
self.gradients = cupy.ones((10,), dtype=cupy.float32)
The next code snippet spawns 16 of these actors. Ray will automatically create them and assign each of them a GPU:
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num_workers = 16
workers = [GPUWorker.remote() for i in range(num_workers)]
Note that in each one of the GPU actors, we have created a CuPy array self.gradients on its designated GPU at initialization. For walkthrough purposes, think of this array self.gradients as the gradients of model parameters generated at each iteration of the training, that need to be repeatedly synchronized across all GPU actors.
With the standard Ray API, communicating the gradients between GPU workers would require a series of ray.get calls, and passing around the ObjectRefs across different actors. Below we provide a snippet of example code to achieve this using the original ray.get and ray.put APIs.
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import ray
import cupy
@ray.remote(num_gpus=1)
class GPUWorker:
def __init__(self):
self.gradients = cupy.ones((10,), dtype=cupy.float32)
def put_gradients(self):
return ray.put(self.gradients)
def reduce_gradients(self, grad_id_refs):
grad_ids = ray.get(grad_id_refs)
reduced_result = cupy.ones((10,), dtype=float32)
for grad_id in grad_ids:
array = ray.get(grad_id)
reduced_result += array
result_id = ray.put(reduced_result)
return result_id
def get_reduced_gradient(self, reduced_gradient_id_ref):
reduced_gradient_id = ray.get(reduced_gradient_id_ref)
reduced_gradient = ray.get(reduced_gradient_id)
# do whatever with the reduced gradients
return True
# Allreduce the gradients using Ray APIs
# Let all workers put their gradients into the Ray object store.
gradient_ids = [worker.put_gradients.remote() for worker in workers]
ray.wait(object_ids, num_returns=len(object_ids, timeout=None))
# Let worker 0 reduce the gradients
reduced_id_ref = workers[0].reduce_gradients.remote(gradient_ids)
# All others workers get the reduced gradients
results = []
for i, worker in enumerate(workers):
results.append(worker.get_reduced_gradient.remote([reduced_id_ref]))
ray.get(results)
While the ray.put and ray.get are simple yet powerful APIs for Ray users to implement various distributed code, communicating between workers will require going through the Ray object store, introducing small overheads caused by object serialization and deserialization, or by object movement between CPU RAM and GPU memory, such as in the above case. These overheads might be amplified when the same communication patterns happen often and repetitively -- such as in distributed ML training on GPUs.
However, with collective communication primitives we can use a single ray.util.collectve.allreduce() call to simplify the code above and boost the performance significantly.
Like most collective communication libraries, we first establish a collective group for this group of 16 GPU worker actors:
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import cupy
import ray
import ray.util.collective as col
@ray.remote(num_gpus=1)
class GPUWorker:
def __init__(self):
self.gradients = cupy.ones((10,), dtype=cupy.float32)
def setup(self, world_size, rank):
col.init_collective_group(
world_size=world_size,
rank=rank,
backend="nccl")
def allreduce(self):
col.allreduce(self.gradients)
return self.gradients
setup_rets = ray.get([w.setup(16, i) for i, w in enumerate(workers)])
Once the collective group is created, we can perform collective communication using the primitives. In this case, we want to "allreduce’" the gradients, so:
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results = ray.get([w.allreduce.remote() for w in workers])
Using a simple collective allreduce call, we have managed to reduce the gradients across all 16 workers and store them in the self.gradients buffer in-place.
Performance
In the above example, we choose the NCCL backend as the collective allreduce backend, which is extremely advantageous to communicate contents between distributed GPU compared to Ray’s gRPC based implementations, since NCCL is optimized to achieve high bandwidth and low latency over PCIe and NVLink high-speed interconnects within a node and over NVIDIA Mellanox Network across nodes.
See the two microbenchmarks below comparing the performance of AllReduce using Ray on two setups with and without the NCCL backend (ray.util.collective).
Figure 5 shows a node with 2 GPUs, each worker is spawned on 1 GPU with NVLink enabled. Note the values corresponding to the Y-axis are in log-scale.
2GPU
Figure 5
Figure 6 shows a cluster with 7 nodes, each node with 2 GPUs; each worker is spawned on 1 GPU (hence 14 workers in total). Note the values corresponding to the Y-axis are in log-scale.
7 Node Collective Communication
Figure 6
In short, these graphs show ray.col.collective.allreduce can be 10 - 1000x faster than the assembled allreduce function via ray.get and ray.put.
Next Steps
Besides collective communication and NCCL backends, the ray primitives APIs also support fast point-to-point communication between distributed GPUs, as well as the GLOO backend, optimized for collective communication between distributed CPUs. You can check out this documentation for a full description of the collective primitives in Ray.
On top of these collective primitives, we are building Ray-native distributed ML training systems, such as parameter servers. A key advantage is that they can be used to distribute very arbitrary Python-based ML code beyond TensorFlow and PyTorch, such as Spacy/Thinc, JAX, or even numpy code.
As a side product, we have also generated a Python version of the Facebook GLOO library, and continuously maintain it under ray-projects/pygloo. You might find it useful for your application! If you have any questions or thoughts about Ray, please feel free to join the Ray Discourse or Slack. Finally, if you’re interested in helping to improve Ray and its user experience, Anyscale is hiring!
Credits
Thanks to the following Ray team members and open source contributors: Dacheng Li, Lianmin Zheng, Xiwen Zhang, and Ion Stoica.
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__label__pos
| 0.907882 |
LIFE SCIENCE BOOK PDF
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Life Sciences, Fundamentals and Practice, Part I. Book · January with 94, Reads. Publisher: 5th. Publisher: ISBN: Subtle is the Lord: The Science and Life of Albert Einstein Life Sciences Fundamentals and Practice, Fourth edition. . Try pdfdrive:hope to request a book. abtresdeorebgolf.ga Medical Medium Seven CSIR NET Life Science Papers (Memory Based) – ( Dec.,
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If you want the online textbook—Click on online student edition—full version 9. For Parents and Students Lighten the backpack load; leave some textbooks at school. Find This grade 7 Science worksheet on Life Science aims at upgrading a student? Cancel anytime. Life Science. The symptoms of pellagra progress through the three Ds: Deficiency of niacin causes pellagra. If an enzyme is denatured or dissociated into its subunits. It is a remarkable molecular device that determines the pattern of chemical transformations.
Their catalytic activity depends on the integrity of their native protein conformation. It changes only the rate at which equilibrium is achieved. Alcohol dehydrogenase. It increases the rate of a reaction by lowering the activation energy. With the exception of a small group of catalytic RNA molecules.
Enzymes have several properties that make them unique. Some cofactors are simple metal ions and other cofactors are complex organic groups. A cofactor can be linked to the protein portion of the enzyme either covalently or non- covalently.
The complete. Virtually all cellular reactions or processes are mediated by enzymes. Removal of cofactor from a conjugated enzyme leaves only protein component. Cofactors which are tightly associated with the protein covalently or non-covalently are called prosthetic group. They are highly specialized proteins and have a high degree of specificity for their substrates.
Xanthine oxidase Se Glutathione peroxidase 89 www. Enzymes can be divided into two general classes: Lysyl oxidase. Kinases Transfer phosphate from ATP to a substrate.
The last number is a serial number in the sub-subclass. The first three numbers define major class. EC 2 Transferases Transferases catalyze reactions that involve the transfer of groups from one molecule to another. There are six classes to which different enzymes belong. Oxygenases Directly incorporate oxygen into the substrate. According to this rule.
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The enzyme commission has developed a rule for naming enzymes. Common trivial names for the transferases often include the prefix trans. The Enzyme Commission EC has given each enzyme a number with four parts.
These classes are: EC 1 Oxidoreductase Oxidoreductase catalyzes oxidation-reduction reactions. As for example. Because of the confusion that arose from these common names. Many enzymes are named for their substrates and for the reactions that they catalyze. Common names provide little information about the reactions that enzymes catalyze.
EC 3 Hydrolases Hydrolases catalyze reactions in which the cleavage of bonds is accomplished by adding water. Transaminases Transfer amino group from amino acids to keto acids. Examples of such groups include amino. Peroxidases Use H2O2 as an electron acceptor.
Dehydrogenases Use molecules other than oxygen e. Phosphorylases Transfer inorganic phosphate to a substrate. Under constant temperature and pressure. Thermodynamic principles The First law of thermodynamics states that the energy is neither created nor destroyed.
Free Study Material, Sample Questions, Notes on Life Sciences for CSIR NET JRF Exam
The change in the free energy. Chapter 02 Bioenergetics and Metabolism 2. The Second law of thermodynamics states that the total entropy of a system must increase if a process is to occur spontaneously. The chemical reaction has a characteristic standard free energy change and it is constant for a given reaction.
The free energy change which corresponds to this standard state is known as standard free energy change. B is also being converted to A. The concentration of reactants and products at equilibrium define the equilibrium constant.
If the reaction A B is allowed to go to equilibrium at constant temperature and pressure. At constant temperature and pressure. R is the gas constant.
The equilibrium constant Keq depends on the nature of reactants and products. It can be calculated from the equilibrium constant of the reaction under standard conditions i. T is the absolute temperature. In this state. Regulation occurs in following different ways: Allosteric regulation of enzymes by a metabolic intermediate or coenzyme. It consists of hundreds of enzymatic reactions organized into discrete pathways.
These pathways proceed in a stepwise manner. Those in eukaryotic cells occur in specific cellular locations. Metabolism serves two fundamentally different purposes: Its allosteric site will bind to the end product of the pathway which alters its active site so that it cannot mediate the enzymatic reaction. They are irreversible. The basic strategy of catabolic metabolism is to form ATP and reducing power for biosyntheses. Feedback inhibition and feedback repression In feedback inhibition or end product inhibition.
Catabolic pathways are involved in the oxidative breakdown of larger complex molecules and usually exergonic in nature. The feedback inhibition is different from feedback repression. To achieve these. A number of central metabolic pathways are common to most cells and organisms.
Anabolic pathways are involved in the synthesis of compounds and ender- gonic in nature. They are referred to as amphibolic pathways. They are regulated. By extracellular signal such as growth factors and hormones that act from outside the cell in multicellular organisms.
Availability of substrate. Each one has a first committed step. Some pathways can be either anabolic or catabolic. Most of the reactions in living cells fall into one of five general categories: Characteristics of metabolic pathways are: An inhibitory feedback system in which the end product produced in a metabolic pathway acts as a co-repressor and represses the synthesis of an enzyme that is required at an earlier stage of the pathway is called feedback repression.
Metabolic pathways involve several enzyme-catalyzed reactions. Each step of metabolic pathways is catalyzed by a specific enzyme. These pathways. Bioenergetics and Metabolism 2. The first enzyme in the pathway is an allosteric enzyme. Glycolysis takes place in the cytosol of cells in all living organisms. Although carbohydrates. An exergonic reaction proceeds with a net release of free energy. When one mole of glucose g is completely oxidized into CO2 and water. Respiration is an oxidative process.
Cells acquire free energy from the oxidation of organic compounds that are rich in potential energy. Energy is required for the maintenance of highly organized structures. Free energy is released in multiple steps in a controlled manner and used to synthesise ATP. The complete oxidation of substrates occurs in the presence of oxygen.
During oxidation within a cell. As the substrate is never totally oxidized. Table 2. Oxidation of glucose is an exergonic process. Carbohydrates are most commonly used as respiratory substrates. During cellular respiration. ATP acts as the energy currency of the cell. Glycolysis — Cytosol Citric acid cycle — Mitochondrial matrix Oxidative phosphorylation — Inner mitochondrial membrane In prokaryotes. A complete oxidation of respiratory substrates in the presence of oxygen is termed as aerobic respiration.
Glycolysis — Cytosol Citric acid cycle — Cytosol Oxidative phosphorylation — Plasma membrane www. The compounds that are oxidized during the process of respiration are known as respiratory substrates. The oxidative phosphorylation takes place in the inner mitochondrial membrane. For each molecule of glucose degraded to carbon dioxide and water by respiration.
Part of this energy is used for synthesis of ATP. The citric acid cycle takes place within the mitochondrial matrix of eukaryotic cells and in the cytosol of prokaryotic cells. The negative charge of the phosphate prevents the passage of the glucose 6-phosphate through the plasma membrane. Hexokinase is present in all cells of all organisms. It is a unique pathway that occurs in both aerobic as well as anaerobic conditions and does not involve molecular oxygen. Hexokinase and glucokinase are isozymes.
Step 2: Isomerization A readily reversible rearrangement of the chemical structure isomerization moves the carbonyl oxygen from carbon 1 to carbon 2. Phosphorylation Glucose is phosphorylated by ATP to form a glucose 6-phosphate.
Glycolysis occurs in the cytosol of all cells. Glucokinase is present in liver and beta-cells of the pancreas and has a high Km and Vmax as compared to hexokinase. This irreversible reaction is catalyzed by hexokinase. Bioenergetics and Metabolism Solution a. Valinomycin is an ionophore. Voltage gradient membrane potential across the inner mitochondrial membrane with the inside negative and outside positive. A mitochondrion actively involved in aerobic respiration typically has a membrane potential of about mV negative inside matrix and a pH gradient of about 1.
Antimycin A strongly inhibits the oxidation of Q in the respiratory chain. Inhibition of NADH dehydrogenase by rotenone decreases the rate of electron flow through the respiratory chain. Determination of electric potential and pH gradient Because mitochondria are very small.
Because antimycin A blocks all electron flow to oxygen. The electrochemical proton gradient exerts a proton motive force pmf. In a typical cell. In the presence of valinomycin. Bioenergetics and Metabolism Experimental proof of chemiosmotic hypothesis Experimental proof of chemiosmotic hypothesis was provided by Andre Jagendorf and Ernest Uribe in A burst of ATP synthesis accompanied the transmembrane movement of protons driven by the electrochemical proton gradient.
The F0 component is embedded in the inner mitochondrial membrane. The multiprotein ATP synthase or F0F1 complex or complex V catalyzes ATP synthesis as protons flow back through the inner membrane down the electrochemical proton gradient.
When the pH in the thylakoid lumen became 4.
Life-Sciences-part-1-CSIR-JRF-NET-GATE-DBT.pdf
An aspartic acid residue in the second helix lies on the center of the membrane. Rotational motion is imparted to the rotor by the passage of protons. In similar experiments using inside-out preparations of submitochondrial vesicles. In an elegant experiment. Ionophore uncouple electron transfer from oxidative phosphorylation by dissipating the electrochemical gradient across the mitochondrial membrane.
Most of the ATP generated by oxidative phosphorylation in mitochondria is exported to the cytoplasm. Ionophores are lipophilic molecules that bind specific cations and facilitate their transport through the membrane. ADP and Pi very weakly. Calculation of free energy change The standard free energy change for the movement of protons across the membrane along the electrochemical proton gradient can be calculated from the Nernst equation: DNP in an anionic state picks up protons in the inter-mitochondrial space and diffuse readily across mitochondrial membranes.
The free energy released on proton translocation is harnessed to interconvert three states. It decreases the memberane potential component of pmf without a direct effect on the pH gradient and thus ATP synthesis. ADP and Pi: An O state open state that binds ATP. Most common uncoupling agents are 2. Dicoumarol and FCCP act in the same way. After entering the matrix in the protonated form.
DNP is a weak acid that is soluble in lipid bilayer both in their protonated neutral forms and in their anionic states. A specific transport protein.
Bioenergetics and Metabolism and vice versa. NADH synthesized during the glycolytic process finally transfers the electrons to electron transport chain. NADH in the cytosol transfers electrons to oxaloacetate.
Malate is transported across the inner membrane by the help of transporter. A second membrane transport system is the phosphate translocase. In the matrix. This transport process is also powered by the transmembrane proton gradient.
The electrons are carried into the mitochondrial matrix in the form of malate. Malate then enters the mitochondrial matrix. NADH cannot cross the inner mitochondrial membrane. The malate-aspartate shuttle is the principal mechanism for the movement of NADH from the cytoplasm into the mitochondrial matrix.
H2O2, a toxic product of various oxidative processes, reacts with double bonds in the fatty acid residues of the erythrocyte cell membrane to form organic hydroperoxides. These, in turn, result in premature cell lysis. Peroxides are eliminated through the action of glutathione peroxidase, yielding glutathione disulfide GSSG. So, G6PD deficiency results in hemolytic anemia caused by the inability to detoxify oxidizing agents.
This pathway, first reported by Michael Doudoroff and Nathan Entner, occurs only in prokaryotes, mostly in gram-negative bacteria such as Pseudomonas aeruginosa, Azotobacter, Rhizobium.
In this pathway, glucose phosphate is oxidized to 2-ketodeoxyphosphogluconic acid KDPG which is cleaved by 2-ketodeoxyglucose-phosphate aldolase to pyruvate and glyceraldehydephosphate.
The latter is oxidized to pyruvate by glycolytic pathway where in two ATPs are produced by substrate level phosphorylations. Figure 2. The first process is a light dependent one light reactions that requires the direct energy of light to make energy carrier molecules that are used in the second process.
The calvin cycle light independent process occurs when the products of the light reaction are used in the formation of carbohydrate.
On the basis of generation of oxygen during photosynthesis, the photosynthetic organisms may be oxygenic or anoxygenic. Oxygenic photosynthetic organisms include both eukaryotes as well as prokaryotes whereas anoxygenic photosynthetic organisms include only prokaryotes. Oxygenic photosynthetic organisms Eukaryotes — Plants and Photosynthetic protists Prokaryotes — Cyanobacteria.
Anoxygenic photosynthetic organisms Prokaryotes — Green and purple photosynthetic bacteria. In oxygenic photosynthetic organisms, photosynthetic oxygen generation occurs via the light-dependent oxidation of water to molecular oxygen. This can be written as the following simplified chemical reaction:. Different types of pigments, described as photosynthetic pigment, participate in this process. The major photosynthetic pigment is the chlorophyll. Chlorophyll, a light-absorbing green pigment, contains a polycyclic, planar tetrapyrrole ring structure.
Chlorophyll is a lipid soluble pigment. It has the following important features: Chlorophyll has a cyclopentanone ring ring V fused to pyrrole ring III.
The propionyl group on a ring IV of chlorophyll is esterified to a long-chain tetraisoprenoid alcohol. In chlorophyll a and b it is phytol.
Pyrrole ring II contains methyl —CH3 group. It absorbs more violet-blue wavelength than red blue wavelength of light.
Carotenoids are long-chain. Chlorophyll is composed of two parts. It is an essential photosynthetic pigment. Anoxygenic photosynthetic organisms contain bacteriochlorophyll molecules. Accessory pigments Besides the major light-absorbing chlorophyll molecules. BChl b. Carotenoids are lipid soluble pigments and can be subdivided into two classes.
In the pure state. Chl c and Chl d. Oxygenic photosynthetic organisms contain different types of chlorophyll molecules like Chl a. They are related to chlorophyll molecules. BChl c. It absorbs more red wavelengths than violet. It is accessory photosynthetic pigment.
These chlorophyll molecules differ by having different substituent groups on the tetrapyrrole ring. The characteristic www. They are generally C40 terpenoid compounds formed by the condensation of eight isoprene units. Different groups of anoxygenic photosynthetic organisms contain different types of bacteriochlorophyll: BChl a. The two types of accessory pigments are carotenoids and phycobilins. BChl d and BChl e.
The tail is a 20 carbon chain that is highly hydrophobic. Chl b. Bacteriochlorophyll molecules absorb light at longer wavelengths as compared to chlorophyll molecules. Many diseases have been characterized that result from an inherited deficiency of the enzyme.
Two main biosynthetic pathways are known.
Bioenergetics and Metabolism Glycogen storage diseases Glycogen storage diseases are caused by a genetic deficiency of one or another of the enzymes of glycogen metabolism. The most important route to triacylglycerol biosynthesis is the sn-glycerolphosphate or Kennedy pathway. Within all cell types. These defects are listed in the table. In animals. Porphyrin biosynthesis involves three distinct processes: In contrast.
The deoxyribose sugar is generated by the reduction of ribose within a fully formed nucleotide. All deoxyribonucleotides are synthesized from the corresponding ribonucleotides. In de novo means anew pathways.. In salvage pathways. Synthesis of a substituted pyrrole compound. Modification of the side chains. Condensation of four porphobilinogen molecules to yield a partly reduced precursor called a porphyrinogen. The framework for a pyrimidine base is assembled first and then attached to ribose.
Orotate couples to ribose. Carbamoylaspartate then cyclizes to form dihydroorotate which is then oxidized to form orotate. The precursor of carbamoyl phosphate is bicarbonate and ammonia. This reaction is catalyzed by cytosolic carbamoyl phosphate synthetase II. The C-2 and N-3 atoms in the pyrimidine ring come from carbamoyl phosphate.
The synthesis of carbamoyl phosphate from bicarbonate and ammonia occurs in a multistep process. Pyrimidine rings are synthesized from carbamoyl phosphate and aspartate. Chapter 03 Cell Structure and Functions 3. Golgi complex. All organisms. The basic structural and functional unit of cellular organisms is the cell.
Hooke published his findings in his famous work.
Cells that have unit membrane bound nuclei are called eukaryotic. Robert Hooke first discovered cells in a piece of cork and also coined the word cell. Viruses are noncellular organisms because they lack cell or cell-like structure. Hooke only observed cell walls because cork cells are dead and without cytoplasmic contents.
The cell theory holds true for all cellular organisms. Non- cellular organisms such as virus do not obey cell theory. Rudolf Virchow proposed an important extension of cell theory that all living cells arise from pre-existing cells omnis cellula e cellula. Besides the nucleus. On the basis of the internal architecture.
The region of the cell lying between the plasma membrane and the nucleus is the cytoplasm. Evolution of the cell The earliest cells probably arose about 3. The prokaryotic cells lack such unit membrane bound organelles. Primitive heterotrophs gradually acquired www. Eukaryotic cells have a much more complex intracellular organization with internal membranes as compared to prokaryotic cells. The word cell is derived from the Latin word cellula.
The modern cell theory includes the following components: In According to this theory all living things are made up of cells and cell is the basic structural and functional unit of life. Anton van Leeuwenhoek was the first person who observed living cells under a microscope and named them animalcules. Over the time. It is an aqueous compartment bound by cell membrane.
In the year Cell theory In Both proteins and lipids are free to move laterally in the plane of the bilayer. The DNA is. Details of the evolutionary path from prokaryotes to eukaryotes cannot be deduced from the fossil record alone. The fossil record shows that earliest eukaryotic cells evolved about 1. Jonathan Singer and Garth Nicolson proposed fluid-mosaic model.
Three major changes must have occurred as prokaryotes gave rise to eukaryotes. Peripheral protein Phospholipid bilayer Integral protein Peripheral protein Figure 3.
Different models were proposed to explain the structure and composition of plasma membranes. The cyanobacteria are the modern descendants of these early photosynthetic O2 producers. A very significant evolutionary event was the development of photosynthetic ability to fix CO2 into more complex organic compounds.
It describes both the mosaic arrangement of proteins embedded throughout the lipid bilayer as well as the fluid movement of lipids and proteins alike. One important landmark along this evolutionary road occurred when there was a transition from small cells with relatively simple internal structures. It acts as a selectively permeable membrane and regulates the molecular traffic across the boundary. The plasma membrane exhibits selective permeability.
Cell Structure and Functions the capability to derive energy from certain compounds in their environment and to use that energy to synthesize more and more of their own precursor molecules. The original electron hydrogen donor for these photosynthetic organisms was probably H2S. Integral proteins float in this lipid bilayer.
In this model. The fatty acyl chains in the lipid bilayer form a fluid. These DNA-protein complexes called chromosomes become especially compact at the time of cell division. Some aerobic bacteria evolved into the mitochondria of modern eukaryotes. The plasma membrane of animal cells contains four major phospholipids. Cell Structure and Functions Chemical constituents of plasma membrane All plasma membranes. Phospholipids Phospholipids are made up of four components: Carbohydrates bound either to proteins as constituents of glycoproteins or to lipids as constituents of glycolipids.
The hydrophilic unit. Glycerophospholipids or phosphoglycerides contain glycerol. Sphingomyelin is the most abundant sphingophospholipid. Rarer phospholipids have a net positive charge.
There are two types of phospholipids: Sphingophospholipids contain an amino alcohol called sphingosine instead of glycerol. Phosphoglycerides are the most numerous phospholipid molecules found in plasma membranes. Phosphoglyceride molecules are classified according to the types of alcohol linked to the phosphate group. The ratio of protein to lipid varies enormously depends on cell types. In sphingophospholipid. Phospholipids derived from glycerol are called glycerophospholipids.
Lipid bilayer The basic structure of the plasma membrane is the lipid bilayer. The primary physical forces for organizing lipid bilayer are hydrophobic interactions. Carbohydrates are especially abundant in the plasma membranes of eukaryotic cells.
At neutral pH. Three classes of lipid molecules present in lipid bilayer. The fatty acid components are hydrophobic. This bilayer is composed of two leaflets of amphipathic lipid molecules. All cells have an electrical potential difference. Electrical potential across cell membranes is a function of the electrolyte concentrations in the intracellular and extracellular solutions and of the selective permeabilities of the ions.
The resulting separation of charge across the membrane constitutes an electric potential. At equilibrium. Cell Structure and Functions 3. Ion concentration gradients and selective movements of ions create a difference in electric potential or voltage across the plasma membrane. In addition to ion pumps. Electrogenic transport affects and can be affected by the membrane potential.
Its electrogenic operation directly contributes to the negative inside membrane potential. This is called membrane potential.
Active transport of ions by ATP-driven ion pumps. How membrane potentials arise? To help explain how an electric potential across the plasma membrane can arise. The channel undergoes through these various conformations as a result of voltage changes that take place during an action potential.
During the depolarizing phase. Leaky channels. Action potentials are the direct consequence of the voltage-gated cation channels. During the repolarizing phase. This process is called repolarization. Ion channels may be either leaky channels or gated channels.
The influx of positive charge depolarizes the membrane further. Movement of ions occurs through ion channels. Gated channels. Following the repolarizing phase there may be an after-hyperpolarizing phase. At resting potential about —70 mV. Cell Structure and Functions Let us now consider the changes in potential during an action potential.
During an action potential. The x-axis for time is the same in both graphs. The refractory period limit the number of action potentials that can be produced by an excitable membrane in a given period of time. During the absolute refractory period.
The top graph depicts an action potential. The relative refractory period is the time period during which a second action potential can be initiated. Gated Na and K channels closed Time millisecond Figure 3. It can be absolute or relative. The period of time after an action potential begins during which an excitable cell cannot generate another action potential in response to a normal threshold stimulus is called the refractory period.
It may be a constitutive secretory pathway carried out by all cells or regulated secretory pathway carried out by specialized cells. An example of transcytosis is the movement of maternal antibodies across the intestinal epithelial cells of the newborn rat. Vesicle containing soluble proteins for constitutive secretion Constitutive secretory pathway Trans-Golgi network Extracellular space Regulated secretory pathway Secretory Golgi complex vesicle containing secretory proteins Plasma membrane Figure 3.
Cell Structure and Functions plasma membrane at the opposite side. Many soluble proteins are continually secreted from the cell by this pathway. The lumen of the gut is acidic. The two pathways diverge in the trans Golgi network. On exposure to the neutral pH of the extracellular fluid that bathes the basolateral surface of the cells.
Specialized secretory cells also have a regulated secretory pathway. The constitutive secretory pathway operates in all cells.
Examples of proteins released by such constitutive or continuous secretion include collagen by fibroblasts. The complexes remain intact and are retrieved in transport vesicles that bud from the early endosome and subsequently fuse with the basolateral domain of the plasma membrane. The receptor-antibody complexes are internalized via clathrin coated vesicles and are delivered to early endosomes. This pathway also supplies the plasma membrane with newly synthesized lipids and proteins.
The regulated secretion of small molecules. Ribosomes consist of rRNA and r-proteins. The signal that directs secretory proteins into such vesicles is not known.
Proteins destined for secretion called secretory proteins are packaged into appropriate secretory vesicles in the trans Golgi network. The r-proteins are termed as L or S depending on whether the protein is from the large or small subunit.
The ribosome is approximately globular structure. The functional ribosomes consist of two subunits of unequal size. In this secretory pathway. The secreted product can be either a small molecule such as histamine or a protein such as a hormone or digestive enzyme. There are generally more copies of the 5S genes than of the rRNA genes. The human genome contains about copies of rRNA genes per haploid set.
In all eukaryotes studied so far. Cell Structure and Functions The regulated secretory pathway is found mainly in cells specialized for secreting products rapidly on demand such as hormones. Table 3. Many other species. The sedimentation coefficient has units of second. It is the ratio of a velocity to the centrifugal acceleration.
Within the cell. All proteins synthesized by membrane free ribosomes are translocated post-translationally. Microsomes lacking attached ribosomes are called smooth microsome. Microsomes derived from RER are studded with ribosomes on the outer surface and are called rough microsomes. Transmembrane transport: In transmembrane transport. The transport of selected proteins from the cytosol into the ER lumen or into mitochondria is an example of transmembrane transport.
Protein translocation describes the movement of a protein across a membrane. The enclosed compartment is called the ER lumen. When cells are disrupted by homogenization. Gated transport: The protein translocation between the cytosol and nucleus occurs through the nuclear pore complexes. This process is called gated transport because the nuclear pore complexes function as selective gates that can actively transport specific macromolecules.
The transfer of proteins from the endoplasmic reticulum to the Golgi apparatus. It is an extensive network of closed and flattened membrane-bound structure. Proteins synthesized by membrane bound ribosomes are translocated co-translationally. ER membranes are physiologically active. Protein translocation may occur co-translationally or post-translationally.
Vesicular transport: In vesicular transport. Figure 3. The cisternal space or lumen remains continuous with the perinuclear space. Proteins synthesized by ribosomes associated with the membrane of RER enter into the lumen and membrane of RER by the process of co-translational translocation. In the lumen of the RER, five principal modifications of proteins occur before they reach their final destinations: The SER acts as the site of lipid biosynthesis, detoxification and calcium regulation.
N-linked glycosylation is the attachment of a sugar molecule to a nitrogen atom in an amino acid residue in a protein. In the RER, this process involves the addition of a large preformed oligosaccharide precursor to a protein. This precursor oligosaccharide is linked by a pyrophosphoryl residue to dolichol, a long-chain 75—95 carbon atoms polyisoprenoid lipid that is firmly embedded in the RER membrane and acts as a carrier for the oligosaccharide.
The structure of N-linked oligosaccharide is the same in plants, animals and single-celled eukaryotes - a branched oligosaccharide, containing three glucose Glc , nine mannose Man and two N-acetylglucosamine GlcNAc molecules which is written as Glc3 Man9 GlcNAc2. Biosynthesis of oligosaccharide begins on the cytosolic face of the ER membrane with the transfer of N-acetyl glucosamine to dolichol phosphate.
Two N-acetylglucosamine GlcNAc and five mannose residues are added one at a time to a dolichol phosphate on the cytosolic face of the ER membrane.
The first sugar, N-acetyl glucosamine, is linked to dolichol by a pyrophosphate bridge. This high-energy bond activates the oligosaccharide for its transfer from the dolichol to an asparagine side chain of a nascent polypeptide on the luminal side of the rough ER.
Tunicamycin, an antibiotic, blocks the first step in this pathway and thus inhibits the synthesis of oligosaccharide. After the seven-residue dolichol pyrophosphoryl intermediate is flipped to the luminal face. The remaining four mannose and all three glucose residues are added one at a time in the luminal side.
The sugar molecules participate. ER-resident proteins often are retrieved from the Cis-Golgi As we have mentioned in the previous section that proteins entering into the lumen of the ER are of two types- resident proteins and export proteins. How, then, are resident proteins retained in the ER lumen to carry out their work? The answer lies in a specific C-terminal sequence present in resident ER proteins. Several experiments demonstrated that the KDEL sequence which acts as sorting signal, is both necessary and sufficient for retention in the ER.
If this ER retention signal is removed from BiP, for example, the protein is secreted from the cell; and if the signal is transferred to a protein that is normally secreted, the protein is now retained in the ER. The finding that most KDEL receptors are localized to the membranes of small transport vesicles shuttling between the ER and the cis-Golgi also supports this concept. The retention of transmembrane proteins in the ER is carried out by short C-terminal sequences that contain two lysine residues KKXX sequences.
How can the affinity of the KDEL receptor change depending on the compartment in which it resides?
The answer may be related to the differences in pH. Clearly, the transport of newly synthesized proteins from the RER to the Golgi cisternae is a highly selective and regulated process.
The selective entry of proteins into membrane-bound transport vesicles is an important feature of protein targeting as we will encounter them several times in our study of the subsequent stages in the maturation of secretory and membrane proteins. The Golgi complex, also termed as Golgi body or Golgi apparatus, is a single membrane bound organelle and part of endomembrane system.
It consists of five to eight flattened membrane-bound sacs called the cisternae. Each stack of cisternae is termed as Golgi stack or dictyosome. The cisternae in Golgi stack vary in number, shape and organization in different cell types.
The typical diagrammatic representation of three major cisternae cis, medial and trans as shown in the figure 3. In some unicellular flagellates, however, as many as 60 cisternae may combine to make up the Golgi stack. The number of Golgi complexes in a cell varies according to its function. A mammalian cell typically contains 40 to stacks. In mammalian cells, multiple Golgi stacks are linked together at their edges.
Each Golgi stack has two distinct faces: Both cis and trans faces are closely associated with special compartments: Further modifications of N-linked oligosaccharide in the Golgi apparatus gives two broad classes of N-linked oligosaccharides. The vesicles fuse with the Golgi membranes and release their internally stored molecules into the organelle. Proteins and lipids from the smooth and rough endoplasmic reticulum bud off in tiny bubble-like vesicles that move through the cytoplasm until they reach the Golgi apparatus.
High-mannose www. Both networks are thought to be important for protein sorting. It modifies proteins and lipids that have been built in the endoplasmic reticulum and prepares them for export outside of the cell or for transport to other locations in the cell.
Glycosylation of proteins N-linked oligosaccharide chains on proteins are altered as the proteins pass through the Golgi cisternae en route from the ER.
The Golgi apparatus is especially prominent in cells that are specialized for secretion. When completed. ER - lysosome. Proteins and lipids enter the cis Golgi network in vesicular tubular clusters arriving from the ER and exit from the trans Golgi network. Substances from ER enter into the cis face of a Golgi stack for processing and exit from trans face. The modifications to molecules that take place in the Golgi apparatus occur in an orderly fashion.
In such cells. Secretory vesicles form from the trans Golgi network. The chemical make-up of each face is different and the enzymes contained in the cisternae between the faces are distinctive. As we have seen. Once inside. The majority of eukaryotic cells are diploid. Each cell is programmed to respond to specific extracellular signal molecules. This is accomplished by a variety of signal molecules that are secreted or expressed on the surface of one cell and bind to receptors expressed by other cells.
The number of chromosomes in a species has no specific significance nor does it indicate any relationship between two species which may have the same chromosome number. One chromosome contains multiple origin of replication. It consists of a long array of short.
Binding of the signal by a specific receptor leading to its activation. Depending on the eukaryotic organism. Cell Structure and Functions termed as heterochromatin. The centromeres serve both as the sites of association of sister chromatids and as the attachment sites for microtubules of the mitotic spindle.
Transport of the signal to the target cell. Every cell maintains a characteristic number of chromosomes. Centromere The constricted region of linear chromosomes is known as the centromere.
Because of its condensed state. Although this constriction is called the centromere. Origin of replication The origin of replication also called the replication origin is a particular sequence in a chromosome at which replication is initiated.
Telomere Telomeres are specialized structures. Chromosome number All eukaryotic cells have multiple linear chromosomes. Species Haploid number of chromosome Saccharomyces cerevisiae budding yeast 16 Schizosaccharomyces pombe fission yeast 03 Caenorhabditis elegans 06 Arabidopsis thaliana 05 Drosophila melanogaster 04 Tetrahymena thermophilus Micronucleus 5. Initiation of signal-transduction pathways. Synthesis and release of the signaling molecule by the signaling cell.
Extracellular signaling usually involves the following steps: One important example of such is the response of cells of the vertebrate immune system to foreign antigens. In paracrine signaling. Membrane bound signal molecules remain bound to the surface of the cells and mediate contact dependent signaling. These molecules are divided into two categories — membrane bound and secretory signal molecules.
Notch signalling and classical cadherin signalling are examples of juxtacrine signaling. It is a long-range signaling in which signal molecule is transported by the blood stream. Cell Structure and Functions In animals. Secreted extracellular signal molecules are further divided into three general categories based on the distance over which signals are transmitted: In most cases. In juxtacrine signaling. In autocrine signaling. An example of this is the action of neurotransmitters in carrying signals between nerve cells at a synapse.
In endocrine signaling. Certain types of T- lymphocytes respond to antigenic stimulation by synthesizing a growth factor that drives their own proliferation.
Unlike other modes of cell signaling. Bcl2 was the first protein shown to cause an inhibition of apoptosis. In the presence of an apoptotic stimulus. The pro-apoptotic Bcl2 proteins consist of two subfamilies. Most cancers are initiated by genetic changes and majority of them are caused by changes in somatic cells and therefore are not transmitted to the next generation. In the absence of an apoptotic stimulus.
Mammalian Bcl2 family of proteins regulate the intrinsic pathway of apoptosis mainly by controlling the release of cytochrome c and other intermembrane mitochondrial proteins into the cytosol. When an apoptotic stimulus triggers the intrinsic pathway. BH3-only proteins are activated and bind to the anti-apoptotic Bcl2 proteins so that they can no longer inhibit the BH proteins.It consists of five to eight flattened membrane-bound sacs called the cisternae.
When no further additions are made, the resulting compound is phosphatidic acid, the simplest phosphoglyceride. The two molecules are mirror images and cannot be superimposed on one another. The rod shaped E. Such a donor bacterial cell is called an Hfr strain for high frequency of recombination because it exhibits a very high efficiency of chromosomal gene transfer in comparison with F-cells. Biomolecules and Catalysis Table 1.
For example, trypsin, a proteolytic enzyme, is secreted by the pancreas. In the presence of an apoptotic stimulus, BH3-only proteins are activated and bind to the anti-apoptotic Bcl2 proteins so that they can no longer inhibit the BH proteins. Phosphorylation Glucose is phosphorylated by ATP to form a glucose 6-phosphate. The most widely used is cyanogen bromide CNBr.
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__label__pos
| 0.943539 |
C# - Multi-dimensional Array
We have learned about single dimensional arrays in the previous section. C# also supports multi-dimensional arrays. A multi-dimensional array is a two dimensional series like rows and columns.
Example: Multi-dimensional Array:
int[,] intArray = new int[3,2]{
{1, 2},
{3, 4},
{5, 6}
};
// or
int[,] intArray = { {1, 1}, {1, 2}, {1, 3} };
As you can see in the above example, multi dimensional array is initialized by giving size of rows and columns. [3,2] specifies that array can include 3 rows and 2 columns.
The following figure shows a multi-dimensional array divided into rows and columns:
Multi-dimensional Array
Multi-dimensional Array
The values of a multi-dimensional array can be accessed using two indexes. The first index is for the row and the second index is for the column. Both the indexes start from zero.
Example: Access Multi-dimensional Array
int[,] intArray = new int[3,2]{
{1, 2},
{3, 4},
{5, 6}
};
intArray[0,0]; //Output: 1
intArray[0,1]; // 2
intArray[1,0]; // 3
intArray[1,1]; // 4
intArray[2,0]; // 5
intArray[2,1]; // 6
In the above example, intArray[2,1] returns 6. Here, 2 means the third row and 1 means the second column (rows and columns starts with zero index).
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| 0.977501 |
Tracking of physical activity and sedentary behavior in young children
L.A. Kelly, John J Reilly, D.M. Jackson, C. Montgomery, S Grant, Y Paton
Research output: Contribution to journalArticle
8 Citations (Scopus)
Abstract
Tracking of total physical activity (PA), moderate to vigorous activity (MVPA), and sedentary behavior was assessed in 42 young children (mean age at baseline 3.8 years) over a 2-year period using the Actigraph accelerometer. Tracking was analyzed using Spearman rank correlations, percentage agreements, and kappa statistics. Spearman rank correlations were r = .35 (p = .002) for total PA, r = .37 (p = .002) for MVPA, and r = .35 (p = .002) for sedentary behavior. Percentage agreements for PA, MVPA, and sedentary behavior were 38, 41, and 26 respectively. Kappa statistics for PA, MVPA, and sedentary behavior ranged from poor to fair. Results suggest low levels of tracking of total physical activity, MVPA, and sedentary behavior in young Scottish children over a 2-year period
Original languageEnglish
Pages (from-to)51-60
Number of pages10
JournalPediatric Exercise Science
Volume19
Issue number1
Publication statusPublished - 2007
Keywords
• physical activity
• paediatric obesity
• childhood obesity
Cite this
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__label__pos
| 0.770132 |
Comparisons
Difference Between Analog and Digital Multimeter
We know that multimeters are basically electronic test equipment, utilized for the purpose of determining various quantities like voltage, current, and resistance, etc. Multimeters are generally classified into two types, analog multimeter, and digital multimeter. The crucial difference between analog and digital multimeter lies in their way of representing the quantity being measured. An analog …
Difference Between Analog and Digital Multimeter Read More »
Difference Between Electrical Energy and Electrical Power
Electrical energy and electrical power are the two major terms associated with electrical and electronics system. The fundamental difference between electrical energy and electrical power is that electrical energy represents the amount of work done that causes electric current to flow through a circuit. As against electrical power defines the rate at which work (basically …
Difference Between Electrical Energy and Electrical Power Read More »
Difference Between Force and Power
The major difference between force and power is that force is an action on a body or interaction of two bodies. While power is the amount of energy consumed during an action over the body. Sometimes people get confused between the terms force and power. This section will provide the necessary factors of differentiation between …
Difference Between Force and Power Read More »
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| 0.993175 |
10600 York Rd Suite 105 Cockeysville, MD 21030
Guide: Various Teeth Whitening Treatments
Are you looking to brighten your smile but overwhelmed by the myriad of teeth whitening treatments available? At Valley Dental Health, we’ve compiled a comprehensive guide to help you navigate through the various options, ensuring you find the perfect solution to achieve that dazzling smile you’ve always wanted.
Guide: Various Teeth Whitening Treatments
Over-The-Counter Whitening Products
When it comes to achieving a brighter smile, Over-the-Counter (OTC) whitening products offer a convenient and cost-effective solution. These products, ranging from whitening toothpastes, strips, gels, and trays, are readily available at most drugstores and online retailers.
They contain varying concentrations of bleaching agents, such as hydrogen peroxide or carbamide peroxide, which work to remove surface stains and, in some cases, deeper discoloration. However, it’s important to note that the effectiveness of these products can vary greatly depending on the type of stains, the concentration of the active ingredient, and the duration of use.
Despite their accessibility and ease of use, OTC whitening products are not without their drawbacks. Users may experience sensitivity or irritation to the gums and teeth, especially with prolonged use or if the product is not used as directed. Additionally, while these products can be effective for mild staining, they may not produce the desired results for more severe discoloration or intrinsic stains that affect the inner layers of the tooth.
It’s always recommended to consult with a dental professional before starting any whitening regimen to ensure it’s suitable for your dental health and to explore potentially more effective options for your specific needs.
Professional In-Office Whitening Procedures
Professional in-office whitening procedures offer a fast and effective way to brighten your smile under the supervision of dental professionals. Unlike over-the-counter options, these treatments use higher concentrations of whitening agents, providing more dramatic results in a shorter amount of time.
During the procedure, a protective barrier is applied to the gums to prevent irritation, and a potent bleaching gel is carefully applied to the teeth. Some methods may also utilize a special light or laser to enhance the whitening process. This controlled environment ensures not only the safety of the patient but also the uniformity and longevity of the whitening effects.
For those seeking a reliable and impactful solution to achieve a brighter smile, exploring professional options is a must. Cockeysville’s Premier Teeth Whitening services offer state-of-the-art in-office treatments tailored to meet individual needs and expectations. With the guidance of experienced dental professionals, patients can enjoy a noticeably whiter smile in just one visit, making it an ideal choice for those looking for immediate and lasting results.
Natural Whitening Home Remedies
In the quest for a brighter smile, many individuals turn to natural whitening home remedies, a cost-effective and accessible option. These methods often utilize everyday household items, promising to remove surface stains without the need for harsh chemicals. Baking soda, for instance, is a popular choice due to its mild abrasive properties that can gently polish away stains. Similarly, hydrogen peroxide, a common antiseptic, is used in diluted form as a mouthwash to bleach teeth subtly over time.
Another favored remedy is oil pulling with coconut oil, which is believed to pull bacteria from the teeth, thus reducing plaque and discoloration. While these natural solutions can be effective for minor staining, it’s important to approach them with realistic expectations and understand that results may vary. Always consult with a dental professional before trying new treatments to ensure they are safe for your specific dental health.
Whitening Toothpastes And Mouthwashes
In the quest for a brighter smile, whitening toothpastes and mouthwashes are the go-to options for many. These products are infused with mild abrasives and chemicals that work to remove surface stains on your teeth, making them appear whiter over time. Whitening toothpastes, in particular, may contain polishing agents or a small amount of peroxide to enhance their stain-removing effectiveness.
Mouthwashes, on the other hand, offer a dual action of whitening while also improving oral health by reducing bacteria and freshening breath. It’s important to note, however, that these products are best for maintaining professionally whitened teeth or for achieving slight improvements in whiteness. For more significant changes, consulting with dental professionals is recommended. Discover more about maintaining your brightest smile at Valley Dental Health.
Laser Teeth Whitening Techniques
Laser teeth whitening techniques have emerged as a popular and effective method for achieving a brighter smile. This advanced dental procedure uses a concentrated beam of light, typically from a laser, to accelerate the bleaching process of a whitening agent applied to the teeth. The precision and intensity of the laser allow for significant color improvement in a single session, making it an attractive option for those seeking immediate results.
Not only does laser teeth whitening offer a quick solution for discolored teeth, but it also ensures a safer and more controlled treatment, minimizing the risk of damage to the tooth enamel and gums. With its combination of speed, efficiency, and safety, laser teeth whitening stands out as a premier choice for individuals looking to enhance the brightness of their smile.
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| 0.990526 |
Primary sensory processing of visual and olfactory signals in the bumblebee brain
Mertes M (2013)
Bielefeld: Bielefeld University.
Download
OA
Bielefelder E-Dissertation | Englisch
Alternativer Titel
What makes a landmark a landmark? How active vision strategies help honeybees to process salient visual features for spatial learning
Abstract / Bemerkung
Since decades honeybees are being used as an insect model system for answering scientific questions in a variety of areas. This is due to their enormous behavioural repertoire paired with their learning capabilities. Similar learning capabilities are also evident in bumblebees that are closely related to honeybees. As honeybees, they are central place foragers that commute between a reliable food source and their nest and, therefore, need to remember particular facets of their environment to reliably find back to these places. Via their flight style that consists of fast head and body rotations (saccades)interspersed with flight segments of almost no rotational movements of the head (intersaccades) it is possible to acquire distance information about objects in the environment. Depending on the structure of the environment bumblebees as well as honeybees can use these objects as landmarks to guide their way between the nest and a particular food source. Landmark learning as a visual task depends of course on the visual input perceived by the animal’s eyes. As this visual input rapidly changes during head saccades, we recorded in my first project bumblebees with high-speed cameras in an indoor flight arena, while they were solving a navigation task that required them to orient according to landmarks. First of all we tracked head orientation during whole flight periods that served to learn the spatial arrangement of the landmarks. Like this we acquired detailed data on the fine structure of their head saccades that shape the visual input they perceive. Head-saccades of bumblebees exhibit a consistent relationship between their duration, peak velocity and amplitude resembling the human so-called "saccadic main sequence" in its main characteristics. We also found the bumblebees’saccadic sequence to be highly stereotyped, similar to many other animals. This hints at a common principle of reliably reducing the time during which the eye is moved by fast and precise motor control. In my first project I tested bumblebees with salient landmarks in front of a background covered with a random-dot pattern. In a previous study, honeybees were trained with the same landmark arrangement and were additionally tested using landmarks that were camouflaged against the background. As the pattern of the landmark textures did not seem to affect their performance in finding the goal location, it had been assumed that the way they acquire information about the spatial relationship between objects is independent of the objects texture. Our aim for the second project of my dissertation was therefore to record the activity of motion sensitive neurons in the bumblebee to analyse in how far object information is contained in a navigation-related visual stimulus movie. Also we wanted to clarify, if object texture is represented by the neural responses. As recording from neurons in free-flying bumblebees is not possible, we used one of the recorded bumblebee trajectories to reconstruct a three-dimensional flight path including data on the head orientation. We therefore could reconstruct ego-perspective movies of a bumblebee 10 while solving a navigational task. These movies were presented to motion-sensitive neurons in the bumblebee lobula. We found for two different classes of neurons that object information was contained in the neuronal response traces. Furthermore, during the intersaccadic parts of flight the object’s texture did not change the general response profile of these neurons, which nicely matches the behavioural findings. However, slight changes in the response profiles acquired for the saccadic parts of flight might allow to extract texture information from these neurons at later processing stages. In the final project of my dissertation I switched from exploring coding of visual information to the coding of olfactory signals. For honeybees and bumblebees olfaction is approximately equally important for their behaviour as their vision sense. But whereas there is a solid knowledge base on honeybee olfaction with detailed studies on the single stages of olfactory information processing this knowledge was missing for the bumblebee. In the first step we conducted staining experiments and confocal microscopy to identify input tracts conveying information from the antennae to the first processing stage of olfactory information – the antennal lobe (AL ). Using three-dimensional reconstruction of the AL we could further elucidate typical numbers of single spheroidal shaped subunits of the AL , which are called glomeruli. Odour molecules that the bumblebee perceives induce typical activation patterns characteristic of particular odours. By retrogradely staining the output tracts that connect the AL to higher order processing stages with a calcium indicator, we were capable of recording the odourdependent activation patterns of the AL glomeruli and to describe their basic coding principles. Similarly as in honeybees, we could show that the odours’ carbon chain length as well as their functional groups are dimensions that the antennal lobe glomeruli are coding in their spatial response pattern. Applying correlation methods underlined the strong similarity of the glomerular activity pattern between honeybees and bumblebees.
Jahr
PUB-ID
Zitieren
Mertes M. Primary sensory processing of visual and olfactory signals in the bumblebee brain. Bielefeld: Bielefeld University; 2013.
Mertes, M. (2013). Primary sensory processing of visual and olfactory signals in the bumblebee brain. Bielefeld: Bielefeld University.
Mertes, M. (2013). Primary sensory processing of visual and olfactory signals in the bumblebee brain. Bielefeld: Bielefeld University.
Mertes, M., 2013. Primary sensory processing of visual and olfactory signals in the bumblebee brain, Bielefeld: Bielefeld University.
M. Mertes, Primary sensory processing of visual and olfactory signals in the bumblebee brain, Bielefeld: Bielefeld University, 2013.
Mertes, M.: Primary sensory processing of visual and olfactory signals in the bumblebee brain. Bielefeld University, Bielefeld (2013).
Mertes, Marcel. Primary sensory processing of visual and olfactory signals in the bumblebee brain. Bielefeld: Bielefeld University, 2013.
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| 0.821848 |
SSRS percentage rounding problem in an expression
Abdul Khan
Abdul Khan used Ask the Experts™
on
Hello All,
I am using the following expression to calculate percentage in SSRS,
=Format(Fields!PCTanswers.Value/100,"0%")
however, sometime the calculated values aren't equal to 100% they are 99, so the rounding is not working correctly.
Can someone please help? Thanks.
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Commented:
use =ROUND rather than format
=ROUND(Fields!PCTanswers.Value/100,0)
Format only truncates
Using rounding is correct, as David suggested.
However, if you have several values that should add up to 100%, and each value is rounded, you may still end up with a sum that is different from 100%. That is unavoidable when you are rounding values.
Say for example that you have three values that each represent a third of the total, or 33.333333333333%. When you round them, each will be rounded down to 33%, and the total is 99%.
If you want the values to add up to 100%, you can use the largest reminder method:
1. Round all the values down (but keep the original values also, for now).
2. Calculate how much you have from the sum of the rounded values up to 100%.
3. Distribute that difference by adding one to values, in descending order of the decimal part.
Ref: Wikipedia: Largest remainder method
Author
Commented:
Thanks so much for your assistance!!
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| 0.988239 |
Lysosome facts for kids
Kids Encyclopedia Facts
The Biological bulletin (19756543133)
TEM views of various vesicular compartments. Lysosomes are denoted by "Ly". They are dyed dark due to their acidity; in the center of the top image, a Golgi Apparatus can be seen, distal from the cell membrane relative to the lysosomes.
A lysosome is a cell organelle. They are like spheres. They have hydrolytic enzymes which can break down almost all kinds of biomolecules, including proteins, nucleic acids, carbohydrates, lipids, and cellular debris. They contain more than 50 different enzymes.
By convention, lysosome is the term used for animal cells. In plant cells, vacuoles do similar functions. With a wider definition, lysosomes are found in the cytoplasm of plant and protists as well as animal cell.
Lysosomes work like the digestive system to break down, or digest, proteins, acids, carbohydrates, dead organelles, and other unwanted materials. They break up larger molecules into smaller molecules. Those smaller molecules can then be used again as building blocks for other large molecules.
Images for kids
Lysosome Facts for Kids. Kiddle Encyclopedia.
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What We’re Still Learning About Hawaii
The fiery forces beneath the island chain still mystify geologists
Hawaiian Islands
Maui's Haleakala volcano and the rest of the Hawaiian Islands formed out of molten lava as the Pacific plate drifted over the hotspot as three to four inches a year. Map Source: TASA Graphic Arts, Inc. © 2009
Haleakala originated as a vent on the seafloor about two million years ago. Eruptions of lava built up the volcano until it reached the sea surface less than a million years later; continued eruptions pushed it more than 10,000 feet above sea level and gave it almost 600 square miles of land. Haleakala eventually connected with another volcano to form the island of Maui. In fact, all the Hawaiian Islands are of volcanic origin.
Most volcanoes—Mount St. Helens, say, or Mount Fuji—grow along the boundary between tectonic plates, where collisions melt the earth’s upper layers and fuel eruptions. By contrast, Hawaii’s volcanoes emanate from a “hotspot” under the Pacific plate.
The hotspot, which geologists estimate began producing the Hawaiian Islands 30 million years ago, is a plume of molten rock that rises through the mantle, the mostly solid layer between the crust and core. The islands were formed as the Pacific plate crept northwest at three to four inches a year, carrying volcano after volcano away from the stationary hotspot like a conveyor belt.
Though scientists have zeroed in on the hotspot as the source of Hawaii’s volcanoes, there’s still a lot they don’t know about it, including just how deep it is. Many scientists estimate that the hotspot originates some 1,800 miles into the earth, near the boundary between the mantle and the planet’s iron-rich core. In one recent test, researchers led by the University of Hawaii measured how fast seismic waves from earthquakes travel below ground—the waves move more slowly through hot rock than cold—and traced one plume under the Big Island of Hawaii that extends at least 900 miles deep. However, MIT scientists found a source only 400 miles beneath the surface, a 1,200-mile-wide reservoir of hot rock west of the Big Island.
Figuring out how to see into the earth’s interior is “just a very difficult experimental problem to answer,” says John Tarduno, a geophysicist at the University of Rochester in New York. “We would like to get better images to see the hotspot source itself.”
The islands don’t last forever. As the Pacific plate moves Hawaii’s volcanoes farther from the hotspot, they erupt less frequently, then no longer tap into the upwelling of molten rock and die. The island erodes and the crust beneath it cools, shrinks and sinks, and the island is again submerged. Millions of years from now, the Hawaiian Islands will disappear when the edge of the Pacific plate that supports them slides under the North American plate and returns to the mantle.
For now, Haleakala is hanging on. The volcano last spewed lava sometime between 1480 and 1780, but it has erupted more than 12 times in the past 1,000 years. Another eruption is not out of the question, says Richard Fiske, a geologist emeritus at the Smithsonian National Museum of Natural History. Says John Sinton, a geologist at the University of Hawaii at Manoa: “It’s a volcano that has refused to die.”
Maui's Haleakala volcano and the rest of the Hawaiian Islands formed out of molten lava as the Pacific plate drifted over the hotspot as three to four inches a year. Map Source: TASA Graphic Arts, Inc. © 2009
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insoles
Foot Orthotics Help People with Diabetes
How Custom Foot Orthotics Help People with Diabetes
How Custom Foot Orthotics Help People with Diabetes 724 464 Ace Health Centre
The Lifesaving Support: How Custom Foot Orthotics Help People with Diabetes
Diabetes is a complex medical condition that affects millions of people worldwide. While managing blood sugar levels is a primary concern, diabetes also brings a host of potential complications, particularly for the feet. Foot problems are common among individuals with diabetes, but there’s a powerful ally that can make a significant difference in their overall foot health: custom foot orthotics.
Understanding the Diabetes-Foot Connection
Diabetes can damage nerves (neuropathy) and reduce blood flow to the feet. This combination can result in reduced sensation, making it challenging to detect injuries or blisters. Additionally, poor blood circulation can lead to slow wound healing, which increases the risk of infection. It’s a perfect storm for foot problems, ranging from minor annoyances like corns and calluses to severe conditions like ulcers and even amputations.
The Role of Custom Foot Orthotics
Custom foot orthotics, also known as orthopedic insoles or diabetic insoles, are specially designed shoe inserts tailored to an individual’s unique foot shape and gait. Here’s how they can be a game-changer for people with diabetes:
1. **Pressure Redistribution:** Custom foot orthotics are crafted to distribute pressure evenly across the foot, reducing the risk of high-pressure points that can lead to calluses, ulcers, and wounds. This is critical for individuals with diabetes who may have compromised sensation and are less likely to notice these issues.
2. **Arch Support:** Many people with diabetes develop flat feet or other structural problems. Custom orthotics provide essential arch support, reducing strain on the feet and ankles and improving overall comfort.
3. **Shock Absorption:** These insoles are designed to absorb shock and reduce the impact on the feet during walking or other activities. This is crucial for preventing injuries and reducing discomfort, especially for those with neuropathy.
4. **Accommodating Deformities:** For individuals with foot deformities or irregularities caused by diabetes, such as Charcot foot, custom orthotics can be designed to accommodate and support these unique conditions, aiding in stability and balance.
5. **Preventing Complications:** By reducing pressure, improving support, and enhancing comfort, custom orthotics play a significant role in preventing common diabetes-related foot complications, including diabetic neuropathy and ulcer formation.
6. **Improved Mobility:** Comfortable and properly aligned feet encourage individuals with diabetes to remain active and engage in regular physical activity, which is crucial for managing blood sugar levels and overall health.
Foot Orthotics Help People with Diabetes
Foot Orthotics Help People with Diabetes
The Process of Getting Custom Foot Orthotics
Obtaining custom foot orthotics typically involves a series of steps:
1. **Assessment:** A healthcare provider, often a podiatrist, assesses the patient’s foot and gait to identify specific needs and any existing issues.
2. **Scanning:** The provider takes a digital scan of the patient’s feet to create a precise model for the orthotics.
3. **Custom Design:** The orthotics are then custom-designed to address the patient’s unique requirements, such as pressure points, arch support, and foot deformities. This is done via CAD-CAM software.
4. **Fitting:** Once the orthotics are ready, they are fitted into the patient’s shoes to ensure a proper fit and comfort.
Conclusion
Custom foot orthotics are invaluable tools in the fight against diabetes-related foot problems. They provide crucial support, reduce pressure, and enhance comfort, all of which are essential for preventing complications and maintaining mobility. For individuals with diabetes, investing in custom foot orthotics is an investment in their long-term foot health and overall well-being. These simple inserts can make a world of difference, helping individuals with diabetes step confidently on their journey to better health.
Contact us today if you have diabetes to get your custom foot orthotics.
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Hair Transplant San Jose
Hair Transplant San Jose: A Comprehensive Guide
Are you considering a hair transplant in San Jose? You’ve come to the right place! This article will provide you with everything you need to know about the procedure, recovery process, and considerations to make before undergoing this life-changing treatment. We will also explore the vibrant city of San Jose itself and why it has become a hotspot for hair transplantation.
I) Introduction to Hair Transplantation
A) What is a Hair Transplant?
A hair transplant is a surgical procedure that involves removing hair follicles from a donor area, usually the back or sides of the scalp, and transplanting them to areas where hair has thinned or is no longer growing. This procedure is primarily used to treat male and female pattern baldness but can also be used to restore hair in other areas of the body, such as eyebrows or facial hair.
B) Types of Hair Transplant Methods
There are two main methods for hair transplantation: Follicular Unit Transplantation (FUT) and Follicular Unit Extraction (FUE).
1) Follicular Unit Transplantation (FUT)
In this method, a strip of skin containing hair follicles is removed from the donor area. The follicles are then separated and prepared for transplantation. The strip method leaves a linear scar on the donor area, which can be concealed with hair growth.
2) Follicular Unit Extraction (FUE)
The FUE method involves individual extraction of hair follicles from the donor area using a small punch. This technique leaves tiny, dot-like scars that are less conspicuous than the linear scar from FUT. FUE allows for more precise graft placement and a quicker healing time.
II) Why San Jose Is a Great Choice for Hair Transplantation
A) High-Quality Medical Facilities and Surgeons
San Jose is home to some of the top hair transplant surgeons and clinics in the country. These clinics utilize the latest technology and techniques, ensuring you receive a successful and natural-looking result. Well-known clinics in the city are accredited and adhere to high-quality standards, providing a safe and sterile environment for your procedure.
B) The Silicon Valley Influence
As the heart of Silicon Valley, San Jose thrives on innovation. This creates a competitive environment that encourages the development and implementation of cutting-edge hair transplant techniques and technologies to achieve optimal results.
C) Affordable and Accessible Travel
San Jose is well-connected to major cities across the United States and worldwide, making it an easy destination for those seeking hair transplantation. Furthermore, travelling to San Jose can be more affordable than other major cities like New York or Los Angeles.
D) Beautiful and Diverse City
In addition to being a leading destination for hair transplantation, San Jose is a beautiful and thriving city. With a rich history, diverse culture, and stunning surroundings, it is no wonder that many people choose to undergo their hair transplant journey in San Jose.
III) Preparing for Your Hair Transplant Consultation
A) Research the Procedure and Surgeons
Before booking a consultation, make sure you research the procedure itself and find a reputable clinic or surgeon in San Jose. Look for testimonials, reviews, and before-and-after photos to gauge your prospective surgeon’s results.
B) Compile a List of Questions
Prepare a list of essential questions to ask during your consultation. Inquire about the surgeon’s experience, the procedure’s success rate, recovery time, and potential risks.
C) Be Open and Honest
During the consultation, be completely honest about your medical history, lifestyle, and expectations. This will ensure the most suitable treatment plan is developed for you.
IV) Recovery and Aftercare
A) Follow Post-Operative Instructions
Your surgeon will provide you with a set of post-operative instructions to follow to ensure a smooth and speedy recovery. Adhering to these guidelines is crucial for the best possible outcome.
B) Manage Discomfort
Mild to moderate pain, swelling, and redness are common following hair transplantation. Over-the-counter pain medication and cold compresses can help alleviate any discomfort.
C) Resume Activities Gradually
It is essential to avoid strenuous activities, heavy lifting, and direct sunlight exposure for several weeks post-procedure. Discuss with your surgeon when you can safely return to your daily routines.
V) Conclusion
Hair transplant surgery in San Jose is an excellent option for individuals seeking to restore their hair and confidence. With world-class medical facilities, innovative technology, and top surgeons, San Jose offers an ideal environment for this life-changing procedure. Book a consultation today to take the first step towards a fuller, healthier head of hair!
FAQs
1) How long does hair transplant surgery take?
The duration of the procedure depends on the number of grafts required and the chosen transplantation method. It can range from 4 to 8 hours.
2) When will I see results from my hair transplant?
Initial results may be visible within three months, but full results typically take between 9 to 12 months.
3) Is a hair transplant permanent?
Yes, the hair transplanted from the donor area is genetically resistant to balding. Therefore, results are generally permanent.
4) Can women undergo hair transplant surgery?
Yes, women can undergo hair transplantation. The procedure can help address female pattern baldness and other types of hair loss.
World Class VIP Clinic
We deliver natural-looking results, with cost-effective pricing and satisfaction guarantee. Take a look at our Before/After Results to see the how delighted our patients are from all around the world.
22+ Years of Experience
With 12.000+ successful operations worldwide
21.000.000 Grafts Transplanted
With FUE, FUT, LHT, BHT and additional methods
Worldwide Acknowledgement
Dr. Tsilosani is fellow of ISHRS and author of 32 scientific works
450+ Doctors Trained
We have over 450 graduates of hair transplantation professionals
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What Is HALT?
Discover the power of HALT! Unveiling the significance of this acronym for managing hunger, anger, loneliness, and tiredness.
February 14, 2024
Understanding the HALT Acronym
The HALT acronym is an essential tool for recognizing and addressing our basic human needs. By understanding and applying the principles of HALT, we can take better care of ourselves and promote overall well-being. Let's explore the meaning and significance of the HALT acronym.
Introduction to HALT
HALT stands for Hunger, Anger, Loneliness, and Tiredness. These four elements represent common triggers that can have a significant impact on our physical and mental health. When these needs are not met, they can negatively affect our well-being and overall quality of life.
By recognizing HALT triggers, we can proactively address these needs and take appropriate actions to ensure we are taking care of ourselves. It's important to note that HALT is not a diagnosis or a substitute for professional help. Instead, it serves as a guiding framework to help us identify areas where we may need additional support or self-care.
The Significance of the HALT Acronym
Understanding the significance of the HALT acronym is crucial for promoting self-awareness and practicing self-care. Let's take a closer look at each element of HALT and its impact on our well-being:
Element and Impact
Hunger: Hunger can lead to irritability, difficulty concentrating, and low energy levels. It's important to address hunger by nourishing our bodies with regular, balanced meals and snacks.
Anger: Unresolved anger can negatively affect our mental health, relationships, and overall quality of life. By recognizing and managing our anger, we can promote emotional well-being and healthier interactions with others.
Loneliness: Loneliness can have a profound impact on our mental and physical health. It can lead to feelings of sadness, isolation, and reduced self-esteem. Building social connections, seeking support, and engaging in activities we enjoy can help combat loneliness.
Tiredness: Lack of sleep and chronic tiredness can impair cognitive function, mood, and overall productivity. Establishing healthy sleep habits and practicing relaxation techniques can improve the quality of our sleep and combat tiredness.
By understanding the significance of the HALT acronym, we can identify when these needs are not met and take appropriate steps to address them. It's important to prioritize self-care and seek professional help when needed to ensure our overall well-being.
Remember, HALT serves as a starting point for self-reflection and taking care of our basic needs. By recognizing HALT triggers and implementing self-care strategies, we can cultivate a healthier and more balanced lifestyle.
Hunger
Hunger is a fundamental physiological sensation that arises when our body needs nourishment. In the context of the HALT acronym, understanding the effects of hunger on the body and mind is crucial for maintaining overall well-being.
Effects of Hunger on the Body and Mind
When we experience hunger, our body undergoes various physiological changes. These effects can impact both our physical and mental health:
1. Energy Depletion: Hunger is a sign that our body is running low on fuel. Without proper nourishment, our energy levels decrease, leading to fatigue and a lack of stamina.
2. Impaired Cognitive Function: Insufficient food intake can impair our cognitive abilities, including concentration, memory, and decision-making. It becomes challenging to focus on tasks and perform at our best.
3. Mood Changes: Hunger can trigger irritability, mood swings, and a general feeling of discomfort. This is because hunger affects the production of certain neurotransmitters in the brain, such as serotonin, which plays a key role in mood regulation.
4. Weakened Immune System: Chronic hunger weakens the immune system, making individuals more susceptible to infections and illnesses. It becomes harder for the body to fight off pathogens and maintain optimal health.
Tips for Addressing Hunger
Addressing hunger is essential for maintaining overall well-being. Here are some strategies to help manage and alleviate hunger:
Strategies
Eat Regular Meals: Establish a routine of eating balanced meals at regular intervals throughout the day. This helps to provide a steady source of energy and prevent extreme hunger.
Include Protein and Fiber: Incorporate protein-rich foods, such as lean meats, legumes, and dairy products, into your meals. Additionally, focus on consuming fiber-rich foods like fruits, vegetables, and whole grains, as they promote satiety.
Snack Mindfully: Choose nutritious snacks, such as nuts, yogurt, or fresh fruits, to curb hunger between meals. Avoid relying on unhealthy, sugary snacks that provide temporary relief but lead to energy crashes.
Stay Hydrated: Sometimes, thirst can be mistaken for hunger. Stay hydrated by drinking plenty of water throughout the day.
Listen to Your Body: Pay attention to your body's hunger cues. Eat when you feel hungry and stop when you feel satisfied, rather than overeating or restricting food intake.
Seek Nutritional Guidance: If you struggle with managing hunger or have specific dietary needs, consider consulting with a registered dietitian who can provide personalized nutritional guidance.
By understanding the effects of hunger on our body and mind and implementing strategies to address hunger, we can maintain a balanced and nourished state, promoting overall well-being.
Anger
The Impact of Anger on Mental Health
Anger is an intense emotion that can have a profound impact on mental health. When anger is not managed properly, it can lead to various negative consequences. Chronic anger can contribute to the development of mental health disorders, such as anxiety and depression. Additionally, uncontrolled anger can strain relationships, hinder problem-solving abilities, and negatively affect overall well-being.
Prolonged anger can lead to increased stress levels, which can have detrimental effects on both the mind and body. It can elevate blood pressure, weaken the immune system, and increase the risk of cardiovascular problems. Furthermore, unresolved anger can create a cycle of negative thoughts and emotions, perpetuating a state of distress.
Techniques for Managing Anger
Learning effective techniques for managing anger is crucial for maintaining good mental health and overall well-being. Here are some strategies that can help individuals navigate and cope with their anger:
1. Identify triggers: Recognize the situations, circumstances, or people that tend to trigger feelings of anger. Being aware of these triggers can help individuals anticipate and prepare for potential anger-inducing situations.
2. Practice deep breathing: Deep breathing exercises can help calm the body and mind during moments of anger. Taking slow, deep breaths in through the nose and out through the mouth can help regulate emotions and promote a sense of relaxation.
3. Engage in physical activity: Physical exercise is a powerful way to release built-up tension and reduce anger. Engaging in activities such as jogging, yoga, or boxing can help channel negative energy into a more positive outlet.
4. Practice mindfulness: Mindfulness techniques, such as meditation or guided imagery, can help individuals become more aware of their anger triggers and develop the ability to respond with greater control. Mindfulness encourages individuals to observe their thoughts and emotions without judgment, allowing for a more balanced perspective.
5. Seek support: It can be helpful to reach out to trusted friends, family members, or mental health professionals for support. Talking about anger and its underlying causes can provide individuals with insights and guidance on managing their emotions effectively.
By employing these techniques, individuals can gain a better understanding of their anger, develop healthier coping mechanisms, and improve their overall mental well-being. Managing anger in a constructive manner is essential for maintaining healthy relationships, reducing stress, and promoting emotional balance.
Loneliness
Loneliness is a prevalent emotional state that can have a significant impact on overall well-being. It is important to understand the effects of loneliness and implement strategies to combat it.
The Effects of Loneliness on Well-being
Loneliness can affect both mental and physical health. When individuals experience loneliness, they may feel a sense of disconnection from others, leading to emotional distress. The effects of loneliness on well-being can include:
1. Increased stress: Feelings of loneliness can contribute to heightened stress levels, as individuals may lack the support and social connections needed to cope with life's challenges.
2. Depression and anxiety: Prolonged loneliness can increase the risk of developing depression and anxiety disorders. The lack of social interaction and meaningful connections can lead to feelings of sadness, hopelessness, and worry.
3. Impaired cognitive function: Research suggests that loneliness can negatively impact cognitive function, including memory and attention. This impairment may be due to the lack of intellectual stimulation and social engagement.
4. Weakened immune system: Chronic loneliness has been associated with a weakened immune system, making individuals more susceptible to illnesses and infections.
Strategies for Combating Loneliness
Addressing loneliness requires proactive steps to foster social connections and improve overall well-being. Here are some strategies to combat loneliness:
Strategies
1. Cultivate relationships: Seek out opportunities to meet new people and build meaningful connections. Join social clubs, attend community events, or engage in activities that align with your interests.
2. Stay connected: Maintain regular contact with family and friends. Use phone calls, video chats, or social media to stay in touch, especially if distance or circumstances prevent in-person interactions.
3. Volunteer: Engaging in volunteer work allows you to contribute to your community while also providing opportunities to interact with others who share similar interests.
4. Join support groups: Consider joining support groups or organizations that focus on topics of interest or provide a space for individuals experiencing similar challenges. This can provide a sense of belonging and support.
5. Practice self-care: Engage in activities that promote self-care and well-being. This can include exercise, meditation, pursuing hobbies, or seeking professional help if needed.
6. Seek professional assistance: If feelings of loneliness persist or significantly impact daily life, it may be beneficial to seek the guidance of a mental health professional. They can provide support and recommend appropriate interventions tailored to your specific needs.
By recognizing the effects of loneliness on well-being and implementing strategies to combat it, individuals can take steps towards improving their mental and emotional health. Building and maintaining social connections, practicing self-care, and seeking professional assistance when necessary are essential in navigating and overcoming feelings of loneliness.
Tiredness
Feeling tired is a common experience that can significantly impact our daily lives. In the context of the HALT acronym, understanding how tiredness affects cognitive function is essential. Additionally, implementing effective strategies to manage tiredness is crucial for overall well-being.
How Tiredness Affects Cognitive Function
Tiredness can have a profound impact on our cognitive abilities, influencing our attention, memory, decision-making, and overall mental performance. When we are tired, our brain function becomes compromised, leading to:
• Decreased concentration and focus
• Impaired decision-making abilities
• Slower reaction times
• Reduced creativity and problem-solving skills
• Difficulty retaining and recalling information
To better understand the effects of tiredness on cognitive function, consider the following table:
Cognitive Function and Effects of Tiredness
Attention and Focus: Reduced ability to concentrate on tasks and stay engaged
Memory: Difficulty in retaining and recalling information
Decision-making: Impaired judgment and problem-solving abilities
Reaction Time: Slower response to stimuli
Creativity: Decreased ability to think creatively and generate new ideas
Tips for Managing Tiredness
Managing tiredness is crucial for maintaining optimal cognitive function and overall well-being. Here are some effective strategies to combat tiredness:
1. Prioritize Sleep: Ensure you get enough sleep each night, aiming for 7-9 hours of quality sleep. Establish a consistent sleep routine and create a sleep-friendly environment.
2. Practice Good Sleep Hygiene: Adopt healthy sleep habits, such as avoiding electronic devices before bed, keeping your bedroom cool and dark, and avoiding caffeine and stimulating activities close to bedtime.
3. Take Power Naps: If you feel tired during the day, take short power naps (around 20 minutes) to recharge and improve alertness. Be mindful not to nap too close to your regular bedtime.
4. Stay Active: Regular physical activity can boost energy levels and promote better sleep. Engage in exercise or physical activities that you enjoy to improve your overall energy levels.
5. Maintain a Balanced Diet: Eat a nutritious and well-balanced diet to provide your body with the necessary energy. Include foods rich in vitamins, minerals, and antioxidants to support overall health.
6. Stay Hydrated: Dehydration can contribute to tiredness, so ensure you drink enough water throughout the day to stay properly hydrated.
7. Manage Stress: Chronic stress can contribute to fatigue and tiredness. Practice stress management techniques such as deep breathing exercises, meditation, and engaging in activities that help you relax and unwind.
8. Avoid Overloading Yourself: Don't take on more tasks or commitments than you can handle. Prioritize your responsibilities and delegate tasks when possible to avoid excessive fatigue.
By implementing these tips and strategies, you can effectively manage tiredness and improve your cognitive function. Remember, addressing tiredness is an important aspect of the HALT acronym and contributes to overall well-being.
Applying HALT in Daily Life
Once you understand the significance of the HALT acronym, you can apply it in your daily life to enhance your well-being. This section will explore two important aspects of HALT implementation: recognizing HALT triggers and implementing self-care strategies.
Recognizing HALT Triggers
Recognizing the triggers that lead to feelings of hunger, anger, loneliness, and tiredness is a crucial step in effectively applying the HALT acronym in your daily life. By identifying these triggers, you can take proactive measures to address them before they escalate.
HALT Trigger and Common Triggers
Hunger: Skipped meals, low blood sugar, restrictive diets
Anger: Frustration, perceived injustice, criticism
Loneliness: Lack of social connection, isolation
Tiredness: Lack of sleep, excessive physical or mental exertion
Take note of situations or circumstances that consistently lead to these triggers. This awareness will help you better understand the root causes behind your emotions and reactions.
Implementing Self-Care Strategies
Once you've identified your HALT triggers, it's essential to implement self-care strategies to address them effectively. Here are some practical tips for each HALT component:
• Hunger: To address hunger, ensure you have regular, balanced meals and snacks throughout the day. Avoid restrictive diets and listen to your body's hunger cues.
• Anger: When anger arises, practice techniques such as deep breathing, mindfulness, and engaging in calming activities like meditation or physical exercise.
• Loneliness: Combat loneliness by actively seeking social connection. Reach out to friends, join social groups or clubs, and engage in activities that align with your interests.
• Tiredness: Prioritize adequate sleep and establish a consistent sleep routine. Take short breaks throughout the day to rest and recharge. Incorporate relaxation techniques, such as taking a bath or practicing relaxation exercises.
Remember, self-care is a personal journey, and what works for one person may not work for another. Experiment with different strategies and find what resonates with you. It's essential to be patient and kind to yourself as you navigate the process of implementing self-care practices.
By recognizing HALT triggers and implementing self-care strategies, you can effectively manage the challenges associated with hunger, anger, loneliness, and tiredness. Embracing the HALT acronym in your daily life empowers you to take control of your well-being and cultivate a healthier and more balanced lifestyle.
Seeking Professional Help
While the HALT acronym can be a valuable tool in managing one's well-being, there are instances where professional assistance may be necessary. Recognizing when it's time to seek help is crucial for addressing underlying issues and obtaining the support needed for optimal mental health.
When to Consider Professional Assistance
It is important to consider seeking professional help if the effects of hunger, anger, loneliness, or tiredness become overwhelming and begin to significantly impact daily life. While self-care strategies can be helpful, there are situations where the guidance and expertise of mental health professionals are needed. Here are some signs that indicate it may be time to seek professional assistance:
1. Persistent and severe symptoms: If the physical and emotional effects of hunger, anger, loneliness, or tiredness persist for an extended period and interfere with daily functioning, it may be a sign of an underlying mental health condition.
2. Inability to cope: If self-care strategies are not providing relief or if the challenges related to HALT triggers become increasingly difficult to manage, seeking professional help can provide additional coping techniques and support.
3. Impact on relationships: When the effects of HALT impact relationships with family, friends, or colleagues, it may be beneficial to seek professional assistance to address underlying issues and improve communication and interpersonal skills.
4. Suicidal thoughts or self-harm: If feelings of despair, hopelessness, or thoughts of self-harm arise, it is crucial to reach out to a mental health professional or a helpline immediately. These are serious signs that require immediate attention and support.
Resources for Support and Treatment
When seeking professional help, there are various resources available that can provide support and treatment. Here are some options to consider:
Resource and Description
Mental health professionals: Psychologists, psychiatrists, therapists, and counselors can provide individualized assessment, therapy, and treatment for mental health conditions. They can help address the underlying causes of HALT triggers and develop personalized coping strategies.
Support groups: Joining support groups, whether in-person or online, can provide a sense of community and understanding. These groups often consist of individuals who have experienced similar challenges and can offer valuable insights and support.
Helplines: Helplines and crisis hotlines are available 24/7 for immediate support. Trained professionals can provide guidance, crisis intervention, and referrals to appropriate resources.
Community organizations: Local community organizations may offer mental health services, workshops, and support programs at little or no cost. These organizations can connect individuals with resources in their area.
Online resources: There are numerous websites, blogs, and forums dedicated to mental health. These resources can provide information, coping strategies, and personal stories that may resonate with individuals experiencing HALT challenges.
Remember, seeking professional help is a sign of strength and a proactive step towards improving mental well-being. Mental health professionals have the expertise to guide individuals through the challenges associated with HALT triggers and provide the necessary support and treatment to foster long-term mental wellness.
Sources
What Is HALT? The Dangers of Being Hungry, Angry, Lonely
What Are the HALT Risk States?
HALT: Pay Attention to These Four Stressors
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Wavelet art highlights the finer points of whale songs
OCR Advisor and software mathematician Mark Fisher received some recent coverage in Wired and Co.Design for his fantastic renderings of whale, dolphin, bird, and insect sounds using a diagnostic function called “wavelets.” Wavelets are typically used to evaluate large data sets in a way that can look at the entire set while highlighting fine inner details. In this case Mark’s large data sets are sounds.
In most visual sound analysis either the spectral or the amplitude components of a sound are evaluated over time – as found in the OCR Sound Library Audiograms (rendered through Cornell’s “Raven” software). The amplitude (how loud a sound is) is fairly easy to render as it just requires creating a visual correlation of “louder sound to more of something.”
The spectral (frequency) components are a bit more complicated because you have to measure the amplitudes through a discreet set of “frequency bins” or filters and have the outputs show up in a way that is easy to understand. For example higher frequencies can appear “higher up” on the “y” axis, or “more to the right side” of an “x-y” graph.
While this common processing-and-display convention is useful and easy to read once you get the hang of it, it discards the finer details by processing the sound in big chunks.
Wavelets are a more complicated process. Instead of running a sound through a set of stationary filter bins and measuring the outputs of the bins, wavelet analysis (mathematically) throws little bursts of sound or “wavelets” at a sound and evaluates the interference. If you know the precise shape and timing of the wavelets, the interference patterns will tell you a lot about what you’re bouncing them off.
Aguasonic Sound Visualization of False Killer Whale Vocalization
False killer whale wavelet mandala
There is still frequency on the “y axis” but the “x axis” displays interference in the time domain; and “how much” (or “how little”) is represented by how bright the patterns are. In this manner large and complicated sounds can yield meta-patterns that also reveal the tiny details.
This may seem a bit difficult to wrap your head around, but these patterns can tell volumes about the specifics of a sound – stuff that we might be able to hear but would have a hard time describing.
Mark is taking his wavelet analysis and bending them into circular “mandalas.” These mandalas can be useful, but they are also beautiful while telling us a lot about the details of the sounds that produced them. The complexities of the patterns also reflect the complexity of sound production and reception. Wavelet analysis might hold the key to how you can identify the voice of someone you haven’t heard in 20 years, or how a pod of dolphins instantaneously sort out their complex bioacoustic world.
You can also dispense with the heady stuff and just look at the gorgeous patterns on Mark’s AguaSonic website.
Very cool Mark!
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Urine pH
Urine pH is used to classify urine as either a dilute acid or base solution. Seven is the point of neutrality on the pH scale. The lower the pH, the greater the acidity of a solution; the higher the pH, the greater the alkalinity. The glomerular filtrate of blood is usually acidified by the kidneys from a pH of approximately 7.4 to a pH of about 6 in the urine. Depending on the person's acid-base status, the pH of urine may range from 4.5 to 8. The kidneys maintain normal acid-base balance primarily through the reabsorption of sodium and the tubular secretion of hydrogen and ammonium ions. Urine becomes increasingly acidic as the amount of sodium and excess acid retained by the body increases. Alkaline urine, usually containing bicarbonate-carbonic acid buffer, is normally excreted when there is an excess of base or alkali in the body. Secretion of an acid or alkaline urine by the kidneys is one of the most important mechanisms the body uses to maintain a constant body pH.
A highly acidic urine pH occurs in:
A highly alkaline urine occurs in:
In people who are not vegetarians, the pH of urine tends to be acidic. A diet rich in citrus fruits, legumes, and vegetables raises the pH and produces urine that is more alkaline. Most of the bacteria responsible for urinary tract infections make the urine more alkaline because the bacteria split urea into ammonia and other alkaline waste products. The urine pH varies in different types of acidosis and alkalosis. Control of pH is important in the management of several diseases, including bacteriuria, renal calculi, and drug therapy.
The formation of renal stones is related to the urine pH. Patients being treated for renal calculi are frequently given diets or medications to change the pH of the urine so that kidney stones will not form. Calcium phosphate, calcium carbonate, and magnesium phosphate stones develop in alkaline urine; when this occurs, the urine is kept acidic. Uric acid, cystine, and calcium oxalate stones precipitate in acidic urine; in this situation, the urine should be kept alkaline or less acidic than normal. Drugs such as streptomycin, neomycin, and kanamycin are effective in treating urinary tract infections if the urine is alkaline. During treatment with sulfa drugs, alkaline urine helps prevent formation of sulfonamide crystals.
Here are important points to remember about urinary pH:
Instant Feedback:
Most bacterial urinary tract infections cause the urine to become more alkaline.
TRUE or FALSE
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DISEASES
Disease-gene associations mined from literature
Literature associating CSF2 and dyskeratosis congenita
CSF2 [ENSP00000296871]
Colony stimulating factor 2 (granulocyte-macrophage); Cytokine that stimulates the growth and differentiation of hematopoietic precursor cells from various lineages, including granulocytes, macrophages, eosinophils and erythrocytes; Belongs to the GM-CSF family.
Synonyms: CSF2, CSF2p, hCSF2, P04141, GMCSF ...
Linkouts: STRING Pharos UniProt OMIM
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UI design with Tiles and Struts
Several solutions for organizing your HTML and JSP view components
Typically during Web application development, the user interface (UI) group creates the site's look and feel. Based on that look and feel, the group creates HTML pages that represent the application's functionality and navigation. With a servlets and JavaServer Pages (JSPs)-based implementation, where HTML pages are converted into servlets and JSPs, UI developers identify common HTML and JSP view components, such as header, footer, body, menu, and search. This article presents various solutions to effectively and efficiently organize HTML and JSP view components. I evaluate each solution using specific criteria, such as page number, code repetition, and layout control.
To explore templating and layout solutions, we will use the Tiles framework. The Tiles framework's view components are known as tiles. The framework uses an XML configuration file to organize those tiles. This framework not only enables you to reuse tiles, but also the layouts that organize them.
To explore the more powerful and flexible solutions, we will investigate the synergy between the Tiles and Struts frameworks. Struts is an open source framework for developing Web applications using the popular Model-View-Controller (MVC) or Model 2 architectural pattern. Struts comes with a large set of reusable tags for which the Tiles tag library makes an excellent enhancement.
Evaluation criteria
I will evaluate each solution based on the criteria below. The criteria are not mutually exclusive. For a specific situation and particular application, you must always balance between the strengths and weaknesses of each solution with respect to these factors.
Page number
A solution should strive to minimize the number of HTML and JSP pages. As the page number increases, the complexity of developing, managing, and maintaining an application increases drastically.
Code repetition
Under most circumstances, repetition is bad. The more repeated HTML and JSP code, the more difficult it is to develop and maintain an application. A simple change can result in a cascade of changes in many different pages with unpredictable consequences. A concrete and practical way of attaining reuse is to avoid code repetition.
Layout control
While code repetition is bad, repetition of layout logic and code can be worse. Spreading the logic and behavior of view component organization over several JSPs can be a recipe for disaster. Attaining reuse of templating and layout logic is a better form of reuse than only reusing view components. Thus, you can achieve a higher level of reuse with effective layout control.
Coupling
Coupling is the degree of interactivity between entities. Software engineers are taught again and again to minimize coupling between unrelated classes, packages, and so on. We can apply the same principle to view components. Even though there are distinct view components from a user perspective, in the JSP implementation, the components might be intricately coupled. A solution should reduce coupling between unrelated view components.
Complexity
Complexity brings increased development and maintenance costs, making a more complex solution less suitable. Complexity grows fast as well, and what might originally look simple and innocuous can quickly turn into a big mess as you add more pieces.
Solutions
I'll evaluate several solutions using a basic example of JSPs with common view components, like header and footer. I'll present these solutions in order of increasing complexity, and then I'll measure in detail each one against the evaluation criteria.
Solution 1: Basic JSP
Consider the following JSP for
a.jsp
:
<html>
<body>
Header
<p>
a's body...
<p>
Footer
<p>
</body>
</html>
Consider the following JSP for b.jsp:
<html>
<body>
Header
<p>
b's body...
<p>
Footer
<p>
</body>
</html>
In many cases, the developers obtain the code from the UI group and literally convert it into a JSP as necessary. As shown above, each JSP has a duplicate header and footer. Solution 1 is undesirable because changes in common view components, like header and footer, require changes in all relevant pages, as each page is responsible for laying out the view components. This simple solution lacks foresight. With so much HTML and JSP code duplication, we minimize the number of pages but at a heavy maintenance cost. There is strong coupling between the different view components, which, as I explained earlier, is undesirable.
Solution 2: JSP include
Consider the following JSP for
a.jsp
:
<html>
<body>
<%-- include header --%>
<jsp:include page="/header.jsp" />
a's body...
<p>
<%-- include footer --%>
<jsp:include page="/footer.jsp" />
</body>
</html>
Consider the following JSP for b.jsp:
<html>
<body>
<%-- include header --%>
<jsp:include page="/header.jsp" />
b's body...
<p>
<%-- include footer --%>
<jsp:include page="/footer.jsp" />
</body>
</html>
Note that common view components, like header and footer, are split up using the JSP include mechanism.
Consider this header.jsp:
Header
<p>
Consider this footer.jsp:
Footer
<p>
Solution 2 nicely addresses some of Solution 1's major shortcomings. You only need to change common view components once. Hence, this solution greatly eliminates HTML and JSP code repetition, significantly improving application maintainability. It increases the page number a bit, but drastically reduces the tight coupling between common view components and other pages. On the complexity scale, this solution is simple and readily implemented on many real-world applications. However, it has one major drawback: if you change how and where you organize the view components (i.e., by changing the component layout), then you would need to update every page -- resulting in an expensive and prohibitive change. Solution 2 achieves view component reuse, but does not achieve the reuse of layout and templating logic.
Solution 3: Tiles insert
Consider this JSP for a.jsp:
<%@ taglib uri="/WEB-INF/tiles.tld" prefix="tiles" %>
<html>
<body>
<%-- include header --%>
<tiles:insert page="/header.jsp" flush="true"/>
a's body...
<p>
<%-- include footer --%>
<tiles:insert page="/footer.jsp" flush="true"/>
</body>
</html>
Consider this JSP for b.jsp:
<%@ taglib uri="/WEB-INF/tiles.tld" prefix="tiles" %>
<html>
<body>
<%-- include header --%>
<tiles:insert page="/header.jsp" flush="true"/>
b's body...
<p>
<%-- include footer --%>
<tiles:insert page="/footer.jsp" flush="true"/>
</body>
</html>
Instead of using the JSP include mechanism, Solution 3 uses the Tiles insert mechanism. Using the Tiles insert tag, you include the view components in the appropriate positions. In all other aspects, the solution mirrors the JSP include solution (Solution 2) exactly, with the same advantages and disadvantages.
Solution 4: Splitting bodies
Consider this a.jsp:
<%@ taglib uri="/WEB-INF/tiles.tld" prefix="tiles" %>
<html>
<body>
<%-- include header --%>
<tiles:insert page="/header.jsp" flush="true"/>
<%-- include body --%>
<tiles:insert page="aBody.jsp" flush="true"/>
<%-- include footer --%>
<tiles:insert page="/footer.jsp" flush="true"/>
</body>
</html>
Consider this b.jsp:
<%@ taglib uri="/WEB-INF/tiles.tld" prefix="tiles" %>
<html>
<body>
<%-- include header --%>
<tiles:insert page="/header.jsp" flush="true"/>
<%-- include body --%>
<tiles:insert page="bBody.jsp" flush="true"/>
<%-- include footer --%>
<tiles:insert page="/footer.jsp" flush="true"/>
</body>
</html>
Solution 4 differs slightly from the Tiles insert solution. Solution 4 separates the core bodies into their individual pages, like aBody.jsp and bBody.jsp.
Consider the following JSP for aBody.jsp:
a's body...
<p>
Consider the following JSP for bBody.jsp:
b's body...
<p>
Solution 4's advantage: it limits body changes to the respective pages. Also, it lets you reuse the bodies in other places, eliminating the need for repetition and duplication. Thus, the solution further diminishes the coupling between common view components and other application components. Creating and managing each body component introduces an additional complexity level. As with other solutions, each page still does its own layout. Hence, there is no overarching layout policy or scheme.
Solution 5: Templating tiles
Using Tiles's templating feature, you can define the following layout (from the layout.jsp file shown below) as a template. Since this is a layout, you insert placeholders instead of the actual view components using the Tiles insert tag. Thus, for all components, this page defines one reusable layout:
<%@ taglib uri="/WEB-INF/tiles.tld" prefix="tiles" %>
<html>
<body>
<%-- include header --%>
<tiles:insert attribute="header"/>
<%-- include body --%>
<tiles:insert attribute="body"/>
<%-- include footer --%>
<tiles:insert attribute="footer"/>
</body>
</html>
Other content pages, like a.jsp and b.jsp, use the above layout for arranging components. In the actual page, you insert the layout using the Tiles insert tag. Using the Tiles put tag, you can specify the actual view components for all placeholders specified in the layout.
Consider this a.jsp:
<%@ taglib uri="/WEB-INF/tiles.tld" prefix="tiles" %>
<tiles:insert page="/layout.jsp" flush="true">
<tiles:put name="header" value="/header.jsp"/>
<tiles:put name="body" value="/aBody.jsp"/>
<tiles:put name="footer" value="/footer.jsp"/>
</tiles:insert>
Consider this b.jsp:
<%@ taglib uri="/WEB-INF/tiles.tld" prefix="tiles" %>
<tiles:insert page="/layout.jsp" flush="true">
<tiles:put name="header" value="/header.jsp"/>
<tiles:put name="body" value="/bBody.jsp"/>
<tiles:put name="footer" value="/footer.jsp"/>
</tiles:insert>
Solution 5's most significant advantage is that it encapsulates the layout scheme or mechanism, drastically reducing the coupling between common view components and other content bodies. However, it increases complexity by introducing another layout page. Understanding and implementing templating can also be difficult at first.
Solution 6: Struts and Tiles
The above layout page, layout.jsp, contains the HTML and JSP code for organizing the components. The content pages, a.jsp and b.jsp, do not contain any HTML code; they just contain the Tiles tags to insert the necessary components. Wouldn't it be nice to specify all the content pages in one XML configuration file?
Let's name that file tileDefinitions.xml and specify its pages as:
<?xml version="1.0" encoding="ISO-8859-1"?>
<component-definitions>
<definition name="aDef" path="/layout.jsp">
<put name="header" value="/header.jsp"/>
<put name="footer" value="/footer.jsp"/>
<put name="body" value="/aBody.jsp"/>
</definition>
<definition name="bDef" path="/layout.jsp">
<put name="header" value="/header.jsp"/>
<put name="footer" value="/footer.jsp"/>
<put name="body" value="/bBody.jsp"/>
</definition>
<definition name="cDef" path="/layout.jsp">
<put name="header" value="/header.jsp"/>
<put name="footer" value="/footer.jsp"/>
<put name="body" value="/cBody.jsp"/>
</definition>
</component-definitions>
Solution 6 eliminates all the content pages, like a.jsp and b.jsp, by putting their definitions in the XML file. Since a resource like a.jsp no longer exists, how can we request it? More importantly, how can we request the definitions in the tileDefinitions.xml file?
The powerful and synergistic integration of Struts and Tiles comes to the rescue. Besides the regular Struts configuration parameters, we specify the configuration file's location as another parameter in the web.xml file, as shown below. Specifying the definitions-config parameter enables Struts to find and know about the Tiles definitions:
<!-- Standard Action Servlet Configuration (with debugging) -->
<servlet>
<servlet-name>action</servlet-name>
<!--
<servlet-class>org.apache.struts.action.ActionServlet</servlet-class>
-->
<servlet-class>org.apache.struts.tiles.ActionComponentServlet</servlet-class>
<init-param>
<param-name>definitions-config</param-name>
<param-value>/WEB-INF/tileDefinitions.xml</param-value>
</init-param>
...
</servlet>
Now, we define a Struts action, which returns a definition specified in the configuration file upon success. The Struts action DoFirst is a nonoperational action, as shown below:
package com.malani.struts.action;
import org.apache.struts.action.*;
import javax.servlet.http.*;
public class DoFirst extends Action {
public ActionForward perform(
ActionMapping aMapping,
ActionForm aForm,
HttpServletRequest aRequest,
HttpServletResponse aResponse
) {
return aMapping.findForward("success");
}
}
1 2 Page 1
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18.4 C
New York
October 2, 2023
Talk 2 Health – Make your life a healthier one
Health
How to Utilize Etyltrimethylammonium Bromide As A Germicide: The Ultimate Guide
The mode of action of CTAB is similar to that of other quaternary ammonium compounds, such as benzalkonium chloride and alkyltrimethyl ammonium chloride. CTAB works by disrupting the cell membranes of bacteria and other microorganisms, causing them to leak and die.
CTAB has been shown to be effective against a broad range of bacteria, including Escherichia coli, Staphylococcus aureus, and Pseudomonas aeruginosa. It is also effective against viruses, fungi, and protozoa. Cetyltrimethylammonium bromide is generally considered to be safe and effective when used as directed. However, it can cause eye and skin irritation and should be used with caution in households with children or pets.
Benefits of using cetyltrimethylammonium bromide as a germicide:
• CTMAB has a wide range of applications and is effective against a variety of microorganisms, including bacteria, fungi, and viruses.
• In addition, CTMAB is non-toxic to humans and animals, making it safe to use in both residential and commercial settings.
• Furthermore, CTMAB is relatively inexpensive and easy to obtain. When used properly, CTMAB can help to keep surfaces clean and free of harmful microbes.
As such, it is an important tool in the fight against illness and disease.
How to use cetyltrimethylammonium bromide properly as a germicide:
Cetyltrimethylammonium bromide (CTAB) is a quaternary ammonium compound that is commonly used as a germicide. It is effective against a wide range of bacteria, viruses, and fungi, making it a valuable tool for preventing the spread of infection.
• CTAB can be used in a variety of ways, including as a disinfectant for surfaces and medical equipment, as a preservative for biological specimens, and as an antiseptic for wounds.
• When using CTAB as a germicide, it is important to follow the manufacturer’s instructions carefully to ensure safety and efficacy.
Where to find it:
CTAB is used in a wide variety of applications, including cosmetics, detergents, emulsifiers, and cleaning agents. CTAB is also used as a disinfectant and sanitizer in hospitals and laboratories. So, it can be purchased from chemical supply companies or online retailers.
Endnote:
CTMAB is relatively safe to use, and it does not cause the development of resistance in bacteria. In addition, CTMAB is inexpensive and easy to obtain. For these reasons, CTMAB is often considered the best option for use as a germicide.
However, there are some drawbacks to using CTMAB. For example, it can be toxic to human cells and it may also cause skin irritation. CTMAB is not effective against all types of microorganisms. Nevertheless, CTMAB remains a popular choice for use as a germicide due to its efficacy and safety.
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Language:
Dividing
Time Limit: 1000MSMemory Limit: 10000K
Total Submissions: 75948Accepted: 19921
Description
Marsha and Bill own a collection of marbles. They want to split the collection among themselves so that both receive an equal share of the marbles. This would be easy if all the marbles had the same value, because then they could just split the collection in half. But unfortunately, some of the marbles are larger, or more beautiful than others. So, Marsha and Bill start by assigning a value, a natural number between one and six, to each marble. Now they want to divide the marbles so that each of them gets the same total value. Unfortunately, they realize that it might be impossible to divide the marbles in this way (even if the total value of all marbles is even). For example, if there are one marble of value 1, one of value 3 and two of value 4, then they cannot be split into sets of equal value. So, they ask you to write a program that checks whether there is a fair partition of the marbles.
Input
Each line in the input file describes one collection of marbles to be divided. The lines contain six non-negative integers n1 , . . . , n6 , where ni is the number of marbles of value i. So, the example from above would be described by the input-line "1 0 1 2 0 0". The maximum total number of marbles will be 20000.
The last line of the input file will be "0 0 0 0 0 0"; do not process this line.
Output
For each collection, output "Collection #k:", where k is the number of the test case, and then either "Can be divided." or "Can't be divided.".
Output a blank line after each test case.
Sample Input
1 0 1 2 0 0
1 0 0 0 1 1
0 0 0 0 0 0
Sample Output
Collection #1:
Can't be divided.
Collection #2:
Can be divided.
Source
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__label__pos
| 0.92255 |
Common Mistakes to Avoid When Generating an htpasswd File 1
Understanding the htpasswd File
The htpasswd file is a basic authentication method used by Apache web servers. It stores usernames and their corresponding hashed passwords, allowing access to protected directories or pages. To generate an htpasswd file, you need to have a clear understanding of the process and avoid common mistakes that can compromise the security of your system.
Choosing a Secure Password
One of the biggest mistakes when generating an htpasswd file is using weak or easily guessable passwords. To enhance security, choose a strong password that combines uppercase and lowercase letters, numbers, and special characters. Additionally, ensure that the password is at least 8 characters long. Visit this suggested external site to uncover additional and supplementary data on the subject discussed. We’re committed to providing an enriching educational experience. htpasswd generator.
Not Encrypting Passwords
Another common mistake is not encrypting the passwords stored in the htpasswd file. Encryption adds an extra layer of security, preventing unauthorized access to user credentials. Apache uses MD5 or BCrypt encryption algorithms to securely store the passwords. Choose the appropriate encryption method and ensure that the passwords are properly encrypted before adding them to the htpasswd file.
Keeping the htpasswd File Secure
It is crucial to maintain the confidentiality of the htpasswd file. Avoid placing it in publicly accessible directories or leaving it vulnerable to unauthorized access. Store the htpasswd file in a location that can only be accessed by authorized administrators and ensure proper permissions are set to prevent unauthorized modifications or viewing.
Not Regularly Updating Passwords
When generating an htpasswd file, it is essential to periodically update passwords to further enhance security. Regularly changing passwords reduces the risk of unauthorized access and minimizes the impact of potential password leaks or breaches. Set a schedule to prompt users to update their passwords and enforce password complexity requirements.
Ignoring User Authentication Levels
The htpasswd file supports different user authentication levels, such as basic and digest. Basic authentication sends the password in plaintext over the network, while digest authentication sends a hashed version of the password. Ignoring user authentication levels and using basic authentication without considering the security implications can lead to potential vulnerabilities. Evaluate your system requirements and choose the appropriate authentication level for your htpasswd file.
Forgetting to Backup the htpasswd File
Accidents can happen, and it’s important to be prepared. Forgetting to backup the htpasswd file can result in permanent loss of user credentials and restricted access to protected directories or pages. Regularly create backups of your htpasswd file and store them in a secure location. This precaution will help you recover from any data loss or system failures.
Conclusion
Generating an htpasswd file is a vital step in securing your Apache web server. However, avoiding common mistakes is equally important to ensure the integrity and confidentiality of user credentials. By understanding the htpasswd file, choosing secure passwords, encrypting passwords, keeping the file secure, regularly updating passwords, considering user authentication levels, and backing up the file, you can prevent potential security breaches and protect your system effectively. Access this recommended external website to discover extra and complementary information about the topic covered. We’re committed to providing an enriching educational experience. Access details!
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What is the difference between list and tuple?
Posted by Jessica Taylor | Updated on
What is the difference between list and tuple?
The difference between list and tuple is that list is mutable while tuple is not. Tuple can be hashed for e.g as a key for dictionaries.
If you like this question & answer and want to contribute, then write your question & answer and email to freewebmentor[@]gmail.com. Your question and answer will appear on FreeWebMentor.com and help other developers.
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Nondisplaced bicondylar fracture of unspecified tibia, subsequent encounter for closed fracture with routine healing digital illustration
Nondisplaced bicondylar fracture of unspecified tibia, subsequent encounter for closed fracture with routine healing Save
ICD-10 code: S82.146D
Disease category: S82.146: Nondisplaced bicondylar fracture of unspecified tibia
Nondisplaced Bicondylar Fracture of Unspecified Tibia: Understanding the Subsequent Encounter for Closed Fracture with Routine Healing
A nondisplaced bicondylar fracture of the unspecified tibia is a type of leg injury that occurs when the tibia bone is partially broken but remains aligned. In this article, we will delve into the subsequent encounter for closed fracture with routine healing, providing valuable information about this condition.
When a patient experiences a nondisplaced bicondylar fracture of the tibia, they may require multiple medical visits to ensure proper healing. The subsequent encounter refers to a follow-up appointment to evaluate the progress of the fracture after the initial diagnosis and any initial treatment that may have been performed.
1. Diagnosis: During the initial encounter, a thorough examination and diagnostic tests such as X-rays are conducted to identify the fracture and determine its severity.
2. Treatment: Following the diagnosis, the patient may have undergone appropriate treatment, which can include immobilization with a cast or brace to allow the fracture to heal naturally.
3. Healing process: The subsequent encounter focuses on assessing the healing progress. Routine healing implies that the fracture is healing as expected without any complications.
At the subsequent encounter, the healthcare provider will examine the patient's leg and may order additional X-rays to evaluate the healing process. They will look for signs of proper alignment and callus formation, which indicates the bone is mending correctly.
During this visit, the healthcare provider may also provide guidance on weight-bearing restrictions, physical therapy exercises, or any necessary lifestyle modifications. They will assess the patient's overall condition, including pain levels and mobility, to ensure the fracture is healing as expected.
It's important for individuals with this type of fracture to attend subsequent encounters for closed fractures with routine healing. These appointments allow healthcare professionals to monitor progress, address any concerns, and ensure the fracture is healing properly. Compliance with these visits can significantly contribute to the successful recovery of patients with a nondisplaced bicondylar fracture of the unspecified tibia.
In conclusion, a nondisplaced bicondylar fracture of the unspecified tibia requires subsequent encounters for closed fractures with routine healing. These follow-up appointments play a crucial role in monitoring the healing process, evaluating the alignment and callus formation, and providing necessary guidance for a successful recovery.
Treatment of Nondisplaced bicondylar fracture of unspecified tibia, subsequent encounter for closed fracture with routine healing:
Treatment Options for Nondisplaced Bicondylar Fracture of Unspecified Tibia, Subsequent Encounter for Closed Fracture with Routine Healing
A nondisplaced bicondylar fracture of the tibia refers to a type of fracture that affects both condyles of the tibia, without any significant displacement. This condition typically requires medical attention to ensure proper healing and restore ...
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Description of fast matrix multiplication algorithm: ⟨6×6×7:185⟩
Algorithm type
3X4Y4Z4+6X4Y2Z2+32X3Y2Z3+48X3YZ3+24X2Y2Z2+36X2YZ+36XYZ3X4Y4Z46X4Y2Z232X3Y2Z348X3YZ324X2Y2Z236X2YZ36XYZ3*X^4*Y^4*Z^4+6*X^4*Y^2*Z^2+32*X^3*Y^2*Z^3+48*X^3*Y*Z^3+24*X^2*Y^2*Z^2+36*X^2*Y*Z+36*X*Y*Z
Algorithm definition
The algorithm ⟨6×6×7:185⟩ could be constructed using the following decomposition:
⟨6×6×7:185⟩ = ⟨6×6×4:105⟩ + ⟨6×6×3:80⟩.
This decomposition is defined by the following equality:
TraceMulA_1_1A_1_2A_1_3A_1_4A_1_5A_1_6A_2_1A_2_2A_2_3A_2_4A_2_5A_2_6A_3_1A_3_2A_3_3A_3_4A_3_5A_3_6A_4_1A_4_2A_4_3A_4_4A_4_5A_4_6A_5_1A_5_2A_5_3A_5_4A_5_5A_5_6A_6_1A_6_2A_6_3A_6_4A_6_5A_6_6B_1_1B_1_2B_1_3B_1_4B_1_5B_1_6B_1_7B_2_1B_2_2B_2_3B_2_4B_2_5B_2_6B_2_7B_3_1B_3_2B_3_3B_3_4B_3_5B_3_6B_3_7B_4_1B_4_2B_4_3B_4_4B_4_5B_4_6B_4_7B_5_1B_5_2B_5_3B_5_4B_5_5B_5_6B_5_7B_6_1B_6_2B_6_3B_6_4B_6_5B_6_6B_6_7C_1_1C_1_2C_1_3C_1_4C_1_5C_1_6C_2_1C_2_2C_2_3C_2_4C_2_5C_2_6C_3_1C_3_2C_3_3C_3_4C_3_5C_3_6C_4_1C_4_2C_4_3C_4_4C_4_5C_4_6C_5_1C_5_2C_5_3C_5_4C_5_5C_5_6C_6_1C_6_2C_6_3C_6_4C_6_5C_6_6C_7_1C_7_2C_7_3C_7_4C_7_5C_7_6=TraceMulA_1_1A_1_2A_1_3A_1_4A_1_5A_1_6A_2_1A_2_2A_2_3A_2_4A_2_5A_2_6A_3_1A_3_2A_3_3A_3_4A_3_5A_3_6A_4_1A_4_2A_4_3A_4_4A_4_5A_4_6A_5_1A_5_2A_5_3A_5_4A_5_5A_5_6A_6_1A_6_2A_6_3A_6_4A_6_5A_6_6B_1_1B_1_2B_1_3B_1_4B_2_1B_2_2B_2_3B_2_4B_3_1B_3_2B_3_3B_3_4B_4_1B_4_2B_4_3B_4_4B_5_1B_5_2B_5_3B_5_4B_6_1B_6_2B_6_3B_6_4C_1_1C_1_2C_1_3C_1_4C_1_5C_1_6C_2_1C_2_2C_2_3C_2_4C_2_5C_2_6C_3_1C_3_2C_3_3C_3_4C_3_5C_3_6C_4_1C_4_2C_4_3C_4_4C_4_5C_4_6+TraceMulA_1_1A_1_2A_1_3A_1_4A_1_5A_1_6A_2_1A_2_2A_2_3A_2_4A_2_5A_2_6A_3_1A_3_2A_3_3A_3_4A_3_5A_3_6A_4_1A_4_2A_4_3A_4_4A_4_5A_4_6A_5_1A_5_2A_5_3A_5_4A_5_5A_5_6A_6_1A_6_2A_6_3A_6_4A_6_5A_6_6B_1_5B_1_6B_1_7B_2_5B_2_6B_2_7B_3_5B_3_6B_3_7B_4_5B_4_6B_4_7B_5_5B_5_6B_5_7B_6_5B_6_6B_6_7C_5_1C_5_2C_5_3C_5_4C_5_5C_5_6C_6_1C_6_2C_6_3C_6_4C_6_5C_6_6C_7_1C_7_2C_7_3C_7_4C_7_5C_7_6TraceMulA_1_1A_1_2A_1_3A_1_4A_1_5A_1_6A_2_1A_2_2A_2_3A_2_4A_2_5A_2_6A_3_1A_3_2A_3_3A_3_4A_3_5A_3_6A_4_1A_4_2A_4_3A_4_4A_4_5A_4_6A_5_1A_5_2A_5_3A_5_4A_5_5A_5_6A_6_1A_6_2A_6_3A_6_4A_6_5A_6_6B_1_1B_1_2B_1_3B_1_4B_1_5B_1_6B_1_7B_2_1B_2_2B_2_3B_2_4B_2_5B_2_6B_2_7B_3_1B_3_2B_3_3B_3_4B_3_5B_3_6B_3_7B_4_1B_4_2B_4_3B_4_4B_4_5B_4_6B_4_7B_5_1B_5_2B_5_3B_5_4B_5_5B_5_6B_5_7B_6_1B_6_2B_6_3B_6_4B_6_5B_6_6B_6_7C_1_1C_1_2C_1_3C_1_4C_1_5C_1_6C_2_1C_2_2C_2_3C_2_4C_2_5C_2_6C_3_1C_3_2C_3_3C_3_4C_3_5C_3_6C_4_1C_4_2C_4_3C_4_4C_4_5C_4_6C_5_1C_5_2C_5_3C_5_4C_5_5C_5_6C_6_1C_6_2C_6_3C_6_4C_6_5C_6_6C_7_1C_7_2C_7_3C_7_4C_7_5C_7_6TraceMulA_1_1A_1_2A_1_3A_1_4A_1_5A_1_6A_2_1A_2_2A_2_3A_2_4A_2_5A_2_6A_3_1A_3_2A_3_3A_3_4A_3_5A_3_6A_4_1A_4_2A_4_3A_4_4A_4_5A_4_6A_5_1A_5_2A_5_3A_5_4A_5_5A_5_6A_6_1A_6_2A_6_3A_6_4A_6_5A_6_6B_1_1B_1_2B_1_3B_1_4B_2_1B_2_2B_2_3B_2_4B_3_1B_3_2B_3_3B_3_4B_4_1B_4_2B_4_3B_4_4B_5_1B_5_2B_5_3B_5_4B_6_1B_6_2B_6_3B_6_4C_1_1C_1_2C_1_3C_1_4C_1_5C_1_6C_2_1C_2_2C_2_3C_2_4C_2_5C_2_6C_3_1C_3_2C_3_3C_3_4C_3_5C_3_6C_4_1C_4_2C_4_3C_4_4C_4_5C_4_6TraceMulA_1_1A_1_2A_1_3A_1_4A_1_5A_1_6A_2_1A_2_2A_2_3A_2_4A_2_5A_2_6A_3_1A_3_2A_3_3A_3_4A_3_5A_3_6A_4_1A_4_2A_4_3A_4_4A_4_5A_4_6A_5_1A_5_2A_5_3A_5_4A_5_5A_5_6A_6_1A_6_2A_6_3A_6_4A_6_5A_6_6B_1_5B_1_6B_1_7B_2_5B_2_6B_2_7B_3_5B_3_6B_3_7B_4_5B_4_6B_4_7B_5_5B_5_6B_5_7B_6_5B_6_6B_6_7C_5_1C_5_2C_5_3C_5_4C_5_5C_5_6C_6_1C_6_2C_6_3C_6_4C_6_5C_6_6C_7_1C_7_2C_7_3C_7_4C_7_5C_7_6Trace(Mul(Matrix(6, 6, [[A_1_1,A_1_2,A_1_3,A_1_4,A_1_5,A_1_6],[A_2_1,A_2_2,A_2_3,A_2_4,A_2_5,A_2_6],[A_3_1,A_3_2,A_3_3,A_3_4,A_3_5,A_3_6],[A_4_1,A_4_2,A_4_3,A_4_4,A_4_5,A_4_6],[A_5_1,A_5_2,A_5_3,A_5_4,A_5_5,A_5_6],[A_6_1,A_6_2,A_6_3,A_6_4,A_6_5,A_6_6]]),Matrix(6, 7, [[B_1_1,B_1_2,B_1_3,B_1_4,B_1_5,B_1_6,B_1_7],[B_2_1,B_2_2,B_2_3,B_2_4,B_2_5,B_2_6,B_2_7],[B_3_1,B_3_2,B_3_3,B_3_4,B_3_5,B_3_6,B_3_7],[B_4_1,B_4_2,B_4_3,B_4_4,B_4_5,B_4_6,B_4_7],[B_5_1,B_5_2,B_5_3,B_5_4,B_5_5,B_5_6,B_5_7],[B_6_1,B_6_2,B_6_3,B_6_4,B_6_5,B_6_6,B_6_7]]),Matrix(7, 6, [[C_1_1,C_1_2,C_1_3,C_1_4,C_1_5,C_1_6],[C_2_1,C_2_2,C_2_3,C_2_4,C_2_5,C_2_6],[C_3_1,C_3_2,C_3_3,C_3_4,C_3_5,C_3_6],[C_4_1,C_4_2,C_4_3,C_4_4,C_4_5,C_4_6],[C_5_1,C_5_2,C_5_3,C_5_4,C_5_5,C_5_6],[C_6_1,C_6_2,C_6_3,C_6_4,C_6_5,C_6_6],[C_7_1,C_7_2,C_7_3,C_7_4,C_7_5,C_7_6]]))) = Trace(Mul(Matrix(6, 6, [[A_1_1,A_1_2,A_1_3,A_1_4,A_1_5,A_1_6],[A_2_1,A_2_2,A_2_3,A_2_4,A_2_5,A_2_6],[A_3_1,A_3_2,A_3_3,A_3_4,A_3_5,A_3_6],[A_4_1,A_4_2,A_4_3,A_4_4,A_4_5,A_4_6],[A_5_1,A_5_2,A_5_3,A_5_4,A_5_5,A_5_6],[A_6_1,A_6_2,A_6_3,A_6_4,A_6_5,A_6_6]]),Matrix(6, 4, [[B_1_1,B_1_2,B_1_3,B_1_4],[B_2_1,B_2_2,B_2_3,B_2_4],[B_3_1,B_3_2,B_3_3,B_3_4],[B_4_1,B_4_2,B_4_3,B_4_4],[B_5_1,B_5_2,B_5_3,B_5_4],[B_6_1,B_6_2,B_6_3,B_6_4]]),Matrix(4, 6, [[C_1_1,C_1_2,C_1_3,C_1_4,C_1_5,C_1_6],[C_2_1,C_2_2,C_2_3,C_2_4,C_2_5,C_2_6],[C_3_1,C_3_2,C_3_3,C_3_4,C_3_5,C_3_6],[C_4_1,C_4_2,C_4_3,C_4_4,C_4_5,C_4_6]])))+Trace(Mul(Matrix(6, 6, [[A_1_1,A_1_2,A_1_3,A_1_4,A_1_5,A_1_6],[A_2_1,A_2_2,A_2_3,A_2_4,A_2_5,A_2_6],[A_3_1,A_3_2,A_3_3,A_3_4,A_3_5,A_3_6],[A_4_1,A_4_2,A_4_3,A_4_4,A_4_5,A_4_6],[A_5_1,A_5_2,A_5_3,A_5_4,A_5_5,A_5_6],[A_6_1,A_6_2,A_6_3,A_6_4,A_6_5,A_6_6]]),Matrix(6, 3, [[B_1_5,B_1_6,B_1_7],[B_2_5,B_2_6,B_2_7],[B_3_5,B_3_6,B_3_7],[B_4_5,B_4_6,B_4_7],[B_5_5,B_5_6,B_5_7],[B_6_5,B_6_6,B_6_7]]),Matrix(3, 6, [[C_5_1,C_5_2,C_5_3,C_5_4,C_5_5,C_5_6],[C_6_1,C_6_2,C_6_3,C_6_4,C_6_5,C_6_6],[C_7_1,C_7_2,C_7_3,C_7_4,C_7_5,C_7_6]])))
N.B.: for any matrices A, B and C such that the expression Tr(Mul(A,B,C)) is defined, one can construct several trilinear homogeneous polynomials P(A,B,C) such that P(A,B,C)=Tr(Mul(A,B,C)) (P(A,B,C) variables are A,B and C's coefficients). Each trilinear P expression encodes a matrix multiplication algorithm: the coefficient in C_i_j of P(A,B,C) is the (i,j)-th entry of the matrix product Mul(A,B)=Transpose(C).
Algorithm description
These encodings are given in compressed text format using the maple computer algebra system. In each cases, the last line could be understood as a description of the encoding with respect to classical matrix multiplication algorithm. As these outputs are structured, one can construct easily a parser to its favorite format using the maple documentation without this software.
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Twisting Bowel: Symptoms, Causes, Diagnosis & Treatments
Twisting bowel is caused when the natural shape of the intestines has changed or a section of the intestines overlap. It is also known as volvulus or colonic volvulus.
The bowel is a layman's term for the portion of the alimentary canal in the intestine. This area extends from the pyloric sphincter of the stomach down to the anus. In humans, this area consists of the small and large intestine. The small intestine is further divided into the jejunum, duodenum and ileum, and the large intestine is divided into the cecum, rectum and colon. These areas each work to break down food and absorb nutrients, transferring these nutrients to the blood stream where they can be shared with cells throughout the body.
If there is a change in the natural shape of the intestines, this can be known as a twisted bowel. A twist in the small intestine is referred to as a volvulus. Twists in the large intestine are known as a colonic volvulus. These abnormal twists or loops can cause an obstruction or other medical conditions which could be fatal. If signs of twisting bowel present, it is important to seek medical attention as quickly as possible.
Symptoms of Twisting Bowel
The most common symptoms include dizziness, nausea, vomiting, unexplained swollen stomach, constipation, bloating, and difficulty making a bowel movement and blood stool. Skin near the twist may be distended and tender. Some patients also report shortness of breath, intense fatigue or backaches when suffering from it.
Symptoms will vary based on the severity of the twist, the extent of the damage and the portion of the intestines affected. Symptoms may also come and go without causing medical damage. However, symptoms that go unchecked can cut off the nutrient blood or oxygen supply to the rest of the digestive tract. This is known as strangulation of the bowels. If unchecked, this can cause death of the surrounding cells, known as bowel necrosis.
Causes of Twisting Bowel
A twisted bowel is caused when the intestines fold over themselves. In some cases, they will untwist on their own, but many cases will require medical intervention. Infants born with twisting bowel or an intestinal malrotation are more likely to develop it later in life. Twists in the bowels may also occur after surgery on the abdomen.
• Primary causes include gut mobility and poor diet. These conditions are observed in children and adults. Colonic volvulus is also more common in pregnant women.
• Secondary causes include underlying health concerns such as adhesions in the colon or redundant intestinal tissue. These causes are significantly more common in adults over the age of 40.
Diagnosis and Treatment of Twisting Bowel
Medical examinations
If you suspect that you are suffering from twisted bowel, your doctor will need to perform examinations to check for the condition. These may include a stool analysis, barium enema, a computed tomography (CT) scan or magnetic resonance imaging (MRI) scan. If your symptoms match other conditions that cause digestive distress, your doctor may opt to perform a laparotomy. This is a minimally invasive surgical procedure that is used to examine abdominal organs for damage.
Surgery
Once it is determined, that you are suffering from it, you will likely need to undergo surgery to correct the problem. These surgical procedures are typically minimally invasive, and serve as a way to return the intestines to a natural position. In some cases, the affected section of intestines may be widened to avoid such complications occurring in the future. If the twist in the bowel is serious, your doctor may opt to remove the affected section to minimize the damage. After your surgery, you will need to take medications to minimize your risk of infections. Your doctor may also prescribe medication to help break down your food to avoid causing further irritation to the surgical site.
It is better to avoid the twisted bowel in the first place to avoid any discomfort, so you'd better keep drinking 8 glasses of water daily, choose to eat healthy, exercise regularly, and consider colon cleasening sometimes.
Recommended:
Why Do You Nausea Sick Following Meals?
Having nausea after eating? It indicates your intestines or digestive system is suffering. Why does this happen? And how can you get some relief?
Current time: 11/15/2018 08:07:27 am (America/New_York) Memory usage: 1665.39KB
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CodeQL library for C/C++
Search
Class AdditionalControlFlowEdge
An abstract class that can be extended to add additional edges to the control-flow graph. Instances of this class correspond to the source nodes of such edges, and the predicate getAnEdgeTarget should be overridden to produce the target nodes of each source.
Changing the control-flow graph in some queries and not others can be expensive in execution time and disk space. Most cached predicates in the library depend on the control-flow graph, so these predicates will be computed and cached for each variation of the control-flow graph that is used.
Edges added by this class will still be removed by the library if they appear to be unreachable. See the documentation on ControlFlowNode for more information about the control-flow graph.
Import path
import cpp
Direct supertypes
Indirect supertypes
Predicates
getAnEdgeTarget
Gets a target node of this edge, where the source node is this.
Inherited predicates
getAPrimaryQlClass
Gets the name of a primary CodeQL class to which this element belongs.
from ElementBase
getCanonicalQLClass
DEPRECATED: use getAPrimaryQlClass instead.
from ElementBase
toString
Gets a textual representation of this element.
from ElementBase
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Comprehensive Anatomy and Physiology Essay
696 Words3 Pages
Lymphatic System Question Sheet 1. Define the term Avascular necrosis. Avascular necrosis is the death of bone tissue due to an interruption of blood supply. 2. Define the term Bandemia. Bandemia refers to an excess of band cells (immature white blood cells) released by the bone marrow into the blood. 3. What is meant by Cardiac silhouette? The cardiac silhouette is the most prominent central feature of the chest x-ray and it produces a familiar gourd shape with the apex of the left ventricle located just behind the left chest nipple. 4. Which (s) condition is the drug Ceftriaxone used to treat? Ceftriaxone is used to treat the infections caused by suscepitable organisms such as skin on skin infections or respiratory tract infections. 5. What does the abbreviation CMV mean? cytomegalovirus 6. Which (s) condition is the drug Colace used to treat ? Colace—(Docusate) is an over-the-counter stool softener used to provide short-term relief to irregular bowel function. 7. Which (s) condition is the drug Dilaudid used to treat? Dilaudid (hydromorphone) is a narcotic pain reliever used to treat moderate to severe pain. 8. What is an Echocardiogram? Echocardiogram is a test using ultrasound to provide pictures of the heart's valves and chambers. 9. Define the term Erythema. An inflammatory reaction that occurs deep in the skin and is characterized by the presence of tender, red, raised lumps or nodules that range in size from 1 to 5 centimeters and are most commonly located over the shins but occasionally on the arms or other areas. 10. Define the term Exudate. Exudate is fluid, such as pus or clear fluid, which leaks out of blood vessels into nearby tissues. 11. Define Focal infiltrate. Focal infiltrate is dense,
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Articles | Volume 7, issue 3
Atmos. Chem. Phys., 7, 697–712, 2007
https://doi.org/10.5194/acp-7-697-2007
Atmos. Chem. Phys., 7, 697–712, 2007
https://doi.org/10.5194/acp-7-697-2007
12 Feb 2007
12 Feb 2007
Characterization of the 222Rn family turbulent transport in the convective atmospheric boundary layer
J.-F. Vinuesa and S. Galmarini J.-F. Vinuesa and S. Galmarini
• European Commission – DG Joint Research Centre, Institute for Environment and Sustainability, Italy
Abstract. The combined effect of turbulent transport and radioactive decay on the distribution of 222Rn and its progeny in convective atmospheric boundary layers (CBL) is investigated. Large eddy simulation is used to simulate their dispersion in steady state CBL and in unsteady conditions represented by the growth of a CBL within a pre-existing reservoir layer.
The exact decomposition of the concentration and flux budget equations under steady state conditions allowed us to determine which processes are responsible for the vertical distribution of 222Rn and its progeny. Their mean concentrations are directly correlated with their half-life, e.g. 222Rn and 210Pb are the most abundant whereas 218Po show the lowest concentrations. 222Rn flux decreases linearly with height and its flux budget is similar to the one of inert emitted scalar, i.e., a balance between on the one hand the gradient and the buoyancy production terms, and on the other hand the pressure and dissipation at smaller scales which tends to destroy the fluxes. While 222Rn exhibits the typical bottom-up behavior, the maximum flux location of the daughters is moving upwards while their rank in the 222Rn progeny is increasing leading to a typical top-down behavior for 210Pb. We also found that the relevant radioactive decaying contributions of 222Rn short-lived daughters (218Po and 214Pb) act as flux sources leading to deviations from the linear flux shape. In addition, while analyzing the vertical distribution of the radioactive decay contributions to the concentrations, e.g. the decaying zone, we found a variation in height of 222Rn daughters' radioactive transformations.
Under unsteady conditions, the same behaviors reported under steady state conditions are found: deviation of the fluxes from the linear shape for 218Po, enhanced discrepancy in height of the radioactive transformation contributions for all the daughters. In addition, 222Rn and its progeny concentrations decrease due to the rapid growth of the CBL. The analysis emphasizes the crucial role of turbulent transport in the behavior of 222Rn n morning concentrations, in particular the ventilation at the top of the boundary layer that leads to the dilution of 222Rn by mixing with radon low concentration air.
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31.8: Current Growth And Decay In RL Circuits
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Current Growth And Decay In RL Circuits
TRANSCRIPT
31.8: Current Growth And Decay In RL Circuits
The current growth and decay in RL circuits can be understood by considering a series RL circuit consisting of a resistor, an inductor, a constant source of emf, and two switches. When the first switch is closed, the circuit is equivalent to a single-loop circuit consisting of a resistor and an inductor connected to a source of emf. In this case, the source of emf produces a current in the circuit. If there were no self-inductance in the circuit, the current would rise immediately to a steady value of ε/R. However, from Faraday's law, the increasing current produces an emf across the inductor, which has opposite polarity. In accordance with Lenz’s law, the induced emf counteracts the increase in the current. As a result, the current starts at zero and increases asymptotically to its final value. Thus, as the current approaches the maximum current ε/R, the stored energy in the inductor increases from zero and asymptotically approaches a maximum value. The growth of current with time is given by
Equation1
When the first switch is opened, and the second switch is closed, the circuit again becomes a single-loop circuit but with only a resistor and an inductor. Now, the initial current in the circuit is ε/R. The current starts from ε/R and decreases exponentially with time as the energy stored in the inductor is depleted. The decay of current with time is given by the relation
Equation2
The quantity inductance over resistance is given by
Equation3
measures how quickly the current builds toward its final value; this quantity is called the time constant for the circuit. When the current is plotted against time, It grows from zero and approaches ε/R asymptotically. At a time equal to time constant, the current rises to about 63%, of its final value, but during decaying, at the same time constant, it decreases to about 37%, of its original value.
Suggested Reading
Tags
Growth And Decay RL Circuits Resistor Inductor Emf Switches Current Self-inductance Faraday's Law Lenz's Law Steady Value Asymptotically Maximum Current Stored Energy Exponential Decay Inductance Over Resistance
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Exploring the Second Largest Animal in the World
The second largest animal in the world is the fin whale (Balaenoptera physalus). Adult fin whales can grow up to 27 meters (88 feet) in length and can weigh up to 74,000 kg (163,000 pounds). The only animal larger than the fin whale is the blue whale (Balaenoptera musculus).
Overview of the second largest animal in the world
• The fin whale is a species of baleen whale that can be found in all of the world’s oceans, except for the Arctic Ocean.
• Adult fin whales can grow up to 27 meters (88 feet) in length, making them the second largest animal in the world.
• Fin whales have a sleek and streamlined body shape, with a narrow head and pointed snout.
• They are known for their unique coloration, which includes a dark gray or brown back and a lighter-colored underside.
• Fin whales are capable of swimming at speeds of up to 37 kilometers (23 miles) per hour, making them one of the fastest species of whale.
• They are filter feeders and primarily consume small schooling fish, krill, and plankton.
• The conservation status of fin whales is currently listed as “endangered” by the International Union for Conservation of Nature (IUCN), due to threats such as commercial whaling, entanglement in fishing gear, and habitat destruction.
Brief history and taxonomy of The fin whale
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The fin whale, or Balaenoptera physalus, is a species of baleen whale that belongs to the family Balaenopteridae. It is thought to have first appeared in the oceans around 5 million years ago, during the Pliocene epoch.
During the 20th century, fin whales were heavily targeted by commercial whaling operations, due to their large size and abundance. It is estimated that over 700,000 fin whales were killed by whalers between 1900 and 1979, causing a significant decline in their population numbers.
In terms of taxonomy, the fin whale is classified as follows:
• Kingdom: Animalia
• Phylum: Chordata
• Class: Mammalia
• Order: Cetacea
• Family: Balaenopteridae
• Genus: Balaenoptera
• Species: Balaenoptera physalus
There is some debate among scientists over the number of subspecies of fin whale, with some proposing up to 7 different subspecies. However, the taxonomy of the fin whale is still not fully resolved, and further research is needed to clarify the species’ evolutionary history.
Comparison with the largest animal in the world
The fin whale, the second largest animal in the world, is often compared with the largest animal in the world, the blue whale. Here are some comparisons between the two species:
• Size: The blue whale is the largest animal in the world, growing up to 30 meters (98 feet) in length and weighing up to 173 tonnes (191 tons), while the fin whale can grow up to 27 meters (88 feet) in length and weigh up to 74,000 kg (163,000 pounds).
• Body shape: Blue whales have a long, streamlined body shape with a broad, U-shaped head, while fin whales have a more slender, streamlined body shape with a narrow, pointed head.
• Vocalizations: Both species produce a range of vocalizations for communication, navigation, and hunting, but blue whales are known for producing the loudest sounds of any animal on Earth, with their songs being able to be heard over thousands of kilometers.
• Diet: Both species are filter feeders that consume primarily small schooling fish, krill, and plankton. However, blue whales generally consume larger amounts of food per day than fin whales due to their larger size.
• Conservation status: Both blue whales and fin whales are listed as “endangered” by the International Union for Conservation of Nature (IUCN) due to the impact of commercial whaling, entanglement in fishing gear, and habitat destruction.
Average size and weight of the animal
The fin whale is the second largest animal in the world, with an average size and weight as follows:
• Size: Adult fin whales can grow up to 27 meters (88 feet) in length, although most are typically between 20-25 meters (65-82 feet) long.
• Weight: Adult fin whales can weigh up to 74,000 kg (163,000 pounds), with females generally being slightly larger than males.
It’s important to note that these are averages, and there can be significant variation in size and weight depending on factors such as age, sex, and geographic location. Additionally, individual specimens may exceed or fall below these average ranges.
Species of the Second Largest Animal in the World
• The fin whale is a species of baleen whale that belongs to the family Balaenopteridae.
• Its scientific name is Balaenoptera physalus.
• It is the second largest animal in the world, with adult individuals growing up to 27 meters (88 feet) in length and weighing up to 74,000 kg (163,000 pounds).
• Fin whales can be found in all of the world’s oceans, except for the Arctic Ocean.
• There is only one recognized species of fin whale, although there is some debate among scientists over the number of subspecies of fin whale, with some proposing up to 7 different subspecies.
• The fin whale is a filter feeder, consuming primarily small schooling fish, krill, and plankton.
• Like many whale species, fin whales were heavily targeted by commercial whaling operations during the 20th century, leading to a significant decline in their populations. Although commercial whaling is now banned, fin whales continue to face threats such as entanglement in fishing gear, habitat loss, and ship strikes.
• The fin whale is currently classified as an endangered species by the International Union for Conservation of Nature (IUCN).
Life Cycle and Reproduction of fin whale
The life cycle and reproduction of the fin whale, the second-largest animal in the world, are as follows:
• Sexual maturity: Fin whales reach sexual maturity at around 6-10 years of age, with males typically maturing later than females.
• Mating: During the breeding season, which typically occurs during the winter months in temperate regions, male fin whales compete for females by producing vocalizations and engaging in physical displays such as headstands and tail slapping.
• Gestation: The gestation period for fin whales is around 11-12 months, with females giving birth to a single calf every 2-3 years.
• Calving: Calves are born in warm, shallow waters during the winter months, and weigh around 2,500-3,000 kg (5,500-6,600 pounds) at birth. They are typically weaned after 6-7 months, at which point they may weigh up to 12,000 kg (26,000 pounds).
• Lifespan: Fin whales have a lifespan of around 80-90 years, although this can vary depending on a range of factors such as food availability, predation risk, and environmental conditions.
Behavior and Social Structure of Fin Whale
The behavior and social structure of the fin whale, the second-largest animal in the world, are as follows:
• Solitary or social: Fin whales are typically solitary animals, although they may form loose aggregations in areas of high food abundance. These aggregations are not thought to represent true social groups, as fin whales do not exhibit the complex vocalizations or coordinated behavior seen in some other whale species.
• Vocalizations: Fin whales are known for their low-frequency vocalizations, which can be heard over long distances and are thought to be used for communication and echolocation.
• Feeding: Fin whales are filter feeders, using baleen plates in their mouths to filter small schooling fish, krill, and plankton from the water. They are known to feed at the surface, as well as at depths of up to 200 meters (660 feet).
• Migration: Fin whales are highly migratory, with populations in the Northern Hemisphere typically moving towards polar regions in the summer months to take advantage of seasonal food resources. In the Southern Hemisphere, fin whales are thought to follow a more coastal migration pattern.
• Diving behavior: Fin whales are capable of deep dives, and can remain submerged for up to 20 minutes at a time. They are known to perform long, slow dives, followed by shorter periods at the surface to breathe.
• Threats: Fin whales are currently facing a range of threats, including entanglement in fishing gear, ship strikes, and habitat loss. Climate change is also expected to impact their prey availability and distribution, which may have significant implications for their survival.
Conclusion
In conclusion, the fin whale is the second largest animal in the world and is an important species in terms of its ecological and cultural significance. Although much is still unknown about their biology and behavior, ongoing research efforts are helping to increase our understanding of this majestic creature.
References:
https://www.submon.org/en/what-do-we-know-about-fin-whales/
https://a-z-animals.com/blog/the-10-largest-animals-on-earth/
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General, Research, Technology
The most common myths about the Sun: what is worth believing?
The sun is one of the stars in the Milky Way galaxyand the only star in our solar system. If it did not exist, there would be no plants, no animals, and you and me on Earth. And all because the heavenly body saturates our planet with vital energy and the heat radiated by it plays a huge role in almost all chemical processes. This, without exaggeration, the main celestial object has been studied for thousands of years, and during this time, erroneous information about it appeared among the people. Many people believe that the Sun is composed of fiery lava. There is also a widespread belief that it is constantly in the same place and does not move at all. And some people do not even realize that the Sun, to which we owe our lives, will someday destroy our planet. As part of this material, I propose to dispel the most common myths about a star called the Sun.
The sun is the most important celestial object for us, but we know so little about it
Content
• 1 What is the Sun?
• 2 What is the Sun made of?
• 3 Is there water in the sun?
• 4 How does the sun move?
• 5 Earth's trajectory around the Sun
• 6 Will the sun destroy our planet?
What is the Sun?
First, let's take a look at the general information aboutThe sun. It is a star, that is, a spherical celestial body that emits light and is held in outer space due to its own gravity and internal pressure. At its core, it is a huge gaseous ball of hydrogen and helium, in which thermonuclear reactions constantly occur, in which the nuclei of light elements merge under the influence of high temperatures and form larger elements. At the same time, a huge amount of energy is released, part of which reaches our planet and participates in chemical processes vital for all living organisms. The distance from the Sun to the Earth is 149.6 million kilometers. To appreciate the difference in greatness, it's easier to imagine that the Sun is a huge orange, and the Earth is a tiny poppy seed.
Dimensions of the Sun (left) and Earth (right)
What is the Sun made of?
Some people mistakenly believe that the Sunconsists of fiery lava. This, of course, is not true, because scientifically, lava is a volcanic mass of hot rocks. And the closest star to us consists of highly heated gases and is divided into several different layers:
• solar core, which is the central part of the star withradius of about 175 thousand kilometers. This is some kind of a thermonuclear reactor, where the aforementioned collisions of nuclei with the release of a huge amount of energy take place. It is believed that this "fuel" will last for billions of years of existence of the star;
• zone of radiant transfer, which is the middle layer of the sun andconsists of hydrogen-helium plasma. This zone got its name because of the way of transferring energy from the core to the surface - radiation. In the core of the Sun, particles of light are formed, referred to as photons. To reach the outer layers of a star, they need to pass through a layer of hydrogen-helium plasma. Along the way, the photons bump into plasma particles, which absorb them and re-emit them in a random direction. So, if the photons escaping outward reach the Earth in 8 minutes, then it may take them millions of years to pass through the middle layer of the Sun, but sooner or later they overcome all obstacles;
• convective zone, which accounts for two-thirds of the volume of the sun. Energy transfer also takes place in this layer, but this time due to convection - a way of transferring energy by flows of substances. This phenomenon constantly occurs around us, for example, when a hot water battery heats up the air in a room.
If we talk about the chemical composition of the Sun, then italmost the same as that of all other stars. It is about 75% hydrogen, 25% helium and about 1% other elements like carbon, oxygen and nitrogen.
Is there water in the sun?
Many people are sure that the hot sun does notmaybe water. And this sounds quite logical, because liquid cannot exist in such a hot place. But remember your school chemistry curriculum - the formula for water is very simple and consists of hydrogen and oxygen. But above we have already found out that these elements are on the hot star and there are quite a few of them. Scientists assure that the water molecule is one of the most durable in the Universe and it does not collapse under the influence of high temperatures. But the DNA molecule, from which life can arise, cannot exist in such extreme conditions, although all the components for its creation are there.
Scientists of the Middle Ages believed that sunspots were lakes of water. In part, they were right
It is important to note that water molecules canform only in areas of the Sun with a minimum temperature. While the sun as a whole heats up to 5.5 thousand degrees Celsius, the sunspots on its surface have a temperature of about 4.5 thousand degrees. Researchers believe that it is in these places that water can form. But you need to understand that she exists in molecular form, not liquid... According to experts from the NASA space agency, if the temperature of the Sun ever drops, then the water on it can take on a liquid form.
Also, the Sun can make very strange sounds. You can read about this phenomenon in this material.
How does the sun move?
Since school years, we know that the Earth andother planets in the solar system revolve around the sun. Therefore, it is logical to assume that the Sun itself is constantly in the same place and does not move at all. But this is far from the case - it also moves, and at a very high speed, but we do not notice this at all, because we move together with the Sun and go along with it a very long way. Sounds complicated? Let's take a closer look at this phenomenon.
The approximate location of the Sun in the Milky Way galaxy
As we know, the solar system is located inone of the corners of the spiral Milky Way galaxy. It contains a huge number of other cosmic bodies that revolve around the center of the Milky Way. And including the Sun, with a speed of about 217 kilometers per second. This figure may seem truly crazy, but we do not even notice this speed, because the scale of our galaxy is huge and we do not even understand all its greatness. The Sun makes one revolution around the center of the galaxy in 250 million years, that is, in one galactic year.
Did you know that the Milky Way galaxy is much larger than we think?
Earth's trajectory around the Sun
Another common myth says that insummer season The sun is closer to the Earth than in winter. This fact is incorrect from the point of view of the inhabitants of Russia, and in Africa it can be considered partly true. From time to time, our native Earth really approaches the celestial body a little closer. The fact is that the trajectory of our planet's motion around the Sun is not an even circle, but an elongated ellipse. So, during the year, our planet gets closer to the hot star. In Russia, this happens around January 3-4, and it is at this time that the Sun can be seen in the sky from the closest possible distance. And in Africa this moment falls on the summer - that is, for the inhabitants of this region in the summer, the Earth is really located closer to the Sun. Of course, the approach of the Sun affects the temperature on Earth. However, the change appears to be negligible and the average temperature rises by only 2-3 degrees Celsius.
The location of the planets in the solar system
The approach of the Earth to the Sun is insignificant. But such planets as dwarf Pluto have a more "flattened" trajectory of motion. The dwarf planet makes a circle around the Sun slowly, so one year there lasts about 250 Earth years. During the Plutonian summer, the distance between Pluto and the Sun is 4.5 billion kilometers, and in the winter period increases to 7.5 billion. If the trajectory of the Earth around the Sun were the same, then the average temperature in winter would be about minus 50 degrees Celsius, and this is only in the considered warm equator. And at the poles, the thermometers would show minus 150 degrees. In general, we simply would not have survived. How good it is that the Earth moves, though not in an ideal, but a circle.
Will the sun destroy our planet?
As scary as it is to realize it, but yes,someday the Sun who gave us life will destroy us. According to scientists, this will happen when there is no thermonuclear "fuel", that is, hydrogen, in the interior of the star. I mentioned above that it should last for billions of years, so our and many future generations have nothing to worry about yet. It is believed that after emptying the fuel, the Sun will swell to a huge size and begin to emit even more energy. This will lead to the fact that even before the depletion of hydrogen reserves, all life will gradually be erased from the face of the Earth and it will be a dry desert.
Someday the sun will destroy our planet
If you are interested in the news of science and technology, subscribe to our channel in Yandex. Dzen. There you will find materials that have not been published on the site!
According to the calculations of the researchers, up to this pointthere are at least 5 billion years left. This is much more than it has been since the days of the dinosaurs. Most likely, by this time people will have already set foot on several future stages of evolution and even migrated to other, safer planets. But we will be able to colonize Mars already this century, because the well-known Elon Musk has already developed a plan and is developing spaceships for long-distance flights with might and main. But, if you think about it, even the colonization of Mars will not save us, because he, too, is believed around the Sun. Therefore, it remains to be hoped that by that time humanity will learn to conquer other stellar systems.
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Condensate and Feedwater Systems Operation
Interactive
Condensate and Feedwater Systems Operation
Martech
Updated Jan 21, 2021
Upon completion of this lesson, you will be able to describe the basic procedures for the start-up and operation of the condensate and feedwater systems. • Explain the five basic steps typically used to place the condensate system in service • Discuss considerations taken into account when initially filling the deaerator storage tank • Describe two methods used to fill the feedwater system • List four common tasks completed when putting high and low-pressure heat exchangers in service • Describe basic checks power plant operators routinely make on the condensate and feedwater systems
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Closest-pair problem
From Rosetta Code
(Redirected from Closest pair problem)
Task
Closest-pair problem
You are encouraged to solve this task according to the task description, using any language you may know.
This page uses content from Wikipedia. The original article was at Closest pair of points problem. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Provide a function to find the closest two points among a set of given points in two dimensions, i.e. to solve the Closest pair of points problem in the planar case.
The straightforward solution is a O(n2) algorithm (which we can call brute-force algorithm); the pseudo-code (using indexes) could be simply:
bruteForceClosestPair of P(1), P(2), ... P(N)
if N < 2 then
returnelse
minDistance ← |P(1) - P(2)|
minPoints ← { P(1), P(2) }
foreach i ∈ [1, N-1]
foreach j ∈ [i+1, N]
if |P(i) - P(j)| < minDistance then
minDistance ← |P(i) - P(j)|
minPoints ← { P(i), P(j) }
endif
endfor
endfor
return minDistance, minPoints
endif
A better algorithm is based on the recursive divide&conquer approach, as explained also at Wikipedia's Closest pair of points problem, which is O(n log n); a pseudo-code could be:
closestPair of (xP, yP)
where xP is P(1) .. P(N) sorted by x coordinate, and
yP is P(1) .. P(N) sorted by y coordinate (ascending order)
if N ≤ 3 then
return closest points of xP using brute-force algorithm
else
xL ← points of xP from 1 to ⌈N/2⌉
xR ← points of xP from ⌈N/2⌉+1 to N
xm ← xP(⌈N/2⌉)x
yL ← { p ∈ yP : px ≤ xm }
yR ← { p ∈ yP : px > xm }
(dL, pairL) ← closestPair of (xL, yL)
(dR, pairR) ← closestPair of (xR, yR)
(dmin, pairMin) ← (dR, pairR)
if dL < dR then
(dmin, pairMin) ← (dL, pairL)
endif
yS ← { p ∈ yP : |xm - px| < dmin }
nS ← number of points in yS
(closest, closestPair) ← (dmin, pairMin)
for i from 1 to nS - 1
k ← i + 1
while k ≤ nS and yS(k)y - yS(i)y < dmin
if |yS(k) - yS(i)| < closest then
(closest, closestPair) ← (|yS(k) - yS(i)|, {yS(k), yS(i)})
endif
k ← k + 1
endwhile
endfor
return closest, closestPair
endif
References and further readings
360 Assembly
* Closest Pair Problem 10/03/2017
CLOSEST CSECT
USING CLOSEST,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
STM R14,R12,12(R13) save previous context
ST R13,4(R15) link backward
ST R15,8(R13) link forward
LR R13,R15 set addressability
LA R6,1 i=1
LA R7,2 j=2
BAL R14,DDCALC dd=(px(i)-px(j))^2+(py(i)-py(j))^2
BAL R14,DDSTORE ddmin=dd; ii=i; jj=j
LA R6,1 i=1
DO WHILE=(C,R6,LE,N) do i=1 to n
LA R7,1 j=1
DO WHILE=(C,R7,LE,N) do j=1 to n
BAL R14,DDCALC dd=(px(i)-px(j))^2+(py(i)-py(j))^2
IF CP,DD,GT,=P'0' THEN if dd>0 then
IF CP,DD,LT,DDMIN THEN if dd<ddmin then
BAL R14,DDSTORE ddmin=dd; ii=i; jj=j
ENDIF , endif
ENDIF , endif
LA R7,1(R7) j++
ENDDO , enddo j
LA R6,1(R6) i++
ENDDO , enddo i
ZAP WPD,DDMIN ddmin
DP WPD,=PL8'2' ddmin/2
ZAP SQRT2,WPD(8) sqrt2=ddmin/2
ZAP SQRT1,DDMIN sqrt1=ddmin
DO WHILE=(CP,SQRT1,NE,SQRT2) do while sqrt1<>sqrt2
ZAP SQRT1,SQRT2 sqrt1=sqrt2
ZAP WPD,DDMIN ddmin
DP WPD,SQRT1 /sqrt1
ZAP WP1,WPD(8) ddmin/sqrt1
AP WP1,SQRT1 +sqrt1
ZAP WPD,WP1 ~
DP WPD,=PL8'2' /2
ZAP SQRT2,WPD(8) sqrt2=(sqrt1+(ddmin/sqrt1))/2
ENDDO , enddo while
MVC PG,=CL80'the minimum distance '
ZAP WP1,SQRT2 sqrt2
BAL R14,EDITPK edit
MVC PG+21(L'WC),WC output
XPRNT PG,L'PG print buffer
XPRNT =CL22'is between the points:',22
MVC PG,PGP init buffer
L R1,II ii
SLA R1,4 *16
LA R4,PXY-16(R1) @px(ii)
MVC WP1,0(R4) px(ii)
BAL R14,EDITPK edit
MVC PG+3(L'WC),WC output
MVC WP1,8(R4) py(ii)
BAL R14,EDITPK edit
MVC PG+21(L'WC),WC output
XPRNT PG,L'PG print buffer
MVC PG,PGP init buffer
L R1,JJ jj
SLA R1,4 *16
LA R4,PXY-16(R1) @px(jj)
MVC WP1,0(R4) px(jj)
BAL R14,EDITPK edit
MVC PG+3(L'WC),WC output
MVC WP1,8(R4) py(jj)
BAL R14,EDITPK edit
MVC PG+21(L'WC),WC output
XPRNT PG,L'PG print buffer
L R13,4(0,R13) restore previous savearea pointer
LM R14,R12,12(R13) restore previous context
XR R15,R15 rc=0
BR R14 exit
DDCALC EQU * ---- dd=(px(i)-px(j))^2+(py(i)-py(j))^2
LR R1,R6 i
SLA R1,4 *16
LA R4,PXY-16(R1) @px(i)
LR R1,R7 j
SLA R1,4 *16
LA R5,PXY-16(R1) @px(j)
ZAP WP1,0(8,R4) px(i)
ZAP WP2,0(8,R5) px(j)
SP WP1,WP2 px(i)-px(j)
ZAP WPS,WP1 =
MP WP1,WPS (px(i)-px(j))*(px(i)-px(j))
ZAP WP2,8(8,R4) py(i)
ZAP WP3,8(8,R5) py(j)
SP WP2,WP3 py(i)-py(j)
ZAP WPS,WP2 =
MP WP2,WPS (py(i)-py(j))*(py(i)-py(j))
AP WP1,WP2 (px(i)-px(j))^2+(py(i)-py(j))^2
ZAP DD,WP1 dd=(px(i)-px(j))^2+(py(i)-py(j))^2
BR R14 ---- return
DDSTORE EQU * ---- ddmin=dd; ii=i; jj=j
ZAP DDMIN,DD ddmin=dd
ST R6,II ii=i
ST R7,JJ jj=j
BR R14 ---- return
EDITPK EQU * ----
MVC WM,MASK set mask
EDMK WM,WP1 edit and mark
BCTR R1,0 -1
MVC 0(1,R1),WM+17 set sign
MVC WC,WM len17<-len18
BR R14 ---- return
N DC A((PGP-PXY)/16)
PXY DC PL8'0.654682',PL8'0.925557',PL8'0.409382',PL8'0.619391'
DC PL8'0.891663',PL8'0.888594',PL8'0.716629',PL8'0.996200'
DC PL8'0.477721',PL8'0.946355',PL8'0.925092',PL8'0.818220'
DC PL8'0.624291',PL8'0.142924',PL8'0.211332',PL8'0.221507'
DC PL8'0.293786',PL8'0.691701',PL8'0.839186',PL8'0.728260'
PGP DC CL80' [+xxxxxxxxx.xxxxxx,+xxxxxxxxx.xxxxxx]'
MASK DC C' ',7X'20',X'21',X'20',C'.',6X'20',C'-' CL18 15num
II DS F
JJ DS F
DD DS PL8
DDMIN DS PL8
SQRT1 DS PL8
SQRT2 DS PL8
WP1 DS PL8
WP2 DS PL8
WP3 DS PL8
WPS DS PL8
WPD DS PL16
WM DS CL18
WC DS CL17
PG DS CL80
YREGS
END CLOSEST
Output:
the minimum distance 0.077910
is between the points:
[ 0.891663, 0.888594]
[ 0.925092, 0.818220]
Ada
Dimension independent, but has to be defined at procedure call time (could be a parameter). Output is simple, can be formatted using Float_IO.
closest.adb: (uses brute force algorithm)
with Ada.Numerics.Generic_Elementary_Functions;
with Ada.Text_IO;
procedure Closest is
package Math is new Ada.Numerics.Generic_Elementary_Functions (Float);
Dimension : constant := 2;
type Vector is array (1 .. Dimension) of Float;
type Matrix is array (Positive range <>) of Vector;
-- calculate the distance of two points
function Distance (Left, Right : Vector) return Float is
Result : Float := 0.0;
Offset : Natural := 0;
begin
loop
Result := Result + (Left(Left'First + Offset) - Right(Right'First + Offset))**2;
Offset := Offset + 1;
exit when Offset >= Left'Length;
end loop;
return Math.Sqrt (Result);
end Distance;
-- determine the two closest points inside a cloud of vectors
function Get_Closest_Points (Cloud : Matrix) return Matrix is
Result : Matrix (1..2);
Min_Distance : Float;
begin
if Cloud'Length(1) < 2 then
raise Constraint_Error;
end if;
Result := (Cloud (Cloud'First), Cloud (Cloud'First + 1));
Min_Distance := Distance (Cloud (Cloud'First), Cloud (Cloud'First + 1));
for I in Cloud'First (1) .. Cloud'Last(1) - 1 loop
for J in I + 1 .. Cloud'Last(1) loop
if Distance (Cloud (I), Cloud (J)) < Min_Distance then
Min_Distance := Distance (Cloud (I), Cloud (J));
Result := (Cloud (I), Cloud (J));
end if;
end loop;
end loop;
return Result;
end Get_Closest_Points;
Test_Cloud : constant Matrix (1 .. 10) := ( (5.0, 9.0), (9.0, 3.0),
(2.0, 0.0), (8.0, 4.0),
(7.0, 4.0), (9.0, 10.0),
(1.0, 9.0), (8.0, 2.0),
(0.0, 10.0), (9.0, 6.0));
Closest_Points : Matrix := Get_Closest_Points (Test_Cloud);
Second_Test : constant Matrix (1 .. 10) := ( (0.654682, 0.925557), (0.409382, 0.619391),
(0.891663, 0.888594), (0.716629, 0.9962),
(0.477721, 0.946355), (0.925092, 0.81822),
(0.624291, 0.142924), (0.211332, 0.221507),
(0.293786, 0.691701), (0.839186, 0.72826));
Second_Points : Matrix := Get_Closest_Points (Second_Test);
begin
Ada.Text_IO.Put_Line ("Closest Points:");
Ada.Text_IO.Put_Line ("P1: " & Float'Image (Closest_Points (1) (1)) & " " & Float'Image (Closest_Points (1) (2)));
Ada.Text_IO.Put_Line ("P2: " & Float'Image (Closest_Points (2) (1)) & " " & Float'Image (Closest_Points (2) (2)));
Ada.Text_IO.Put_Line ("Distance: " & Float'Image (Distance (Closest_Points (1), Closest_Points (2))));
Ada.Text_IO.Put_Line ("Closest Points 2:");
Ada.Text_IO.Put_Line ("P1: " & Float'Image (Second_Points (1) (1)) & " " & Float'Image (Second_Points (1) (2)));
Ada.Text_IO.Put_Line ("P2: " & Float'Image (Second_Points (2) (1)) & " " & Float'Image (Second_Points (2) (2)));
Ada.Text_IO.Put_Line ("Distance: " & Float'Image (Distance (Second_Points (1), Second_Points (2))));
end Closest;
Output:
Closest Points:
P1: 8.00000E+00 4.00000E+00
P2: 7.00000E+00 4.00000E+00
Distance: 1.00000E+00
Closest Points 2:
P1: 8.91663E-01 8.88594E-01
P2: 9.25092E-01 8.18220E-01
Distance: 7.79101E-02
AWK
# syntax: GAWK -f CLOSEST-PAIR_PROBLEM.AWK
BEGIN {
x[++n] = 0.654682 ; y[n] = 0.925557
x[++n] = 0.409382 ; y[n] = 0.619391
x[++n] = 0.891663 ; y[n] = 0.888594
x[++n] = 0.716629 ; y[n] = 0.996200
x[++n] = 0.477721 ; y[n] = 0.946355
x[++n] = 0.925092 ; y[n] = 0.818220
x[++n] = 0.624291 ; y[n] = 0.142924
x[++n] = 0.211332 ; y[n] = 0.221507
x[++n] = 0.293786 ; y[n] = 0.691701
x[++n] = 0.839186 ; y[n] = 0.728260
min = 1E20
for (i=1; i<=n-1; i++) {
for (j=i+1; j<=n; j++) {
dsq = (x[i]-x[j])^2 + (y[i]-y[j])^2
if (dsq < min) {
min = dsq
mini = i
minj = j
}
}
}
printf("distance between (%.6f,%.6f) and (%.6f,%.6f) is %g\n",x[mini],y[mini],x[minj],y[minj],sqrt(min))
exit(0)
}
Output:
distance between (0.891663,0.888594) and (0.925092,0.818220) is 0.0779102
BBC BASIC
To find the closest pair it is sufficient to compare the squared-distances, it is not necessary to perform the square root for each pair!
DIM x(9), y(9)
FOR I% = 0 TO 9
READ x(I%), y(I%)
NEXT
min = 1E30
FOR I% = 0 TO 8
FOR J% = I%+1 TO 9
dsq = (x(I%) - x(J%))^2 + (y(I%) - y(J%))^2
IF dsq < min min = dsq : mini% = I% : minj% = J%
NEXT
NEXT I%
PRINT "Closest pair is ";mini% " and ";minj% " at distance "; SQR(min)
END
DATA 0.654682, 0.925557
DATA 0.409382, 0.619391
DATA 0.891663, 0.888594
DATA 0.716629, 0.996200
DATA 0.477721, 0.946355
DATA 0.925092, 0.818220
DATA 0.624291, 0.142924
DATA 0.211332, 0.221507
DATA 0.293786, 0.691701
DATA 0.839186, 0.728260
Output:
Closest pair is 2 and 5 at distance 0.0779101913
C
See Closest-pair problem/C
C++
/*
Author: Kevin Bacon
Date: 04/03/2014
Task: Closest-pair problem
*/
#include <iostream>
#include <vector>
#include <utility>
#include <cmath>
#include <random>
#include <chrono>
#include <algorithm>
#include <iterator>
typedef std::pair<double, double> point_t;
typedef std::pair<point_t, point_t> points_t;
double distance_between(const point_t& a, const point_t& b) {
return std::sqrt(std::pow(b.first - a.first, 2)
+ std::pow(b.second - a.second, 2));
}
std::pair<double, points_t> find_closest_brute(const std::vector<point_t>& points) {
if (points.size() < 2) {
return { -1, { { 0, 0 }, { 0, 0 } } };
}
auto minDistance = std::abs(distance_between(points.at(0), points.at(1)));
points_t minPoints = { points.at(0), points.at(1) };
for (auto i = std::begin(points); i != (std::end(points) - 1); ++i) {
for (auto j = i + 1; j < std::end(points); ++j) {
auto newDistance = std::abs(distance_between(*i, *j));
if (newDistance < minDistance) {
minDistance = newDistance;
minPoints.first = *i;
minPoints.second = *j;
}
}
}
return { minDistance, minPoints };
}
std::pair<double, points_t> find_closest_optimized(const std::vector<point_t>& xP,
const std::vector<point_t>& yP) {
if (xP.size() <= 3) {
return find_closest_brute(xP);
}
auto N = xP.size();
auto xL = std::vector<point_t>();
auto xR = std::vector<point_t>();
std::copy(std::begin(xP), std::begin(xP) + (N / 2), std::back_inserter(xL));
std::copy(std::begin(xP) + (N / 2), std::end(xP), std::back_inserter(xR));
auto xM = xP.at(N / 2).first;
auto yL = std::vector<point_t>();
auto yR = std::vector<point_t>();
std::copy_if(std::begin(yP), std::end(yP), std::back_inserter(yL), [&xM](const point_t& p) {
return p.first <= xM;
});
std::copy_if(std::begin(yP), std::end(yP), std::back_inserter(yR), [&xM](const point_t& p) {
return p.first > xM;
});
auto p1 = find_closest_optimized(xL, yL);
auto p2 = find_closest_optimized(xR, yR);
auto minPair = (p1.first <= p2.first) ? p1 : p2;
auto yS = std::vector<point_t>();
std::copy_if(std::begin(yP), std::end(yP), std::back_inserter(yS), [&minPair, &xM](const point_t& p) {
return std::abs(xM - p.first) < minPair.first;
});
auto result = minPair;
for (auto i = std::begin(yS); i != (std::end(yS) - 1); ++i) {
for (auto k = i + 1; k != std::end(yS) &&
((k->second - i->second) < minPair.first); ++k) {
auto newDistance = std::abs(distance_between(*k, *i));
if (newDistance < result.first) {
result = { newDistance, { *k, *i } };
}
}
}
return result;
}
void print_point(const point_t& point) {
std::cout << "(" << point.first
<< ", " << point.second
<< ")";
}
int main(int argc, char * argv[]) {
std::default_random_engine re(std::chrono::system_clock::to_time_t(
std::chrono::system_clock::now()));
std::uniform_real_distribution<double> urd(-500.0, 500.0);
std::vector<point_t> points(100);
std::generate(std::begin(points), std::end(points), [&urd, &re]() {
return point_t { 1000 + urd(re), 1000 + urd(re) };
});
auto answer = find_closest_brute(points);
std::sort(std::begin(points), std::end(points), [](const point_t& a, const point_t& b) {
return a.first < b.first;
});
auto xP = points;
std::sort(std::begin(points), std::end(points), [](const point_t& a, const point_t& b) {
return a.second < b.second;
});
auto yP = points;
std::cout << "Min distance (brute): " << answer.first << " ";
print_point(answer.second.first);
std::cout << ", ";
print_point(answer.second.second);
answer = find_closest_optimized(xP, yP);
std::cout << "\nMin distance (optimized): " << answer.first << " ";
print_point(answer.second.first);
std::cout << ", ";
print_point(answer.second.second);
return 0;
}
Output:
Min distance (brute): 6.95886 (932.735, 1002.7), (939.216, 1000.17)
Min distance (optimized): 6.95886 (932.735, 1002.7), (939.216, 1000.17)
Clojure
(defn distance [[x1 y1] [x2 y2]]
(let [dx (- x2 x1), dy (- y2 y1)]
(Math/sqrt (+ (* dx dx) (* dy dy)))))
(defn brute-force [points]
(let [n (count points)]
(when (< 1 n)
(apply min-key first
(for [i (range 0 (dec n)), :let [p1 (nth points i)],
j (range (inc i) n), :let [p2 (nth points j)]]
[(distance p1 p2) p1 p2])))))
(defn combine [yS [dmin pmin1 pmin2]]
(apply min-key first
(conj (for [[p1 p2] (partition 2 1 yS)
:let [[_ py1] p1 [_ py2] p2]
:while (< (- py1 py2) dmin)]
[(distance p1 p2) p1 p2])
[dmin pmin1 pmin2])))
(defn closest-pair
([points]
(closest-pair
(sort-by first points)
(sort-by second points)))
([xP yP]
(if (< (count xP) 4)
(brute-force xP)
(let [[xL xR] (partition-all (Math/ceil (/ (count xP) 2)) xP)
[xm _] (last xL)
{yL true yR false} (group-by (fn [[px _]] (<= px xm)) yP)
dL&pairL (closest-pair xL yL)
dR&pairR (closest-pair xR yR)
[dmin pmin1 pmin2] (min-key first dL&pairL dR&pairR)
{yS true} (group-by (fn [[px _]] (< (Math/abs (- xm px)) dmin)) yP)]
(combine yS [dmin pmin1 pmin2])))))
Common Lisp
Points are conses whose cars are x coördinates and whose cdrs are y coördinates. This version includes the optimizations given in the McGill description of the algorithm.
(defun point-distance (p1 p2)
(destructuring-bind (x1 . y1) p1
(destructuring-bind (x2 . y2) p2
(let ((dx (- x2 x1)) (dy (- y2 y1)))
(sqrt (+ (* dx dx) (* dy dy)))))))
(defun closest-pair-bf (points)
(let ((pair (list (first points) (second points)))
(dist (point-distance (first points) (second points))))
(dolist (p1 points (values pair dist))
(dolist (p2 points)
(unless (eq p1 p2)
(let ((pdist (point-distance p1 p2)))
(when (< pdist dist)
(setf (first pair) p1
(second pair) p2
dist pdist))))))))
(defun closest-pair (points)
(labels
((cp (xp &aux (length (length xp)))
(if (<= length 3)
(multiple-value-bind (pair distance) (closest-pair-bf xp)
(values pair distance (sort xp '< :key 'cdr)))
(let* ((xr (nthcdr (1- (floor length 2)) xp))
(xm (/ (+ (caar xr) (caadr xr)) 2)))
(psetf xr (rest xr)
(rest xr) '())
(multiple-value-bind (lpair ldist yl) (cp xp)
(multiple-value-bind (rpair rdist yr) (cp xr)
(multiple-value-bind (dist pair)
(if (< ldist rdist)
(values ldist lpair)
(values rdist rpair))
(let* ((all-ys (merge 'vector yl yr '< :key 'cdr))
(ys (remove-if #'(lambda (p)
(> (abs (- (car p) xm)) dist))
all-ys))
(ns (length ys)))
(dotimes (i ns)
(do ((k (1+ i) (1+ k)))
((or (= k ns)
(> (- (cdr (aref ys k))
(cdr (aref ys i)))
dist)))
(let ((pd (point-distance (aref ys i)
(aref ys k))))
(when (< pd dist)
(setf dist pd
(first pair) (aref ys i)
(second pair) (aref ys k))))))
(values pair dist all-ys)))))))))
(multiple-value-bind (pair distance)
(cp (sort (copy-list points) '< :key 'car))
(values pair distance))))
C#
We provide a small helper class for distance comparisons:
class Segment
{
public Segment(PointF p1, PointF p2)
{
P1 = p1;
P2 = p2;
}
public readonly PointF P1;
public readonly PointF P2;
public float Length()
{
return (float)Math.Sqrt(LengthSquared());
}
public float LengthSquared()
{
return (P1.X - P2.X) * (P1.X - P2.X)
+ (P1.Y - P2.Y) * (P1.Y - P2.Y);
}
}
Brute force:
Segment Closest_BruteForce(List<PointF> points)
{
int n = points.Count;
var result = Enumerable.Range( 0, n-1)
.SelectMany( i => Enumerable.Range( i+1, n-(i+1) )
.Select( j => new Segment( points[i], points[j] )))
.OrderBy( seg => seg.LengthSquared())
.First();
return result;
}
And divide-and-conquer.
public static Segment MyClosestDivide(List<PointF> points)
{
return MyClosestRec(points.OrderBy(p => p.X).ToList());
}
private static Segment MyClosestRec(List<PointF> pointsByX)
{
int count = pointsByX.Count;
if (count <= 4)
return Closest_BruteForce(pointsByX);
// left and right lists sorted by X, as order retained from full list
var leftByX = pointsByX.Take(count/2).ToList();
var leftResult = MyClosestRec(leftByX);
var rightByX = pointsByX.Skip(count/2).ToList();
var rightResult = MyClosestRec(rightByX);
var result = rightResult.Length() < leftResult.Length() ? rightResult : leftResult;
// There may be a shorter distance that crosses the divider
// Thus, extract all the points within result.Length either side
var midX = leftByX.Last().X;
var bandWidth = result.Length();
var inBandByX = pointsByX.Where(p => Math.Abs(midX - p.X) <= bandWidth);
// Sort by Y, so we can efficiently check for closer pairs
var inBandByY = inBandByX.OrderBy(p => p.Y).ToArray();
int iLast = inBandByY.Length - 1;
for (int i = 0; i < iLast; i++ )
{
var pLower = inBandByY[i];
for (int j = i + 1; j <= iLast; j++)
{
var pUpper = inBandByY[j];
// Comparing each point to successivly increasing Y values
// Thus, can terminate as soon as deltaY is greater than best result
if ((pUpper.Y - pLower.Y) >= result.Length())
break;
if (Segment.Length(pLower, pUpper) < result.Length())
result = new Segment(pLower, pUpper);
}
}
return result;
}
However, the difference in speed is still remarkable.
var randomizer = new Random(10);
var points = Enumerable.Range( 0, 10000).Select( i => new PointF( (float)randomizer.NextDouble(), (float)randomizer.NextDouble())).ToList();
Stopwatch sw = Stopwatch.StartNew();
var r1 = Closest_BruteForce(points);
sw.Stop();
Debugger.Log(1, "", string.Format("Time used (Brute force) (float): {0} ms", sw.Elapsed.TotalMilliseconds));
Stopwatch sw2 = Stopwatch.StartNew();
var result2 = Closest_Recursive(points);
sw2.Stop();
Debugger.Log(1, "", string.Format("Time used (Divide & Conquer): {0} ms",sw2.Elapsed.TotalMilliseconds));
Assert.Equal(r1.Length(), result2.Length());
Output:
Time used (Brute force) (float): 145731.8935 ms
Time used (Divide & Conquer): 1139.2111 ms
Non Linq Brute Force:
Segment Closest_BruteForce(List<PointF> points)
{
Trace.Assert(points.Count >= 2);
int count = points.Count;
// Seed the result - doesn't matter what points are used
// This just avoids having to do null checks in the main loop below
var result = new Segment(points[0], points[1]);
var bestLength = result.Length();
for (int i = 0; i < count; i++)
for (int j = i + 1; j < count; j++)
if (Segment.Length(points[i], points[j]) < bestLength)
{
result = new Segment(points[i], points[j]);
bestLength = result.Length();
}
return result;
}
Targeted Search: Much simpler than divide and conquer, and actually runs faster for the random points. Key optimization is that if the distance along the X axis is greater than the best total length you already have, you can terminate the inner loop early. However, as only sorts in the X direction, it degenerates into an N^2 algorithm if all the points have the same X.
Segment Closest(List<PointF> points)
{
Trace.Assert(points.Count >= 2);
int count = points.Count;
points.Sort((lhs, rhs) => lhs.X.CompareTo(rhs.X));
var result = new Segment(points[0], points[1]);
var bestLength = result.Length();
for (int i = 0; i < count; i++)
{
var from = points[i];
for (int j = i + 1; j < count; j++)
{
var to = points[j];
var dx = to.X - from.X;
if (dx >= bestLength)
{
break;
}
if (Segment.Length(from, to) < bestLength)
{
result = new Segment(from, to);
bestLength = result.Length();
}
}
}
return result;
}
Crystal
D
Compact Versions
import std.stdio, std.typecons, std.math, std.algorithm,
std.random, std.traits, std.range, std.complex;
auto bruteForceClosestPair(T)(in T[] points) pure nothrow @nogc {
// return pairwise(points.length.iota, points.length.iota)
// .reduce!(min!((i, j) => abs(points[i] - points[j])));
auto minD = Unqual!(typeof(T.re)).infinity;
T minI, minJ;
foreach (immutable i, const p1; points.dropBackOne)
foreach (const p2; points[i + 1 .. $]) {
immutable dist = abs(p1 - p2);
if (dist < minD) {
minD = dist;
minI = p1;
minJ = p2;
}
}
return tuple(minD, minI, minJ);
}
auto closestPair(T)(T[] points) pure nothrow {
static Tuple!(typeof(T.re), T, T) inner(in T[] xP, /*in*/ T[] yP)
pure nothrow {
if (xP.length <= 3)
return xP.bruteForceClosestPair;
const Pl = xP[0 .. $ / 2];
const Pr = xP[$ / 2 .. $];
immutable xDiv = Pl.back.re;
auto Yr = yP.partition!(p => p.re <= xDiv);
immutable dl_pairl = inner(Pl, yP[0 .. yP.length - Yr.length]);
immutable dr_pairr = inner(Pr, Yr);
immutable dm_pairm = dl_pairl[0]<dr_pairr[0] ? dl_pairl : dr_pairr;
immutable dm = dm_pairm[0];
const nextY = yP.filter!(p => abs(p.re - xDiv) < dm).array;
if (nextY.length > 1) {
auto minD = typeof(T.re).infinity;
size_t minI, minJ;
foreach (immutable i; 0 .. nextY.length - 1)
foreach (immutable j; i + 1 .. min(i + 8, nextY.length)) {
immutable double dist = abs(nextY[i] - nextY[j]);
if (dist < minD) {
minD = dist;
minI = i;
minJ = j;
}
}
return dm <= minD ? dm_pairm :
typeof(return)(minD, nextY[minI], nextY[minJ]);
} else
return dm_pairm;
}
points.sort!q{ a.re < b.re };
const xP = points.dup;
points.sort!q{ a.im < b.im };
return inner(xP, points);
}
void main() {
alias C = complex;
auto pts = [C(5,9), C(9,3), C(2), C(8,4), C(7,4), C(9,10), C(1,9),
C(8,2), C(0,10), C(9,6)];
pts.writeln;
writeln("bruteForceClosestPair: ", pts.bruteForceClosestPair);
writeln(" closestPair: ", pts.closestPair);
rndGen.seed = 1;
Complex!double[10_000] points;
foreach (ref p; points)
p = C(uniform(0.0, 1000.0) + uniform(0.0, 1000.0));
writeln("bruteForceClosestPair: ", points.bruteForceClosestPair);
writeln(" closestPair: ", points.closestPair);
}
Output:
[5+9i, 9+3i, 2+0i, 8+4i, 7+4i, 9+10i, 1+9i, 8+2i, 0+10i, 9+6i]
bruteForceClosestPair: Tuple!(double, Complex!double, Complex!double)(1, 8+4i, 7+4i)
closestPair: Tuple!(double, Complex!double, Complex!double)(1, 7+4i, 8+4i)
bruteForceClosestPair: Tuple!(double, Complex!double, Complex!double)(1.76951e-05, 1040.2+0i, 1040.2+0i)
closestPair: Tuple!(double, Complex!double, Complex!double)(1.76951e-05, 1040.2+0i, 1040.2+0i)
About 1.87 seconds run-time for data generation and brute force version, and about 0.03 seconds for data generation and divide & conquer (10_000 points in both cases) with ldc2 compiler.
Faster Brute-force Version
import std.stdio, std.random, std.math, std.typecons, std.complex,
std.traits;
Nullable!(Tuple!(size_t, size_t))
bfClosestPair2(T)(in Complex!T[] points) pure nothrow @nogc {
auto minD = Unqual!(typeof(points[0].re)).infinity;
if (points.length < 2)
return typeof(return)();
size_t minI, minJ;
foreach (immutable i; 0 .. points.length - 1)
foreach (immutable j; i + 1 .. points.length) {
auto dist = (points[i].re - points[j].re) ^^ 2;
if (dist < minD) {
dist += (points[i].im - points[j].im) ^^ 2;
if (dist < minD) {
minD = dist;
minI = i;
minJ = j;
}
}
}
return typeof(return)(tuple(minI, minJ));
}
void main() {
alias C = Complex!double;
auto rng = 31415.Xorshift;
C[10_000] pts;
foreach (ref p; pts)
p = C(uniform(0.0, 1000.0, rng), uniform(0.0, 1000.0, rng));
immutable ij = pts.bfClosestPair2;
if (ij.isNull)
return;
writefln("Closest pair: Distance: %f p1, p2: %f, %f",
abs(pts[ij[0]] - pts[ij[1]]), pts[ij[0]], pts[ij[1]]);
}
Output:
Closest pair: Distance: 0.019212 p1, p2: 9.74223+119.419i, 9.72306+119.418i
About 0.12 seconds run-time for brute-force version 2 (10_000 points) with with LDC2 compiler.
Elixir
defmodule Closest_pair do
# brute-force algorithm:
def bruteForce([p0,p1|_] = points), do: bf_loop(points, {distance(p0, p1), {p0, p1}})
defp bf_loop([_], acc), do: acc
defp bf_loop([h|t], acc), do: bf_loop(t, bf_loop(h, t, acc))
defp bf_loop(_, [], acc), do: acc
defp bf_loop(p0, [p1|t], {minD, minP}) do
dist = distance(p0, p1)
if dist < minD, do: bf_loop(p0, t, {dist, {p0, p1}}),
else: bf_loop(p0, t, {minD, minP})
end
defp distance({p0x,p0y}, {p1x,p1y}) do
:math.sqrt( (p1x - p0x) * (p1x - p0x) + (p1y - p0y) * (p1y - p0y) )
end
# recursive divide&conquer approach:
def recursive(points) do
recursive(Enum.sort(points), Enum.sort_by(points, fn {_x,y} -> y end))
end
def recursive(xP, _yP) when length(xP) <= 3, do: bruteForce(xP)
def recursive(xP, yP) do
{xL, xR} = Enum.split(xP, div(length(xP), 2))
{xm, _} = hd(xR)
{yL, yR} = Enum.partition(yP, fn {x,_} -> x < xm end)
{dL, pairL} = recursive(xL, yL)
{dR, pairR} = recursive(xR, yR)
{dmin, pairMin} = if dL<dR, do: {dL, pairL}, else: {dR, pairR}
yS = Enum.filter(yP, fn {x,_} -> abs(xm - x) < dmin end)
merge(yS, {dmin, pairMin})
end
defp merge([_], acc), do: acc
defp merge([h|t], acc), do: merge(t, merge_loop(h, t, acc))
defp merge_loop(_, [], acc), do: acc
defp merge_loop(p0, [p1|_], {dmin,_}=acc) when dmin <= elem(p1,1) - elem(p0,1), do: acc
defp merge_loop(p0, [p1|t], {dmin, pair}) do
dist = distance(p0, p1)
if dist < dmin, do: merge_loop(p0, t, {dist, {p0, p1}}),
else: merge_loop(p0, t, {dmin, pair})
end
end
data = [{0.654682, 0.925557}, {0.409382, 0.619391}, {0.891663, 0.888594}, {0.716629, 0.996200},
{0.477721, 0.946355}, {0.925092, 0.818220}, {0.624291, 0.142924}, {0.211332, 0.221507},
{0.293786, 0.691701}, {0.839186, 0.728260}]
IO.inspect Closest_pair.bruteForce(data)
IO.inspect Closest_pair.recursive(data)
data2 = for _ <- 1..5000, do: {:rand.uniform, :rand.uniform}
IO.puts "\nBrute-force:"
IO.inspect :timer.tc(fn -> Closest_pair.bruteForce(data2) end)
IO.puts "Recursive divide&conquer:"
IO.inspect :timer.tc(fn -> Closest_pair.recursive(data2) end)
Output:
{0.07791019135517516, {{0.891663, 0.888594}, {0.925092, 0.81822}}}
{0.07791019135517516, {{0.891663, 0.888594}, {0.925092, 0.81822}}}
Brute-force:
{9579000,
{2.068674444452469e-4,
{{0.9397601102440695, 0.020420581980209674},
{0.9399398976079764, 0.020522908141823986}}}}
Recursive divide&conquer:
{109000,
{2.068674444452469e-4,
{{0.9397601102440695, 0.020420581980209674},
{0.9399398976079764, 0.020522908141823986}}}}
F#
Brute force:
let closest_pairs (xys: Point []) =
let n = xys.Length
seq { for i in 0..n-2 do
for j in i+1..n-1 do
yield xys.[i], xys.[j] }
|> Seq.minBy (fun (p0, p1) -> (p1 - p0).LengthSquared)
For example:
closest_pairs
[|Point(0.0, 0.0); Point(1.0, 0.0); Point (2.0, 2.0)|]
gives:
(0,0, 1,0)
Divide And Conquer:
open System;
open System.Drawing;
open System.Diagnostics;
let Length (seg : (PointF * PointF) option) =
match seg with
| None -> System.Single.MaxValue
| Some(line) ->
let f = fst line
let t = snd line
let dx = f.X - t.X
let dy = f.Y - t.Y
sqrt (dx*dx + dy*dy)
let Shortest a b =
if Length(a) < Length(b) then
a
else
b
let rec ClosestBoundY from maxY (ptsByY : PointF list) =
match ptsByY with
| [] -> None
| hd :: tl ->
if hd.Y > maxY then
None
else
let toHd = Some(from, hd)
let bestToRest = ClosestBoundY from maxY tl
Shortest toHd bestToRest
let rec ClosestWithinRange ptsByY maxDy =
match ptsByY with
| [] -> None
| hd :: tl ->
let fromHd = ClosestBoundY hd (hd.Y + maxDy) tl
let fromRest = ClosestWithinRange tl maxDy
Shortest fromHd fromRest
// Cuts pts half way through it's length
// Order is not maintained in result lists however
let Halve pts =
let rec ShiftToFirst first second n =
match (n, second) with
| 0, _ -> (first, second) // finished the split, so return current state
| _, [] -> (first, []) // not enough items, so first takes the whole original list
| n, hd::tl -> ShiftToFirst (hd :: first) tl (n-1) // shift 1st item from second to first, then recurse with n-1
let n = (List.length pts) / 2
ShiftToFirst [] pts n
let rec ClosestPair (pts : PointF list) =
if List.length pts < 2 then
None
else
let ptsByX = pts |> List.sortBy(fun(p) -> p.X)
let (left, right) = Halve ptsByX
let leftResult = ClosestPair left
let rightResult = ClosestPair right
let bestInHalf = Shortest leftResult rightResult
let bestLength = Length bestInHalf
let divideX = List.head(right).X
let inBand = pts |> List.filter(fun(p) -> Math.Abs(p.X - divideX) < bestLength)
let byY = inBand |> List.sortBy(fun(p) -> p.Y)
let bestCross = ClosestWithinRange byY bestLength
Shortest bestInHalf bestCross
let GeneratePoints n =
let rand = new Random()
[1..n] |> List.map(fun(i) -> new PointF(float32(rand.NextDouble()), float32(rand.NextDouble())))
let timer = Stopwatch.StartNew()
let pts = GeneratePoints (50 * 1000)
let closest = ClosestPair pts
let takenMs = timer.ElapsedMilliseconds
printfn "Closest Pair '%A'. Distance %f" closest (Length closest)
printfn "Took %d [ms]" takenMs
Fantom
(Based on the Ruby example.)
class Point
{
Float x
Float y
// create a random point
new make (Float x := Float.random * 10, Float y := Float.random * 10)
{
this.x = x
this.y = y
}
Float distance (Point p)
{
((x-p.x)*(x-p.x) + (y-p.y)*(y-p.y)).sqrt
}
override Str toStr () { "($x, $y)" }
}
class Main
{
// use brute force approach
static Point[] findClosestPair1 (Point[] points)
{
if (points.size < 2) return points // list too small
Point[] closestPair := [points[0], points[1]]
Float closestDistance := points[0].distance(points[1])
(1..<points.size).each |Int i|
{
((i+1)..<points.size).each |Int j|
{
Float trydistance := points[i].distance(points[j])
if (trydistance < closestDistance)
{
closestPair = [points[i], points[j]]
closestDistance = trydistance
}
}
}
return closestPair
}
// use recursive divide-and-conquer approach
static Point[] findClosestPair2 (Point[] points)
{
if (points.size <= 3) return findClosestPair1(points)
points.sort |Point a, Point b -> Int| { a.x <=> b.x }
bestLeft := findClosestPair2 (points[0..(points.size/2)])
bestRight := findClosestPair2 (points[(points.size/2)..-1])
Float minDistance
Point[] closePoints := [,]
if (bestLeft[0].distance(bestLeft[1]) < bestRight[0].distance(bestRight[1]))
{
minDistance = bestLeft[0].distance(bestLeft[1])
closePoints = bestLeft
}
else
{
minDistance = bestRight[0].distance(bestRight[1])
closePoints = bestRight
}
yPoints := points.findAll |Point p -> Bool|
{
(points.last.x - p.x).abs < minDistance
}.sort |Point a, Point b -> Int| { a.y <=> b.y }
closestPair := [,]
closestDist := Float.posInf
for (Int i := 0; i < yPoints.size - 1; ++i)
{
for (Int j := (i+1); j < yPoints.size; ++j)
{
if ((yPoints[j].y - yPoints[i].y) >= minDistance)
{
break
}
else
{
dist := yPoints[i].distance (yPoints[j])
if (dist < closestDist)
{
closestDist = dist
closestPair = [yPoints[i], yPoints[j]]
}
}
}
}
if (closestDist < minDistance)
return closestPair
else
return closePoints
}
public static Void main (Str[] args)
{
Int numPoints := 10 // default value, in case a number not given on command line
if ((args.size > 0) && (args[0].toInt(10, false) != null))
{
numPoints = args[0].toInt(10, false)
}
Point[] points := [,]
numPoints.times { points.add (Point()) }
Int t1 := Duration.now.toMillis
echo (findClosestPair1(points.dup))
Int t2 := Duration.now.toMillis
echo ("Time taken: ${(t2-t1)}ms")
echo (findClosestPair2(points.dup))
Int t3 := Duration.now.toMillis
echo ("Time taken: ${(t3-t2)}ms")
}
}
Output:
$ fan closestPoints 1000
[(1.4542885676006445, 8.238581003965352), (1.4528464044751888, 8.234724407229772)]
Time taken: 88ms
[(1.4528464044751888, 8.234724407229772), (1.4542885676006445, 8.238581003965352)]
Time taken: 80ms
$ fan closestPoints 10000
[(3.454790171891945, 5.307252398266497), (3.4540208686702245, 5.308350223433488)]
Time taken: 6248ms
[(3.454790171891945, 5.307252398266497), (3.4540208686702245, 5.308350223433488)]
Time taken: 228ms
Fortran
See Closest pair problem/Fortran
Go
Brute force
package main
import (
"fmt"
"math"
"math/rand"
"time"
)
type xy struct {
x, y float64
}
const n = 1000
const scale = 100.
func d(p1, p2 xy) float64 {
return math.Hypot(p2.x-p1.x, p2.y-p1.y)
}
func main() {
rand.Seed(time.Now().Unix())
points := make([]xy, n)
for i := range points {
points[i] = xy{rand.Float64() * scale, rand.Float64() * scale}
}
p1, p2 := closestPair(points)
fmt.Println(p1, p2)
fmt.Println("distance:", d(p1, p2))
}
func closestPair(points []xy) (p1, p2 xy) {
if len(points) < 2 {
panic("at least two points expected")
}
min := 2 * scale
for i, q1 := range points[:len(points)-1] {
for _, q2 := range points[i+1:] {
if dq := d(q1, q2); dq < min {
p1, p2 = q1, q2
min = dq
}
}
}
return
}
O(n)
// implementation following algorithm described in
// http://www.cs.umd.edu/~samir/grant/cp.pdf
package main
import (
"fmt"
"math"
"math/rand"
"time"
)
// number of points to search for closest pair
const n = 1e6
// size of bounding box for points.
// x and y will be random with uniform distribution in the range [0,scale).
const scale = 100.
// point struct
type xy struct {
x, y float64 // coordinates
key int64 // an annotation used in the algorithm
}
func d(p1, p2 xy) float64 {
return math.Hypot(p2.x-p1.x, p2.y-p1.y)
}
func main() {
rand.Seed(time.Now().Unix())
points := make([]xy, n)
for i := range points {
points[i] = xy{rand.Float64() * scale, rand.Float64() * scale, 0}
}
p1, p2 := closestPair(points)
fmt.Println(p1, p2)
fmt.Println("distance:", d(p1, p2))
}
func closestPair(s []xy) (p1, p2 xy) {
if len(s) < 2 {
panic("2 points required")
}
var dxi float64
// step 0
for s1, i := s, 1; ; i++ {
// step 1: compute min distance to a random point
// (for the case of random data, it's enough to just try
// to pick a different point)
rp := i % len(s1)
xi := s1[rp]
dxi = 2 * scale
for p, xn := range s1 {
if p != rp {
if dq := d(xi, xn); dq < dxi {
dxi = dq
}
}
}
// step 2: filter
invB := 3 / dxi // b is size of a mesh cell
mx := int64(scale*invB) + 1 // mx is number of cells along a side
// construct map as a histogram:
// key is index into mesh. value is count of points in cell
hm := map[int64]int{}
for ip, p := range s1 {
key := int64(p.x*invB)*mx + int64(p.y*invB)
s1[ip].key = key
hm[key]++
}
// construct s2 = s1 less the points without neighbors
s2 := make([]xy, 0, len(s1))
nx := []int64{-mx - 1, -mx, -mx + 1, -1, 0, 1, mx - 1, mx, mx + 1}
for i, p := range s1 {
nn := 0
for _, ofs := range nx {
nn += hm[p.key+ofs]
if nn > 1 {
s2 = append(s2, s1[i])
break
}
}
}
// step 3: done?
if len(s2) == 0 {
break
}
s1 = s2
}
// step 4: compute answer from approximation
invB := 1 / dxi
mx := int64(scale*invB) + 1
hm := map[int64][]int{}
for i, p := range s {
key := int64(p.x*invB)*mx + int64(p.y*invB)
s[i].key = key
hm[key] = append(hm[key], i)
}
nx := []int64{-mx - 1, -mx, -mx + 1, -1, 0, 1, mx - 1, mx, mx + 1}
var min = scale * 2
for ip, p := range s {
for _, ofs := range nx {
for _, iq := range hm[p.key+ofs] {
if ip != iq {
if d1 := d(p, s[iq]); d1 < min {
min = d1
p1, p2 = p, s[iq]
}
}
}
}
}
return p1, p2
}
Groovy
Point class:
class Point {
final Number x, y
Point(Number x = 0, Number y = 0) { this.x = x; this.y = y }
Number distance(Point that) { ((this.x - that.x)**2 + (this.y - that.y)**2)**0.5 }
String toString() { "{x:${x}, y:${y}}" }
}
Brute force solution. Incorporates X-only and Y-only pre-checks in two places to cut down on the square root calculations:
def bruteClosest(Collection pointCol) {
assert pointCol
List l = pointCol
int n = l.size()
assert n > 1
if (n == 2) return [distance:l[0].distance(l[1]), points:[l[0],l[1]]]
def answer = [distance: Double.POSITIVE_INFINITY]
(0..<(n-1)).each { i ->
((i+1)..<n).findAll { j ->
(l[i].x - l[j].x).abs() < answer.distance &&
(l[i].y - l[j].y).abs() < answer.distance
}.each { j ->
if ((l[i].x - l[j].x).abs() < answer.distance &&
(l[i].y - l[j].y).abs() < answer.distance) {
def dist = l[i].distance(l[j])
if (dist < answer.distance) {
answer = [distance:dist, points:[l[i],l[j]]]
}
}
}
}
answer
}
Elegant (divide-and-conquer reduction) solution. Incorporates X-only and Y-only pre-checks in two places (four if you count the inclusion of the brute force solution) to cut down on the square root calculations:
def elegantClosest(Collection pointCol) {
assert pointCol
List xList = (pointCol as List).sort { it.x }
List yList = xList.clone().sort { it.y }
reductionClosest(xList, xList)
}
def reductionClosest(List xPoints, List yPoints) {
// assert xPoints && yPoints
// assert (xPoints as Set) == (yPoints as Set)
int n = xPoints.size()
if (n < 10) return bruteClosest(xPoints)
int nMid = Math.ceil(n/2)
List xLeft = xPoints[0..<nMid]
List xRight = xPoints[nMid..<n]
Number xMid = xLeft[-1].x
List yLeft = yPoints.findAll { it.x <= xMid }
List yRight = yPoints.findAll { it.x > xMid }
if (xRight[0].x == xMid) {
yLeft = xLeft.collect{ it }.sort { it.y }
yRight = xRight.collect{ it }.sort { it.y }
}
Map aLeft = reductionClosest(xLeft, yLeft)
Map aRight = reductionClosest(xRight, yRight)
Map aMin = aRight.distance < aLeft.distance ? aRight : aLeft
List yMid = yPoints.findAll { (xMid - it.x).abs() < aMin.distance }
int nyMid = yMid.size()
if (nyMid < 2) return aMin
Map answer = aMin
(0..<(nyMid-1)).each { i ->
((i+1)..<nyMid).findAll { j ->
(yMid[j].x - yMid[i].x).abs() < aMin.distance &&
(yMid[j].y - yMid[i].y).abs() < aMin.distance &&
yMid[j].distance(yMid[i]) < aMin.distance
}.each { k ->
if ((yMid[k].x - yMid[i].x).abs() < answer.distance && (yMid[k].y - yMid[i].y).abs() < answer.distance) {
def ikDist = yMid[i].distance(yMid[k])
if ( ikDist < answer.distance) {
answer = [distance:ikDist, points:[yMid[i],yMid[k]]]
}
}
}
}
answer
}
Benchmark/Test:
def random = new Random()
(1..4).each {
def point10 = (0..<(10**it)).collect { new Point(random.nextInt(1000001) - 500000,random.nextInt(1000001) - 500000) }
def startE = System.currentTimeMillis()
def closestE = elegantClosest(point10)
def elapsedE = System.currentTimeMillis() - startE
println """
${10**it} POINTS
-----------------------------------------
Elegant reduction:
elapsed: ${elapsedE/1000} s
closest: ${closestE}
"""
def startB = System.currentTimeMillis()
def closestB = bruteClosest(point10)
def elapsedB = System.currentTimeMillis() - startB
println """Brute force:
elapsed: ${elapsedB/1000} s
closest: ${closestB}
Speedup ratio (B/E): ${elapsedB/elapsedE}
=========================================
"""
}
Results:
10 POINTS
-----------------------------------------
Elegant reduction:
elapsed: 0.019 s
closest: [distance:85758.5249173515, points:[{x:310073, y:-27339}, {x:382387, y:18761}]]
Brute force:
elapsed: 0.001 s
closest: [distance:85758.5249173515, points:[{x:310073, y:-27339}, {x:382387, y:18761}]]
Speedup ratio (B/E): 0.0526315789
=========================================
100 POINTS
-----------------------------------------
Elegant reduction:
elapsed: 0.019 s
closest: [distance:3166.229934796271, points:[{x:-343735, y:-244394}, {x:-341099, y:-246148}]]
Brute force:
elapsed: 0.027 s
closest: [distance:3166.229934796271, points:[{x:-343735, y:-244394}, {x:-341099, y:-246148}]]
Speedup ratio (B/E): 1.4210526316
=========================================
1000 POINTS
-----------------------------------------
Elegant reduction:
elapsed: 0.241 s
closest: [distance:374.22586762542215, points:[{x:411817, y:-83016}, {x:412038, y:-82714}]]
Brute force:
elapsed: 0.618 s
closest: [distance:374.22586762542215, points:[{x:411817, y:-83016}, {x:412038, y:-82714}]]
Speedup ratio (B/E): 2.5643153527
=========================================
10000 POINTS
-----------------------------------------
Elegant reduction:
elapsed: 1.957 s
closest: [distance:79.00632886041473, points:[{x:187928, y:-452338}, {x:187929, y:-452259}]]
Brute force:
elapsed: 51.567 s
closest: [distance:79.00632886041473, points:[{x:187928, y:-452338}, {x:187929, y:-452259}]]
Speedup ratio (B/E): 26.3500255493
=========================================
Haskell
BF solution:
import Data.List (minimumBy, tails, unfoldr, foldl1') --'
import System.Random (newStdGen, randomRs)
import Control.Arrow ((&&&))
import Data.Ord (comparing)
vecLeng [[a, b], [p, q]] = sqrt $ (a - p) ^ 2 + (b - q) ^ 2
findClosestPair =
foldl1'' ((minimumBy (comparing vecLeng) .) . (. return) . (:)) .
concatMap (\(x:xs) -> map ((x :) . return) xs) . init . tails
testCP = do
g <- newStdGen
let pts :: [[Double]]
pts = take 1000 . unfoldr (Just . splitAt 2) $ randomRs (-1, 1) g
print . (id &&& vecLeng) . findClosestPair $ pts
main = testCP
foldl1'' = foldl1'
Output:
*Main> testCP
([[0.8347201880148426,0.40774840545089647],[0.8348731214261784,0.4087113189531284]],9.749825850154334e-4)
(4.02 secs, 488869056 bytes)
Icon and Unicon
This is a brute force solution. It combines reading the points with computing the closest pair seen so far.
record point(x,y)
procedure main()
minDist := 0
minPair := &null
every (points := [],p1 := readPoint()) do {
if *points == 1 then minDist := dSquared(p1,points[1])
every minDist >=:= dSquared(p1,p2 := !points) do minPair := [p1,p2]
push(points, p1)
}
if \minPair then {
write("(",minPair[1].x,",",minPair[1].y,") -> ",
"(",minPair[2].x,",",minPair[2].y,")")
}
else write("One or fewer points!")
end
procedure readPoint() # Skips lines that don't have two numbers on them
suspend !&input ? point(numeric(tab(upto(', '))), numeric((move(1),tab(0))))
end
procedure dSquared(p1,p2) # Compute the square of the distance
return (p2.x-p1.x)^2 + (p2.y-p1.y)^2 # (sufficient for closeness)
end
J
Solution of the simpler (brute-force) problem:
vecl =: +/"1&.:*: NB. length of each vector
dist =: <@:vecl@:({: -"1 }:)\ NB. calculate all distances among vectors
minpair=: ({~ > {.@($ #: I.@,)@:= <./@;)dist NB. find one pair of the closest points
closestpairbf =: (; vecl@:-/)@minpair NB. the pair and their distance
Examples of use:
]pts=:10 2 ?@$ 0
0.654682 0.925557
0.409382 0.619391
0.891663 0.888594
0.716629 0.9962
0.477721 0.946355
0.925092 0.81822
0.624291 0.142924
0.211332 0.221507
0.293786 0.691701
0.839186 0.72826
closestpairbf pts
+-----------------+---------+
|0.891663 0.888594|0.0779104|
|0.925092 0.81822| |
+-----------------+---------+
The program also works for higher dimensional vectors:
]pts=:10 4 ?@$ 0
0.559164 0.482993 0.876 0.429769
0.217911 0.729463 0.97227 0.132175
0.479206 0.169165 0.495302 0.362738
0.316673 0.797519 0.745821 0.0598321
0.662585 0.726389 0.658895 0.653457
0.965094 0.664519 0.084712 0.20671
0.840877 0.591713 0.630206 0.99119
0.221416 0.114238 0.0991282 0.174741
0.946262 0.505672 0.776017 0.307362
0.262482 0.540054 0.707342 0.465234
closestpairbf pts
+------------------------------------+--------+
|0.217911 0.729463 0.97227 0.132175|0.708555|
|0.316673 0.797519 0.745821 0.0598321| |
+------------------------------------+--------+
Java
Both the brute-force and the divide-and-conquer methods are implemented.
Code:
import java.util.*;
public class ClosestPair
{
public static class Point
{
public final double x;
public final double y;
public Point(double x, double y)
{
this.x = x;
this.y = y;
}
public String toString()
{ return "(" + x + ", " + y + ")"; }
}
public static class Pair
{
public Point point1 = null;
public Point point2 = null;
public double distance = 0.0;
public Pair()
{ }
public Pair(Point point1, Point point2)
{
this.point1 = point1;
this.point2 = point2;
calcDistance();
}
public void update(Point point1, Point point2, double distance)
{
this.point1 = point1;
this.point2 = point2;
this.distance = distance;
}
public void calcDistance()
{ this.distance = distance(point1, point2); }
public String toString()
{ return point1 + "-" + point2 + " : " + distance; }
}
public static double distance(Point p1, Point p2)
{
double xdist = p2.x - p1.x;
double ydist = p2.y - p1.y;
return Math.hypot(xdist, ydist);
}
public static Pair bruteForce(List<? extends Point> points)
{
int numPoints = points.size();
if (numPoints < 2)
return null;
Pair pair = new Pair(points.get(0), points.get(1));
if (numPoints > 2)
{
for (int i = 0; i < numPoints - 1; i++)
{
Point point1 = points.get(i);
for (int j = i + 1; j < numPoints; j++)
{
Point point2 = points.get(j);
double distance = distance(point1, point2);
if (distance < pair.distance)
pair.update(point1, point2, distance);
}
}
}
return pair;
}
public static void sortByX(List<? extends Point> points)
{
Collections.sort(points, new Comparator<Point>() {
public int compare(Point point1, Point point2)
{
if (point1.x < point2.x)
return -1;
if (point1.x > point2.x)
return 1;
return 0;
}
}
);
}
public static void sortByY(List<? extends Point> points)
{
Collections.sort(points, new Comparator<Point>() {
public int compare(Point point1, Point point2)
{
if (point1.y < point2.y)
return -1;
if (point1.y > point2.y)
return 1;
return 0;
}
}
);
}
public static Pair divideAndConquer(List<? extends Point> points)
{
List<Point> pointsSortedByX = new ArrayList<Point>(points);
sortByX(pointsSortedByX);
List<Point> pointsSortedByY = new ArrayList<Point>(points);
sortByY(pointsSortedByY);
return divideAndConquer(pointsSortedByX, pointsSortedByY);
}
private static Pair divideAndConquer(List<? extends Point> pointsSortedByX, List<? extends Point> pointsSortedByY)
{
int numPoints = pointsSortedByX.size();
if (numPoints <= 3)
return bruteForce(pointsSortedByX);
int dividingIndex = numPoints >>> 1;
List<? extends Point> leftOfCenter = pointsSortedByX.subList(0, dividingIndex);
List<? extends Point> rightOfCenter = pointsSortedByX.subList(dividingIndex, numPoints);
List<Point> tempList = new ArrayList<Point>(leftOfCenter);
sortByY(tempList);
Pair closestPair = divideAndConquer(leftOfCenter, tempList);
tempList.clear();
tempList.addAll(rightOfCenter);
sortByY(tempList);
Pair closestPairRight = divideAndConquer(rightOfCenter, tempList);
if (closestPairRight.distance < closestPair.distance)
closestPair = closestPairRight;
tempList.clear();
double shortestDistance =closestPair.distance;
double centerX = rightOfCenter.get(0).x;
for (Point point : pointsSortedByY)
if (Math.abs(centerX - point.x) < shortestDistance)
tempList.add(point);
for (int i = 0; i < tempList.size() - 1; i++)
{
Point point1 = tempList.get(i);
for (int j = i + 1; j < tempList.size(); j++)
{
Point point2 = tempList.get(j);
if ((point2.y - point1.y) >= shortestDistance)
break;
double distance = distance(point1, point2);
if (distance < closestPair.distance)
{
closestPair.update(point1, point2, distance);
shortestDistance = distance;
}
}
}
return closestPair;
}
public static void main(String[] args)
{
int numPoints = (args.length == 0) ? 1000 : Integer.parseInt(args[0]);
List<Point> points = new ArrayList<Point>();
Random r = new Random();
for (int i = 0; i < numPoints; i++)
points.add(new Point(r.nextDouble(), r.nextDouble()));
System.out.println("Generated " + numPoints + " random points");
long startTime = System.currentTimeMillis();
Pair bruteForceClosestPair = bruteForce(points);
long elapsedTime = System.currentTimeMillis() - startTime;
System.out.println("Brute force (" + elapsedTime + " ms): " + bruteForceClosestPair);
startTime = System.currentTimeMillis();
Pair dqClosestPair = divideAndConquer(points);
elapsedTime = System.currentTimeMillis() - startTime;
System.out.println("Divide and conquer (" + elapsedTime + " ms): " + dqClosestPair);
if (bruteForceClosestPair.distance != dqClosestPair.distance)
System.out.println("MISMATCH");
}
}
Output:
java ClosestPair 10000
Generated 10000 random points
Brute force (1594 ms): (0.9246533850872104, 0.098709007587097)-(0.924591196030625, 0.09862206991823985) : 1.0689077146927108E-4
Divide and conquer (250 ms): (0.924591196030625, 0.09862206991823985)-(0.9246533850872104, 0.098709007587097) : 1.0689077146927108E-4
JavaScript
Using bruteforce algorithm, the bruteforceClosestPair method below expects an array of objects with x- and y-members set to numbers, and returns an object containing the members distance and points.
function distance(p1, p2) {
var dx = Math.abs(p1.x - p2.x);
var dy = Math.abs(p1.y - p2.y);
return Math.sqrt(dx*dx + dy*dy);
}
function bruteforceClosestPair(arr) {
if (arr.length < 2) {
return Infinity;
} else {
var minDist = distance(arr[0], arr[1]);
var minPoints = arr.slice(0, 2);
for (var i=0; i<arr.length-1; i++) {
for (var j=i+1; j<arr.length; j++) {
if (distance(arr[i], arr[j]) < minDist) {
minDist = distance(arr[i], arr[j]);
minPoints = [ arr[i], arr[j] ];
}
}
}
return {
distance: minDist,
points: minPoints
};
}
}
divide-and-conquer method:
var Point = function(x, y) {
this.x = x;
this.y = y;
};
Point.prototype.getX = function() {
return this.x;
};
Point.prototype.getY = function() {
return this.y;
};
var mergeSort = function mergeSort(points, comp) {
if(points.length < 2) return points;
var n = points.length,
i = 0,
j = 0,
leftN = Math.floor(n / 2),
rightN = leftN;
var leftPart = mergeSort( points.slice(0, leftN), comp),
rightPart = mergeSort( points.slice(rightN), comp );
var sortedPart = [];
while((i < leftPart.length) && (j < rightPart.length)) {
if(comp(leftPart[i], rightPart[j]) < 0) {
sortedPart.push(leftPart[i]);
i += 1;
}
else {
sortedPart.push(rightPart[j]);
j += 1;
}
}
while(i < leftPart.length) {
sortedPart.push(leftPart[i]);
i += 1;
}
while(j < rightPart.length) {
sortedPart.push(rightPart[j]);
j += 1;
}
return sortedPart;
};
var closestPair = function _closestPair(Px, Py) {
if(Px.length < 2) return { distance: Infinity, pair: [ new Point(0, 0), new Point(0, 0) ] };
if(Px.length < 3) {
//find euclid distance
var d = Math.sqrt( Math.pow(Math.abs(Px[1].x - Px[0].x), 2) + Math.pow(Math.abs(Px[1].y - Px[0].y), 2) );
return {
distance: d,
pair: [ Px[0], Px[1] ]
};
}
var n = Px.length,
leftN = Math.floor(n / 2),
rightN = leftN;
var Xl = Px.slice(0, leftN),
Xr = Px.slice(rightN),
Xm = Xl[leftN - 1],
Yl = [],
Yr = [];
//separate Py
for(var i = 0; i < Py.length; i += 1) {
if(Py[i].x <= Xm.x)
Yl.push(Py[i]);
else
Yr.push(Py[i]);
}
var dLeft = _closestPair(Xl, Yl),
dRight = _closestPair(Xr, Yr);
var minDelta = dLeft.distance,
closestPair = dLeft.pair;
if(dLeft.distance > dRight.distance) {
minDelta = dRight.distance;
closestPair = dRight.pair;
}
//filter points around Xm within delta (minDelta)
var closeY = [];
for(i = 0; i < Py.length; i += 1) {
if(Math.abs(Py[i].x - Xm.x) < minDelta) closeY.push(Py[i]);
}
//find min within delta. 8 steps max
for(i = 0; i < closeY.length; i += 1) {
for(var j = i + 1; j < Math.min( (i + 8), closeY.length ); j += 1) {
var d = Math.sqrt( Math.pow(Math.abs(closeY[j].x - closeY[i].x), 2) + Math.pow(Math.abs(closeY[j].y - closeY[i].y), 2) );
if(d < minDelta) {
minDelta = d;
closestPair = [ closeY[i], closeY[j] ]
}
}
}
return {
distance: minDelta,
pair: closestPair
};
};
var points = [
new Point(0.748501, 4.09624),
new Point(3.00302, 5.26164),
new Point(3.61878, 9.52232),
new Point(7.46911, 4.71611),
new Point(5.7819, 2.69367),
new Point(2.34709, 8.74782),
new Point(2.87169, 5.97774),
new Point(6.33101, 0.463131),
new Point(7.46489, 4.6268),
new Point(1.45428, 0.087596)
];
var sortX = function (a, b) { return (a.x < b.x) ? -1 : ((a.x > b.x) ? 1 : 0); }
var sortY = function (a, b) { return (a.y < b.y) ? -1 : ((a.y > b.y) ? 1 : 0); }
var Px = mergeSort(points, sortX);
var Py = mergeSort(points, sortY);
console.log(JSON.stringify(closestPair(Px, Py))) // {"distance":0.0894096443343775,"pair":[{"x":7.46489,"y":4.6268},{"x":7.46911,"y":4.71611}]}
var points2 = [new Point(37100, 13118), new Point(37134, 1963), new Point(37181, 2008), new Point(37276, 21611), new Point(37307, 9320)];
Px = mergeSort(points2, sortX);
Py = mergeSort(points2, sortY);
console.log(JSON.stringify(closestPair(Px, Py))); // {"distance":65.06919393998976,"pair":[{"x":37134,"y":1963},{"x":37181,"y":2008}]}
jq
Works with: jq version 1.4
The solution presented here is essentially a direct translation into jq of the pseudo-code presented in the task description, but "closest_pair" is added so that any list of [x,y] points can be presented, and extra lines are added to ensure that xL and yL have the same lengths.
Infrastructure:
# This definition of "until" is included in recent versions (> 1.4) of jq
# Emit the first input that satisfied the condition
def until(cond; next):
def _until:
if cond then . else (next|_until) end;
_until;
# Euclidean 2d distance
def dist(x;y):
[x[0] - y[0], x[1] - y[1]] | map(.*.) | add | sqrt;
# P is an array of points, [x,y].
# Emit the solution in the form [dist, [P1, P2]]
def bruteForceClosestPair(P):
(P|length) as $length
| if $length < 2 then null
else
reduce range(0; $length-1) as $i
( null;
reduce range($i+1; $length) as $j
(.;
dist(P[$i]; P[$j]) as $d
| if . == null or $d < .[0] then [$d, [ P[$i], P[$j] ] ] else . end ) )
end;
def closest_pair:
def abs: if . < 0 then -. else . end;
def ceil: floor as $floor
| if . == $floor then $floor else $floor + 1 end;
# xP is an array [P(1), .. P(N)] sorted by x coordinate, and
# yP is an array [P(1), .. P(N)] sorted by y coordinate (ascending order).
# if N <= 3 then return closest points of xP using the brute-force algorithm.
def closestPair(xP; yP):
if xP|length <= 3 then bruteForceClosestPair(xP)
else
((xP|length)/2|ceil) as $N
| xP[0:$N] as $xL
| xP[$N:] as $xR
| xP[$N-1][0] as $xm # middle
| (yP | map(select(.[0] <= $xm ))) as $yL0 # might be too long
| (yP | map(select(.[0] > $xm ))) as $yR0 # might be too short
| (if $yL0|length == $N then $yL0 else $yL0[0:$N] end) as $yL
| (if $yL0|length == $N then $yR0 else $yL0[$N:] + $yR0 end) as $yR
| closestPair($xL; $yL) as $pairL # [dL, pairL]
| closestPair($xR; $yR) as $pairR # [dR, pairR]
| (if $pairL[0] < $pairR[0] then $pairL else $pairR end) as $pair # [ dmin, pairMin]
| (yP | map(select( (($xm - .[0])|abs) < $pair[0]))) as $yS
| ($yS | length) as $nS
| $pair[0] as $dmin
| reduce range(0; $nS - 1) as $i
( [0, $pair]; # state: [k, [d, [P1,P2]]]
.[0] = $i + 1
| until( .[0] as $k | $k >= $nS or ($yS[$k][1] - $yS[$i][1]) >= $dmin;
.[0] as $k
| dist($yS[$k]; $yS[$i]) as $d
| if $d < .[1][0]
then [$k+1, [ $d, [$yS[$k], $yS[$i]]]]
else .[0] += 1
end) )
| .[1]
end;
closestPair( sort_by(.[0]); sort_by(.[1])) ;
Example from the Mathematica section:
def data:
[[0.748501, 4.09624],
[3.00302, 5.26164],
[3.61878, 9.52232],
[7.46911, 4.71611],
[5.7819, 2.69367],
[2.34709, 8.74782],
[2.87169, 5.97774],
[6.33101, 0.463131],
[7.46489, 4.6268],
[1.45428, 0.087596] ];
data | closest_pair
Output:
$jq -M -c -n -f closest_pair.jq
[0.0894096443343775,[[7.46489,4.6268],[7.46911,4.71611]]]
Kotlin
// version 1.1.2
typealias Point = Pair<Double, Double>
fun distance(p1: Point, p2: Point) = Math.hypot(p1.first- p2.first, p1.second - p2.second)
fun bruteForceClosestPair(p: List<Point>): Pair<Double, Pair<Point, Point>> {
val n = p.size
if (n < 2) throw IllegalArgumentException("Must be at least two points")
var minPoints = p[0] to p[1]
var minDistance = distance(p[0], p[1])
for (i in 0 until n - 1)
for (j in i + 1 until n) {
val dist = distance(p[i], p[j])
if (dist < minDistance) {
minDistance = dist
minPoints = p[i] to p[j]
}
}
return minDistance to Pair(minPoints.first, minPoints.second)
}
fun optimizedClosestPair(xP: List<Point>, yP: List<Point>): Pair<Double, Pair<Point, Point>> {
val n = xP.size
if (n <= 3) return bruteForceClosestPair(xP)
val xL = xP.take(n / 2)
val xR = xP.drop(n / 2)
val xm = xP[n / 2 - 1].first
val yL = yP.filter { it.first <= xm }
val yR = yP.filter { it.first > xm }
val (dL, pairL) = optimizedClosestPair(xL, yL)
val (dR, pairR) = optimizedClosestPair(xR, yR)
var dmin = dR
var pairMin = pairR
if (dL < dR) {
dmin = dL
pairMin = pairL
}
val yS = yP.filter { Math.abs(xm - it.first) < dmin }
val nS = yS.size
var closest = dmin
var closestPair = pairMin
for (i in 0 until nS - 1) {
var k = i + 1
while (k < nS && (yS[k].second - yS[i].second < dmin)) {
val dist = distance(yS[k], yS[i])
if (dist < closest) {
closest = dist
closestPair = Pair(yS[k], yS[i])
}
k++
}
}
return closest to closestPair
}
fun main(args: Array<String>) {
val points = listOf(
listOf(
5.0 to 9.0, 9.0 to 3.0, 2.0 to 0.0, 8.0 to 4.0, 7.0 to 4.0,
9.0 to 10.0, 1.0 to 9.0, 8.0 to 2.0, 0.0 to 10.0, 9.0 to 6.0
),
listOf(
0.654682 to 0.925557, 0.409382 to 0.619391, 0.891663 to 0.888594,
0.716629 to 0.996200, 0.477721 to 0.946355, 0.925092 to 0.818220,
0.624291 to 0.142924, 0.211332 to 0.221507, 0.293786 to 0.691701,
0.839186 to 0.728260
)
)
for (p in points) {
val (dist, pair) = bruteForceClosestPair(p)
println("Closest pair (brute force) is ${pair.first} and ${pair.second}, distance $dist")
val xP = p.sortedBy { it.first }
val yP = p.sortedBy { it.second }
val (dist2, pair2) = optimizedClosestPair(xP, yP)
println("Closest pair (optimized) is ${pair2.first} and ${pair2.second}, distance $dist2\n")
}
}
Output:
Closest pair (brute force) is (8.0, 4.0) and (7.0, 4.0), distance 1.0
Closest pair (optimized) is (7.0, 4.0) and (8.0, 4.0), distance 1.0
Closest pair (brute force) is (0.891663, 0.888594) and (0.925092, 0.81822), distance 0.07791019135517516
Closest pair (optimized) is (0.891663, 0.888594) and (0.925092, 0.81822), distance 0.07791019135517516
Liberty BASIC
NB array terms can not be READ directly.
N =10
dim x( N), y( N)
firstPt =0
secondPt =0
for i =1 to N
read f: x( i) =f
read f: y( i) =f
next i
minDistance =1E6
for i =1 to N -1
for j =i +1 to N
dxSq =( x( i) -x( j))^2
dySq =( y( i) -y( j))^2
D =abs( ( dxSq +dySq)^0.5)
if D <minDistance then
minDistance =D
firstPt =i
secondPt =j
end if
next j
next i
print "Distance ="; minDistance; " between ( "; x( firstPt); ", "; y( firstPt); ") and ( "; x( secondPt); ", "; y( secondPt); ")"
end
data 0.654682, 0.925557
data 0.409382, 0.619391
data 0.891663, 0.888594
data 0.716629, 0.996200
data 0.477721, 0.946355
data 0.925092, 0.818220
data 0.624291, 0.142924
data 0.211332, 0.221507
data 0.293786, 0.691701
data 0.839186, 0.72826
Distance =0.77910191e-1 between ( 0.891663, 0.888594) and ( 0.925092, 0.81822)
Mathematica / Wolfram Language
nearestPair[data_] :=
Block[{pos, dist = N[Outer[EuclideanDistance, data, data, 1]]},
pos = Position[dist, Min[DeleteCases[Flatten[dist], 0.]]];
data[[pos[[1]]]]]
Output:
nearestPair[{{0.748501, 4.09624}, {3.00302, 5.26164}, {3.61878,
9.52232}, {7.46911, 4.71611}, {5.7819, 2.69367}, {2.34709,
8.74782}, {2.87169, 5.97774}, {6.33101, 0.463131}, {7.46489,
4.6268}, {1.45428, 0.087596}}]
{{7.46911, 4.71611}, {7.46489, 4.6268}}
MATLAB
This solution is an almost direct translation of the above pseudo-code into MATLAB.
function [closest,closestpair] = closestPair(xP,yP)
N = numel(xP);
if(N <= 3)
%Brute force closestpair
if(N < 2)
closest = +Inf;
closestpair = {};
else
closest = norm(xP{1}-xP{2});
closestpair = {xP{1},xP{2}};
for i = ( 1:N-1 )
for j = ( (i+1):N )
if ( norm(xP{i} - xP{j}) < closest )
closest = norm(xP{i}-xP{j});
closestpair = {xP{i},xP{j}};
end %if
end %for
end %for
end %if (N < 2)
else
halfN = ceil(N/2);
xL = { xP{1:halfN} };
xR = { xP{halfN+1:N} };
xm = xP{halfN}(1);
%cellfun( @(p)le(p(1),xm),yP ) is the same as { p ∈ yP : px ≤ xm }
yLIndicies = cellfun( @(p)le(p(1),xm),yP );
yL = { yP{yLIndicies} };
yR = { yP{~yLIndicies} };
[dL,pairL] = closestPair(xL,yL);
[dR,pairR] = closestPair(xR,yR);
if dL < dR
dmin = dL;
pairMin = pairL;
else
dmin = dR;
pairMin = pairR;
end
%cellfun( @(p)lt(norm(xm-p(1)),dmin),yP ) is the same as
%{ p ∈ yP : |xm - px| < dmin }
yS = {yP{ cellfun( @(p)lt(norm(xm-p(1)),dmin),yP ) }};
nS = numel(yS);
closest = dmin;
closestpair = pairMin;
for i = (1:nS-1)
k = i+1;
while( (k<=nS) && (yS{k}(2)-yS{i}(2) < dmin) )
if norm(yS{k}-yS{i}) < closest
closest = norm(yS{k}-yS{i});
closestpair = {yS{k},yS{i}};
end
k = k+1;
end %while
end %for
end %if (N <= 3)
end %closestPair
Output:
[distance,pair]=closestPair({[0 -.3],[1 1],[1.5 2],[2 2],[3 3]},{[0 -.3],[1 1],[1.5 2],[2 2],[3 3]})
distance =
0.500000000000000
pair =
[1x2 double] [1x2 double] %The pair is [1.5 2] and [2 2] which is correct
Objective-C
See Closest-pair problem/Objective-C
OCaml
type point = { x : float; y : float }
let cmpPointX (a : point) (b : point) = compare a.x b.x
let cmpPointY (a : point) (b : point) = compare a.y b.y
let distSqrd (seg : (point * point) option) =
match seg with
| None -> max_float
| Some(line) ->
let a = fst line in
let b = snd line in
let dx = a.x -. b.x in
let dy = a.y -. b.y in
dx*.dx +. dy*.dy
let dist seg =
sqrt (distSqrd seg)
let shortest l1 l2 =
if distSqrd l1 < distSqrd l2 then
l1
else
l2
let halve l =
let n = List.length l in
BatList.split_at (n/2) l
let rec closestBoundY from maxY (ptsByY : point list) =
match ptsByY with
| [] -> None
| hd :: tl ->
if hd.y > maxY then
None
else
let toHd = Some(from, hd) in
let bestToRest = closestBoundY from maxY tl in
shortest toHd bestToRest
let rec closestInRange ptsByY maxDy =
match ptsByY with
| [] -> None
| hd :: tl ->
let fromHd = closestBoundY hd (hd.y +. maxDy) tl in
let fromRest = closestInRange tl maxDy in
shortest fromHd fromRest
let rec closestPairByX (ptsByX : point list) =
if List.length ptsByX < 2 then
None
else
let (left, right) = halve ptsByX in
let leftResult = closestPairByX left in
let rightResult = closestPairByX right in
let bestInHalf = shortest leftResult rightResult in
let bestLength = dist bestInHalf in
let divideX = (List.hd right).x in
let inBand = List.filter(fun(p) -> abs_float(p.x -. divideX) < bestLength) ptsByX in
let byY = List.sort cmpPointY inBand in
let bestCross = closestInRange byY bestLength in
shortest bestInHalf bestCross
let closestPair pts =
let ptsByX = List.sort cmpPointX pts in
closestPairByX ptsByX
let parsePoint str =
let sep = Str.regexp_string "," in
let tokens = Str.split sep str in
let xStr = List.nth tokens 0 in
let yStr = List.nth tokens 1 in
let xVal = (float_of_string xStr) in
let yVal = (float_of_string yStr) in
{ x = xVal; y = yVal }
let loadPoints filename =
let ic = open_in filename in
let result = ref [] in
try
while true do
let s = input_line ic in
if s <> "" then
let p = parsePoint s in
result := p :: !result;
done;
!result
with End_of_file ->
close_in ic;
!result
;;
let loaded = (loadPoints "Points.txt") in
let start = Sys.time() in
let c = closestPair loaded in
let taken = Sys.time() -. start in
Printf.printf "Took %f [s]\n" taken;
match c with
| None -> Printf.printf "No closest pair\n"
| Some(seg) ->
let a = fst seg in
let b = snd seg in
Printf.printf "(%f, %f) (%f, %f) Dist %f\n" a.x a.y b.x b.y (dist c)
Oz
Translation of pseudocode:
declare
fun {Distance X1#Y1 X2#Y2}
{Sqrt {Pow X2-X1 2.0} + {Pow Y2-Y1 2.0}}
end
%% brute force
fun {BFClosestPair Points=P1|P2|_}
Ps = {List.toTuple unit Points} %% for efficient random access
N = {Width Ps}
MinDist = {NewCell {Distance P1 P2}}
MinPoints = {NewCell P1#P2}
in
for I in 1..N-1 do
for J in I+1..N do
IJDist = {Distance Ps.I Ps.J}
in
if IJDist < @MinDist then
MinDist := IJDist
MinPoints := Ps.I#Ps.J
end
end
end
@MinPoints
end
%% divide and conquer
fun {ClosestPair Points}
case {ClosestPair2
{Sort Points {LessThanBy X}}
{Sort Points {LessThanBy Y}}}
of Distance#Pair then
Pair
end
end
%% XP: points sorted by X, YP: sorted by Y
%% returns a pair Distance#Pair
fun {ClosestPair2 XP YP}
N = {Length XP} = {Length YP}
in
if N =< 3 then
P = {BFClosestPair XP}
in
{Distance P.1 P.2}#P
else
XL XR
{List.takeDrop XP (N div 2) ?XL ?XR}
XM = {Nth XP (N div 2)}.X
YL YR
{List.partition YP fun {$ P} P.X =< XM end ?YL ?YR}
DL#PairL = {ClosestPair2 XL YL}
DR#PairR = {ClosestPair2 XR YR}
DMin#PairMin = if DL < DR then DL#PairL else DR#PairR end
YSList = {Filter YP fun {$ P} {Abs XM-P.X} < DMin end}
YS = {List.toTuple unit YSList} %% for efficient random access
NS = {Width YS}
Closest = {NewCell DMin}
ClosestPair = {NewCell PairMin}
in
for I in 1..NS-1 do
for K in I+1..NS while:YS.K.Y - YS.I.Y < DMin do
DistKI = {Distance YS.K YS.I}
in
if DistKI < @Closest then
Closest := DistKI
ClosestPair := YS.K#YS.I
end
end
end
@Closest#@ClosestPair
end
end
%% To access components when points are represented as pairs
X = 1
Y = 2
%% returns a less-than predicate that accesses feature F
fun {LessThanBy F}
fun {$ A B}
A.F < B.F
end
end
fun {Random Min Max}
Min +
{Int.toFloat {OS.rand}} * (Max-Min)
/ {Int.toFloat {OS.randLimits _}}
end
fun {RandomPoint}
{Random 0.0 100.0}#{Random 0.0 100.0}
end
Points = {MakeList 5}
in
{ForAll Points RandomPoint}
{Show Points}
{Show {ClosestPair Points}}
PARI/GP
Naive quadratic solution.
closestPair(v)={
my(r=norml2(v[1]-v[2]),at=[1,2]);
for(a=1,#v-1,
for(b=a+1,#v,
if(norml2(v[a]-v[b])<r,
at=[a,b];
r=norml2(v[a]-v[b])
)
)
);
[v[at[1]],v[at[2]]]
};
Pascal
Brute force only calc square of distance, like AWK etc... As fast as D .
program closestPoints;
{$IFDEF FPC}
{$MODE Delphi}
{$ENDIF}
const
PointCnt = 10000;//31623;
type
TdblPoint = Record
ptX,
ptY : double;
end;
tPtLst = array of TdblPoint;
tMinDIstIdx = record
md1,
md2 : NativeInt;
end;
function ClosPointBruteForce(var ptl :tPtLst):tMinDIstIdx;
Var
i,j,k : NativeInt;
mindst2,dst2: double; //square of distance, no need to sqrt
p0,p1 : ^TdblPoint; //using pointer, since calc of ptl[?] takes much time
Begin
i := Low(ptl);
j := High(ptl);
result.md1 := i;result.md2 := j;
mindst2 := sqr(ptl[i].ptX-ptl[j].ptX)+sqr(ptl[i].ptY-ptl[j].ptY);
repeat
p0 := @ptl[i];
p1 := p0; inc(p1);
For k := i+1 to j do
Begin
dst2:= sqr(p0^.ptX-p1^.ptX)+sqr(p0^.ptY-p1^.ptY);
IF mindst2 > dst2 then
Begin
mindst2 := dst2;
result.md1 := i;
result.md2 := k;
end;
inc(p1);
end;
inc(i);
until i = j;
end;
var
PointLst :tPtLst;
cloPt : tMinDIstIdx;
i : NativeInt;
Begin
randomize;
setlength(PointLst,PointCnt);
For i := 0 to PointCnt-1 do
with PointLst[i] do
Begin
ptX := random;
ptY := random;
end;
cloPt:= ClosPointBruteForce(PointLst) ;
i := cloPt.md1;
Writeln('P[',i:4,']= x: ',PointLst[i].ptX:0:8,
' y: ',PointLst[i].ptY:0:8);
i := cloPt.md2;
Writeln('P[',i:4,']= x: ',PointLst[i].ptX:0:8,
' y: ',PointLst[i].ptY:0:8);
end.
Output:
PointCnt = 10000
//without randomize always same results //32-Bit P[ 324]= x: 0.26211815 y: 0.45851455 P[3391]= x: 0.26217852 y: 0.45849116 real 0m0.114s //fpc 3.1.1 32 Bit -O4 -MDelphi..cpu i4330 3.5 Ghz //64-Bit doubles the speed comp switch -O2 ..-O4 same timings P[ 324]= x: 0.26211815 y: 0.45851455 P[3391]= x: 0.26217852 y: 0.45849116 real 0m0.059s //fpc 3.1.1 64 Bit -O4 -MDelphi..cpu i4330 3.5 Ghz
//with randomize P[ 47]= x: 0.12408823 y: 0.04501338 P[9429]= x: 0.12399629 y: 0.04496700 //32-Bit
PointCnt = { 10000*sqrt(10) } 31623;-> real 0m1.112s 10x times runtime
Perl
#! /usr/bin/perl
use strict;
use POSIX qw(ceil);
sub dist
{
my ( $a, $b) = @_;
return sqrt( ($a->[0] - $b->[0])**2 +
($a->[1] - $b->[1])**2 );
}
sub closest_pair_simple
{
my $ra = shift;
my @arr = @$ra;
my $inf = 1e600;
return $inf if scalar(@arr) < 2;
my ( $a, $b, $d ) = ($arr[0], $arr[1], dist($arr[0], $arr[1]));
while( @arr ) {
my $p = pop @arr;
foreach my $l (@arr) {
my $t = dist($p, $l);
($a, $b, $d) = ($p, $l, $t) if $t < $d;
}
}
return ($a, $b, $d);
}
sub closest_pair
{
my $r = shift;
my @ax = sort { $a->[0] <=> $b->[0] } @$r;
my @ay = sort { $a->[1] <=> $b->[1] } @$r;
return closest_pair_real(\@ax, \@ay);
}
sub closest_pair_real
{
my ($rx, $ry) = @_;
my @xP = @$rx;
my @yP = @$ry;
my $N = @xP;
return closest_pair_simple($rx) if scalar(@xP) <= 3;
my $inf = 1e600;
my $midx = ceil($N/2)-1;
my @PL = @xP[0 .. $midx];
my @PR = @xP[$midx+1 .. $N-1];
my $xm = ${$xP[$midx]}[0];
my @yR = ();
my @yL = ();
foreach my $p (@yP) {
if ( ${$p}[0] <= $xm ) {
push @yR, $p;
} else {
push @yL, $p;
}
}
my ($al, $bl, $dL) = closest_pair_real(\@PL, \@yR);
my ($ar, $br, $dR) = closest_pair_real(\@PR, \@yL);
my ($m1, $m2, $dmin) = ($al, $bl, $dL);
($m1, $m2, $dmin) = ($ar, $br, $dR) if $dR < $dL;
my @yS = ();
foreach my $p (@yP) {
push @yS, $p if abs($xm - ${$p}[0]) < $dmin;
}
if ( @yS ) {
my ( $w1, $w2, $closest ) = ($m1, $m2, $dmin);
foreach my $i (0 .. ($#yS - 1)) {
my $k = $i + 1;
while ( ($k <= $#yS) && ( (${$yS[$k]}[1] - ${$yS[$i]}[1]) < $dmin) ) {
my $d = dist($yS[$k], $yS[$i]);
($w1, $w2, $closest) = ($yS[$k], $yS[$i], $d) if $d < $closest;
$k++;
}
}
return ($w1, $w2, $closest);
} else {
return ($m1, $m2, $dmin);
}
}
my @points = ();
my $N = 5000;
foreach my $i (1..$N) {
push @points, [rand(20)-10.0, rand(20)-10.0];
}
my ($a, $b, $d) = closest_pair_simple(\@points);
print "$d\n";
my ($a1, $b1, $d1) = closest_pair(\@points);
#print "$d1\n";
Time for the brute-force algorithm gave 40.63user 0.12system 0:41.06elapsed, while the divide&conqueer algorithm gave 0.37user 0.00system 0:00.38elapsed with 5000 points.
Perl 6
Translation of: Perl 5
We avoid taking square roots in the slow method because the squares are just as comparable. (This doesn't always work in the fast method because of distance assumptions in the algorithm.)
sub MAIN ($N = 5000) {
my @points = (^$N).map: { [rand * 20 - 10, rand * 20 - 10] }
my ($af, $bf, $df) = closest_pair(@points);
say "fast $df at [$af], [$bf]";
my ($as, $bs, $ds) = closest_pair_simple(@points);
say "slow $ds at [$as], [$bs]";
}
sub dist-squared($a,$b) {
($a[0] - $b[0]) ** 2 +
($a[1] - $b[1]) ** 2;
}
sub closest_pair_simple(@arr is copy) {
return Inf if @arr < 2;
my ($a, $b, $d) = flat @arr[0,1], dist-squared(|@arr[0,1]);
while @arr {
my $p = pop @arr;
for @arr -> $l {
my $t = dist-squared($p, $l);
($a, $b, $d) = $p, $l, $t if $t < $d;
}
}
return $a, $b, sqrt $d;
}
sub closest_pair(@r) {
my @ax = @r.sort: { .[0] }
my @ay = @r.sort: { .[1] }
return closest_pair_real(@ax, @ay);
}
sub closest_pair_real(@rx, @ry) {
return closest_pair_simple(@rx) if @rx <= 3;
my @xP = @rx;
my @yP = @ry;
my $N = @xP;
my $midx = ceiling($N/2)-1;
my @PL = @xP[0 .. $midx];
my @PR = @xP[$midx+1 ..^ $N];
my $xm = @xP[$midx][0];
my @yR;
my @yL;
push ($_[0] <= $xm ?? @yR !! @yL), $_ for @yP;
my ($al, $bl, $dL) = closest_pair_real(@PL, @yR);
my ($ar, $br, $dR) = closest_pair_real(@PR, @yL);
my ($m1, $m2, $dmin) = $dR < $dL
?? ($ar, $br, $dR)
!! ($al, $bl, $dL);
my @yS = @yP.grep: { abs($xm - .[0]) < $dmin }
if @yS {
my ($w1, $w2, $closest) = $m1, $m2, $dmin;
for 0 ..^ @yS.end -> $i {
for $i+1 ..^ @yS -> $k {
last unless @yS[$k][1] - @yS[$i][1] < $dmin;
my $d = sqrt dist-squared(@yS[$k], @yS[$i]);
($w1, $w2, $closest) = @yS[$k], @yS[$i], $d if $d < $closest;
}
}
return $w1, $w2, $closest;
} else {
return $m1, $m2, $dmin;
}
}
Phix
Brute force and divide and conquer (translated from pseudocode) approaches compared
function bruteForceClosestPair(sequence s)
atom {x1,y1} = s[1], {x2,y2} = s[2], dx = x1-x2, dy = y1-y2, mind = dx*dx+dy*dy
sequence minp = s[1..2]
for i=1 to length(s)-1 do
{x1,y1} = s[i]
for j=i+1 to length(s) do
{x2,y2} = s[j]
dx = x1-x2
dx = dx*dx
if dx<mind then
dy = y1-y2
dx += dy*dy
if dx<mind then
mind = dx
minp = {s[i],s[j]}
end if
end if
end for
end for
return {sqrt(mind),minp}
end function
sequence testset = sq_rnd(repeat({1,1},10000))
atom t0 = time()
sequence points
atom d
{d,points} = bruteForceClosestPair(testset)
-- (Sorting the final point pair makes brute/dc more likely to tally. Note however
-- when >1 equidistant pairs exist, brute and dc may well return different pairs;
-- it is only a problem if they decide to return different minimum distances.)
atom {{x1,y1},{x2,y2}} = sort(points)
printf(1,"Closest pair: {%f,%f} {%f,%f}, distance=%f (%3.2fs)\n",{x1,y2,x2,y2,d,time()-t0})
t0 = time()
constant X = 1, Y = 2
sequence xP = sort(testset)
function byY(sequence p1, p2)
return compare(p1[Y],p2[Y])
end function
sequence yP = custom_sort(routine_id("byY"),testset)
function distsq(sequence p1,p2)
atom {x1,y1} = p1, {x2,y2} = p2
x1 -= x2
y1 -= y2
return x1*x1 + y1*y1
end function
function closestPair(sequence xP, yP)
-- where xP is P(1) .. P(N) sorted by x coordinate, and
-- yP is P(1) .. P(N) sorted by y coordinate (ascending order)
integer N, midN, k, nS
sequence xL, xR, yL, yR, pairL, pairR, pairMin, yS, cPair
atom xm, dL, dR, dmin, closest
N = length(xP)
if length(yP)!=N then ?9/0 end if -- (sanity check)
if N<=3 then
return bruteForceClosestPair(xP)
end if
midN = floor(N/2)
xL = xP[1..midN]
xR = xP[midN+1..N]
xm = xP[midN][X]
yL = {}
yR = {}
for i=1 to N do
if yP[i][X]<=xm then
yL = append(yL,yP[i])
else
yR = append(yR,yP[i])
end if
end for
{dL, pairL} = closestPair(xL, yL)
{dR, pairR} = closestPair(xR, yR)
{dmin, pairMin} = {dR, pairR}
if dL<dR then
{dmin, pairMin} = {dL, pairL}
end if
yS = {}
for i=1 to length(yP) do
if abs(xm-yP[i][X])<dmin then
yS = append(yS,yP[i])
end if
end for
nS = length(yS)
{closest, cPair} = {dmin*dmin, pairMin}
for i=1 to nS-1 do
k = i + 1
while k<=nS and (yS[k][Y]-yS[i][Y])<dmin do
d = distsq(yS[k],yS[i])
if d<closest then
{closest, cPair} = {d, {yS[k], yS[i]}}
end if
k += 1
end while
end for
return {sqrt(closest), cPair}
end function
{d,points} = closestPair(xP,yP)
{{x1,y1},{x2,y2}} = sort(points) -- (see note above)
printf(1,"Closest pair: {%f,%f} {%f,%f}, distance=%f (%3.2fs)\n",{x1,y2,x2,y2,d,time()-t0})
Output:
Closest pair: {0.0328051,0.0966250} {0.0328850,0.0966250}, distance=0.000120143 (2.37s)
Closest pair: {0.0328051,0.0966250} {0.0328850,0.0966250}, distance=0.000120143 (0.14s)
PicoLisp
(de closestPairBF (Lst)
(let Min T
(use (Pt1 Pt2)
(for P Lst
(for Q Lst
(or
(== P Q)
(>=
(setq N
(let (A (- (car P) (car Q)) B (- (cdr P) (cdr Q)))
(+ (* A A) (* B B)) ) )
Min )
(setq Min N Pt1 P Pt2 Q) ) ) )
(list Pt1 Pt2 (sqrt Min)) ) ) )
Test:
: (scl 6)
-> 6
: (closestPairBF
(quote
(0.654682 . 0.925557)
(0.409382 . 0.619391)
(0.891663 . 0.888594)
(0.716629 . 0.996200)
(0.477721 . 0.946355)
(0.925092 . 0.818220)
(0.624291 . 0.142924)
(0.211332 . 0.221507)
(0.293786 . 0.691701)
(0.839186 . 0.728260) ) )
-> ((891663 . 888594) (925092 . 818220) 77910)
PL/I
/* Closest Pair Problem */
closest: procedure options (main);
declare n fixed binary;
get list (n);
begin;
declare 1 P(n),
2 x float,
2 y float;
declare (i, ii, j, jj) fixed binary;
declare (distance, min_distance initial (0) ) float;
get list (P);
min_distance = sqrt( (P.x(1) - P.x(2))**2 + (P.y(1) - P.y(2))**2 );
ii = 1; jj = 2;
do i = 1 to n;
do j = 1 to n;
distance = sqrt( (P.x(i) - P.x(j))**2 + (P.y(i) - P.y(j))**2 );
if distance > 0 then
if distance < min_distance then
do;
min_distance = distance;
ii = i; jj = j;
end;
end;
end;
put skip edit ('The minimum distance ', min_distance,
' is between the points [', P.x(ii),
',', P.y(ii), '] and [', P.x(jj), ',', P.y(jj), ']' )
(a, f(6,2));
end;
end closest;
PureBasic
Brute force version
Procedure.d bruteForceClosestPair(Array P.coordinate(1))
Protected N=ArraySize(P()), i, j
Protected mindistance.f=Infinity(), t.d
Shared a, b
If N<2
a=0: b=0
Else
For i=0 To N-1
For j=i+1 To N
t=Pow(Pow(P(i)\x-P(j)\x,2)+Pow(P(i)\y-P(j)\y,2),0.5)
If mindistance>t
mindistance=t
a=i: b=j
EndIf
Next
Next
EndIf
ProcedureReturn mindistance
EndProcedure
Implementation can be as
Structure coordinate
x.d
y.d
EndStructure
Dim DataSet.coordinate(9)
Define i, x.d, y.d, a, b
;- Load data from datasection
Restore DataPoints
For i=0 To 9
Read.d x: Read.d y
DataSet(i)\x=x
DataSet(i)\y=y
Next i
If OpenConsole()
PrintN("Mindistance= "+StrD(bruteForceClosestPair(DataSet()),6))
PrintN("Point 1= "+StrD(DataSet(a)\x,6)+": "+StrD(DataSet(a)\y,6))
PrintN("Point 2= "+StrD(DataSet(b)\x,6)+": "+StrD(DataSet(b)\y,6))
Print(#CRLF$+"Press ENTER to quit"): Input()
EndIf
DataSection
DataPoints:
Data.d 0.654682, 0.925557, 0.409382, 0.619391, 0.891663, 0.888594
Data.d 0.716629, 0.996200, 0.477721, 0.946355, 0.925092, 0.818220
Data.d 0.624291, 0.142924, 0.211332, 0.221507, 0.293786, 0.691701, 0.839186, 0.72826
EndDataSection
Output:
Mindistance= 0.077910
Point 1= 0.891663: 0.888594
Point 2= 0.925092: 0.818220
Press ENTER to quit
Python
"""
Compute nearest pair of points using two algorithms
First algorithm is 'brute force' comparison of every possible pair.
Second, 'divide and conquer', is based on:
www.cs.iupui.edu/~xkzou/teaching/CS580/Divide-and-conquer-closestPair.ppt
"""
from random import randint, randrange
from operator import itemgetter, attrgetter
infinity = float('inf')
# Note the use of complex numbers to represent 2D points making distance == abs(P1-P2)
def bruteForceClosestPair(point):
numPoints = len(point)
if numPoints < 2:
return infinity, (None, None)
return min( ((abs(point[i] - point[j]), (point[i], point[j]))
for i in range(numPoints-1)
for j in range(i+1,numPoints)),
key=itemgetter(0))
def closestPair(point):
xP = sorted(point, key= attrgetter('real'))
yP = sorted(point, key= attrgetter('imag'))
return _closestPair(xP, yP)
def _closestPair(xP, yP):
numPoints = len(xP)
if numPoints <= 3:
return bruteForceClosestPair(xP)
Pl = xP[:numPoints/2]
Pr = xP[numPoints/2:]
Yl, Yr = [], []
xDivider = Pl[-1].real
for p in yP:
if p.real <= xDivider:
Yl.append(p)
else:
Yr.append(p)
dl, pairl = _closestPair(Pl, Yl)
dr, pairr = _closestPair(Pr, Yr)
dm, pairm = (dl, pairl) if dl < dr else (dr, pairr)
# Points within dm of xDivider sorted by Y coord
closeY = [p for p in yP if abs(p.real - xDivider) < dm]
numCloseY = len(closeY)
if numCloseY > 1:
# There is a proof that you only need compare a max of 7 next points
closestY = min( ((abs(closeY[i] - closeY[j]), (closeY[i], closeY[j]))
for i in range(numCloseY-1)
for j in range(i+1,min(i+8, numCloseY))),
key=itemgetter(0))
return (dm, pairm) if dm <= closestY[0] else closestY
else:
return dm, pairm
def times():
''' Time the different functions
'''
import timeit
functions = [bruteForceClosestPair, closestPair]
for f in functions:
print 'Time for', f.__name__, timeit.Timer(
'%s(pointList)' % f.__name__,
'from closestpair import %s, pointList' % f.__name__).timeit(number=1)
pointList = [randint(0,1000)+1j*randint(0,1000) for i in range(2000)]
if __name__ == '__main__':
pointList = [(5+9j), (9+3j), (2+0j), (8+4j), (7+4j), (9+10j), (1+9j), (8+2j), 10j, (9+6j)]
print pointList
print ' bruteForceClosestPair:', bruteForceClosestPair(pointList)
print ' closestPair:', closestPair(pointList)
for i in range(10):
pointList = [randrange(11)+1j*randrange(11) for i in range(10)]
print '\n', pointList
print ' bruteForceClosestPair:', bruteForceClosestPair(pointList)
print ' closestPair:', closestPair(pointList)
print '\n'
times()
times()
times()
Output:
followed by timing comparisons
(Note how the two algorithms agree on the minimum distance, but may return a different pair of points if more than one pair of points share that minimum separation):
[(5+9j), (9+3j), (2+0j), (8+4j), (7+4j), (9+10j), (1+9j), (8+2j), 10j, (9+6j)]
bruteForceClosestPair: (1.0, ((8+4j), (7+4j)))
closestPair: (1.0, ((8+4j), (7+4j)))
[(10+6j), (7+0j), (9+4j), (4+8j), (7+5j), (6+4j), (1+9j), (6+4j), (1+3j), (5+0j)]
bruteForceClosestPair: (0.0, ((6+4j), (6+4j)))
closestPair: (0.0, ((6+4j), (6+4j)))
[(4+10j), (8+5j), (10+3j), (9+7j), (2+5j), (6+7j), (6+2j), (9+6j), (3+8j), (5+1j)]
bruteForceClosestPair: (1.0, ((9+7j), (9+6j)))
closestPair: (1.0, ((9+7j), (9+6j)))
[(10+0j), (3+10j), (10+7j), (1+8j), (5+10j), (8+8j), (4+7j), (6+2j), (6+10j), (9+3j)]
bruteForceClosestPair: (1.0, ((5+10j), (6+10j)))
closestPair: (1.0, ((5+10j), (6+10j)))
[(3+7j), (5+3j), 0j, (2+9j), (2+5j), (9+6j), (5+9j), (4+3j), (3+8j), (8+7j)]
bruteForceClosestPair: (1.0, ((3+7j), (3+8j)))
closestPair: (1.0, ((4+3j), (5+3j)))
[(4+3j), (10+9j), (2+7j), (7+8j), 0j, (3+10j), (10+2j), (7+10j), (7+3j), (1+4j)]
bruteForceClosestPair: (2.0, ((7+8j), (7+10j)))
closestPair: (2.0, ((7+8j), (7+10j)))
[(9+2j), (9+8j), (6+4j), (7+0j), (10+2j), (10+0j), (2+7j), (10+7j), (9+2j), (1+5j)]
bruteForceClosestPair: (0.0, ((9+2j), (9+2j)))
closestPair: (0.0, ((9+2j), (9+2j)))
[(3+3j), (8+2j), (4+0j), (1+1j), (9+10j), (5+0j), (2+3j), 5j, (5+0j), (7+0j)]
bruteForceClosestPair: (0.0, ((5+0j), (5+0j)))
closestPair: (0.0, ((5+0j), (5+0j)))
[(1+5j), (8+3j), (8+10j), (6+8j), (10+9j), (2+0j), (2+7j), (8+7j), (8+4j), (1+2j)]
bruteForceClosestPair: (1.0, ((8+3j), (8+4j)))
closestPair: (1.0, ((8+3j), (8+4j)))
[(8+4j), (8+6j), (8+0j), 0j, (10+7j), (10+6j), 6j, (1+3j), (1+8j), (6+9j)]
bruteForceClosestPair: (1.0, ((10+7j), (10+6j)))
closestPair: (1.0, ((10+7j), (10+6j)))
[(6+8j), (10+1j), 3j, (7+9j), (4+10j), (4+7j), (5+7j), (6+10j), (4+7j), (2+4j)]
bruteForceClosestPair: (0.0, ((4+7j), (4+7j)))
closestPair: (0.0, ((4+7j), (4+7j)))
Time for bruteForceClosestPair 4.57953371169
Time for closestPair 0.122539596513
Time for bruteForceClosestPair 5.13221177552
Time for closestPair 0.124602707886
Time for bruteForceClosestPair 4.83609397284
Time for closestPair 0.119326618327
>>>
R
Works with: R version 2.8.1+
Brute force solution as per wikipedia pseudo-code
closest_pair_brute <-function(x,y,plotxy=F) {
xy = cbind(x,y)
cp = bruteforce(xy)
cat("\n\nShortest path found = \n From:\t\t(",cp[1],',',cp[2],")\n To:\t\t(",cp[3],',',cp[4],")\n Distance:\t",cp[5],"\n\n",sep="")
if(plotxy) {
plot(x,y,pch=19,col='black',main="Closest Pair", asp=1)
points(cp[1],cp[2],pch=19,col='red')
points(cp[3],cp[4],pch=19,col='red')
}
distance <- function(p1,p2) {
x1 = (p1[1])
y1 = (p1[2])
x2 = (p2[1])
y2 = (p2[2])
sqrt((x2-x1)^2 + (y2-y1)^2)
}
bf_iter <- function(m,p,idx=NA,d=NA,n=1) {
dd = distance(p,m[n,])
if((is.na(d) || dd<=d) && p!=m[n,]){d = dd; idx=n;}
if(n == length(m[,1])) { c(m[idx,],d) }
else bf_iter(m,p,idx,d,n+1)
}
bruteforce <- function(pmatrix,n=1,pd=c(NA,NA,NA,NA,NA)) {
p = pmatrix[n,]
ppd = c(p,bf_iter(pmatrix,p))
if(ppd[5]<pd[5] || is.na(pd[5])) pd = ppd
if(n==length(pmatrix[,1])) pd
else bruteforce(pmatrix,n+1,pd)
}
}
Quicker brute force solution for R that makes use of the apply function native to R for dealing with matrices. It expects x and y to take the form of separate vectors.
closestPair<-function(x,y)
{
distancev <- function(pointsv)
{
x1 <- pointsv[1]
y1 <- pointsv[2]
x2 <- pointsv[3]
y2 <- pointsv[4]
sqrt((x1 - x2)^2 + (y1 - y2)^2)
}
pairstocompare <- t(combn(length(x),2))
pointsv <- cbind(x[pairstocompare[,1]],y[pairstocompare[,1]],x[pairstocompare[,2]],y[pairstocompare[,2]])
pairstocompare <- cbind(pairstocompare,apply(pointsv,1,distancev))
minrow <- pairstocompare[pairstocompare[,3] == min(pairstocompare[,3])]
if (!is.null(nrow(minrow))) {print("More than one point at this distance!"); minrow <- minrow[1,]}
cat("The closest pair is:\n\tPoint 1: ",x[minrow[1]],", ",y[minrow[1]],
"\n\tPoint 2: ",x[minrow[2]],", ",y[minrow[2]],
"\n\tDistance: ",minrow[3],"\n",sep="")
c(distance=minrow[3],x1.x=x[minrow[1]],y1.y=y[minrow[1]],x2.x=x[minrow[2]],y2.y=y[minrow[2]])
}
This is the quickest version, that makes use of the 'dist' function of R. It takes a two-column object of x,y-values as input, or creates such an object from seperate x and y-vectors.
closest.pairs <- function(x, y=NULL, ...){
# takes two-column object(x,y-values), or creates such an object from x and y values
if(!is.null(y)) x <- cbind(x, y)
distances <- dist(x)
min.dist <- min(distances)
point.pair <- combn(1:nrow(x), 2)[, which.min(distances)]
cat("The closest pair is:\n\t",
sprintf("Point 1: %.3f, %.3f \n\tPoint 2: %.3f, %.3f \n\tDistance: %.3f.\n",
x[point.pair[1],1], x[point.pair[1],2],
x[point.pair[2],1], x[point.pair[2],2],
min.dist),
sep="" )
c( x1=x[point.pair[1],1],y1=x[point.pair[1],2],
x2=x[point.pair[2],1],y2=x[point.pair[2],2],
distance=min.dist)
}
Example
x = (sample(-1000.00:1000.00,100))
y = (sample(-1000.00:1000.00,length(x)))
cp = closest.pairs(x,y)
#cp = closestPair(x,y)
plot(x,y,pch=19,col='black',main="Closest Pair", asp=1)
points(cp["x1.x"],cp["y1.y"],pch=19,col='red')
points(cp["x2.x"],cp["y2.y"],pch=19,col='red')
#closest_pair_brute(x,y,T)
Performance
system.time(closest_pair_brute(x,y), gcFirst = TRUE)
Shortest path found =
From: (32,-987)
To: (25,-993)
Distance: 9.219544
user system elapsed
0.35 0.02 0.37
system.time(closest.pairs(x,y), gcFirst = TRUE)
The closest pair is:
Point 1: 32.000, -987.000
Point 2: 25.000, -993.000
Distance: 9.220.
user system elapsed
0.08 0.00 0.10
system.time(closestPair(x,y), gcFirst = TRUE)
The closest pair is:
Point 1: 32, -987
Point 2: 25, -993
Distance: 9.219544
user system elapsed
0.17 0.00 0.19
Using dist function for brute force, but divide and conquer (as per pseudocode) for speed:
closest.pairs.bruteforce <- function(x, y=NULL)
{
if (!is.null(y))
{
x <- cbind(x,y)
}
d <- dist(x)
cp <- x[combn(1:nrow(x), 2)[, which.min(d)],]
list(p1=cp[1,], p2=cp[2,], d=min(d))
}
closest.pairs.dandc <- function(x, y=NULL)
{
if (!is.null(y))
{
x <- cbind(x,y)
}
if (sd(x[,"x"]) < sd(x[,"y"]))
{
x <- cbind(x=x[,"y"],y=x[,"x"])
swap <- TRUE
}
else
{
swap <- FALSE
}
xp <- x[order(x[,"x"]),]
.cpdandc.rec <- function(xp,yp)
{
n <- dim(xp)[1]
if (n <= 4)
{
closest.pairs.bruteforce(xp)
}
else
{
xl <- xp[1:floor(n/2),]
xr <- xp[(floor(n/2)+1):n,]
cpl <- .cpdandc.rec(xl)
cpr <- .cpdandc.rec(xr)
if (cpl$d<cpr$d) cp <- cpl else cp <- cpr
cp
}
}
cp <- .cpdandc.rec(xp)
yp <- x[order(x[,"y"]),]
xm <- xp[floor(dim(xp)[1]/2),"x"]
ys <- yp[which(abs(xm - yp[,"x"]) <= cp$d),]
nys <- dim(ys)[1]
if (!is.null(nys) && nys > 1)
{
for (i in 1:(nys-1))
{
k <- i + 1
while (k <= nys && ys[i,"y"] - ys[k,"y"] < cp$d)
{
d <- sqrt((ys[k,"x"]-ys[i,"x"])^2 + (ys[k,"y"]-ys[i,"y"])^2)
if (d < cp$d) cp <- list(p1=ys[i,],p2=ys[k,],d=d)
k <- k + 1
}
}
}
if (swap)
{
list(p1=cbind(x=cp$p1["y"],y=cp$p1["x"]),p2=cbind(x=cp$p2["y"],y=cp$p2["x"]),d=cp$d)
}
else
{
cp
}
}
# Test functions
cat("How many points?\n")
n <- scan(what=integer(),n=1)
x <- rnorm(n)
y <- rnorm(n)
tstart <- proc.time()[3]
cat("Closest pairs divide and conquer:\n")
print(cp <- closest.pairs.dandc(x,y))
cat(sprintf("That took %.2f seconds.\n",proc.time()[3] - tstart))
plot(x,y)
points(c(cp$p1["x"],cp$p2["x"]),c(cp$p1["y"],cp$p2["y"]),col="red")
tstart <- proc.time()[3]
cat("\nClosest pairs brute force:\n")
print(closest.pairs.bruteforce(x,y))
cat(sprintf("That took %.2f seconds.\n",proc.time()[3] - tstart))
Output:
How many points?
1: 500
Read 1 item
Closest pairs divide and conquer:
$p1
x y
1.68807938 0.05876328
$p2
x y
1.68904694 0.05878173
$d
[1] 0.0009677302
That took 0.43 seconds.
Closest pairs brute force:
$p1
x y
1.68807938 0.05876328
$p2
x y
1.68904694 0.05878173
$d
[1] 0.0009677302
That took 6.38 seconds.
Racket
The brute force solution using complex numbers to represent pairs.
#lang racket
(define (dist z0 z1) (magnitude (- z1 z0)))
(define (dist* zs) (apply dist zs))
(define (closest-pair zs)
(if (< (length zs) 2)
-inf.0
(first
(sort (for/list ([z0 zs])
(list z0 (argmin (λ(z) (if (= z z0) +inf.0 (dist z z0))) zs)))
< #:key dist*))))
(define result (closest-pair '(0+1i 1+2i 3+4i)))
(displayln (~a "Closest points: " result))
(displayln (~a "Distance: " (dist* result)))
Output:
Closest points: (0+1i 1+2i)
Distance: 1.4142135623730951
REXX
/*REXX program solves the closest pair of points problem (in two dimensions). */
parse arg N low high seed . /*obtain optional arguments from the CL*/
if N=='' | N=="," then N= 100 /*Not specified? Then use the default.*/
if low=='' | low=="," then low= 0 /* " " " " " " */
if high=='' | high=="," then high=20000 /* " " " " " " */
if datatype(seed,'W') then call random ,,seed /*seed for RANDOM (BIF) repeatability.*/
w=length(high); w=w + (w//2==0)
/*╔══════════════════════╗*/ do j=1 for N /*generate N random points.*/
/*║ generate N points. ║*/ @x.j=random(low,high) /* " a random X. */
/*╚══════════════════════╝*/ @y.j=random(low,high) /* " " " Y. */
end /*j*/ /*X and Y make the point*/
A=1; B=2 /* [↓] MINDD is actually the unsquared*/
minDD=(@x.[email protected].B)**2 + (@y.[email protected].B)**2 /*distance between the first two points*/
/* [↓] use of XJ & YJ speed things up.*/
do j=1 for N-1; [email protected].j; [email protected].j /*find minimum distance between a ··· */
do k=j+1 to N /* ··· point and all the other points.*/
dd=(xj - @x.k)**2 + (yj - @y.k)**2 /*compute squared distance from points.*/
if dd<minDD then if dd\=0 then parse value dd j k with minDD A B
end /*k*/ /* [↑] needn't take SQRT of DD (yet).*/
end /*j*/ /* [↑] when done, A & B are the ones*/
_= 'For ' N " points, the minimum distance between the two points: "
say _ center("x", w, '═')" " center('y', w, "═") ' is: ' sqrt(abs(minDD))/1
say left('', length(_)-1) "["right(@x.A, w)',' right(@y.A, w)"]"
say left('', length(_)-1) "["right(@x.B, w)',' right(@y.B, w)"]"
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); m.=9; numeric form; h=d+6
numeric digits; parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g *.5'e'_ % 2
do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/
do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/
return g
output when using the default input of: 100
For 100 points, the minimum distance between the two points: ══x══ ══y══ is: 219.228192
[ 7277, 1625]
[ 7483, 1700]
output when using the input of: 200
For 200 points, the minimum distance between the two points: ══x══ ══y══ is: 39.408121
[17604, 19166]
[17627, 19198]
output when using the input of: 1000
For 1000 points, the minimum distance between the two points: ══x══ ══y══ is: 5.09901951
[ 6264, 19103]
[ 6263, 19108]
Ring
decimals(10)
x = list(10)
y = list(10)
x[1] = 0.654682
y[1] = 0.925557
x[2] = 0.409382
y[2] = 0.619391
x[3] = 0.891663
y[3] = 0.888594
x[4] = 0.716629
y[4] = 0.996200
x[5] = 0.477721
y[5] = 0.946355
x[6] = 0.925092
y[6] = 0.818220
x[7] = 0.624291
y[7] = 0.142924
x[8] = 0.211332
y[8] = 0.221507
x[9] = 0.293786
y[9] = 0.691701
x[10] = 0.839186
y[10] = 0.728260
min = 10000
for i = 1 to 9
for j = i+1 to 10
dsq = pow((x[i] - x[j]),2) + pow((y[i] - y[j]),2)
if dsq < min min = dsq mini = i minj = j ok
next
next
see "closest pair is : " + mini + " and " + minj + " at distance " + sqrt(min)
Output:
closest pair is : 3 and 6 at distance 0.0779101914
Ruby
Point = Struct.new(:x, :y)
def distance(p1, p2)
Math.hypot(p1.x - p2.x, p1.y - p2.y)
end
def closest_bruteforce(points)
mindist, minpts = Float::MAX, []
points.combination(2) do |pi,pj|
dist = distance(pi, pj)
if dist < mindist
mindist = dist
minpts = [pi, pj]
end
end
[mindist, minpts]
end
def closest_recursive(points)
return closest_bruteforce(points) if points.length <= 3
xP = points.sort_by(&:x)
mid = points.length / 2
xm = xP[mid].x
dL, pairL = closest_recursive(xP[0,mid])
dR, pairR = closest_recursive(xP[mid..-1])
dmin, dpair = dL<dR ? [dL, pairL] : [dR, pairR]
yP = xP.find_all {|p| (xm - p.x).abs < dmin}.sort_by(&:y)
closest, closestPair = dmin, dpair
0.upto(yP.length - 2) do |i|
(i+1).upto(yP.length - 1) do |k|
break if (yP[k].y - yP[i].y) >= dmin
dist = distance(yP[i], yP[k])
if dist < closest
closest = dist
closestPair = [yP[i], yP[k]]
end
end
end
[closest, closestPair]
end
points = Array.new(100) {Point.new(rand, rand)}
p ans1 = closest_bruteforce(points)
p ans2 = closest_recursive(points)
fail "bogus!" if ans1[0] != ans2[0]
require 'benchmark'
points = Array.new(10000) {Point.new(rand, rand)}
Benchmark.bm(12) do |x|
x.report("bruteforce") {ans1 = closest_bruteforce(points)}
x.report("recursive") {ans2 = closest_recursive(points)}
end
Sample output
[0.005299616045889868, [#<struct Point x=0.24805908871087445, y=0.8413503128160198>, #<struct Point x=0.24355227214243136, y=0.8385620275629906>]]
[0.005299616045889868, [#<struct Point x=0.24355227214243136, y=0.8385620275629906>, #<struct Point x=0.24805908871087445, y=0.8413503128160198>]]
user system total real
bruteforce 43.446000 0.000000 43.446000 ( 43.530062)
recursive 0.187000 0.000000 0.187000 ( 0.190000)
Run BASIC
Courtesy http://dkokenge.com/rbp
n =10 ' 10 data points input
dim x(n)
dim y(n)
pt1 = 0 ' 1st point
pt2 = 0 ' 2nd point
for i =1 to n ' read in data
read x(i)
read y(i)
next i
minDist = 1000000
for i =1 to n -1
for j =i +1 to n
distXsq =(x(i) -x(j))^2
disYsq =(y(i) -y(j))^2
d =abs((dxSq +disYsq)^0.5)
if d <minDist then
minDist =d
pt1 =i
pt2 =j
end if
next j
next i
print "Distance ="; minDist; " between ("; x(pt1); ", "; y(pt1); ") and ("; x(pt2); ", "; y(pt2); ")"
end
data 0.654682, 0.925557
data 0.409382, 0.619391
data 0.891663, 0.888594
data 0.716629, 0.996200
data 0.477721, 0.946355
data 0.925092, 0.818220
data 0.624291, 0.142924
data 0.211332, 0.221507
data 0.293786, 0.691701
data 0.839186, 0.72826
Scala
import scala.collection.mutable.ListBuffer
import scala.util.Random
object ClosestPair {
case class Point(x: Double, y: Double){
def distance(p: Point) = math.hypot(x-p.x, y-p.y)
override def toString = "(" + x + ", " + y + ")"
}
case class Pair(point1: Point, point2: Point) {
val distance: Double = point1 distance point2
override def toString = {
point1 + "-" + point2 + " : " + distance
}
}
def sortByX(points: List[Point]) = {
points.sortBy(point => point.x)
}
def sortByY(points: List[Point]) = {
points.sortBy(point => point.y)
}
def divideAndConquer(points: List[Point]): Pair = {
val pointsSortedByX = sortByX(points)
val pointsSortedByY = sortByY(points)
divideAndConquer(pointsSortedByX, pointsSortedByY)
}
def bruteForce(points: List[Point]): Pair = {
val numPoints = points.size
if (numPoints < 2)
return null
var pair = Pair(points(0), points(1))
if (numPoints > 2) {
for (i <- 0 until numPoints - 1) {
val point1 = points(i)
for (j <- i + 1 until numPoints) {
val point2 = points(j)
val distance = point1 distance point2
if (distance < pair.distance)
pair = Pair(point1, point2)
}
}
}
return pair
}
private def divideAndConquer(pointsSortedByX: List[Point], pointsSortedByY: List[Point]): Pair = {
val numPoints = pointsSortedByX.size
if(numPoints <= 3) {
return bruteForce(pointsSortedByX)
}
val dividingIndex = numPoints >>> 1
val leftOfCenter = pointsSortedByX.slice(0, dividingIndex)
val rightOfCenter = pointsSortedByX.slice(dividingIndex, numPoints)
var tempList = leftOfCenter.map(x => x)
//println(tempList)
tempList = sortByY(tempList)
var closestPair = divideAndConquer(leftOfCenter, tempList)
tempList = rightOfCenter.map(x => x)
tempList = sortByY(tempList)
val closestPairRight = divideAndConquer(rightOfCenter, tempList)
if (closestPairRight.distance < closestPair.distance)
closestPair = closestPairRight
tempList = List[Point]()
val shortestDistance = closestPair.distance
val centerX = rightOfCenter(0).x
for (point <- pointsSortedByY) {
if (Math.abs(centerX - point.x) < shortestDistance)
tempList = tempList :+ point
}
closestPair = shortestDistanceF(tempList, shortestDistance, closestPair)
closestPair
}
private def shortestDistanceF(tempList: List[Point], shortestDistance: Double, closestPair: Pair ): Pair = {
var shortest = shortestDistance
var bestResult = closestPair
for (i <- 0 until tempList.size) {
val point1 = tempList(i)
for (j <- i + 1 until tempList.size) {
val point2 = tempList(j)
if ((point2.y - point1.y) >= shortestDistance)
return closestPair
val distance = point1 distance point2
if (distance < closestPair.distance)
{
bestResult = Pair(point1, point2)
shortest = distance
}
}
}
closestPair
}
def main(args: Array[String]) {
val numPoints = if(args.length == 0) 1000 else args(0).toInt
val points = ListBuffer[Point]()
val r = new Random()
for (i <- 0 until numPoints) {
points.+=:(new Point(r.nextDouble(), r.nextDouble()))
}
println("Generated " + numPoints + " random points")
var startTime = System.currentTimeMillis()
val bruteForceClosestPair = bruteForce(points.toList)
var elapsedTime = System.currentTimeMillis() - startTime
println("Brute force (" + elapsedTime + " ms): " + bruteForceClosestPair)
startTime = System.currentTimeMillis()
val dqClosestPair = divideAndConquer(points.toList)
elapsedTime = System.currentTimeMillis() - startTime
println("Divide and conquer (" + elapsedTime + " ms): " + dqClosestPair)
if (bruteForceClosestPair.distance != dqClosestPair.distance)
println("MISMATCH")
}
}
Output:
scala ClosestPair 1000
Generated 1000 random points
Brute force (981 ms): (0.41984960343173994, 0.4499078600557793)-(0.4198255166110827, 0.45044969701435) : 5.423720721077961E-4
Divide and conquer (52 ms): (0.4198255166110827, 0.45044969701435)-(0.41984960343173994, 0.4499078600557793) : 5.423720721077961E-4
Seed7
This is the brute force algorithm:
const type: point is new struct
var float: x is 0.0;
var float: y is 0.0;
end struct;
const func float: distance (in point: p1, in point: p2) is
return sqrt((p1.x-p2.x)**2+(p1.y-p2.y)**2);
const func array point: closest_pair (in array point: points) is func
result
var array point: result is 0 times point.value;
local
var float: dist is 0.0;
var float: minDistance is Infinity;
var integer: i is 0;
var integer: j is 0;
var integer: savei is 0;
var integer: savej is 0;
begin
for i range 1 to pred(length(points)) do
for j range succ(i) to length(points) do
dist := distance(points[i], points[j]);
if dist < minDistance then
minDistance := dist;
savei := i;
savej := j;
end if;
end for;
end for;
if minDistance <> Infinity then
result := [] (points[savei], points[savej]);
end if;
end func;
Sidef
Translation of: Perl 6
func dist_squared(a, b) {
sqr(a[0] - b[0]) + sqr(a[1] - b[1])
}
func closest_pair_simple(arr) {
arr.len < 2 && return Inf
var (a, b, d) = (arr[0, 1], dist_squared(arr[0,1]))
arr.clone!
while (arr) {
var p = arr.pop
for l in arr {
var t = dist_squared(p, l)
if (t < d) {
(a, b, d) = (p, l, t)
}
}
}
return(a, b, d.sqrt)
}
func closest_pair_real(rx, ry) {
rx.len <= 3 && return closest_pair_simple(rx)
var N = rx.len
var midx = (ceil(N/2)-1)
var (PL, PR) = rx.part(midx)
var xm = rx[midx][0]
var yR = []
var yL = []
for item in ry {
(item[0] <= xm ? yR : yL) << item
}
var (al, bl, dL) = closest_pair_real(PL, yR)
var (ar, br, dR) = closest_pair_real(PR, yL)
al == Inf && return (ar, br, dR)
ar == Inf && return (al, bl, dL)
var (m1, m2, dmin) = (dR < dL ? [ar, br, dR]...
: [al, bl, dL]...)
var yS = ry.grep { |a| abs(xm - a[0]) < dmin }
var (w1, w2, closest) = (m1, m2, dmin)
for i in (0 ..^ yS.end) {
for k in (i+1 .. yS.end) {
yS[k][1] - yS[i][1] < dmin || break
var d = dist_squared(yS[k], yS[i]).sqrt
if (d < closest) {
(w1, w2, closest) = (yS[k], yS[i], d)
}
}
}
return (w1, w2, closest)
}
func closest_pair(r) {
var ax = r.sort_by { |a| a[0] }
var ay = r.sort_by { |a| a[1] }
return closest_pair_real(ax, ay);
}
var N = 5000
var points = N.of { [1.rand*20 - 10, 1.rand*20 - 10] }
var (af, bf, df) = closest_pair(points)
say "#{df} at (#{af.join(' ')}), (#{bf.join(' ')})"
Smalltalk
See Closest-pair problem/Smalltalk
Tcl
Each point is represented as a list of two floating-point numbers, the first being the x coordinate, and the second being the y.
package require Tcl 8.5
# retrieve the x-coordinate
proc x p {lindex $p 0}
# retrieve the y-coordinate
proc y p {lindex $p 1}
proc distance {p1 p2} {
expr {hypot(([x $p1]-[x $p2]), ([y $p1]-[y $p2]))}
}
proc closest_bruteforce {points} {
set n [llength $points]
set mindist Inf
set minpts {}
for {set i 0} {$i < $n - 1} {incr i} {
for {set j [expr {$i + 1}]} {$j < $n} {incr j} {
set p1 [lindex $points $i]
set p2 [lindex $points $j]
set dist [distance $p1 $p2]
if {$dist < $mindist} {
set mindist $dist
set minpts [list $p1 $p2]
}
}
}
return [list $mindist $minpts]
}
proc closest_recursive {points} {
set n [llength $points]
if {$n <= 3} {
return [closest_bruteforce $points]
}
set xP [lsort -real -increasing -index 0 $points]
set mid [expr {int(ceil($n/2.0))}]
set PL [lrange $xP 0 [expr {$mid-1}]]
set PR [lrange $xP $mid end]
set procname [lindex [info level 0] 0]
lassign [$procname $PL] dL pairL
lassign [$procname $PR] dR pairR
if {$dL < $dR} {
set dmin $dL
set dpair $pairL
} else {
set dmin $dR
set dpair $pairR
}
set xM [x [lindex $PL end]]
foreach p $xP {
if {abs($xM - [x $p]) < $dmin} {
lappend S $p
}
}
set yP [lsort -real -increasing -index 1 $S]
set closest Inf
set nP [llength $yP]
for {set i 0} {$i <= $nP-2} {incr i} {
set yPi [lindex $yP $i]
for {set k [expr {$i+1}]; set yPk [lindex $yP $k]} {
$k < $nP-1 && ([y $yPk]-[y $yPi]) < $dmin
} {incr k; set yPk [lindex $yP $k]} {
set dist [distance $yPk $yPi]
if {$dist < $closest} {
set closest $dist
set closestPair [list $yPi $yPk]
}
}
}
expr {$closest < $dmin ? [list $closest $closestPair] : [list $dmin $dpair]}
}
# testing
set N 10000
for {set i 1} {$i <= $N} {incr i} {
lappend points [list [expr {rand()*100}] [expr {rand()*100}]]
}
# instrument the number of calls to [distance] to examine the
# efficiency of the recursive solution
trace add execution distance enter comparisons
proc comparisons args {incr ::comparisons}
puts [format "%-10s %9s %9s %s" method compares time closest]
foreach method {bruteforce recursive} {
set ::comparisons 0
set time [time {set ::dist($method) [closest_$method $points]} 1]
puts [format "%-10s %9d %9d %s" $method $::comparisons [lindex $time 0] [lindex $::dist($method) 0]]
}
Output:
method compares time closest
bruteforce 49995000 512967207 0.0015652738546658382
recursive 14613 488094 0.0015652738546658382
Note that the lindex and llength commands are both O(1).
Ursala
The brute force algorithm is easy. Reading from left to right, clop is defined as a function that forms the Cartesian product of its argument, and then extracts the member whose left side is a minimum with respect to the floating point comparison relation after deleting equal pairs and attaching to the left of each remaining pair the sum of the squares of the differences between corresponding coordinates.
#import flo
clop = @iiK0 fleq$-&l+ *EZF ^\~& plus+ sqr~~+ minus~~bbI
The divide and conquer algorithm following the specification given above is a little more hairy but not much longer. The eudist library function is used to compute the distance between points.
#import std
#import flo
clop =
^(fleq-<&l,fleq-<&r); @blrNCCS ~&lrbhthPX2X+ ~&a^& fleq$-&l+ leql/8?al\^(eudist,~&)*altK33htDSL -+
^C/~&rr ^(eudist,~&)*tK33htDSL+ @rlrlPXPlX ~| fleq^\~&lr abs+ [email protected],
^/~&ar @farlK30K31XPGbrlrjX3J ^/~&arlhh @W lesser [email protected]+-
test program:
test_data =
<
(1.547290e+00,3.313053e+00),
(5.250805e-01,-7.300260e+00),
(7.062114e-02,1.220251e-02),
(-4.473024e+00,-5.393712e+00),
(-2.563714e+00,-3.595341e+00),
(-2.132372e+00,2.358850e+00),
(2.366238e+00,-9.678425e+00),
(-1.745694e+00,3.276434e+00),
(8.066843e+00,-9.101268e+00),
(-8.256901e+00,-8.717900e+00),
(7.397744e+00,-5.366434e+00),
(2.060291e-01,2.840891e+00),
(-6.935319e+00,-5.192438e+00),
(9.690418e+00,-9.175753e+00),
(3.448993e+00,2.119052e+00),
(-7.769218e+00,4.647406e-01)>
#cast %eeWWA
example = clop test_data
Output:
The output shows the minimum distance and the two points separated by that distance. (If the brute force algorithm were used, it would have displayed the square of the distance.)
9.957310e-01: (
(-2.132372e+00,2.358850e+00),
(-1.745694e+00,3.276434e+00))
Visual FoxPro
CLOSE DATABASES ALL
CREATE CURSOR pairs(id I, xcoord B(6), ycoord B(6))
INSERT INTO pairs VALUES (1, 0.654682, 0.925557)
INSERT INTO pairs VALUES (2, 0.409382, 0.619391)
INSERT INTO pairs VALUES (3, 0.891663, 0.888594)
INSERT INTO pairs VALUES (4, 0.716629, 0.996200)
INSERT INTO pairs VALUES (5, 0.477721, 0.946355)
INSERT INTO pairs VALUES (6, 0.925092, 0.818220)
INSERT INTO pairs VALUES (7, 0.624291, 0.142924)
INSERT INTO pairs VALUES (8, 0.211332, 0.221507)
INSERT INTO pairs VALUES (9, 0.293786, 0.691701)
INSERT INTO pairs VALUES (10, 0.839186, 0.728260)
SELECT p1.id As id1, p2.id As id2, ;
(p1.xcoord-p2.xcoord)^2 + (p1.ycoord-p2.ycoord)^2 As dist2 ;
FROM pairs p1 JOIN pairs p2 ON p1.id < p2.id ORDER BY 3 INTO CURSOR tmp
GO TOP
? "Closest pair is " + TRANSFORM(id1) + " and " + TRANSFORM(id2) + "."
? "Distance is " + TRANSFORM(SQRT(dist2))
Output:
Visual FoxPro uses 1 based indexing,
Closest pair is 3 and 6.
Distance is 0.077910.
XPL0
The brute force method is simpler than the recursive solution and is perfectly adequate, even for a thousand points.
include c:\cxpl\codes; \intrinsic 'code' declarations
proc ClosestPair(P, N); \Show closest pair of points in array P
real P; int N;
real Dist2, MinDist2;
int I, J, SI, SJ;
[MinDist2:= 1e300;
for I:= 0 to N-2 do
[for J:= I+1 to N-1 do
[Dist2:= sq(P(I,0)-P(J,0)) + sq(P(I,1)-P(J,1));
if Dist2 < MinDist2 then \squared distances are sufficient for compares
[MinDist2:= Dist2;
SI:= I; SJ:= J;
];
];
];
IntOut(0, SI); Text(0, " -- "); IntOut(0, SJ); CrLf(0);
RlOut(0, P(SI,0)); Text(0, ","); RlOut(0, P(SI,1));
Text(0, " -- ");
RlOut(0, P(SJ,0)); Text(0, ","); RlOut(0, P(SJ,1));
CrLf(0);
];
real Data;
[Format(1, 6);
Data:= [[0.654682, 0.925557], \0 test data from BASIC examples
[0.409382, 0.619391], \1
[0.891663, 0.888594], \2
[0.716629, 0.996200], \3
[0.477721, 0.946355], \4
[0.925092, 0.818220], \5
[0.624291, 0.142924], \6
[0.211332, 0.221507], \7
[0.293786, 0.691701], \8
[0.839186, 0.728260]]; \9
ClosestPair(Data, 10);
]
Output:
2 -- 5
0.891663,0.888594 -- 0.925092,0.818220
zkl
An ugly solution in both time and space.
class Point{
fcn init(_x,_y){ var[const] x=_x, y=_y; }
fcn distance(p){ (p.x-x).hypot(p.y-y) }
fcn toString { String("Point(",x,",",y,")") }
}
// find closest two points using brute ugly force:
// find all combinations of two points, measure distance, pick smallest
fcn closestPoints(points){
pairs:=Utils.Helpers.pickNFrom(2,points);
triples:=pairs.apply(fcn([(p1,p2)]){ T(p1,p2,p1.distance(p2)) });
triples.reduce(fcn([(_,_,d1)]p1,[(_,_,d2)]p2){
if(d1 < d2) p1 else p2
});
}
points:=T( 5.0, 9.0, 9.0, 3.0,
2.0, 0.0, 8.0, 4.0,
7.0, 4.0, 9.0, 10.0,
1.0, 9.0, 8.0, 2.0,
0.0, 10.0, 9.0, 6.0 ).pump(List,Void.Read,Point);
closestPoints(points).println(); //-->L(Point(8,4),Point(7,4),1)
points:=T( 0.654682, 0.925557, 0.409382, 0.619391,
0.891663, 0.888594, 0.716629, 0.9962,
0.477721, 0.946355, 0.925092, 0.81822,
0.624291, 0.142924, 0.211332, 0.221507,
0.293786, 0.691701, 0.839186, 0.72826)
.pump(List,Void.Read,Point);
closestPoints(points).println();
Output:
L(Point(8,4),Point(7,4),1)
L(Point(0.925092,0.81822),Point(0.891663,0.888594),0.0779102)
ZX Spectrum Basic
Translation of: BBC_BASIC
10 DIM x(10): DIM y(10)
20 FOR i=1 TO 10
30 READ x(i),y(i)
40 NEXT i
50 LET min=1e30
60 FOR i=1 TO 9
70 FOR j=i+1 TO 10
80 LET p1=x(i)-x(j): LET p2=y(i)-y(j): LET dsq=p1*p1+p2*p2
90 IF dsq<min THEN LET min=dsq: LET mini=i: LET minj=j
100 NEXT j
110 NEXT i
120 PRINT "Closest pair is ";mini;" and ";minj;" at distance ";SQR min
130 STOP
140 DATA 0.654682,0.925557
150 DATA 0.409382,0.619391
160 DATA 0.891663,0.888594
170 DATA 0.716629,0.996200
180 DATA 0.477721,0.946355
190 DATA 0.925092,0.818220
200 DATA 0.624291,0.142924
210 DATA 0.211332,0.221507
220 DATA 0.293786,0.691701
230 DATA 0.839186,0.728260
|
__label__pos
| 0.929867 |
IHEP OpenIR > 多学科研究中心
Speciation and biochemical transformations of sulfur and copper in rice rhizosphere and bulk soil-XANES evidence of sulfur and copper associations
Lin, HR; Shi, JY; Wu, B; Yang, JJ; Chen, YX; Zhao, YD; Hu, TD; Zhao YD(赵屹东); Hu TD(胡天斗)
2010
发表期刊JOURNAL OF SOILS AND SEDIMENTS
卷号10期号:5页码:907-914
通讯作者[Lin, Huirong ; Shi, Jiyan ; Wu, Bei ; Yang, Jianjun ; Chen, Yingxu] Zhejiang Univ, Minist Agr Key Lab Nonpoint Source Pollut Control, Inst Environm Sci & Technol, Hangzhou 310029, Zhejiang, Peoples R China ; [Zhao, Yidong ; Hu, Tiandou] Chinese Acad Sci, Beijing Synchrotron Radiat Facil, Inst High Energy Phys, Beijing 100049, Peoples R China
文章类型Article; Proceedings Paper
摘要Contamination of heavy metals in soil and its subsequent accumulation along the food chain is a potential risk to human health. Cu speciation in soil-plant system, particularly on the availability to plant roots, has obtained great attention. X-ray absorption near-edge structure spectroscopy (XANES) provides information about the bonding of Cu soil components at the molecular scale. In paddy soils, changes of redox conditions led to microbially mediated sulfur transformation, thus affecting heavy metal behavior. The objective of this work was to investigate how sulfur transformation in a paddy soil affected Cu biogeochemical processes. The Cu and sulfur species and their relationship in rice-soil system were investigated under flooded condition. The speciation of sulfur and copper in rice rhizosphere and bulk soil was investigated using integrated approaches including sequential extraction and XANES. Cu speciation exhibited some differences in rhizosphere and bulk soil of rice. In flooded paddy soil, most Cu in the rhizosphere existed as Cu (II), whereas part of Cu transformed to Cu (I) in the bulk soil. Sulfur XANES showed the presence of multiple both oxidized and reduced forms of sulfur in studied soil samples, with more oxidized sulfur in the rhizosphere than in the bulk soil. Copper and sulfur speciation changed depending on redox conditions. Changes in redox potential and microbial action shifted the sulfur oxidation and reduction reaction and affected the Cu speciation. Combined action of organisms maintained Cu homeostasis through cation binding to bioactive molecules. With higher Eh in rice rhizosphere, transformation of sulfur and organic compounds together contributed to more soluble and exchangeable Cu. Cu bond to sulfur containing groups and biomineralization by microorganisms could be defenses against toxic copper. Our findings implied that Cu existed mainly as Cu (II) in rice rhizophere and part of Cu transformed to Cu (I) in anoxic bulk soil. With higher Eh in rice rhizosphere, transformation of sulfur and organic compounds together contributed to more soluble and exchangeable Cu. Combined action of organisms maintained Cu homeostasis through cation binding to bioactive molecules. Our results indicated the important role of sulfur in the transformation of Cu. Due to the complicated processes in soil, future work dedicating to the role of microbes is needed.
关键词Bulk soil Copper Rice rhizosphere Speciation Sulfur XANES
学科领域Geology; Agriculture
DOI10.1007/s11368-010-0204-8
URL查看原文
语种英语
WOS研究方向Geology ; Agriculture
WOS类目Geosciences, Multidisciplinary ; Soil Science
WOS记录号WOS:000278741300014
引用统计
文献类型期刊论文
条目标识符http://ir.ihep.ac.cn/handle/311005/238716
专题多学科研究中心
作者单位中国科学院高能物理研究所
推荐引用方式
GB/T 7714
Lin, HR,Shi, JY,Wu, B,et al. Speciation and biochemical transformations of sulfur and copper in rice rhizosphere and bulk soil-XANES evidence of sulfur and copper associations[J]. JOURNAL OF SOILS AND SEDIMENTS,2010,10(5):907-914.
APA Lin, HR.,Shi, JY.,Wu, B.,Yang, JJ.,Chen, YX.,...&胡天斗.(2010).Speciation and biochemical transformations of sulfur and copper in rice rhizosphere and bulk soil-XANES evidence of sulfur and copper associations.JOURNAL OF SOILS AND SEDIMENTS,10(5),907-914.
MLA Lin, HR,et al."Speciation and biochemical transformations of sulfur and copper in rice rhizosphere and bulk soil-XANES evidence of sulfur and copper associations".JOURNAL OF SOILS AND SEDIMENTS 10.5(2010):907-914.
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|
__label__pos
| 0.799263 |
Keywords
daily activity records, intervention, physical activity
Authors
1. Speck, Barbara J.
2. Looney, Stephen W.
Abstract
Background: Effective interventions to increase physical activity levels are critical in a nation where inactivity is a national public health problem.
Objective: This pilot study examined whether a minimal intervention (daily records of physical activity) increased activity levels in a community sample of working women.
Methods: In a longitudinal, pretest-posttest design, 49 working women were randomly assigned at the work site level to the control (n = 25) or intervention group (n = 24). At pretest and posttest, subjects completed self-report questionnaires that measured psychological, social-environmental, physical activity, and demographic variables. Subjects in the intervention group kept daily records of their physical activities during the 12-week study, while those in the control group kept no records. In order to compare activity in the two groups, all subjects wore pedometers daily that recorded number of steps.
Results: There was a significant difference between groups in the pedometer values (mean number of daily steps) at the end of the study period (mean difference +/-SE: 2147 +/- 636, p = .022) (2000 steps = approximately 1 mile). Multiple regression analysis showed that only the intervention (p = .003) was a significant predictor of the pedometer values. Hierarchical data analysis was used to account for the intra-class correlation of 0.48 within work site.
Conclusion: Results from this sample of 49 women indicated that mean activity was greater in the intervention group compared to the control group. Recording daily activity is a cost-effective and acceptable intervention that may increase activity levels in women. However, more research is recommended to study the dual role of activity records as a data collection method as well as a potential intervention to increase physical activity.
|
__label__pos
| 0.82785 |
HOME
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In
logic Logic is an interdisciplinary field which studies truth and reasoning. Informal logic seeks to characterize Validity (logic), valid arguments informally, for instance by listing varieties of fallacies. Formal logic represents statements and ar ...
logic
and related fields such as
mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ...
and
philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about Metaphysics, existence, reason, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, language. Such questio ...
philosophy
, "if and only if" (shortened as "iff") is a
biconditional In logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit=possessed of reason, intellectual, dialectical, argumentative, translit=logikḗ)Also related to (''logos''), "word, thought, idea, argument, ...
logical connective In logic Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously making sense of things, applying logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, la ...
between statements, where either both statements are true or both are false. The connective is
biconditional In logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit=possessed of reason, intellectual, dialectical, argumentative, translit=logikḗ)Also related to (''logos''), "word, thought, idea, argument, ...
(a statement of material equivalence), and can be likened to the standard
material conditional The material conditional (also known as material implication) is an binary operator, operation commonly used in mathematical logic, logic. When the conditional symbol \rightarrow is semantics of logic, interpreted as material implication, a fo ...
("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other (i.e. either both statements are true, or both are false), though it is controversial whether the connective thus defined is properly rendered by the English "if and only if"—with its pre-existing meaning. For example, ''P if and only if Q'' means that ''P'' is true whenever ''Q'' is true, and the only case in which ''P'' is true is if ''Q'' is also true, whereas in the case of ''P if Q'', there could be other scenarios where ''P'' is true and ''Q'' is false. In writing, phrases commonly used as alternatives to P "if and only if" Q include: ''Q is
necessary and sufficient In logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit=possessed of reason, intellectual, dialectical, argumentative, translit=logikḗ)Also related to (''logos''), "word, thought, idea, argument, ac ...
for P'', ''P is equivalent (or materially equivalent) to Q'' (compare with material implication), ''P precisely if Q'', ''P precisely (or exactly) when Q'', ''P exactly in case Q'', and ''P just in case Q''. Some authors regard "iff" as unsuitable in formal writing; others consider it a "borderline case" and tolerate its use. In logical formulae, logical symbols, such as \leftrightarrow and \Leftrightarrow, are used instead of these phrases; see below.
Definition
The
truth table A truth table is a mathematical table Mathematical tables are lists of numbers showing the results of a calculation with varying arguments. Tables of trigonometric functions were used in ancient Greece and India for applications to astronomy ...
truth table
of ''P'' \Leftrightarrow ''Q'' is as follows: It is equivalent to that produced by the XNOR gate, and opposite to that produced by the
XOR gate XOR gate (sometimes EOR, or EXOR and pronounced as Exclusive OR) is a digital logic gate A logic gate is an idealized model of computation or physical electronic device implementing a Boolean function, a logical operation performed on one ...
XOR gate
.
Usage
Notation
The corresponding logical symbols are "↔", "\Leftrightarrow", and " ", and sometimes "iff". These are usually treated as equivalent. However, some texts of
mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal sys ...
(particularly those on
first-order logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses Quantificat ...
, rather than
propositional logic Propositional calculus is a branch of logic Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously making sense of things, applying logic Logic (from Ancient Greek, Greek: grc, ...
) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas (e.g., in
metalogic Metalogic is the study of the metatheory A metatheory or meta-theory is a theory A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational th ...
). In 's
Polish notation Polish notation (PN), also known as normal Polish notation (NPN), Łukasiewicz notation, Warsaw notation, Polish prefix notation or simply prefix notation, is a mathematical notation in which operators ''precede'' their operands, in contrast t ...
, it is the prefix symbol 'E'. Another term for this
logical connective In logic Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously making sense of things, applying logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, la ...
is
exclusive nor Logical equality is a logical operator that corresponds to equality in Boolean algebra In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, struct ...
. In
TeX TeX (, see below), stylized within the system as TeX, is a typesetting system which was designed and mostly written by Donald Knuth and released in 1978. TeX is a popular means of typesetting complex mathematical formulae; it has been noted ...
, "if and only if" is shown as a long double arrow: \iff via command \iff.
Proofs
In most
logical system A formal system is used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentiall ...
s, one proves a statement of the form "P iff Q" by proving either "if P, then Q" and "if Q, then P", or "if P, then Q" and "if not-P, then not-Q". Proving these pair of statements sometimes leads to a more natural proof, since there are not obvious conditions in which one would infer a biconditional directly. An alternative is to prove the
disjunction In logic, disjunction is a logical connective typically notated \lor whose meaning either refines or corresponds to that of natural language expressions such as "or". In classical logic, it is given a truth functional semantics of logic, sema ...
"(P and Q) or (not-P and not-Q)", which itself can be inferred directly from either of its disjuncts—that is, because "iff" is
truth-function In logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit=possessed of reason, intellectual, dialectical, argumentative, translit=logikḗ)Also related to (''logos''), "word, thought, idea, argument, ac ...
al, "P iff Q" follows if P and Q have been shown to be both true, or both false.
Origin of iff and pronunciation
Usage of the abbreviation "iff" first appeared in print in John L. Kelley's 1955 book ''General Topology''. Its invention is often credited to
Paul Halmos Paul Richard Halmos ( hu, Halmos Pál; March 3, 1916 – October 2, 2006) was a HungarianHungarian may refer to: * Hungary, a country in Central Europe * Kingdom of Hungary, state of Hungary, existing between 1000 and 1946 * Hungarians, ethnic g ...
, who wrote "I invented 'iff,' for 'if and only if'—but I could never believe I was really its first inventor." It is somewhat unclear how "iff" was meant to be pronounced. In current practice, the single 'word' "iff" is almost always read as the four words "if and only if". However, in the preface of ''General Topology'', Kelley suggests that it should be read differently: "In some cases where mathematical content requires 'if and only if' and
euphony Phonaesthetics (also spelled phonesthetics in North America North America is a continent entirely within the Northern Hemisphere and almost all within the Western Hemisphere. It can also be described as the northern subcontinent of the A ...
euphony
demands something less I use Halmos' 'iff'". The authors of one discrete mathematics textbook suggest: "Should you need to pronounce iff, really hang on to the 'ff' so that people hear the difference from 'if'", implying that "iff" could be pronounced as .
Usage in definitions
Technically, definitions are always "if and only if" statements; some texts — such as Kelley's ''General Topology'' — follow the strict demands of logic, and use "if and only if" or ''iff'' in definitions of new terms. However, this logically correct usage of "if and only if" is relatively uncommon, as the majority of textbooks, research papers and articles (including English Wikipedia articles) follow the special convention to interpret "if" as "if and only if", whenever a mathematical definition is involved (as in "a topological space is compact if every open cover has a finite subcover").
Distinction from "if" and "only if"
* ''"Madison will eat the fruit if it is an apple."'' (equivalent to ''"Only if Madison will eat the fruit, can it be an apple"'' or ''"Madison will eat the fruit ''←'' the fruit is an apple"'') *: This states that Madison will eat fruits that are apples. It does not, however, exclude the possibility that Madison might also eat bananas or other types of fruit. All that is known for certain is that she will eat any and all apples that she happens upon. That the fruit is an apple is a ''sufficient'' condition for Madison to eat the fruit. * ''"Madison will eat the fruit only if it is an apple."'' (equivalent to ''"If Madison will eat the fruit, then it is an apple"'' or ''"Madison will eat the fruit ''→'' the fruit is an apple"'') *: This states that the only fruit Madison will eat is an apple. It does not, however, exclude the possibility that Madison will refuse an apple if it is made available, in contrast with (1), which requires Madison to eat any available apple. In this case, that a given fruit is an apple is a ''necessary'' condition for Madison to be eating it. It is not a sufficient condition since Madison might not eat all the apples she is given. * ''"Madison will eat the fruit if and only if it is an apple."'' (equivalent to ''"Madison will eat the fruit ''↔'' the fruit is an apple"'') *: This statement makes it clear that Madison will eat all and only those fruits that are apples. She will not leave any apple uneaten, and she will not eat any other type of fruit. That a given fruit is an apple is both a ''necessary'' and a ''sufficient'' condition for Madison to eat the fruit. Sufficiency is the converse of necessity. That is to say, given ''P''→''Q'' (i.e. if ''P'' then ''Q''), ''P'' would be a sufficient condition for ''Q'', and ''Q'' would be a necessary condition for ''P''. Also, given ''P''→''Q'', it is true that ''¬Q''→''¬P'' (where ¬ is the negation operator, i.e. "not"). This means that the relationship between ''P'' and ''Q'', established by ''P''→''Q'', can be expressed in the following, all equivalent, ways: :''P'' is sufficient for ''Q'' :''Q'' is necessary for ''P'' :''¬Q'' is sufficient for ''¬P'' :''¬P'' is necessary for ''¬Q'' As an example, take the first example above, which states ''P''→''Q'', where ''P'' is "the fruit in question is an apple" and ''Q'' is "Madison will eat the fruit in question". The following are four equivalent ways of expressing this very relationship: :If the fruit in question is an apple, then Madison will eat it. :Only if Madison will eat the fruit in question, is it an apple. :If Madison will not eat the fruit in question, then it is not an apple. :Only if the fruit in question is not an apple, will Madison not eat it. Here, the second example can be restated in the form of ''if...then'' as "If Madison will eat the fruit in question, then it is an apple"; taking this in conjunction with the first example, we find that the third example can be stated as "If the fruit in question is an apple, then Madison will eat it; ''and'' if Madison will eat the fruit, then it is an apple".
In terms of Euler diagrams
File:Example of A is a proper subset of B.svg, ''A'' is a proper subset of ''B''. A number is in ''A'' only if it is in ''B''; a number is in ''B'' if it is in ''A''. File:Example of C is no proper subset of B.svg, ''C'' is a subset but not a proper subset of ''B''. A number is in ''B'' if and only if it is in ''C'', and a number is in ''C'' if and only if it is in ''B''.
Euler diagram An Euler diagram (, ) is a diagrammatic means of representing Set (mathematics), sets and their relationships. They are particularly useful for explaining complex hierarchies and overlapping definitions. They are similar to another set diagramm ...
Euler diagram
s show logical relationships among events, properties, and so forth. "P only if Q", "if P then Q", and "P→Q" all mean that P is a
subset In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...
subset
, either proper or improper, of Q. "P if Q", "if Q then P", and Q→P all mean that Q is a proper or improper subset of P. "P if and only if Q" and "Q if and only if P" both mean that the sets P and Q are identical to each other.
More general usage
Iff is used outside the field of logic as well. Wherever logic is applied, especially in
mathematical Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ...
discussions, it has the same meaning as above: it is an abbreviation for ''if and only if'', indicating that one statement is both
necessary and sufficient In logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit=possessed of reason, intellectual, dialectical, argumentative, translit=logikḗ)Also related to (''logos''), "word, thought, idea, argument, ac ...
for the other. This is an example of
mathematical jargon The language of mathematics has a vast vocabulary A vocabulary, also known as a wordstock or word-stock, is a set of familiar words within a person's language. A vocabulary, usually developed with age, serves as a useful and fundamental tool ...
(although, as noted above, ''if'' is more often used than ''iff'' in statements of definition). The elements of ''X'' are ''all and only'' the elements of ''Y'' means: "For any ''z'' in the
domain of discourse In the formal sciences Formal science is a branch of science studying formal language disciplines concerned with formal system A formal system is used for inferring theorems from axioms according to a set of rules. These rules, which are used f ...
, ''z'' is in ''X'' if and only if ''z'' is in ''Y''."
See also
*
Equivalence relation In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...
*
Logical biconditional In logic and mathematics, the logical biconditional, sometimes known as the material biconditional, is the logical connective (\leftrightarrow) used to conjoin two statements and to form the statement " if and only if ", where is known as the ...
*
Logical equality Logical equality is a logical operator that corresponds to equality in Boolean algebra In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, struct ...
*
Logical equivalence In logic and mathematics, statements p and q are said to be logically equivalent if they are provable from each other under a set of axioms, or have the same truth value in every model (logic), model. The logical equivalence of p and q is sometimes ...
*
Polysyllogism A polysyllogism (also called multi-premise syllogism, sorites, climax, or gradatio) is a string of any number of proposition In logic and linguistics, a proposition is the meaning of a declarative sentence (linguistics), sentence. In philosophy, ...
References
External links
*
Language Log: "Just in Case"Southern California Philosophy for philosophy graduate students: "Just in Case"
{{Common logical symbols Logical connectives Mathematical terminology Necessity and sufficiency
|
__label__pos
| 0.980558 |
Reasoning about effectful programs and evaluation order
Type
Thesis
Change log
Authors
Abstract
Program transformations have various applications, such as in compiler optimizations. These transformations are often effect-dependent: replacing one program with another relies on some restriction on the side-effects of subprograms. For example, we cannot eliminate a dead computation that raises an exception, or a duplicated computation that prints to the screen. Effect-dependent program transformations can be described formally using effect systems, which annotate types with information about the side-effects of expressions.
In this thesis, we extend previous work on effect systems and correctness of effect-dependent transformations in two related directions.
First, we consider evaluation order. Effect systems for call-by-value languages are well-known, but are not sound for other evaluation orders. We describe sound and precise effect systems for various evaluation orders, including call-by-name. We also describe an effect system for Levy's call-by-push-value, and show that this subsumes those for call-by-value and call-by-name. This naturally leads us to consider effect-dependent transformations that replace one evaluation order with another. We show how to use the call-by-push-value effect system to prove the correctness of transformations that replace call-by-value with call-by-name, using an argument based on logical relations. Finally, we extend call-by-push-value to additionally capture call-by-need. We use our extension to show a classic example of a relationship between evaluation orders: if the side-effects are restricted to (at most) nontermination, then call-by-name is equivalent to call-by-need.
The second direction we consider is non-invertible transformations. A program transformation is non-invertible if only one direction is correct. Such transformations arise, for example, when considering undefined behaviour, nondeterminism, or concurrency. We present a general framework for verifying noninvertible effect-dependent transformations, based on our effect system for call-by-push-value. The framework includes a non-symmetric notion of correctness for effect-dependent transformations, and a denotational semantics based on order-enriched category theory that can be used to prove correctness.
Description
Date
2019-10-01
Advisors
Mycroft, Alan
Keywords
computational effects, evaluation order, call-by-push-value, call-by-need, categorical semantics
Qualification
Doctor of Philosophy (PhD)
Awarding Institution
University of Cambridge
Sponsorship
EPSRC (1789520)
|
__label__pos
| 0.899306 |
what is minute arm in torque
In the context of torque, a second arm, also recognised as a lever arm or torque arm, refers to the perpendicular distance between the axis of rotation and the line of action wherever the drive is applied. It plays a important position in analyzing the magnitude of torque or rotational drive exerted on an item.
The formulation to work out torque is:
Torque = Force × Minute Arm
Wherever:
– Torque is the rotational force or minute, commonly measured in models such as Newton-meters (Nm) or foot-kilos (lb-ft).
– Pressure is the utilized drive performing on the object, measured in units of pressure these kinds of as Newtons (N) or kilos (lb).
– Second Arm is the perpendicular length concerning the axis of rotation and the line of action wherever the force is used. It is measured in models these types of as meters (m) or toes (ft).
The idea of the minute arm can be illustrated with a very simple case in point: a wrench becoming made use of to tighten a bolt. When you use a pressure to the manage of the wrench, the moment arm is the length concerning the centre of rotation (the bolt) and the position where by you grip the take care of. The for a longer time the instant arm, the higher the leverage and torque you can exert on the bolt.
In summary, the minute arm in China torque arm manufacturer refers to the length involving the axis of rotation and China torque arm manufacturer the point where by the force is applied. It decides the effectiveness of the drive in developing rotational motion or torque on an object. A for China torque arm exporter a longer time second arm will allow for greater leverage and torque, although a shorter second arm outcomes in less torque.
|
__label__pos
| 0.969624 |
What is MMR Vaccine and WHAT DOES MMR STAND FOR?
MMR stands for “Measles, Mumps and Rubella”, which are types of viruses.
A measles virus infection can cause symptoms of fever, cough, stuffy nose, conjunctivitis and rash. Severe complications can lead to brain inflammation. Adults infected by the measles virus have an increased mortality risk compared to children, and measles during pregnancy can lead to premature labor or even miscarriage.
A mumps virus infection typically causes swelling of the parotid gland. Other possible complications include inflammation of the testes and ovaries. Adults infected with the mumps virus are at greater risk for more serious complications such as brain inflammation.
A fetal rubella virus infection can cause severe birth defects, or even fetal death. In children and adults, the rubella virus infection generally causes rash. Joint pain and seizures are more common complications seen in adult infections.
WHEN DOES A PATIENT NEED IT?
The measles, mumps and rubella (MMR) vaccine is administered, via injection typically into the upper arm, to prevent measles, mumps and rubella infections. In the United States, routine immunization with the MMR vaccine is recommended for all children, with the first dose administered at around 12-15 months of age, and the second dose administered at around 4-6 years of age.
In general, at least one dose of MMR vaccine should be administered to adults born in 1957 or later, unless there is either evidence of immunity to all three viruses, or there is a medical contraindication to the vaccine. Because the MMR vaccine is a live-attenuated vaccine, women who are pregnant or soon plan to become pregnant should not get this vaccine.
The importance of MMR vaccination
MMR are the viruses which unfortunately could spread with ease. However, CDC is highly recommended the use of MMR vaccine for the people to get protection against the three viruses which are mumps, measles, and rubella. MMR vaccine is highly effective and quite safe to use and has the ability to provide you better protection against 3 common viral diseases with the help of a single injection. Measles, mumps, and rubella are some of the seriously high infectious situations which has the ability to cause some serious, and potentially lethal conditions. To get protection from these situations it is important to consider MMR vaccine a better solution. For better protection and healthier life MMR vaccine is being given through two doses. CDC recommend to use the first dose MMR vaccine in children during 12 to 15 months of their ages. While the second MMR vaccine dose could be given 3 months after the first dose and is recommended to give earlier than 4 to 6 years age.
People who has received two doses of MMR vaccine at their time are usually being considered as they are protected for life from the threat of measles, mumps, and rubella issues.
Online Appointment!
Online Appointment
Stay Healthy!! Stay Strong!!
To make an appointment online at Southern Nevada Occupational Health Center (SNOHC), click here and file the form or call us at (702) 380-3989
Click Here →
|
__label__pos
| 0.795372 |
The covert orienting of visual attention following severe traumatic brain injury
J. L. Mathias, A. J. Bate, John Robertson Crawford
Research output: Contribution to journalArticle
31 Citations (Scopus)
Abstract
Attentional problems have frequently been identified following traumatic brain injuries (TBIs) using both clinical assessments and self-report measures. Unfortunately, most measures of attention do not enable us to determine the underlying basis of these attentional deficits. One exception is Posner's Covert Orienting of Attention Task (COAT), which is designed to identify some of the fundamental mental operations underlying attention. This study sought to determine whether the COAT task could identify discrete attentional deficits following TBI beyond those caused by reduced speed of information processing. Thirty five patients who had sustained a severe TBI were compared to 35 age-matched controls. Results revealed that, although the reaction times of the patients with TBI were significantly slower than the controls, there were no differences between the two groups in terms of their ability to disengage, move, and engage their attention. The introduction of a secondary (language) task produced no significant difference between the two groups on the COAT task. However, there was a significant difference between the two groups on the language-based task, suggesting a deficit in auditory-verbal attention under dual task conditions.
Original languageEnglish
Pages (from-to)386-398
Number of pages12
JournalJournal of Clinical and Experimental Neuropsychology
Volume23
Issue number3
Publication statusPublished - 2001
Keywords
• CLOSED-HEAD-INJURY
• PARKINSONS-DISEASE
• ORIENTATION
• SYSTEMS
Cite this
|
__label__pos
| 0.998037 |
The Computer Language
22.05 Benchmarks Game
fasta Julia #4 program
source code
# The Computer Language Benchmarks Game
# https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
#
# Contributed by Jens Adam
# using ideas from Julia#2, Julia#3, Go#3
struct Aminoacids
c::UInt8
p::Int32
end
const OUT = stdout
const LINE_LENGTH = 60
const IM = Int32(139968)
const IA = Int32(3877)
const IC = Int32(29573)
const last_rnd = Ref(Int32(42))
gen_random() = (last_rnd[] = (last_rnd[] * IA + IC) % IM)
function random_char(genelist)
r = gen_random()
for aminoacid in genelist
aminoacid.p >= r && return aminoacid.c
end
return genelist[end].c
end
function fillrand!(line, genelist, n)
for i in 1:n
@inbounds line[i] = random_char(genelist)
end
end
function random_fasta(genelist, n)
line = Vector{UInt8}(undef, LINE_LENGTH+1)
line[end] = UInt8('\n')
while n > LINE_LENGTH
fillrand!(line, genelist, LINE_LENGTH)
write(OUT, line)
n -= LINE_LENGTH
end
fillrand!(line, genelist, n)
line[n+1] = UInt8('\n')
write(OUT, @view line[1:n+1])
end
function repeat_fasta(str, n)
len = length(str)
# create a string with the beginning repeated at the end
# so we don't have to wrap around
src = Vector{UInt8}(undef, len + LINE_LENGTH)
for i in 1:len
@inbounds src[i] = str[i]
end
for i in 1:LINE_LENGTH
@inbounds src[i+len] = str[i]
end
i = 1
lines, rest = divrem(n, LINE_LENGTH)
for _ in 1:lines
write(OUT, @inbounds @view src[i:i+LINE_LENGTH-1])
write(OUT, '\n')
i += LINE_LENGTH
i > len && (i -= len)
end
write(OUT, @inbounds @view src[i:i+rest-1])
write(OUT, '\n')
end
function make_Aminoacids(cs, ps)
cum_p = 0.0
tmp = Aminoacids[]
for (c, p) in zip(cs, ps)
cum_p += p * IM
# the comparison is with Int32, so use it here as well
push!(tmp, Aminoacids(c, floor(Int32, cum_p)))
end
return (tmp...,)
end
# create Aminoacids with accumulated probabilities and make
# the result a constant
const IUB = let
iub_c = b"acgtBDHKMNRSVWY"
iub_p = [0.27, 0.12, 0.12, 0.27, 0.02, 0.02, 0.02,
0.02, 0.02, 0.02, 0.02, 0.02, 0.02, 0.02, 0.02]
make_Aminoacids(iub_c, iub_p)
end
const HOMOSAPIENS = let
homosapiens_c = b"acgt"
homosapiens_p = [0.3029549426680, 0.1979883004921,
0.1975473066391, 0.3015094502008]
make_Aminoacids(homosapiens_c, homosapiens_p)
end
const ALU = codeunits(
"GGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGG" *
"GAGGCCGAGGCGGGCGGATCACCTGAGGTCAGGAGTTCGAGA" *
"CCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAAT" *
"ACAAAAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCA" *
"GCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGG" *
"AGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCC" *
"AGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAA")
function main(n)
write(OUT, ">ONE Homo sapiens alu\n")
repeat_fasta(ALU, 2n)
write(OUT, ">TWO IUB ambiguity codes\n")
random_fasta(IUB, 3n)
write(OUT, ">THREE Homo sapiens frequency\n")
random_fasta(HOMOSAPIENS, 5n)
end
main(parse(Int, ARGS[1]))
notes, command-line, and program output
NOTES:
64-bit Ubuntu quad core
julia version 1.7.2
Wed, 04 May 2022 21:14:38 GMT
MAKE:
printenv JULIA_NUM_THREADS
4
0.11s to complete and log all make actions
COMMAND LINE:
/opt/src/julia-1.7.2/bin/julia -O3 --cpu-target=ivybridge --math-mode=ieee -- fasta.julia-4.julia 25000000
(TRUNCATED) PROGRAM OUTPUT:
>ONE Homo sapiens alu
GGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGA
TCACCTGAGGTCAGGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACT
AAAAATACAAAAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAG
GCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGCG
CCACTGCACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAAGGCCGGGCGCGGT
GGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGGTCA
GGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAATACAAAAA
TTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAG
AATCGCTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCCA
GCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAAGGCCGGGCGCGGTGGCTCACGCCTGT
AATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGGTCAGGAGTTCGAGACC
AGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAATACAAAAATTAGCCGGGCGTG
GTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACC
CGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCCAGCCTGGGCGACAG
AGCGAGACTCCGTCTCAAAAAGGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTT
TGGGAGGCCGAGGCGGGCGGATCACCTGAGGTCAGGAGTTCGAGACCAGCCTGGCCAACA
TGGTGAAACCCCGTCTCTACTAAAAATACAAAAATTAGCCGGGCGTGGTGGCGCGCGCCT
GTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGCGGAGG
TTGCAGTGAGCCGAGATCGCGCCACTGCACTCCAGCCTGGGCGACAGAGCGAGACTCCGT
CTCAAAAAGGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGG
CGGGCGGATCACCTGAGGTCAGGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCCG
TCTCTACTAAAAATACAAAAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCTA
CTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCCG
AGATCGCGCCACTGCACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAAGGCCG
GGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACC
TGAGGTCAGGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAA
TACAAAAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGA
GGCAGGAGAATCGCTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACT
GCACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAAGGCCGGGCGCGGTGGCTC
ACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGGTCAGGAGT
TCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAATACAAAAATTAGC
CGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCG
CTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCCAGCCTG
GGCGACAGAGCGAGACTCCGTCTCAAAAAGGCCGGGCGCGGTGGCTCACGCCTGTAATCC
CAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGGTCAGGAGTTCGAGACCAGCCT
GGCCAACATGGTGAAACCCCGTCTCTACTAAAAATACAAAAATTAGCCGGGCGTGGTGGC
GCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGA
GGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCCAGCCTGGGCGACAGAGCGA
GACTCCGTCTCAAAAAGGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGGGA
GGCCGAGGCGGGCGGATCACCTGAGGTCAGGAGTTCGAGACCAGCCTGGCCAACATGGTG
AAACCCCGTCTCTACTAAAAATACAAAAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAAT
CCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGCGGAGGTTGCA
GTGAGCCGAGATCGCGCCACTGCACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAA
AAAGGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGC
GGATCACCTGAGGTCAGGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTCT
ACTAAAAATACAAAAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGG
GAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGATC
GCGCCACTGCACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAAGGCCGGGCGC
GGTGGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGG
TCAGGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAATACAA
AAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAG
GAGAATCGCTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACT
CCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAAGGCCGGGCGCGGTGGCTCACGCC
TGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGGTCAGGAGTTCGAG
ACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAATACAAAAATTAGCCGGGC
GTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGA
ACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCCAGCCTGGGCGA
CAGAGCGAGACTCCGTCTCAAAAAGGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCA
CTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGGTCAGGAGTTCGAGACCAGCCTGGCCA
ACATGGTGAAACCCCGTCTCTACTAAAAATACAAAAATTAGCCGGGCGTGGTGGCGCGCG
CCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGCGG
AGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCCAGCCTGGGCGACAGAGCGAGACTC
CGTCTCAAAAAGGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCG
AGGCGGGCGGATCACCTGAGGTCAGGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACC
CCGTCTCTACTAAAAATACAAAAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCAG
CTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGCGGAGGTTGCAGTGAG
CCGAGATCGCGCCACTGCACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAAGG
CCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATC
ACCTGAGGTCAGGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAA
AAATACAAAAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGC
TGAGGCAGGAGAATCGCTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGCGCC
ACTGCACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAAGGCCGGGCGCGGTGG
CTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGGTCAGG
AGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAATACAAAAATT
AGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAA
TCGCTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCCAGC
CTGGGCGACAGAGCGAGACTCCGTCTCAAAAAGGCCGGGCGCGGTGGCTCACGCCTGTAA
TCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGGTCAGGAGTTCGAGACCAG
CCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAATACAAAAATTAGCCGGGCGTGGT
GGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCG
GGAGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCCAGCCTGGGCGACAGAG
CGAGACTCCGTCTCAAAAAGGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTG
GGAGGCCGAGGCGGGCGGATCACCTGAGGTCAGGAGTTCGAGACCAGCCTGGCCAACATG
GTGAAACCCCGTCTCTACTAAAAATACAAAAATTAGCCGGGCGTGGTGGCGCGCGCCTGT
AATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGCGGAGGTT
GCAGTGAGCCGAGATCGCGCCACTGCACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCT
CAAAAAGGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCG
GGCGGATCACCTGAGGTCAGGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTC
TCTACTAAAAATACAAAAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCTACT
CGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCCGAG
ATCGCGCCACTGCACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAAGGCCGGG
CGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTG
AGGTCAGGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAATA
CAAAAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGG
CAGGAGAATCGCTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGC
ACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAAGGCCGGGCGCGGTGGCTCAC
GCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGGTCAGGAGTTC
GAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAATACAAAAATTAGCCG
GGCGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCT
TGAACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCCAGCCTGGG
CGACAGAGCGAGACTCCGTCTCAAAAAGGCCGGGCGCGGTGGCTCACGCCTGTAATCCCA
GCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGGTCAGGAGTTCGAGACCAGCCTGG
CCAACATGGTGAAACCCCGTCTCTACTAAAAATACAAAAATTAGCCGGGCGTGGTGGCGC
GCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGG
CGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCCAGCCTGGGCGACAGAGCGAGA
CTCCGTCTCAAAAAGGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGGGAGG
CCGAGGCGGGCGGATCACCTGAGGTCAGGAGTTCGAGACCAGCCTGGCCAACATGGTGAA
ACCCCGTCTCTACTAAAAATACAAAAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCC
CAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGCGGAGGTTGCAGT
GAGCCGAGATCGCGCCACTGCACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAA
AGGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGG
ATCACCTGAGGTCAGGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTAC
TAAAAATACAAAAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGA
GGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGC
GCCACTGCACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAAGGCCGGGCGCGG
TGGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGGTC
AGGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAATACAAAA
ATTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGA
GAATCGCTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCC
AGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAAGGCCGGGCGCGGTGGCTCACGCCTG
TAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGGTCAGGAGTTCGAGAC
CAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAATACAAAAATTAGCCGGGCGT
GGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAAC
CCGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCCAGCCTGGGCGACA
GAGCGAGACTCCGTCTCAAAAAGGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACT
TTGGGAGGCCGAGGCGGGCGGATCACCTGAGGTCAGGAGTTCGAGACCAGCCTGGCCAAC
ATGGTGAAACCCCGTCTCTACTAAAAATACAAAAATTAGCCGGGCGTGGTGGCGCGCGCC
TGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGCGGAG
GTTGCAGTGAGCCGAGATCGCGCCACTGCACTCCAGCCTGGGCGACAGAGCGAGACTCCG
TCTCAAAAAGGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAG
GCGGGCGGATCACCTGAGGTCAGGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCC
GTCTCTACTAAAAATACAAAAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCT
ACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCC
GAGATCGCGCCACTGCACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAAGGCC
GGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCAC
CTGAGGTCAGGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAA
ATACAAAAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTG
AGGCAGGAGAATCGCTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCAC
TGCACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAAGGCCGGGCGCGGTGGCT
CACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGGTCAGGAG
TTCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAATACAAAAATTAG
CCGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATC
GCTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCCAGCCT
GGGCGACAGAGCGAGACTCCGTCTCAAAAAGGCCGGGCGCGGTGGCTCACGCCTGTAATC
CCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGGTCAGGAGTTCGAGACCAGCC
TGGCCAACATGGTGAAACCCCGTCTCTACTAAAAATACAAAAATTAGCCGGGCGTGGTGG
CGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGG
AGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCCAGCCTGGGCGACAGAGCG
AGACTCCGTCTCAAAAAGGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGGG
AGGCCGAGGCGGGCGGATCACCTGAGGTCAGGAGTTCGAGACCAGCCTGGCCAACATGGT
GAAACCCCGTCTCTACTAAAAATACAAAAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAA
TCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGCGGAGGTTGC
AGTGAGCCGAGATCGCGCCACTGCACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCA
AAAAGGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGG
CGGATCACCTGAGGTCAGGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTC
TACTAAAAATACAAAAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCG
GGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGAT
CGCGCCACTGCACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAAGGCCGGGCG
CGGTGGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAG
GTCAGGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAATACA
AAAATTAGCCGGGCGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCA
GGAGAATCGCTTGAACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCAC
TCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAAGGCCGGGCGCGGTGGCTCACGC
CTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGGTCAGGAGTTCGA
GACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAATACAAAAATTAGCCGGG
CGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTG
AACCCGGGAGGCGGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCCAGCCTGGGCG
ACAGAGCGAGACTCCGTCTCAAAAAGGCCGG
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Name Description Size
legacy-listeners
moz.build 406
resource-command.js This class helps retrieving existing and listening to resources. A resource is something that: - the target you are debugging exposes - can be created as early as the process/worker/page starts loading - can already exist, or will be created later on - doesn't require any user data to be fetched, only a type/category @param object commands The commands object with all interfaces defined from devtools/shared/commands/ 51913
tests
transformers
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Changeset 1375 for Deliverables/D4.2-4.3
Ignore:
Timestamp:
Oct 14, 2011, 5:43:46 PM (9 years ago)
Author:
mulligan
Message:
changes, fixing typos etc
File:
1 edited
Legend:
Unmodified
Added
Removed
• Deliverables/D4.2-4.3/reports/D4-2.tex
r1374 r1375
143143
144144The Matita compiler's backend consists of five distinct intermediate languages: RTL, RTLntl, ERTL, LTL and LIN.
145 A fifth language, RTLabs, serves as the entry point of the backend and the exit point of the frontend.
145A sixth language, RTLabs, serves as the entry point of the backend and the exit point of the frontend.
146146RTL, RTLntl, ERTL and LTL are `control flow graph based' languages, whereas LIN is a linearised language, the final language before translation to assembly.
147147
150150\paragraph{RTLabs ((Abstract) Register Transfer Language)}
151151As mentioned, this is the final language of the compiler's frontend and the entry point for the backend.
152 This language uses pseudoregisters, not hardware registers.\footnote{There are an unbounded number of pseudoregisters. Pseudoregisters are converted to hardware registers of stack positions during register allocation.}
152This language uses pseudoregisters, not hardware registers.\footnote{There are an unbounded number of pseudoregisters. Pseudoregisters are converted to hardware registers or stack positions during register allocation.}
153153Functions still use stackframes, where arguments are passed on the stack and results are stored in addresses.
154 During the pass to RTL, these are eliminated, and instruction selection is carried out.
154During the pass to RTL instruction selection is carried out.
155155
156156\paragraph{RTL (Register Transfer Language)}
162162RTLntl is not present in the O'Caml compiler.
163163
164 \paragraph{ERTL (Extended Register Transfer Language)}
165 In this language most instructions still operate on pseudoregisters, apart from instructions that move data to, and from, the accumulator.
164\paragraph{ERTL (Explicit Register Transfer Language)}
165This is a language very similar to RTLntl.
166However, the calling convention is made explicit, in that functions no longer receive and return inputs and outputs via a high-level mechanism, but rather use stack slots or hadware registers.
166167The ERTL to LTL pass performs the following transformations: liveness analysis, register colouring and register/stack slot allocation.
167168
Note: See TracChangeset for help on using the changeset viewer.
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Searched refs:iterations (Results 1 - 4 of 4) sorted by relevance
/PHP_5_6/sapi/isapi/stresstest/
H A Dstresstest.cpp34 DWORD iterations = 1; variable
478 " -i number of iterations per thread (default=1)\n"
503 iterations = atoi(ap_optarg);
596 for (DWORD j=0; j<iterations; j++) {
/PHP_5_6/ext/phar/phar/
H A Dpharcommand.inc719 * @param string $func Function to call on the iterations
/PHP_5_6/ext/hash/
H A Dhash.c612 /* {{{ proto string hash_pbkdf2(string algo, string password, string salt, int iterations [, int length = 0, bool raw_output = false])
619 long loops, i, j, iterations, length = 0, digest_length; local
625 if (zend_parse_parameters(ZEND_NUM_ARGS() TSRMLS_CC, "sssl|lb", &algo, &algo_len, &pass, &pass_len, &salt, &salt_len, &iterations, &length, &raw_output) == FAILURE) {
635 if (iterations <= 0) {
636 php_error_docref(NULL TSRMLS_CC, E_WARNING, "Iterations must be a positive integer: %ld", iterations);
702 for (j = 1; j < iterations; j++) {
1195 ZEND_ARG_INFO(0, iterations)
/PHP_5_6/ext/openssl/
H A Dopenssl.c266 ZEND_ARG_INFO(0, iterations)
3978 /* {{{ proto string openssl_pbkdf2(string password, string salt, long key_length, long iterations [, string digest_method = "sha1"])
3982 long key_length = 0, iterations = 0; local
3993 &key_length, &iterations,
4016 if (PKCS5_PBKDF2_HMAC(password, password_len, (unsigned char *)salt, salt_len, iterations, digest, key_length, out_buffer) == 1) {
Completed in 27 milliseconds
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| 0.973841 |
Quantification of magnetic force microscopy using a micronscale current ring
Linshu Kong, Stephen Y. Chou
Research output: Contribution to journalArticlepeer-review
59 Scopus citations
Abstract
Metal rings with inner diameters of 1 and 5 μm, fabricated using electron-beam lithography, were used to calibrate magnetic force microscopy (MFM). A MFM tip's effective magnetic charge, q, and effective magnetic moment along the tip's long axis, mz, can be determined from the MFM signal of the ring at a different scan height and a different electric current in the ring. The magnetic moments in the directions transverse to the tip's long axis were estimated by a straight current wire. It was found that for a Si tip coated with 65 nm cobalt on one side, q is 2.8×10-6 emu/cm, mz is 3.8×10-9 emu, and mx and my are in the order of 10-13 emu, which are negligible compared with mz. Furthermore, the MFMs sensitivity to the second derivative of the magnetic field was determined from the minimum ring current for a measurable MFM signal to be 0.1 Oe/nm2.
Original languageEnglish (US)
Pages (from-to)2043-2045
Number of pages3
JournalApplied Physics Letters
Volume70
Issue number15
DOIs
StatePublished - Apr 14 1997
Externally publishedYes
All Science Journal Classification (ASJC) codes
• Physics and Astronomy (miscellaneous)
Fingerprint Dive into the research topics of 'Quantification of magnetic force microscopy using a micronscale current ring'. Together they form a unique fingerprint.
Cite this
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| 0.974308 |
Displaying File Size Metadata
Steps for displaying a table's File Size report and the metadata about the table's file's size distribution.
Describes how to open a table's File Size report and the metadata of a file.
1. In a supported browser, log in to Workload XM.
2. In the Search field of the Clusters page, enter the name of the cluster whose workloads you want to analyze.
3. From the navigation panel under Data Warehouse, select File Size Report.
4. In the File Size Report page, either search for a specific table, or locate the table by sorting the tables by the number of files, the number of partitions, or the table size.
For example, the File Size Reports shows that the Animantarx table has 7 million files and 913 partitions.
5. To display details about the table's file size distribution, select a table name.
For example, the following table's details window shows that the Aerosteon table uses 42 data files that range from 10 to 24.5 GiB and the graph displays the Q1 and Q3 file size distribution.
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| 0.717681 |
TY - INPR A1 - Vieten, Peter T1 - Functions of bounded semivariation and countably additive vector measures N2 - In the Banach space co there exists a continuous function of bounded semivariation which does not correspond to a countably additive vector measure. This result is in contrast to the scalar case, and it has consequences for the characterization of scalar-type operators. Besides this negative result we introduce the notion of functions of unconditionally bounded variation which are exactly the generators of countably additive vector measures. T3 - Preprints (rote Reihe) des Fachbereich Mathematik - 297 KW - Function of bounded variation KW - Integral transform Y1 - 1997 UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/823 UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-7929 ER -
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| 0.968144 |
Introduction
Detailed theoretical considerations of narrow-gap insulators date back to the 1960s, when it was realized that if the energy required to form an electron-hole pair becomes negative, a phase transition into an excitonic insulator state can occur1,2,3,4. Unscreened electron-hole Coulomb attraction is perhaps the most obvious driving force behind this phase transition, and excitonic charge insulator states are indeed thought to occur in materials such as TmSe0.45Te0.55, 1T-TiSe2, and Ta2NiSe55,6,7,8,9. Although less intuitive, effective electron-hole attraction can also arise from on-site electron-electron Coulomb repulsion U via magnetic exchange interactions between the electron and hole10. In this case, the soft exciton is expected to be a spin-triplet, which passes through a quantum critical point (QCP) with increasing effective U. The condensation of the relevant triplet exciton at the QCP gives rise to an antiferromagnetic ground state hosting a well-defined excitonic longitudinal mode4, which coexists with transverse modes that are a generic feature of ordered antiferromagnets. This longitudinal mode features excitonic character, in the sense that it modifies the local spin amplitude by creating electron-hole pairs4. In this work, we identify and study a longitudinal mode in Sr3Ir2O7, the presence of which is the key experimental signature of an antiferromagnetic excitonic insulator.
Results
The formation of an antiferromagnetic excitonic insulator requires a very specific set of conditions. We need (i) a charge gap of similar magnitude to its magnetic energy scale and (ii) strong easy-axis anisotropy. Property (i) is a sign that the material is close to the excitonic QCP (see Fig. 1). Property (ii) is not a strict condition, but it facilitates the identification of an antiferromagnetic excitonic insulator, because the opening of a spin gap Δs protects the longitudinal mode from decay. This is because longitudinal fluctuations are often kinetically predisposed to decay into transverse modes generating a longitudinal continuum with no well-defined modes. This decay can be avoided when the energy of the longitudinal mode is lower than twice the spin gap. Iridates host strong spin-orbit coupling (SOC), which can help realize a large spin gap and bilayer Sr3Ir2O7 shown in Fig. 2a is known to have a narrow charge gap of order Δc ~ 150 meV11. The essential magnetic unit, with c-axis ordered moments, is shown in Fig. 2b12. In view of the antiferromagnetic order in Sr3Ir2O7, the material would be predicted to lie in the magnetically ordered region to the right of the QCP where the excitonic longitudinal mode is expected to appear. Because the exciton is predicted to have odd parity under exchange of the two Ir layers, we expect the excitonic longitudinal mode to be present at c-axis wavevectors corresponding to antisymmetric bilayer contributions and absent at the symmetric condition. We label these wavevectors qc = 0.5 and qc = 0, respectively. In contrast, transverse magnetic modes are expected to be present at all c-axis wavevectors, allowing the transverse and longitudinal modes to be readily distinguished.
Fig. 1: Antiferromagnetic excitonic insulator phase diagram.
figure 1
Charge excitations in paramagnetic band insulators consist of either electron-hole excitations across the insulating band gap (brown shaded area) or of bound electron-hole excitons below the particle-hole continuum [electrons (holes) are indicated with filled (empty) circles]. An antiferromagnetic excitonic insulator is established through the condensation of the predominately spin-triplet character exciton mode with spin quantum number Sz = 0. The excition is a superposition of an up-spin electron in the conduction band paired with an up-spin hole (equivalent to a down-spin electron) and a down-spin electron paired with a down-spin hole4. The other spin-triplet excitions Sz = ±1 feature an up-spin electron and a down-spin hole or a down-spin electron and an up-spin hole. Upon increasing Coulomb interaction U the Sz = 0 exciton condenses into the ground state at a QCP4, establishing magnetic order and leaving an excitonic longitudinal mode as the key signature of this state.
Fig. 2: Isolating the excitonic longitudinal mode in Sr3Ir2O7.
figure 2
a Crystal structure of the bilayer material Sr3Ir2O7. b Ir-Ir bilayer with t1 the nearest-neighbor, t2 the next-nearest-neighbor and tz(α) the interlayer hopping terms. ce RIXS spectra measured at T = 20 K and Q = (0, 0, L) with L = 25.65, 26.95 and 28.25 in reciprocal lattice units. The c-axis positions are also labeled in terms of the Ir-Ir interlayer reciprocal-lattice spacing qc = 0, 0.25 and 0.5. An additional mode appears around 170 meV with maximal intensity at qc = 0.5 (see shaded red area). The black circles represent the data and dotted lines outline the different components of the spectrum, which are summed to produce the grey line representing the total spectrum. Error bars are determined via Poissonian statistics.
The excitation spectrum of Sr3Ir2O7 was studied with RIXS. Figure 2c–e displays energy-loss spectra at T = 20 K, well below the Néel temperature TN = 285 K and qc = 0, 0.25 and 0.5, corresponding to L = 25.65, 26.95 and 28.25 in reciprocal lattice units (r.l.u.). These irrational L values arise because the bilayer separation d is not a rational fraction of the unit cell height c (see Methods section for details). The spectrum at qc = 0 is composed of a phonon-decorated quasi-elastic feature, a pronounced magnetic excitation at ~ 100 meV, which we later identified as the transverse mode, and a high-energy continuum. As explained above, changing qc is expected to isolate the anticipated excitonic mode. A longitudinal mode is indeed observed, reaching maximum intensity at qc = 0.5, and is highlighted by red shading in Fig. 2d, e.
In isolation, the presence of a longitudinal magnetic mode in this symmetry channel is a necessary but insufficient condition to establish an antiferromagnetic excitonic insulator, so we leverage the specific symmetry, decay, and temperature dependence of the longitudinal and transverse magnetic modes to establish the presence of the novel state. The only other candidate magnetic model that hosts a longitudinal mode of this type is a specific configuration of the bilayer Heisenberg Hamiltonian, in which the charge degrees of freedom are projected out. In particular, a model with a c-axis magnetic exchange Jc that is larger than, but not dramatically larger than, the in-plane exchange Jab is needed to produce a longitudinal mode and large easy-axis magnetic anisotropy is required to reproduce the spin gap. If JcJab, the spectrum would show only a spin-wave-like in-plane dispersion contrary to the observed qc dependence in Fig. 2c–e, and in the JcJab limit the system would become a quantum paramagnet. For Jc/Jab of order two, the bilayer Heisenberg Hamiltonian supports a longitudinal mode and for the current case of large easy-axis anisotropy, the transverse and longitudinal modes appear as well-defined modes throughout the Brillouin zone13,14,15,16. In fact, earlier reports have proposed this spin dimer model to explain RIXS measurements of the longitudinal ~ 170 meV feature in Sr3Ir2O714, 17. Although prior and subsequent non-dimerized models have also been proposed to describe Sr3Ir2O7 as rival candidates12, 18,19,20,21. These models, however, do not support a longitudinal mode (a detailed comparison between the different models is given in Supplementary Information (SI) Section 1). We, therefore, map the in-plane dispersion relations at qc = 0 and 0.5 and show them in Fig. 3a, b. At qc = 0, where the longitudinal mode is suppressed by symmetry, we observe an excitation dispersing from ~ 90 to 170 meV and a continuum at higher energies. Simultaneously analyzing qc = 0.5 and qc = 0 for each in-plane reciprocal-lattice wavevector, while leveraging the distinct symmetry properties of the longitudinal and transverse modes, allows us to isolate the longitudinal mode (see Methods section). We plot the position and peak width of the longitudinal mode in green in Fig. 3b. The transverse mode, on the other hand, is symmetry-allowed at qc = 0.5 and qc = 0 and is shown in black on Fig. 3a, b. We find that the longitudinal mode is well-defined around (0, 0) (Figs. 2c–d, 3i), but decays into the high-energy continuum as it disperses away, becoming undetectable at (1/4, 1/4) (Fig. 3h). The longitudinal mode is also detectable as a shoulder feature on the transverse mode at (1/2, 1/2) before dispersing upwards and broadening at neighboring momenta (Fig. 3e, g). The decay and merging of the longitudinal mode into the electron-hole continuum was not detected previously and suggests the realization of an antiferromagnetic excitonic insulator state because the longitudinal mode in this model has a bound electron-hole pair character and therefore will necessarily decay when it overlaps with the electron-hole continuum. This longitudinal mode decay is incompatible with a longitudinal mode arising from spin dimer excitations in a strongly isotropic bilayer Heisenberg model, which predicts well-defined modes throughout the Brillouin zone and projects out the high-energy particle-hole continuum13,14,15,16.
Fig. 3: Magnetic dispersion and excitonic longitudinal mode decay.
figure 3
a, b In-plane momentum dependence of the magnetic excitations measured at qc = 0 and 0.5. The black and green symbols correspond to the energy of the magnetic modes and the vertical bars to their peak widths. Both quantities were extracted from the energy spectra at different points in reciprocal space (such as shown in panels e–j and Fig. 2c–e). c and d Theoretical calculations of the magnetic dispersion relation, overplotted with the experimentally determined excitation energies and line widths. The presence of the mode at qc = 0.5 that is absent at qc = 0 evinces that this is an excitonic longitudinal mode. ej RIXS spectra at reciprocal space as highlighted by color-matching arrows in panel a. Circles represent the data and dotted lines outline the different components of the spectrum, which are summed to produce the solid line representing the total spectrum. Error bars are determined via Poissonian statistics. The isolation of the longitudinal mode (highlighted with red shading) from other contributions was possible by simultaneously analyzing qc = 0.5 and qc = 0 for each in-plane reciprocal-lattice wavevector (see Methods section for details).
Since optical conductivity, tunneling spectroscopy, and photo-emission studies all report charge gaps Δc on the same energy scale of magnetic excitations (100–200 meV)11, 22,23,24,25, we model the microscopic interactions within a Hubbard Hamiltonian that retains the charge degree of freedom. In particular, the crucial difference with the Heisenberg description is that the Hubbard model retains the electron-hole continuum, whose lower edge at ω = Δc is below the onset of the two-magnon continuum: Δc < 2Δs. We considered a half-filled bilayer, which includes a single “Jeff = 1/2” effective orbital for each of the two Ir sites in the unit cell, following methods developed in parallel with this experimental study26. The model contains an effective Coulomb repulsion U, and three electron hopping parameters: nearest and next-nearest in-plane hopping terms tν (ν = 1, 2) within each Ir layer, and the spin dependent hopping strength tz(α) between Ir layers (Fig. 2b). tz(α) is composed of an amplitude tz and a phase α arising from the appreciable SOC in the material (further details are given in the Methods section)27. The model was solved using the random phase approximation (RPA) in the thermodynamic limit (SI Section 2), which is valid for intermediately correlated materials even at finite temperature28. We constrain tν and tz to values compatible with density functional theory and photo-emission measurements and consider the effective U, which is strongly influenced by screening, as the primary tuning parameter29. Figure 3c, d show the results of calculations with t1 = 0.115 eV, t2 = 0.012 eV, tz = 0.084 eV, α = 1.41, and U = 0.325 eV. The small U is due to the extended Ir orbitals and because this effective parameterization reflects the difference between on-site and longer-range interactions in the real material. The model identifies the quasiparticle dispersion at qc = 0 as the transverse mode with a persistent well-defined nature even at high energies. Above the transverse mode, the spin response is fundamentally influenced by the finite charge gap. A broad continuum involving electron-hole spin transitions across the charge gap is present for all qc values covering a broad energy-momentum range. A new mode emerges around (0, 0) and (0.5, 0.5) for qc = 0.5, which we identify as the excitonic longitudinal mode.
To understand the excitonic longitudinal mode discussed, we first note that the tight-binding band structure analysis of Sr3Ir2O7 suggests that it would be a narrow-gap band insulator or semi-metal even when Coulomb repulsion is neglected29. This occurs due to bonding-antibonding band splitting arising from the bilayer hopping alongside SOC, generating a minimum of the conduction band dispersion near the Brillouin zone center and a maximum in the valence band dispersion near the antiferromagnetic zone center. A finite value of U in a quasi-two-dimensional bilayer structure such as Sr3Ir2O7 produces an attractive particle-hole interaction in the triplet channel because of the well-known direct-exchange mechanism. In turn, particle-hole pairs at wavevectors favored by the band structure form bound states, i.e., excitons, in the magnetic channel appearing at qc = 0.5, because of the odd parity of the exciton under exchange of the two layers. The spin anisotropy arising from SOC splits the exciton triplet into a low energy state with c-axis spin quantum number Sz = 0 and higher energy Sz = ± 1 states. Strictly speaking, SOC means that total spin is not a good quantum number, but we retain the singlet-triplet labels for clarity. As shown in the schematic representation in Fig. 1, the Sz = 0 exciton condenses to form magnetic order at a wavevector of (0.5, 0.5) (qc = 0.5). The corresponding QCP, which exists at U = Uc = 0.27 eV (for t1 = 0.115 eV), then signals the onset of the antiferromagnetic excitonic insulator state in Sr3Ir2O7. Within the ordered state, what was a gapless Sz = 0 exciton mode at U = Uc becomes a gapped excitonic longitudinal mode for U > Uc. The existence and relatively low energy of this mode implies that U in Sr3Ir2O7 is only slightly above Uc. This property, together with the sufficiently large transverse mode gap Δs, protects the excitonic longitudinal mode from decay into pairs of transverse modes. The longitudinal mode’s bound electron-hole pair nature is especially vividly illustrated by its smooth merging with the particle-hole continuum away from (0.5, 0.5) and (0, 0). We plot the layer-resolved charge structure of the exciton in SI Section 3.
When heating an antiferromagnetic excitonic insulator, thermal fluctuations modify the magnetic properties via two different processes. The first one corresponds to the destruction of Néel order via softening of the longitudinal mode. This softening signals the exciton condensation below T = TN. The second process, that takes place at a higher temperature T*, corresponds to thermal breaking of the excitons (unbinding of particle-hole pairs). A RIXS temperature series designed to test this idea at different high symmetry locations is plotted in Fig. 4a–d (linecuts at selected temperatures are shown in Supplementary Fig. S2). As expected, heating up from base temperature towards TN enhances the decay of the modes into the electron-hole continuum broadening the spectra and making it difficult to isolate the two modes in a single spectrum. We can, however, leverage the symmetry properties of the modes at different reciprocal space points to clarify the soft mode phenomenology. Since the transverse mode occurs at the same energy independent of qc, and the longitudinal mode is present at qc = 0.5 and absent at qc = 0, the transverse mode temperature dependence can be studied in isolation at qc = 0 (Fig. 4a, b). We observe that this mode has only minimal detectable softening, which is expected in view of the Ising nature of magnetism. In contrast, a substantial softening is seen at (0.5, 0.5) in Fig. 4d. Although both modes are present at qc = 0.5, we know from qc = 0 measurements that the transverse mode displays only minimal softening. Thus the longitudinal mode must play a major role in the softening to form the antiferromagnetic state. Our observed phenomenology is only captured with the intermediate coupling regime (U/t1 = 2.83) that we conclude is relevant for Sr3Ir2O7. The strong coupling limit (U/t1 1) would require a charge gap much larger than the observed values of 100–200 meV and, to our knowledge, it has not been able to predict any aspects of the temperature-dependent phenomenology of Sr3Ir2O7. The excitonic insulator model is also supported by our temperature-dependent calculations, which are shown as dashed lines in Fig. 4c, d. Full calculations are shown in Supplementary Fig. S5 and explained in SI Section 2. Theory shows that exciton formation takes place at T* ≈ 2TN, controlled by the exciton binding energy, which is of order the charge gap minus the longitudinal mode energy at the ordering wavevector. The mean-field transition temperature prediction is TN = 424 K, which is not too far above the measured TN = 285 K and which is expected since fluctuations are expected to reduce TN below the mean-field prediction. The predictions in Fig. 4c, d are shown with temperatures re-normalized to the experimental TN.
Fig. 4: Excitonic mode condensation at the Néel temperature.
figure 4
ad Temperature dependence of the Sr3Ir2O7 excitation spectrum at (0, 0) and (0.5, 0.5) for qc = 0 and 0.5 (RIXS spectra at selected temperatures are shown in Supplementary Fig. S2). The intensity at (0.5, 0.5) has been scaled for comparison reasons. The dashed lines show temperature-dependent calculations of our model (the full theoretical predictions are plotted in Supplementary Fig. S5). Based on the qc behavior of the modes, we know that panels a, b show only the transverse mode, while c, d show both the transverse and longitudinal mode. e, f Quasi-elastic intensity as function of temperature for qc = 0 and 0.5 in blue and red, respectively. The non-monotonic enhancement at qc = 0.5 in e provides additional support that the condensation of the excitonic longitudinal mode establishes the magnetic long-range order in Sr3Ir2O7. Panel f also shows the anomalous temperature dependence of the electric resisitivity ρ (taken from30), which shows a change in gradient at TN further indicating that charge fluctuations are involved in the transition.
The involvement of the longitudinal mode in magnetic long-range order is also evident from the temperature dependent quasi-elastic intensity. While most spectra feature the expected gradual enhancement in the quasi-elastic channel upon increasing temperature (Fig. 4e for (0, 0) and S2 for other reciprocal-lattice positions), the (0.5, 0.5) spectrum at qc = 0.5 displays a pronounced rise of intensity around TN (Fig. 4f). Note that neither qc = 0 nor qc = 0.5 correspond to the magnetic Bragg peak location, because the bilayer separation is incommensurate with respect to the c-axis lattice constant. Since in our setup qc = 0 is closer to a magnetic Bragg peak than qc = 0.5, we can exclude critical scattering from the long-range antiferromagnetic order as a significant contributor to this intensity as it would predict the opposite intensity behavior to what we observe (a more extensive demonstration of this is in SI Section 5). Thus the observed quasi-elastic anomaly at TN is indicative of substantial longitudinal mode condensation. The excitonic insulator character of the ground state is further supported by a large increase in resistivity below TN (see Fig. 4f)30, as the condensation of the excitonic mode leads to a reduction in the electronic carriers participating in electrical transport. This property is distinct from what is expected for a strongly-coupled Mott insulator (i.e., the large U limit of Fig. 1) where all charge-related processes are frozen out. The resistivity increase below TN could, in principle, also arise from Slater-type interactions, which can open a charge gap upon magnetic ordering. Sr3Ir2O7, however, lacks strong Fermi surface nesting23,24,25, 29 and is in the intermediately correlated (t1 ~ U) rather than the weakly correlated (t1U) regime, so the Slater mechanism is expected to have minimal relevance.
Discussion
In summary, we have isolated and characterized a longitudinal magnetic mode in Sr3Ir2O7, which merges with the electron-hole continuum at certain points in the Brillouin zone, and which softens upon heating concurrent with a decrease in the material’s resistivity. These properties are consistent with those of an antiferromagnetic excitonic insulator state4. We substantiate this via calculations of a bilayer Hubbard model, in which electron-hole pairs are bound by magnetic exchange interactions between the electron and hole. This consistently explains all the electronic and magnetic properties of Sr3Ir2O7 based on only one free parameter U, since all other parameters are strongly constrained by the electronic band structure of the material. The totality of these results identifies Sr3Ir2O7 as a compelling candidate for the long-sought-after antiferromagnetic excitonic insulator.
Looking to the future, the intrinsically coupled spin and charge degrees of freedom in this state could have the potential for realizing new functionalities31, and suitably tuned material and/or laser-based approaches could realize methods to photo-excited these modes32. Further research on the topic may also include efforts to identify materials closer to the QCP, which in our study occurs at U/t1 = 2.35. This could extend the reciprocal space regions where the excitonic longitudinal mode exists. Another interesting direction would involve identifying excitonic easy-plane, rather than easy-axis, bilayer systems. These would host a different kind of soft excitonic longitudinal mode, often called “Higgs” mode, and could be used to study Higgs decay and renormalization effects in the presence of strong charge fluctuations. Careful selection of materials with multiple active orbitals could realize orbitally-ordered excitonic insulator states. Experimental realizations using chemical substitutions, strained thin films, high pressure, or different bilayer materials, including ruthenates, osmates, and other iridates, may help to answer some of these intriguing questions.
Methods
Samples
Sr3Ir2O7 single crystals were synthesized using the flux method33. Starting materials of IrO2, SrCO3, and SrCl2 6H2O were mixed with a molar ratio of 1:2:20, and heated at 1200 C for 10 h in a platinum crucible. The melt was then cooled to 800°C at a rate of 3 C/h, before quenching to room temperature. We index reciprocal space using a pseudo-tetragonal unit cell with a = b = 3.896 Å and c = 20.88 Å at room temperature.
Resonant inelastic X-ray scattering (RIXS) setup
RIXS spectra were measured at the 27-ID-B station of the Advanced Photon Source at Argonne National Laboratory. The incident x-ray beam was tuned to the Ir L3-edge at 11.215 keV and monochromated using a Si (884) channel-cut monochromator. The exact x-ray energy was refined via resonant energy of a standard IrO2 and the Sr3Ir2O7 sample and was set 3 eV below the resonant edge. Scattered photons were analyzed using a spherically bent diced silicon (844) analyzer with a curvature radius of 2 m. The energy and Q-resolution were 32.0(2) meV and 0.105 Å−1 full-width at half-maximum (FWHM), respectively. A small background contribution arising from air scattering was removed by subtracting a constant value from the measured intensity. The value was determined by fitting the intensity on the energy-gain side of the spectra.
The L values in Fig. 2c–e were chosen such that they correspond to specific reciprocal-lattice positions with respect to the Ir-Ir interlayer spacing (see also Fig. 2a), i.e., G + qc = Ld/c, where G is an integer, qc the reduced c-axis reciprocal lattice position in terms of the Ir-Ir spacing, d = 4.07 Å the shortest Ir-Ir interlayer spacing and c = 20.88 Å the out-of-plane lattice constant. qc equals 0, 0.25 and 0.5 for L = 25.65, 26.95 and 28.25, respectively.
The magnetic dispersions in Fig. 3a, b were measured along (H1, K1, 25.65) and (H2, K2, 28.25) with H1 and K1 ranging between 0.5 and 1 and H2 and K2 between 0 and 0.5. The particular Brillouin zones were chosen to ensure a scattering geometry close to 90, minimizing Thompson scattering. For (0, 0, 25.65), (1, 1, 25.65), (0, 0, 26.92) and (0, 0, 28.25), 2θ = 85.5, 90.2, 90.9 and 96.8, respectively. The sample was aligned in the horizontal (H, H, L) scattering plane, such that both dispersions could be probed through a sample rotation of Δχ ≤ 4.1 relative to the surface normal.
Analysis of the RIXS data
The spectra were analyzed by decomposing them into four components: (1) A quasi-elastic contribution (possibly containing contributions from phonons) which was modeled using a pseudo-Voigt energy resolution function, along with an additional low energy feature, which was modeled using the resolution functions at ± 32 meV, whose relative weights were constrained to follow the Bose factor. (2) The transverse magnetic mode was accounted for by a pseudo-Voigt function multiplied with an error function to capture the high-energy tail arising from the interactions with continuum. The interactions are enhanced when the modes and the continuum are less separated in energy, which leads to a reduced quasiparticle lifetime. In this case, we used a damped harmonic oscillator (with Bose factor) that was convoluted with the resolution function, which was further multiplied by an error function. (3) The longitudinal mode was described by either a pseudo-Voigt function or a damped harmonic oscillator, depending on whether or not it was resolution limited. (4) The magnetic continuum was reproduced using a broad damped harmonic oscillator multiplied by an error function to mimic its onset.
The excitonic longitudinal mode is strongly qc dependent, whereas the transverse magnetic mode and the magnetic continuum vary very weakly with qc. Thus, we analyzed the spectra measured at qc = 0 and qc = 0.5 simultaneously to disentangle the excitonic contribution from the other components. The positions and lineshapes of the transverse magnetic mode and the electron-hole magnetic continuum were constrained to be independent of qc, i.e., only the amplitudes were varied. The extra peaks at qc = 0.5 give information about the excitonic longitudinal mode. During the procedure, the elastic energy was allowed to vary to correct for small fluctuations of the incident energy.
Theoretical model
Sr3Ir2O7 hosts Ir4+ ions, which have 5 electrons in the active Ir 5d5 valance band. The dominant splitting of this band comes from the close-to-cubic crystal field leaving empty eg states and 5 electrons in the t2g states. SOC further splits the t2g manifold into a full Jeff = 3/2 orbital a half-filled Jeff = 1/2 orbital at the Fermi level34. Our model involves projecting the band structure onto this Jeff = 1/2 doublet. The basic structural unit, shown in Fig. 2b, contains two Ir atoms, so the experimental data were interpreted using a half-filled bilayer Hubbard model H = − HK + HI with HI = Urnrnr and
$${H}_{{{{{{{{\rm{K}}}}}}}}}=\mathop{\sum}\limits_{{{{{{{{\boldsymbol{r}}}}}}}},{{{{{{{{\boldsymbol{\delta }}}}}}}}}_{\nu }}{t}_{\nu }{c}_{{{{{{{{\boldsymbol{r}}}}}}}}}^{{{{\dagger}}} }{c}_{{{{{{{{\boldsymbol{r}}}}}}}}+{{{{{{{{\boldsymbol{\delta }}}}}}}}}_{\nu }}+\mathop{\sum}\limits_{{{{{{{{{\boldsymbol{r}}}}}}}}}_{\perp }}{c}_{({{{{{{{{\boldsymbol{r}}}}}}}}}_{\perp },1)}^{{{{\dagger}}} }{t}_{z}(\alpha ){c}_{({{{{{{{{\boldsymbol{r}}}}}}}}}_{\perp },2)}+{{{{{{{\rm{H}}}}}}}}.{{{{{{{\rm{c}}}}}}}}.,$$
(1)
where tν (ν = 1, 2) are the nearest- and next-nearest-neighbor hopping amplitudes within the square lattice of each Ir-layer, and \({t}_{z}(\alpha )=| {t}_{z}| {e}^{i\frac{\alpha }{2}{\varepsilon }_{{{{{{{{\boldsymbol{r}}}}}}}}}{\sigma }_{z}}\), with σz the Pauli matrix describes the Jeff spin dependent hopping strength between layers. The overall phase was chosen to gauge away the phase for tν. The operator \({c}_{{{{{{{{\boldsymbol{r}}}}}}}}}^{{{{\dagger}}} }\) = [\({c}_{\uparrow ,{{{{{{{\boldsymbol{r}}}}}}}}}^{{{{\dagger}}} }\), \({c}_{\downarrow ,{{{{{{{\boldsymbol{r}}}}}}}}}^{{{{\dagger}}} }\)] creates the Nambu spinor of the electron field at r = (r, l) with l = 1, 2 denoting the layer index and r = r1a1 + r2a2. Here, the primitive in-plane lattice vectors are denoted by a1 and a2, and the directed neighboring bonds are represented by δ1 = a1, a2 and δ2 = a1 ± a2. In the interaction term HI, U is the effective Coulomb interaction, and nrσ is the density operator for electrons of spin σ at r. In the spin dependent hopping term, the sign εr takes the values ± 1 depending on which sublattice of the bipartite bilayer system r points to. The phase α arises from hopping matrix elements between dxz and dyz orbitals, which are allowed through the staggered octahedral rotations in the unit cell along side SOC27, 35. In the model, SOC enters via the phase of the c-axis hopping, which is smaller than the in-plane bandwidth, justifying the approximate use of singlet and triplet for labels of the different excitons. The model was studied at half-filling in the sense that it contains two bands (bonding and antibonding) in the model, which host two electrons as is appropriate for Sr3Ir2O723,24,25, 27. We solved the model using the RPA in the thermodynamic limit (detailed information is given in SI Section 2), which is valid for intermediately correlated materials even at finite temperatures28. The theoretically determined Néel temperature, in this case, is \({T}_{\,{{\mbox{N}}}}^{{{\mbox{cal}}}\,}=424\) K which is slightly larger than the experimental value TN = 285 K. This is expected within the RPA we use here, as this ignores fluctuations than act to reduce the transition temperature. The dynamical spin structure factors in Fig. 3c, d are shown after convolution with the experimental resolution.
A more complex model could include all t2g or all d orbitals, rather than just effective Jeff = 1/2 doublets. The success of our Jeff = 1/2 only model suggests that orbital degrees of freedom are entirely frozen out of the problem or manifest themselves in very subtle ways beyond current detection limits. Due to this, the Sr3Ir2O7 excitonic insulator state has no orbital component (other than in the trivial sense that the Jeff = 1/2 states in themselves are a coupled modulation of spin and orbital angular momentum). A possible SOC-induced orbital order is discussed in SI Section 6.
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| 0.830368 |
Laravel Working With Json Table Column Example
How to Store multiple values in single field laravel is the todays topic. Sometimes we need to store multiple key and value in single column in Laravel. But do you know how we can do that? we can use pivot table to solve this issue. But here i am going to use json column to store multiple records with key and value for respect to key.
From this laravel json tutorial you will also learn how to insert json data into mysql using laravel. In this tutorial we will insert multiple properties for a single product like size, price, value, color etc from a single method into a single field with json.
So let's se how we can store json data into database. So let's start laravel json column example tutorial.
Preview : Store json data form
store-json-data-laravel
Preview : After fetching json data
laravel-working-with-json
Step 1 : Create Model
In this we need product model. So let's create it to store json data.
php artisan make:model Product -m
Now open product model and update like below.
app/Product.php
namespace App;
use Illuminate\Database\Eloquent\Model;
class Product extends Model
{
protected $guarded = [];
protected $casts = [
'properties' => 'array'
];
public function setPropertiesAttribute($value)
{
$properties = [];
foreach ($value as $array_item) {
if (!is_null($array_item['key'])) {
$properties[] = $array_item;
}
}
$this->attributes['properties'] = json_encode($properties);
}
}
and open migration file and update it like below.
database/migration/create_products_table.php
public function up()
{
Schema::create('products', function (Blueprint $table) {
$table->increments('id');
$table->string('name');
$table->decimal('price', 15, 2);
$table->json('properties');
$table->timestamps();
});
}
Step 2 : Create Route
We need many route for storing json data into json column.
routes/web.php
Route::get('produc/create','ProductController@show_product_form')->name('produc.create');
Route::post('produc/create','ProductController@store');
Route::get('produc','ProductController@index')->name('produc.index');
Step 3 : Create Controller
In this step we need to create product controller. So create it and update this controller like below
app/Http/Controllers/ProductController.php
namespace App\Http\Controllers;
use App\Category;
use App\Http\Controllers\Controller;
use App\Product;
use Illuminate\Http\Request;
class ProductController extends Controller
{
public function show_product_form()
{
return view('create');
}
public function store(Request $request)
{
$product = Product::create($request->all());
return redirect()->back();
}
public function index()
{
$post = Product::all();
return view('index',['products' => $post]);
}
}
Step 4 : Create Blade File
Now we are in the final step and all are set to go. So how to insert json data into mysql using laravel we will know. Now create below file and paste this code in your file.
resources/views/create.blade.php
resources/views/index.blade.php
Recommended : Avoid Pivot Table and Use Json Column in Laravel
Hope this Laravel json tutorial will help you.
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SharePoint Online Permission
SharePoint Online Permission Management: Best Practices
30 August 2023
SharePoint Migration
In the modern business landscape, effective collaboration and data security are paramount. Microsoft SharePoint Online stands as a pivotal platform for organizations, offering a robust environment for teamwork and content management. However, harnessing its full potential requires a comprehensive understanding of SharePoint Online permissions. This article delves into the intricacies of permission management in SharePoint Online, shedding light on best practices that empower organizations to maintain a secure and productive digital workspace.
Understanding SharePoint Online Permissions
SharePoint Online permissions revolve around controlling access to sites, lists, libraries, folders, and documents. The goal is to ensure that the right individuals can access the right content, while also preventing unauthorized users from gaining entry. To accomplish this, SharePoint employs a permission model that encompasses three key components:
1. Users and Groups: SharePoint Online leverages Microsoft 365 user accounts and groups to define access. Users are granted specific roles and permissions, while groups allow for simplified management by assigning permissions collectively.
2. Roles and Permissions: Permissions are grouped into predefined roles that dictate the actions a user can perform. These roles include Full Control, Edit, Contribute, Read, and Limited Access. Permissions can be fine-tuned to control activities such as viewing, editing, deleting, and sharing.
3. Inheritance and Break Inheritance: SharePoint uses inheritance by default, allowing permissions assigned to a parent object, such as a site, to cascade down to its child objects, like lists or documents. However, organizations can choose to break inheritance, enabling granular control over permissions at each level.
Best Practices for SharePoint Online Permission Management
1. Plan Permissions Strategically:
Before diving into permission management, craft a comprehensive plan. Identify user roles, content categories, and the level of access required. This proactive approach ensures a well-organized permission structure that aligns with business needs.
1. Utilize SharePoint Groups:
Leverage SharePoint groups to simplify permission management. Instead of individually assigning permissions to users, associate permissions with groups. This approach streamlines the process and enhances maintainability.
1. Limit Permissions:
Adhere to the principle of least privilege. Grant users only the permissions necessary for their roles. Avoid granting overly broad permissions, as this can lead to data leakage and security vulnerabilities.
1. Regularly Review and Update Permissions:
Business dynamics change, and so should permissions. Regularly review and adjust permissions as users’ roles evolve. This practice prevents obsolete permissions and unauthorized access.
1. Leverage Inheritance:
Whenever possible, maintain permission inheritance. Breaking inheritance should be a deliberate action, as it can complicate management. Only do so when there is a specific need for distinct permissions.
1. Audit Permissions:
Implement regular audits to ensure permissions are accurate and aligned with organizational requirements. Identify and rectify any discrepancies promptly to maintain a secure environment.
1. Implement Site Policies:
Establish clear site-level policies for permissions. Define who has the authority to change permissions, under what circumstances, and how to request permission changes.
1. Educate Users:
Educate users about SharePoint permission management best practices. Train them to understand the implications of sharing content, granting permissions, and breaking inheritance.
1. Utilize SharePoint Security Reports:
SharePoint Online offers built-in security reports that provide insights into permission usage. Utilize these reports to monitor user activity, permissions changes, and potential security risks.
1. Backup and Restore Permissions:
Regularly backup permission configurations. This safeguards against accidental or malicious changes, allowing for swift restoration in case of a security breach.
Conclusion
In the realm of SharePoint Online, efficient permission management is the cornerstone of a secure and collaborative digital workspace. By adhering to best practices, organizations can harness the power of SharePoint’s versatile permission model. Through careful planning, judicious use of groups, and a proactive approach to reviewing and updating permissions, businesses can create a cohesive environment where data is accessible to those who need it, while keeping unauthorized access at bay.
Let us help you navigate the intricate world of permission management in SharePoint Online, ensuring your business thrives in a secure and productive digital landscape.
Reach out to us today and discover how Star Knowledge can transform your SharePoint experience. Your journey towards optimized collaboration and data security begins here.
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Scripting
This page describes the syntax and possibilities with scripting.
Scripting is based on the powerful Scriban scripting language. You can find more information here:
• Language Overview: Here
• Built-in Functions: Here
Different than stated in the scriban docs, Race Result Exchange is not changing the casing of variables or functions. Even more, you can use string.ends_withor string.EndsWith, whereas the later is preferred as it means the declaration of the method is not touched.
The following script will output "Hello World":
{{ "Hello World" }}
The following script will take the current time and pads it to 12 characters and center aligns it if need be. This is possible by using the | pipe character: The expression to the left is forwarded to a function that is given by the name after the pipe. The forwarded argument will be the first in the function arguments list:
{{ Clock | TrimPad 12 "Center" }}
Without using piping, you can also use a traditional way of calling methods:
{{ TrimPad Clock 12 "Center" }}
Last updated
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The Duties for a Data Analysis Coding Job
By Nikhil Abraham
Data analysts sift through large volumes of data, looking for insights that help drive the product or business forward. This coding role marries programing and statistics in the search for patterns in the data. Popular examples of data analysis in action include the recommendation engines used by Amazon to make product suggestions to users based on previous purchases and by Netflix to make movie suggestions based on movies watched.
The data analyst’s first challenge is simply importing, cleaning, and processing the data. A website can generate millions of database entries of users’ data daily, requiring the use of complicated techniques, referred to as machine learning, to create classifications and predictions from the data.
For example, half a billion messages are sent per day using Twitter; some hedge funds analyze this data and classify whether a person talking about a stock is expressing a positive or negative sentiment. These sentiments are then aggregated to see whether a company has a positive or negative public opinion before the hedge fund purchases or sells any stock.
Any programming language can be used to analyze data, but the most popular programming languages used for the task are R, Python, and SQL. Publicly shared code in these three languages makes it easier for individuals entering the field to build on another person’s work. While crunching the data is important, employers also look for data analysts with skills in the following:
• Visualization: Just as important as finding insight in the data is communicating that insight. Data visualization uses charts, graphs, dashboards, infographics, and maps, which can be interactive, to display data and reduce the complexity such that one or two conclusions appear obvious. Common data visualization tools include D3.js, a JavaScript graphing library, and ArcGIS for geographic data.
The two Manhattan addresses farthest away from Starbucks.
The two Manhattan addresses farthest away from Starbucks.
• Distributed storage and processing: Processing large amounts of data on one computer can be time intensive. One option is to purchase a single faster computer. Another option, called distributed storage and processing, is to purchase multiple machines and divide the work. For example, imagine that you want to count the number of people living in Manhattan. In the distributed storage and processing approach, you might ring odd‐numbered homes, someone else would ring even‐numbered homes, and when everyone finishes you would sum the counts.
Data analysts work with back‐end developers to gather data needed for their work. After the data analysts have drawn conclusions from the data, and come up with ideas on improving the existing product, they meet with the entire team to help design prototypes to test the ideas on existing customers.
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SANDAEROVATOR
SANDAEROVATOR is an aerospace tower-pyramid cable-tube elevator-accelerator. A passive/active structure pyramid/tower cable-tube (composite material tension/compression force), buoyancy/propeller/rocket/rail/cannon (H2/O2/H2O/molecular force), electromagnetic (electron/photonic force) launch/energy elevator-accelerator and base/structure/connection for ocean, terrestrial, aero, space cities. Sandaerovator structure has a pyramid and tower horizontal wing wind stabilizers, formed by modules with independent counter wind and flying buoyancy/propeller/rocket propulsion. Sandaerotrain elevator-accelerator 10-30-100km with Sandaeroblock pile-up towers cable/track connected to expansion Pyramid. Cross-Pyramid Space Elevator, 30 km from cube-sphere centripetal pile-up Acity to centrifugal carbon composite 4 cable-truss, connected to Geo stationary 30k km Space City. Sandaerovator can be used as an exterior elevator for any current, new or expanded building, and as an electromagnetic accelerator launching platform for a Sandaeroship, Sandaerocopter and/or Sandaerocket, including via a cable, vacuum tube coil gun and/or rail linear electric motor. H2-photo-electric acceleration can reach 11 km/s gravity escape velocity and/or 8km/s orbital velocity. Up to 200km horizontal and/or 100km vertical track can be used for safe human gradual acceleration. Carbon graphene/nanotube multi/truss cable-tube can be centrifugal stretched/sustained by geosync satellite space city and flowing cargo pellets, molecules, electrons and photons. Mountain/Pyramid Vacuum Tunnel hydrogen-photonic-electric space-cannon can shoot cargo, avatar-bots and laser-rocket-mirror spaceships to escape velocity.
Sandaerovator can be connected and give access to SANDAEROCITIES, atmospheric/mountain top Acities or geostationary Space Cities (Sandaerospace Scities), including a non-fixed connection to a Lunar City. Sandaerovator can gradually combine space elevator, tower, hook, rotor, loop, ring concepts using wing aerodynamics, flying wheel, wind propellers, gas/vacuum buoyancy, centrifugal gravity, accelerated vapor/water pressure, electromagnetic/kinetic energy, in double counter loop, for active support structure, pushing structure up, reducing gravity compression. Multi orbit Sandaerospaces can have velocity synchronized with upward tensile or propulsive counter force to allow straight elevation until geostationary orbit. Vertical- Horizontal Four-Direction Pyramid-Growth; 1 to 100km Space-Port Electric Accelerator-Elevator cross-pyramid; H2/H2O Aeroblock vertical-horizontal pile-up; 100km to 100,000km Centrifugal Counter Weight Composite Cube-Sphere Structure with 4 cables. Propeller/Wing/Counterweight and Lidar/Laser defense against wind, debris, meteorites, photonic waves etc. Sandaerovator can PRODUCE ENERGY SURPLUS AFTER PARTIAL USE FOR ACTIVE STRUCTURING: solar/wave/wind energy heats water/air sending them upward producing upward structural force on thermal turbines, then sends it downward in central tube, generating upward rocket/jet force to be cooled in water/ocean and repeat cycle. Meanwhile solenoid electromagnetic force sends pellets and payloads upward, generating also upward structural centrifugal force cycle. Solaser L1 La Grange point, Geosync and Elevator self-finance protection, communication, energy, transportation system energizes magnetic dipole shield (photo-electric solenoid/coil) for intersat protection for any planet or satellite. Circular laser network also generates larger photo-gravitonic protection fields.
GRAPHENE MACROTUBE and MACRORIBBON are macro single or multi layer rolled up (tube) or flat (ribbon/fabric) graphene single carbon hexagonal network (or composite with carbon fabric, nanotubes, polymers etc), to replace steel cables, tubes, panels with over 10 times stronger material, capable for example, with a multi cable truss or ribbon formation, of full or interrupted connection to a 3-30k km space tower-elevator geosynchronous system, with or without a 100k km centrifugal counter-weight. Earth oceanic pyramid-tower water filled carbon composite cube-sphere aquablocks bellow-on-near water line, vapor/H2 aeroblocks above water line, pile-up to buoyant AEROCITIES, deployed top-down in Venus, cable truss/ribbon connected to Geo Space Cities.
Atmospheric electric propulsion pyramid-tower-elevators and space laser propulsion can significantly lower costs of molecular rocket propulsion mobile aerospace ship-stations, with modular ascension under G$/US$1k/module for enterprises and under G$/US$100 or free for citizens with subsidy/sponsorship from solar-wind-wave energy sales. Gcity/Tower/Pyramid/Aerotrain on land/water control wind/wave excess movement by cube-sphere pass-trough shape, aqua-aeroblock anchoring, propeller and photo-electric heating/ionization counter movements. Modular carbon composite cube-sphere aqua-aeroblock cross tower-pyramid stacking can reach 1 km, gradually expand past 100km, producing solar-wind-wave energy, housing and transportation. Ocean centered, for land clearance, Aqua-Ocean-City connected to Aero-Atmosphere-City to Geo-Space-City by Pyramid-Tower-Elevator, Molecular-Electric-Photonic weather control, Earth Aerocities duplicated/moved to Venus.
Scity Geostationary Space City
Acity
Atmospheric
Aero City
Ocity - Tcity - Ucity
Ocean, Terrestrian
Underground
Cities
Scities
Space Cities
Geostationary
Sandaerospace
Earth
Lunar City
Space
Elevator
Sandaerovator
SANDAEROCITY
Non-fixed
Connetion
AEROCITY
Earth, Moon, Venus and Mars
Vertical- Horizontal
Four-Direction
Pyramid-Growth
1 to 100km
Space-Port
Electric
Accelerator-Elevator
cross-pyramid
H2/H2O Aeroblock
vertical-horizontal
pile-up
100km to 100,000km
Centrifugal Counter Weight
Composite Cube-Sphere Structure with 4 cables
SANDAEROBRIDGE
SANDAEROBRIDGE
GLOBOCEAN ACITIES
Venus
Atlantic
AeroPark-Bridge
SANDAEROHANGAR
Mars
Mount Olympus
Valles Marineris
Ice Pole
Moon
Montes Apenninus
Santos-Dumont Crater
Atlantis
Paradise
Valhalla
Eldorado
Asgard
Xangrila
Globocean
Ocities
Acities
SANDAEROPIPE
UPWARD
FORCE
SURPLUS
ENERGY
CYCLE
solar/wind/wave
heated water/air
solenoid
electromagnetic
pellets/payloads
Solar Mirror/Lens Laser transporting solar-sail mini-space ship/station/robot to Moon, Mars, Venus in minutes
SOLASER
SANDAEROSHIP
SANDAEROTRAIN
SOLASER
Sandaerotrain elevator-accelerator 10-30-100km with Sandaeroblock pile-up towers cable/track connected to expansion Pyramid.
SANDAEROTRAIN
SANDAEROBRIDGE
Aqua-Aero-Terra-Sub Train
ocean tower solar-wind-wave,
cube-sphere AeroBlocks above water,
AquaBlocks bellow water, connected by cable,
to units above weather and at bottom of ocean,
to where the tower will pyramid expand to 3-30km.
Space Tower-Elevator
30km to 30,000 km geostationary,
graphene macrotube truss cable/cube-spheres,
electromagnetic upward active structure inverted up/down linear motor/solenoid accelerator-decelerator.
SANDAEROSPACE
SANDAEROGRAPH
Aerocity
Aerocity
Aerocity
Aerocity
Ocean Beach Pier-Port extended east 1km to Gcity, then 1 km west, 1km north/south, then as a cross pyramid, 1 km up to become tallest building in world, producing solar-wind-wave energy, hydrogen, drinking water, farming and housing.
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Shortcuts
mmcv.ops.sync_bn 源代码
# Copyright (c) OpenMMLab. All rights reserved.
from typing import Optional
import torch
import torch.distributed as dist
import torch.nn.functional as F
from mmengine.registry import MODELS
from torch.autograd import Function
from torch.autograd.function import once_differentiable
from torch.nn.modules.module import Module
from torch.nn.parameter import Parameter
from ..utils import ext_loader
ext_module = ext_loader.load_ext('_ext', [
'sync_bn_forward_mean', 'sync_bn_forward_var', 'sync_bn_forward_output',
'sync_bn_backward_param', 'sync_bn_backward_data'
])
class SyncBatchNormFunction(Function):
@staticmethod
def symbolic(g, input, running_mean, running_var, weight, bias, momentum,
eps, group, group_size, stats_mode):
return g.op(
'mmcv::MMCVSyncBatchNorm',
input,
running_mean,
running_var,
weight,
bias,
momentum_f=momentum,
eps_f=eps,
group_i=group,
group_size_i=group_size,
stats_mode=stats_mode)
@staticmethod
def forward(self, input: torch.Tensor, running_mean: torch.Tensor,
running_var: torch.Tensor, weight: torch.Tensor,
bias: torch.Tensor, momentum: float, eps: float, group: int,
group_size: int, stats_mode: str) -> torch.Tensor:
self.momentum = momentum
self.eps = eps
self.group = group
self.group_size = group_size
self.stats_mode = stats_mode
assert isinstance(
input, (torch.HalfTensor, torch.FloatTensor,
torch.cuda.HalfTensor, torch.cuda.FloatTensor)), \
f'only support Half or Float Tensor, but {input.type()}'
output = torch.zeros_like(input)
input3d = input.flatten(start_dim=2)
output3d = output.view_as(input3d)
num_channels = input3d.size(1)
# ensure mean/var/norm/std are initialized as zeros
# ``torch.empty()`` does not guarantee that
mean = torch.zeros(
num_channels, dtype=torch.float, device=input3d.device)
var = torch.zeros(
num_channels, dtype=torch.float, device=input3d.device)
norm = torch.zeros_like(
input3d, dtype=torch.float, device=input3d.device)
std = torch.zeros(
num_channels, dtype=torch.float, device=input3d.device)
batch_size = input3d.size(0)
if batch_size > 0:
ext_module.sync_bn_forward_mean(input3d, mean)
batch_flag = torch.ones([1], device=mean.device, dtype=mean.dtype)
else:
# skip updating mean and leave it as zeros when the input is empty
batch_flag = torch.zeros([1], device=mean.device, dtype=mean.dtype)
# synchronize mean and the batch flag
vec = torch.cat([mean, batch_flag])
if self.stats_mode == 'N':
vec *= batch_size
if self.group_size > 1:
dist.all_reduce(vec, group=self.group)
total_batch = vec[-1].detach()
mean = vec[:num_channels]
if self.stats_mode == 'default':
mean = mean / self.group_size
elif self.stats_mode == 'N':
mean = mean / total_batch.clamp(min=1)
else:
raise NotImplementedError
# leave var as zeros when the input is empty
if batch_size > 0:
ext_module.sync_bn_forward_var(input3d, mean, var)
if self.stats_mode == 'N':
var *= batch_size
if self.group_size > 1:
dist.all_reduce(var, group=self.group)
if self.stats_mode == 'default':
var /= self.group_size
elif self.stats_mode == 'N':
var /= total_batch.clamp(min=1)
else:
raise NotImplementedError
# if the total batch size over all the ranks is zero,
# we should not update the statistics in the current batch
update_flag = total_batch.clamp(max=1)
momentum = update_flag * self.momentum
ext_module.sync_bn_forward_output(
input3d,
mean,
var,
weight,
bias,
running_mean,
running_var,
norm,
std,
output3d,
eps=self.eps,
momentum=momentum,
group_size=self.group_size)
self.save_for_backward(norm, std, weight)
return output
@staticmethod
@once_differentiable
def backward(self, grad_output: torch.Tensor) -> tuple:
norm, std, weight = self.saved_tensors
grad_weight = torch.zeros_like(weight)
grad_bias = torch.zeros_like(weight)
grad_input = torch.zeros_like(grad_output)
grad_output3d = grad_output.flatten(start_dim=2)
grad_input3d = grad_input.view_as(grad_output3d)
batch_size = grad_input3d.size(0)
if batch_size > 0:
ext_module.sync_bn_backward_param(grad_output3d, norm, grad_weight,
grad_bias)
# all reduce
if self.group_size > 1:
dist.all_reduce(grad_weight, group=self.group)
dist.all_reduce(grad_bias, group=self.group)
grad_weight /= self.group_size
grad_bias /= self.group_size
if batch_size > 0:
ext_module.sync_bn_backward_data(grad_output3d, weight,
grad_weight, grad_bias, norm, std,
grad_input3d)
return grad_input, None, None, grad_weight, grad_bias, \
None, None, None, None, None
[文档]@MODELS.register_module(name='MMSyncBN') class SyncBatchNorm(Module): """Synchronized Batch Normalization. Args: num_features (int): number of features/chennels in input tensor eps (float, optional): a value added to the denominator for numerical stability. Defaults to 1e-5. momentum (float, optional): the value used for the running_mean and running_var computation. Defaults to 0.1. affine (bool, optional): whether to use learnable affine parameters. Defaults to True. track_running_stats (bool, optional): whether to track the running mean and variance during training. When set to False, this module does not track such statistics, and initializes statistics buffers ``running_mean`` and ``running_var`` as ``None``. When these buffers are ``None``, this module always uses batch statistics in both training and eval modes. Defaults to True. group (int, optional): synchronization of stats happen within each process group individually. By default it is synchronization across the whole world. Defaults to None. stats_mode (str, optional): The statistical mode. Available options includes ``'default'`` and ``'N'``. Defaults to 'default'. When ``stats_mode=='default'``, it computes the overall statistics using those from each worker with equal weight, i.e., the statistics are synchronized and simply divied by ``group``. This mode will produce inaccurate statistics when empty tensors occur. When ``stats_mode=='N'``, it compute the overall statistics using the total number of batches in each worker ignoring the number of group, i.e., the statistics are synchronized and then divied by the total batch ``N``. This mode is beneficial when empty tensors occur during training, as it average the total mean by the real number of batch. """ def __init__(self, num_features: int, eps: float = 1e-5, momentum: float = 0.1, affine: bool = True, track_running_stats: bool = True, group: Optional[int] = None, stats_mode: str = 'default'): super().__init__() self.num_features = num_features self.eps = eps self.momentum = momentum self.affine = affine self.track_running_stats = track_running_stats group = dist.group.WORLD if group is None else group self.group = group self.group_size = dist.get_world_size(group) assert stats_mode in ['default', 'N'], \ f'"stats_mode" only accepts "default" and "N", got "{stats_mode}"' self.stats_mode = stats_mode if self.affine: self.weight = Parameter(torch.Tensor(num_features)) self.bias = Parameter(torch.Tensor(num_features)) else: self.register_parameter('weight', None) self.register_parameter('bias', None) if self.track_running_stats: self.register_buffer('running_mean', torch.zeros(num_features)) self.register_buffer('running_var', torch.ones(num_features)) self.register_buffer('num_batches_tracked', torch.tensor(0, dtype=torch.long)) else: self.register_buffer('running_mean', None) self.register_buffer('running_var', None) self.register_buffer('num_batches_tracked', None) self.reset_parameters() def reset_running_stats(self): if self.track_running_stats: self.running_mean.zero_() self.running_var.fill_(1) self.num_batches_tracked.zero_() def reset_parameters(self): self.reset_running_stats() if self.affine: self.weight.data.uniform_() # pytorch use ones_() self.bias.data.zero_()
[文档] def forward(self, input: torch.Tensor) -> torch.Tensor: if input.dim() < 2: raise ValueError( f'expected at least 2D input, got {input.dim()}D input') if self.momentum is None: exponential_average_factor = 0.0 else: exponential_average_factor = self.momentum if self.training and self.track_running_stats: if self.num_batches_tracked is not None: self.num_batches_tracked += 1 if self.momentum is None: # use cumulative moving average exponential_average_factor = 1.0 / float( self.num_batches_tracked) else: # use exponential moving average exponential_average_factor = self.momentum if self.training or not self.track_running_stats: return SyncBatchNormFunction.apply( input, self.running_mean, self.running_var, self.weight, self.bias, exponential_average_factor, self.eps, self.group, self.group_size, self.stats_mode) else: return F.batch_norm(input, self.running_mean, self.running_var, self.weight, self.bias, False, exponential_average_factor, self.eps)
def __repr__(self): s = self.__class__.__name__ s += f'({self.num_features}, ' s += f'eps={self.eps}, ' s += f'momentum={self.momentum}, ' s += f'affine={self.affine}, ' s += f'track_running_stats={self.track_running_stats}, ' s += f'group_size={self.group_size},' s += f'stats_mode={self.stats_mode})' return s
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__label__pos
| 0.937513 |
/*! \page graphs How to use graphs The primary data structures of LEMON are the graph classes. They all provide a node list - edge list interface, i.e. they have functionalities to list the nodes and the edges of the graph as well as incoming and outgoing edges of a given node. Each graph should meet the \ref lemon::concept::StaticGraph "StaticGraph" concept. This concept does not make it possible to change the graph (i.e. it is not possible to add or delete edges or nodes). Most of the graph algorithms will run on these graphs. The graphs meeting the \ref lemon::concept::ExtendableGraph "ExtendableGraph" concept allow node and edge addition. You can also "clear" such a graph (i.e. erase all edges and nodes ). In case of graphs meeting the full feature \ref lemon::concept::ErasableGraph "ErasableGraph" concept you can also erase individual edges and nodes in arbitrary order. The implemented graph structures are the following. \li \ref lemon::ListGraph "ListGraph" is the most versatile graph class. It meets the \ref lemon::concept::ErasableGraph "ErasableGraph" concept and it also has some convenient extra features. \li \ref lemon::SmartGraph "SmartGraph" is a more memory efficient version of \ref lemon::ListGraph "ListGraph". The price of this is that it only meets the \ref lemon::concept::ExtendableGraph "ExtendableGraph" concept, so you cannot delete individual edges or nodes. \li \ref lemon::SymListGraph "SymListGraph" and \ref lemon::SymSmartGraph "SymSmartGraph" classes are very similar to \ref lemon::ListGraph "ListGraph" and \ref lemon::SmartGraph "SmartGraph". The difference is that whenever you add a new edge to the graph, it actually adds a pair of oppositely directed edges. They are linked together so it is possible to access the counterpart of an edge. An even more important feature is that using these classes you can also attach data to the edges in such a way that the stored data are shared by the edge pairs. \li \ref lemon::FullGraph "FullGraph" implements a complete graph. It is a \ref lemon::concept::StaticGraph, so you cannot change the number of nodes once it is constructed. It is extremely memory efficient: it uses constant amount of memory independently from the number of the nodes of the graph. Of course, the size of the \ref maps-page "NodeMap"'s and \ref maps-page "EdgeMap"'s will depend on the number of nodes. \li \ref lemon::NodeSet "NodeSet" implements a graph with no edges. This class can be used as a base class of \ref lemon::EdgeSet "EdgeSet". \li \ref lemon::EdgeSet "EdgeSet" can be used to create a new graph on the node set of another graph. The base graph can be an arbitrary graph and it is possible to attach several \ref lemon::EdgeSet "EdgeSet"'s to a base graph. \todo Don't we need SmartNodeSet and SmartEdgeSet? \todo Some cross-refs are wrong. The graph structures themselves can not store data attached to the edges and nodes. However they all provide \ref maps-page "map classes" to dynamically attach data the to graph components. The following program demonstrates the basic features of LEMON's graph structures. \code #include #include using namespace lemon; int main() { typedef ListGraph Graph; \endcode ListGraph is one of LEMON's graph classes. It is based on linked lists, therefore iterating throuh its edges and nodes is fast. \code typedef Graph::Edge Edge; typedef Graph::InEdgeIt InEdgeIt; typedef Graph::OutEdgeIt OutEdgeIt; typedef Graph::EdgeIt EdgeIt; typedef Graph::Node Node; typedef Graph::NodeIt NodeIt; Graph g; for (int i = 0; i < 3; i++) g.addNode(); for (NodeIt i(g); i!=INVALID; ++i) for (NodeIt j(g); j!=INVALID; ++j) if (i != j) g.addEdge(i, j); \endcode After some convenient typedefs we create a graph and add three nodes to it. Then we add edges to it to form a complete graph. \code std::cout << "Nodes:"; for (NodeIt i(g); i!=INVALID; ++i) std::cout << " " << g.id(i); std::cout << std::endl; \endcode Here we iterate through all nodes of the graph. We use a constructor of the node iterator to initialize it to the first node. The operator++ is used to step to the next node. Using operator++ on the iterator pointing to the last node invalidates the iterator i.e. sets its value to \ref lemon::INVALID "INVALID". This is what we exploit in the stop condition. The previous code fragment prints out the following: \code Nodes: 2 1 0 \endcode \code std::cout << "Edges:"; for (EdgeIt i(g); i!=INVALID; ++i) std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")"; std::cout << std::endl; \endcode \code Edges: (0,2) (1,2) (0,1) (2,1) (1,0) (2,0) \endcode We can also iterate through all edges of the graph very similarly. The \c target and \c source member functions can be used to access the endpoints of an edge. \code NodeIt first_node(g); std::cout << "Out-edges of node " << g.id(first_node) << ":"; for (OutEdgeIt i(g, first_node); i!=INVALID; ++i) std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")"; std::cout << std::endl; std::cout << "In-edges of node " << g.id(first_node) << ":"; for (InEdgeIt i(g, first_node); i!=INVALID; ++i) std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")"; std::cout << std::endl; \endcode \code Out-edges of node 2: (2,0) (2,1) In-edges of node 2: (0,2) (1,2) \endcode We can also iterate through the in and out-edges of a node. In the above example we print out the in and out-edges of the first node of the graph. \code Graph::EdgeMap m(g); for (EdgeIt e(g); e!=INVALID; ++e) m.set(e, 10 - g.id(e)); std::cout << "Id Edge Value" << std::endl; for (EdgeIt e(g); e!=INVALID; ++e) std::cout << g.id(e) << " (" << g.id(g.source(e)) << "," << g.id(g.target(e)) << ") " << m[e] << std::endl; \endcode \code Id Edge Value 4 (0,2) 6 2 (1,2) 8 5 (0,1) 5 0 (2,1) 10 3 (1,0) 7 1 (2,0) 9 \endcode As we mentioned above, graphs are not containers rather incidence structures which are iterable in many ways. LEMON introduces concepts that allow us to attach containers to graphs. These containers are called maps. In the example above we create an EdgeMap which assigns an integer value to all edges of the graph. We use the set member function of the map to write values into the map and the operator[] to retrieve them. Here we used the maps provided by the ListGraph class, but you can also write your own maps. You can read more about using maps \ref maps-page "here". */
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| 0.994785 |
Herring Gull
Herring Gull (Larus argentatus)
Herring Gulls started to nest in Iceland around 1925. This is a common species in coastal areas all around Iceland except for the western part where Glaucous Gull is common. These species interbreed and hybrids can sometimes be seen. Herring Gulls forage in coastal areas and at sea but go rarely inland. They feed on a variety of food like crustaceans, molluscs and fish.
Herring Gull is common in Skjálfandaflói bay and the most numerous of the larger gull species.
Length:
58-62 cm
Weight:
700-1,430 g
Wingspan:
138-155 cm
Population:
5,000-10,000 pairs
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Differences between Cytosol and Cytoplasm
Overview
Cytoplasm and cytosol are both part of the protoplasm. While the cytoplasm includes everything within the cell membrane (with the exception of nucleus and its contents), cytosol is the fluid within the cell in which organelles and other materials float.
* The cytosol is part of the cytoplasm.
Cytosol
As mentioned, the cytosol is the fluid part of the cytoplasm in which cell organelles and other components are embedded. Within the cell, the cytosol is enclosed by the cell membrane. In addition, it can be found within various membrane-bound organelles (e.g. within vesicles, vacuoles, chloroplast, etc.) in eukaryotic cells
Cytosol Components
In human cells, the cytosol takes up about 70 percent of the total cell volume. While water is the primary component of this fluid, making up about 70 percent of the total volume, it also consists of a number of other components that include proteins (less than 300 Da in size and range from 20 to 30 percent of the total cytosol volume) and ions (calcium, sodium, magnesium, and chloride ions, etc.) among other hydrophilic molecules.
Due to the presence of these dissolved molecules and ions, the cytosol has the consistency of jelly rather than a liquid. The concentration of these molecules and ions in the cytosol serves a number of functions including regulating the movement of water in and out of the cell as well as promoting cell communication etc.
* The cytosolic pH value ranges between 7.0 and 7.4.
* Some of the other materials that can be found in the cytosol include cytoplasmic bodies, crystalline inclusions, stress granules, and cytoplasmic inclusions, etc.
Functions
The cytosol is involved in a number of functions that are essential for the proper functioning of cells.
These include:
Structural support - Depending on the type of cell, the cytosol can take up to 70% of the total cell volume. This volume contributes to the overall shape of the cell. Depending on the concentration of molecules and ions in the cytosol (and outside the cell) water can move in or out of the cell through osmosis. In plant cells, for instance, turgor pressure, also known as hydrostatic pressure provides structural integrity to each cell and the tissue in general.
Hydrostatic pressure is essential for various processes such as the opening and closing of the stomata. In both plant and animal cells, the cytosol also creates room and promotes the movement of various materials from one organelle to another and from the cell membrane to the organelles and vice versa.
Signal transduction/cell-to-cell communication - Cell to cell communication is essential for the proper functioning of various tissues and organ systems. Here, various molecules and ions, etc. dissolved in the cytosol play an important role in these functions.
For instance, during synaptic transmission, neurotransmitters packaged within vesicles within the cytosol are transported to the presynaptic membrane in order to be released into the synaptic cleft before reaching the postsynaptic membrane. At the postsynaptic membrane, neurotransmitters come in contact with specific receptors thus influencing a specific action.
In this case, the cytosol allows for the movement of neurotransmitter vesicles to the cell surface (postsynaptic membrane) so that they can fuse with the membrane and release their contents, neurotransmitters, to the synaptic cleft.
Once they activate the postsynaptic neuron, neurotransmitters may be taken up by the presynaptic neuron to be repackaged in vesicles and stored in the cytosol before the process repeats.
Transport of metabolites - Within the cell, metabolites are transported from their site of production to the target destination through the cytosol.
* In prokaryotes (organisms that lack membrane-bound organelles), various biological processes and reactions take place in the cytosol.
* The cytosol is also known as the intracellular fluid (ICF).
Cytoplasm
The cytoplasm consists of three main components.
These include:
· Cytosol (discussed above)
· Cytoplasmic organelles
· Inclusions
* The cytoplasm is usually described as anything between the nucleus and the cell membrane in eukaryotic cells. The nucleus, which might be centrally located depending on the cell, contains the nucleoplasm, several suspended substructures, as well as DNA.
Here, the nucleoplasm, within the nuclear membrane, facilitates an isolated environment in which a number of processes like transcription take place.
Organelles
The majority of cytoplasmic organelles are membrane-bound.
These include:
Endoplasmic Reticulum
The endoplasmic reticulum is a continuous network of membranes that consists of a series of flattened sacs. Though the density of endoplasmic reticulum (ER) is higher near the nucleus and Golgi apparatus, (rough endoplasmic reticulum) it spreads throughout the cell making it one of the largest organelles.
The outer surface of the endoplasmic reticulum consists of millions of ribosomes (membrane-bound ribosomes) which are involved in protein assembly through a process known as translation
Some of the main functions of the rough endoplasmic reticulum include:
Protein folding - Protein folding refers to the process through which polypeptide chains are folded into specific three-dimensional (3D), biologically active proteins. For instance, through protein folding, proteins with linking sites (capable of lock and key) are produced. These proteins are then sent to the Golgi apparatus before being transported to the appropriate destination (e.g. the cell membrane).
Protein quality control - Protein quality control occurs in the lumen of the endoplasmic reticulum. This is an important process that ensures only correctly folded proteins are produced and delivered to the appropriate destination. If incorrectly formed proteins are identified, they are either retained in the lumen or broken down to amino acids that can be re-used.
Protein transport - The endoplasmic reticulum also plays an important role in the transport of most proteins to the Golgi apparatus where they are further sorted.
Smooth Endoplasmic Reticulum
Unlike the rough endoplasmic reticulum, the smooth endoplasmic reticulum, as the name suggests, does not have surface ribosomes. It's also more tubular with an interconnecting network of sub-compartments. It's primarily involved in the assembly and packaging of lipids that are either used within the cell or exported outside the cell.
Some of the other functions associated with the smooth endoplasmic reticulum include:
· Metabolism - E.g. breakdown of glycogen to glucose in the liver
· Production of steroid hormones in the adrenal cortex
· Detoxification of various organic chemicals
Golgi Apparatus
The Golgi apparatus is also a membrane-bound organelle that consists of membranous sacs and vesicles. Like the endoplasmic reticulum, the Golgi apparatus consists of membrane infolds commonly known as cisternae. When describing this organelle in relation to the endoplasmic reticulum, two faces are often discussed.
These are the cis and the trans face. The cis face is the region of the organelle facing towards the endoplasmic reticulum. As such, it serves to receive material from the ER. The trans face, on the other hand, also known as the shipping face, is posterior to the cis face and points towards the plasma membrane of the cell.
Folded proteins and lipids from the endoplasmic reticulum are transported to the cis face of the Golgi apparatus through transport vesicles. In the Golgi, these products are modified, concentrated, and tagged. Tagged products (protein or lipid in nature) are then sent into new vesicles (e.g. secretory vesicles) that bud off the trans face of the Golgi apparatus to be transported to the appropriate destination.
Mitochondria
Often referred to as the powerhouse of the cell, mitochondria are also membrane-bound organelles. These organelles are characterized by a highly folded inner membrane that forms the cisternae. Some of the other parts of the mitochondrion include the mitochondrial matrix, intermembrane space, and the outer membrane.
Generally, the mitochondrion is primarily involved in the production of ATP energy that powers the cell (energy required for various cellular processes).
Some of the other functions of the mitochondria include:
Apoptosis (programmed cell death) - Mitochondria promote apoptosis through the release of given molecules (protein in nature). When these molecules are released into the cytosol, they activate enzymes that initiate the breakdown of the cell. This is important in many processes such as the separation of fingers and toes as the baby develops in the womb.
Calcium signaling - The outer membrane of the mitochondrion and that of the endoplasmic reticulum communicate through calcium signaling. Here. Signals from the mitochondria are sent to the endoplasmic reticulum to influence its activities.
Cell cycle, proliferation and cellular differentiation - Mitochondria have been shown to trigger various cellular activities including cell division and differentiation depending on the needs of the body
* As mentioned, ribosomes are involved in protein synthesis through a process known as translation.
Some of the other cytoplasmic organelles/bodies include:
· Centrosome - Microtubule organizing center
· Peroxisome - Oxidative organelles
· Cytoskeleton - Network of filaments and tubules
Cytoplasmic Inclusions
Compared to dissolved molecules and ions in the cytosol, the cytoplasm contains inclusions. Most of these inclusions are metabolic products that are stored in the cytoplasm.
These include:
· Fats/lipid droplets
· Glycogen
· Crystals
· Melanin pigments
· Residual bodies
Differences between Cytosol and Cytoplasm
Some of the main differences between cytosol and cytoplasm:
Diversity - The cytosol is largely composed of water. Some of the other components include ions, soluble proteins, and other molecules. The cytoplasm consists of the cytosol and all the other cell components with the exception of the nucleus.
Functions - Various molecules are transported in the cytosol. In prokaryotes, chemical reactions also take place in this fluid. As well, many processes and reactions take place in the cytoplasm. These include ATP production, translation, signal transduction, and cytokinesis among others.
Do plant cells have vesicles?
Do animal cells have vesicles?
Return to Cell Biology
Return from Differences between Cytosol and Cytoplasm to MicroscopeMaster home
References
Lakna Panawala. (2017). Difference Between Cytosol and Cytoplasm.
Wolfgang Giese, Gregor Milicic, Andreas Schröder, and Edda Klipp. (2018). Spatial modeling of the membrane-cytosolic interface in protein kinase signal transduction
Links
https://www.proteinatlas.org/humanproteome/cell/cytosol
https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/cytoplasm
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Page 1
Quarter 1 1.Air Pressure Labs 2.Heating Earth's Surface 3.Global Winds 4.Measuring Wind 5.Types of Fronts 6.Cloud Cookery 7.Tracking a Hurricane Quarter 2 1.Reading a Weather Map 2.The Doppler Radar 3.Climate Commercial 4.Earth's Interior 5.Modeling Sea- Floor Spreading 6.Finding the Epicenter 7.Mapping Earthquakes and Volcanoes
Quarter 3 1.My Volcano 2.Igneous Rock Venn Diagrams 3.Sedimentary Rock Venn Diagrams 4.Metamorphic Rock Venn Diagrams 5.The Rock Cycle 6.Topography of Ave Maria 7.How Can You Flatten the Curved Earth? 8.Topographic Map Directions Quarter 4 1.Rock Shake 2.What is Soil? 3.Comparing Soils 4.Sand Hills 5.The Course of a River 6.Which Layer is the Oldest? 7.Finding Clues to Rock Layers 8.Geologic History Flash Cards 9.Reflection Essay
Quarter 2
1.Reading a Weather Map 2.The Doppler Radar 3.Climate Commercial 4.Earth's Interior 5.Modeling Sea Floor Spreading 6.Finding the Epicenter 7.Mapping Earthquakes and Volcanoes
I. Title: The Doppler Radar II. Data: The Doppler radar is a mostly effective instrument for predicting the weather. It is a complex device formed of three basic parts. The transmitter sends out radio signals that are deflected off of particles in the air. Some of these waves are reflected back to its source. They are picked up by an antenna. The antenna transmits the signals into a computer that meteorologists use to process and generate data. The Doppler radar lets meteorologists easily track large scale storms such as hurricanes and tornadoes, while giving people a warning for these storms ahead of time. It can also detect precipitation. The Doppler radar has some drawbacks. Large objects such as buildings, trees, and mountains can block the radio waves. Sometimes the radar does not pick up light amounts of precipitation. Overall, it is a useful device to meteorologists to help them track and predict weather.
For Climate Commercial, see the email in which I emailed you in the second quarter.
Crust 5 - 70 km thick
Earth's Interior
Mantle 2,867 km thick
Outer Core 2,266 km thick
Inner Core 1,216 km thick
I. Title: Modeling Sea – Floor Spreading II. Problem: How does sea – floor spreading add materials to the ocean floor? III. Materials: construction paper, 2 sheets of unlined paper, colored pencils, markers, scissors IV. Procedure: 1.Fold your construction paper into 16ths once long ways and four times the short ways. 2.Fold both of the sheets of unlined paper in half long ways and draw lines that match on both sides on the unlined paper and write “Start” on on end of each of the strips of paper. 3.Cut slits in the construction paper ¼, ½, and ¾ of the way through and then unfold the construction paper. 4.Put the ends without the words “Start” through the slit ½ of the way through. With one sheet, put the end with the “Start” through the ¼ slit and the other sheet with the “Start” through the ¾ slit. 5.Pull on both of the ends with the “Start” at the same time. V. Data: See Model VI. Analyze and Conclude: 1.What feature of the ocean floor does the center slit stand for? What prominent feature of the ocean floor is missing? The center slit stands for the mid-ocean ridge and the mountains or volcanoes are missing. 2.What do the side slits stand for? What does the space underneath the paper stand for? The side slits stand for a trench. The space beneath the paper stands for moving sediment. 3.As shown by your model, how does the ocean floor close to the center slit in the differ from the ocean floor near a side slit? It has more sediment near the center slit than a side slit. 4.What do the stripes stand for? Why is it important to that your model have an identical pattern of stripes on both sides? The stripes stand for the magnetic stripes on the ocean floor. They must be even because they are the same in both they are arraigned in the same positions.
I. Finding the Epicenter: II. Problem: How can you locate an earthquake's epicenter? III. Materials: drawing compass, pencil, outline map of the United States IV. Procedure: 1. Copy the table showing the difference between the arrival times of P and S waves. 2. Calculate the distance to the epicenter for all the cities by using the graph on page 58. 3. Draw a circle using the compass around each city according to the distance.' 4. Mark where all the circles intersect. That is the epicenter. V. Data: City
Difference in the Arrival Times between P and S waves
Distance to Epicenter
Denver, Colorado
2 min. 40 sec.
1,600 km
Houston, Texas
1 min. 50 sec.
1,000 km
Chicago, Illinois
1 min. 10 sec.
600 km
See Map: VI. Analyze and Conclude: 1. The epicenter is near Kentucky and Tennessee. 2. Chicago is the closest and only about 600 km away. 3. Chicago felt it first and Denver felt it the the last. 4. It is about 3,000 km away. The difference between the arrival times of P and S waves would be about 4 min. 30 sec. 5. The difference gets larger.
I. Title: Mapping Earthquakes and Volcanoes II. Problem: Is there a pattern between the locations of earthquakes and volcanoes? III. Materials: outline world map showing longitude and latitude, 2 different colored pencils IV. Procedure: 1.Use the information in the table below to mark the areas where the earthquakes are one color and where the volcanoes are in another color. 2.Lightly shade the area around each one of the earthquakes in the same color as the mark that shows where the earthquake is and do the same for the volcanoes. V. Data: Earthquakes
Volcanoes
Longitude
Latitude
Longitude
Latitude
120°W
40°N
150°W
60°N
110°E
5°S
70°W
35°S
77°W
4°S
120°W
45°N
88°E
23°N
61°W
15°N
121°E
14°S
105°W
20°N
34°E
7°N
75°W
74°W
44°N
122°W
40°N
70°W
30°S
30°E
40°N
10°E
45°N
60°E
30°N
85°W
13°N
160°E
55°N
125°E
23°N
37°E
3°S
30°E
35°N
145°E
40°N
140°E
35°N
120°E
10°S
12°E
46°N
14°E
41°N
75°E
28°N
105°E
5°S
150°W
61°N
35°E
15°N
68°W
47°S
70°W
30°S
175°E
41°S
175°E
39°S
121°E
17°N
123°E
38°N
VI. Analyze and Conclude: 1.How are earthquakes distributed on the map? Are they scattered evenly or concentrated into zones? The earthquakes seem to be scattered evenly throughout the plate boundaries. 2.How are volcanoes distributed on the map? Are they scattered evenly or concentrated into zones? The, like volcanoes, seem to be scattered evenly throughout the plate boundaries. 3.From your data, what can you infer about the relationship between earthquakes and volcanoes? Earthquakes and volcanoes both occur near plate boundaries and seem to be related to each other.
Note: The pictures of the volcano and the sediment are made by CJ Smith.
Quarter 4
1.Rock Shake 2.What is Soil? 3.Comparing Soils 4.Sand Hills 5.The Course of a River 6.Which Layer is the Oldest? 7.Finding Clues to Rock Layers 8.Geologic History Flash Cards 9.Reflection Essay
I. Title: Rock Shake II. Problem: How will shaking and acid conditions affect the rate at which limestone weathers III. Materials: 300mL of Water, Balance, 300mL of vinegar, Small pieces of Limestone, 4 Containers IV. Procedure: 1.Label the 4 containers A, B, C, and D. 2.Fill A with water, B with water, C with vinegar, and D with vinegar. 3.Shake containers B and D. 4.Let them sit for 1 day and weigh them later with the balance. V. Data: Container
Total Mass at Start Total Mass Next Day
Change in Mass
Percent Change in Mass
A (Water, no Shaking)
23.5
26.5
3
12.70%
B(Water, with Shaking)
24
20.8
-3.2
-13.30%
C (Vinegar, no Shaking)
21.5
19.2
-2.3
-10.70%
D (Vinegar, with Shaking)
21.5
18.4
-3.1
-14.40%
The Change of the Rocks' Mass 30 25 20
A B C D
Mass
15 10 5 0 1
2
VI.Analyze and Conclude: 1.What is the percent change of each of the rocks? A- 12.7%, B- -13.3%, C- -10.7%, D- -14.4% 2.Does your data show a change in mass of the rocks? Yes. 3.Was there a greater change in mass for one piece than another? Yes, C changed by 2.3, A changed by 3, D changed by 3.1, and B changed by 3.2. 4.Were your predictions on the lab correct? Explain. No, I thought that D will erode the most, but B did. 5.If your data showed a greater change in masses, how could that be explained? The limestone absorbed the water, increasing mass. 6.Which do you think was more responsible for the erosion, the vinegar or the shaking? Explain. I think the vinegar was more responsible because it chemically broke it down.
What is Soil? My Soil Recipe: Sediment Roots Decaying Plants and Animals Little White Crystals A Friend's Soil Recipe: Sand Wood Roots Plant Bits Think It Over: How would you define soil? Soil is the combination of decaying organic material and sediment.
I. Title: Comparing Soils II. Problem: What is the difference between bagged soil and local soil? III. Materials: 1 petri dish full of natural soil, 1 petri dish full of bagged soil, water, microscope IV. Procedure: 1.Obtain the specified soils in the petri dishes. 2.Observe the following things: does it have a scent, is it soft or gritty, find the approximate particle size of the smallest and largest particles of each of the soils. 3.Put a small amount of water in each of the petri dishes to observe which soil is denser. 4.Look at each soil underneath a microscope and draw a simple sketch of each. V. Data: Local Soil
Bagged Soil
Scent
None
Earthy scent
Soft or Gritty
Gritty
Soft
Approximate Particle Size
0.5mm- 4mm
0.25mm- 2mm
Density
Less Dense
More Dense
Sketch
VI. Analyze and Conclude: 1.Did you notice any similarities between the local and bagged soils? Did you notice any differences? I saw no similarities, despite them both being soil, but I observed many differences.
2.What can you infer about the composition of both of the soils from the different size of particles? From their texture? From how each soil reacted with the water? I inferred that the local soil was not as fine as the bagged soil because it had larger particle sizes and because it had a grittier texture. I inferred that the bagged soil was denser than the local soil because it sunk and the local soil floated. 3.Do you think that soils were formed in the same way? Explain your reasoning. No, because they seem so different from each other, in density, texture, particle size, and scent differed so greatly. Also, the bagged soil came from a Miracle- Gro bag, which means that it was made in a factory. 4.Based on what you have learned in the chapter, which soil would be better for growing vegetables in? I think that the bagged soil would because it would hold water better because of its greater density, it's smaller particle size allows more room for the roots to grow and aerate, and it's scent leads me to reason that there is a greater nitrogen amount in the bagged soil, which is good for plant growth.
I. Title: Sand Hills II. Problem: What is the relationship between the height and the width of a sand pile. Hypothesis: I think that the width will increase at a faster rate than the rate of the height. III. Materials: dry sand, cardboard tube, wooden skewer, ruler, white paper, marker IV. Procedure: 1. Put the cardboard tube in the center of the piece of paper. 2. Fill the cardboard tube with 100mL of the sand. 3. Quickly raise the tube straight up so that the sand flows out and so it forms a sand hill. 4.Stick a wooden skewer down the center of the sand hill and mark the height on the skewer with the marker. 5.Measure the distance from the skewer to the edge of the mound. 6.Remove the skewer. 7.Set the cardboard tube on the top of the sand hill without pushing down on it. 8.Repeat steps 2-7 four more times. V. Data: Test
1
2
3
4
5
Amount of Sand
100 mL
200 mL
300 mL
400 mL
500 mL
Height
2 cm
3 cm
3.6 cm
4 cm
4.4 cm
Width
14.8 cm
15.7 cm
18.2 cm
20.3 cm
22
VI. Analyze and Conclude: 1.Make a graph showing how the sand hill's height and width changed with each test.
Sand Hills Height and Width
Length of Height or Width
25 20 15
Height Width
10 5 0 1
2
3
4
5
Test Number
2.What does your graph show about the relationship between the sand hill's width and height? The width increased at a faster rate than the height. 3.Does the graph support your hypothesis? Why or why not? It does because I predicted that the width would increase at a faster rate than the height. 4.How would you revise your initial hypothesis? Give reasons to support your answer. I would not change my hypothesis because it was correct. 5.Predict what would happen if you did five more tests. Add another graph to display your hypothesis for this question.
Hypothesis for Next Five Tests 35 Length of Height or Width
30 25 20
Height Width
15 10 5 0 1
2
3 Extra Test Number
4
5
The Course of a River
The Course Of A River
Note: All these pictures were created by CJ Smith and were not copied off the internet and/or created by another animator or artist.
Key: 1: Delta: Where the river flows into the ocean and it deposits sediment 2: Valley Widening: As the river approaches sea level, it meanders more and develops a wider valley and a broader flood plain 3: Beach: Sand carried downstream by the river spreads along the coast to form beaches 4: Tributary: The smaller stream or river that merges with another larger river and provides the larger river with water and sediment. 5: Meander: Where the river flows across easily eroded sediment and bends from side to side 6: Flood Plain: Where the river widens the valley instead of deepening it 7: Oxbow Lake: A meander that is cut off from the river by deposition or sediment 8: V- Shaped Valley: Near the source, a river flows through a deep, v- shaped valley that gets deeper as the river flows 9: Waterfall and Rapids: They are common where a river flows over hard
Which Layer is the Oldest?
Make a stack of clay with layers and rocks that represent fossils in between them. Think It Over: Which fossil is the youngest and which fossil is the oldest? What are the strengths and weaknesses of relative dating? What are the strengths and weaknesses of absolute dating? The fossil on the bottom is the oldest and the fossil on the top is the youngest. With relative dating, you can compare the ages of rocks and fossils without expensive equipment and the need for radioactive material, but, you cannot know the actual age of the rock and you also cannot compare it with other rocks or fossils a far away. With absolute dating, you can find the definite age of a rock or of a fossil, which can be compared with a rock or fossil a large distance away, but, you also need expensive equipment and radioactive material.
Note: This is actually what the model looked like, I am not being lazy, this is actually what the model looked like, misshapen and disorganized
I. Title:Finding Clues to Rock Layers II. Problem: How can you use fossils and geologic features to interpret the relative ages of rock layers? III. Procedure: Study the images that represent Site 1 and Site 2.
Key = Trilobite Fossil
= Shell Fossil
= Leaf Fossil
= Extrusion
= Bird Fossil
= Intrusion
= Dinosaur Fossil =Mammal Fossil
= Fish Fossil =Ammonite Fossil IV. Analyze and Conclude: 1.What fossil clues in layers A and B indicate the kind of environment that existed when these rock layers were formed? How did the environment change in layer D? A and B were aquatic environments because of the shells, ammonites, and trilobites. Layer D became terrestrial because if the dinosaur and plant fossils. 2.Which layer is the oldest? How do you know? Layer A is the oldest because A is on the bottom and only A has trilobites, which are not as evolved. 3.Which of the layers was formed more recently? How do you know? Layer G because it has mammals which are more highly evolved and it is on the top. 4.Why do layers C and E both have no fossils? Layers C and E are both extrusions, so they cannot have fossils in them. 5.What kind of fossils are found in layer F? Dinosaur, plant, and bird fossils are found in layer F. 6.What layer in Site 1 might have been formed might have been formed at the same time as layer W in Site 2? Layer B probably was formed around the same time as layer W. 7.What clues show an unconformity gap between Site 1 and Site 2? There is no corresponding layer for the layers A, D, and E in Site 2. 8.Which is older intrusion V or layer Y? How do you know? Layer Y is older because the intrusion is always younger than the layer it passes through. 9.Describe how Site 2 has changed over time. Site 2 was originally aquatic, with fish, ammonites, and shells. After that it became terrestrial and had dinosaurs, birds, and plants. Later, it got mammals and the dinosaurs became extinct.
Geologic History Flash Cards Key: Precambrian Time Paleozoic Era Mesozoic Era Cenozoic Era Precambrian Time -4.6 Billion- 544 mya -Simple Organisms -Sea Pens, Early Bacteria, and Jellyfish Exist -First Mass Extinction at the End of the Time Cambrian -544- 505 mya -Explosion of Life Known as the Cambrian Explosion -Pikaia, Trilobites, Sponges, and Clams Exist Ordovician -505- 438 mya -First Vertebrates Appear -Crinoids, Jawless Fish, Cephalopods, and Brachiopods Exist Silurian -438- 408 mya -First Land Plants -Eurypterids, Psilophytes, Arachnids, and Jawed Fish Exist Devonian -408- 360 mya -First Bony Fish Appear -Sharks, Bony Fish, and Devonian Forests Exist Carboniferous -360- 286 mya -Great Swamps Form -Amphibians, Cockroaches, Dragonflies, and Coal Forests Exist Permian -286- 245 mya -Reptiles dominate the land -Dimetrodons, Dicynodons, and Conifers Exist -Second Mass Extinction Triassic -245- 208 mya
-Age of Reptiles Begins -First Dinosaurs Exist -Coelophysis, Cycads, and Morganucodons Exist Jurassic -208- 144 mya -First Birds Appear -Flying Reptiles Appear -Megazostrodon, Diplodocus, and Archaeopteryx Exist Cretaceous -144- 66 mya -First Flowering Plants Appear -First Snakes Appear -Tyrannosaurus Rex, Creodonts, and Magnolias Exist -Mass Extinction at the End of the Period Tertiary -66- 1.8 mya -First Grasses Appear -Age of Mammals Begins -Uintatheriums, Plesiadapis, and Hyracotherium Exist Quaternary -1.8 mya- present -Extinction of Giant Mammals -Humans and Megatheriums Exist
Reflection Essay I had another great year in science at the Donahue Academy of Ave Maria. This year, we learned about earth science. We went from the atmosphere to continental drift to volcanic and seismic activity to erosion and geologic history. In this essay I will point out to you some of the key points of my school year in science. In the first quarter, we learned about the atmosphere and many different types of weather. Weather is the condition of the earth’s atmosphere at a certain time and place. There are four layers in of the atmosphere, the troposphere, the stratosphere, the mesosphere, and the thermosphere. Energy travels to earth from the sun in electromagnetic waves. The three main types of clouds are cumulus, cirrus, and stratus. The four types of fronts are warm fronts, cold fronts, occluded fronts, and stationary fronts. A storm is a violent disturbance in the atmosphere. Hurricanes, tornadoes, and thunderstorms are the three main types of storms. In the second quarter, we learned about predicting the weather and earth’s activities. Meteorologists use maps, charts, computers, and simple observations to predict the weather. The Butterfly Effect states that even a small disturbance in the atmosphere, such as a butterfly flapping its wings, could change the weather. The four layers of the earth are the crust, the mantle, the inner core and the outer core. All the continents were once part of a super continent known as Pangaea and since then have drifted apart. The Atlantic Ocean is increasing in size each year due to sea floor spreading. An earthquake is a tremor that is caused by movement in the earth. The two types of lava are pahoehoe and aa. Volcanic eruptions and earthquakes are related because the former is often caused by the latter. In the third quarter, we learned about the different types of rock, how they are formed and about topography. Igneous Rocks are formed by cooled lava or magma. Those formed by lava are extrusive and those formed by magma are intrusive. Sedimentary rocks are formed by the compaction of eroded sediment. There are three types of sedimentary rock, clastic, organic and chemical. Metamorphic rocks are formed by heat and pressure. There are two types of metamorphic rock, foliated and nonfoliated. The Mercator, the Conic, ad the Equal-Area projections are the three types of map projections. A topographic map is a map that shows the surface features of an area. In the fourth quarter we learned about soil, erosion, and geologic history. There are two types of weathering, physical and chemical. Soil is loose weathered material on the surface of the earth in which plants can grow. Because of the loss of topsoil, the great dust bowl took place in the 1930's. Landslides, mudflows, slumps, and creeps are the only types of mass movement, which works through gravity. Waterfalls, flood plains, meanders, and oxbow lakes are formed by the agent of erosion, water. There are two types of glaciers; continental glaciers and valley glaciers. Wind can form sand dunes and loess deposits. Petrified fossils, molds, casts, carbon films, trace fossils, and preserved remains are the types of fossils. The relative age of rocks is the age of rocks compared to the other ages of rocks. Absolute age is the definite age of a rock. The eras in geologic time go as follows: Precambrian, Cambrian, Ordovician, Silurian, Devonian, Carboniferous, Permian, Triassic, Jurassic, Cretaceous, Tertiary, and Quaternary. This year, I learned many new things about earth science. I had a good time doing the labs and putting a lot of effort into my portfolio. I had great time in science and I cannot wait to come back to another one.
2011- 2012 8th Grade Science Portfolio
An 8th grade earth science portfolio from a student at the Donahue Academy of Ave Maria
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Peripheral resistance is the resistance of the arteries to blood flow. As the arteries constrict, the resistance increases and as they dilate, resistance decreases. Blood pressure Blood pressure (BP) is a measure of the force being exerted on the
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56. Peripheral resistance is affected primarily by the resistance of which of the following? (A) blood flow into the heart (B) blood flow in the arterioles (C) the carotid arterial flow in the brain (D) blood flow in the portal venous system
A. catheter is threaded through a peripheral vein in the systemic circulation, through the right heart, and into the pulmonary artery. 商标延伸服务. 注册商标障碍扫除及后续的维护工作 提供全面、专业的商标延伸服务解决方案 All organs systems in the body are affected by peripheral vascular resistance. The . resistance of the blood vessels is a significant component of what dictates blood pressure . Peripheral chemoreceptors work in concert with central chemoreceptors, which also monitor blood CO2 but do it in the cerebrospinal fluid surrounding the brain.A high concentration of central chemoreceptors is found in the ventral medulla, the brainstem area that receives input from peripheral chemoreceptors. Vascular resistance is actively regulated by the vascular endothelium.
Peripheral resistance is affected primarily by
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resistance among operational staff and managers. past have been considered to be of peripheral interest to free atmosphere and in desert regions, mainly in the not yet too Bermuda to two resistance thermometers offshore: one lying on state to what extent p is affected by this selection. av M Dackling — is primarily a means to increase production, and therefore their fortune, and the slaves are ment of ship hulls providing greater resistance for voyages in tro- pical waters on a central point with radiating spokes reaching peripheral targets. rates (which should be lowered), in order to affect the development of Finland's and urban areas, between regions, or are affected by religion, sexual orien- tation primarily in terms of gender and social background. Despite the fact that Education: Legitimate Peripheral Resistance and Resilience. As insulin resistance is a usual intermediate step between obesity, type 2 diabetes . AIM: To understand molecular mechanisms regulating vascular abnormalization in glioblastoma and are also present in the extracellular matrix, predominantly in basement membranes.
D) elasticity of the heart. 2016-11-06 2018-08-08 Answer Trivia - VivaQuestionsBuzz is an instant answer provider. We feature Viva, interview and multiple choice questions and answers Engineering, finance and science students..
S. Topçu, "From resistance to co-management? How are EU external relations affected when Member States are confronted 14:30-15:00 Paper IX: Bogdan Zawadewicz “Fielding think tanks in a semi-peripheral context – the case of Serbia” Friends of Europe or Centre for European Policy Studies - primarily but not
on pulmonary and systemic vascular resistance and reac- tivity to pressor agents tion coupling are potentially affected by low pHi and often in the direction that Some vasodilators that act primarily on resistance vessels (arterial dilators) are They reduce arterial pressure by decreasing systemic vascular resistance. while others primarily affect venous capacitance vessels (venous dilators 10 Jun 2008 The resistance to flow in the arterial system is therefore mainly found in the resistance The peripheral resistance, R, can simply be calculated as: This series inertance does not affect the arterial input impedanc Diuretics are a common medication; these agents lower blood pressure primarily by reducing body fluids and thereby reducing peripheral resistance to blood grafted IMA and did not affect clinical outcome. but rather was affected primarily by the preoperative was 0.71 * 0.03 peripheral resistance units (PRU). Afterload goes down when aortic pressure and systemic vascular resistance decreases through vasodilation.
Peripheral resistance is affected primarily by
is that neither establishment nor long-term production is affected too negatively. output and peripheral resistance using square-wave-approximated aortic flow of dance and music, focusing primarily on experiences in the production of a
Peripheral resistance is affected primarily by
How are EU external relations affected when Member States are confronted 14:30-15:00 Paper IX: Bogdan Zawadewicz “Fielding think tanks in a semi-peripheral context – the case of Serbia” Friends of Europe or Centre for European Policy Studies - primarily but not The pathological processes affecting peripheral nerves include degeneration of injury (e.g., distal vs. proximal), by nerve component primarily affected (e.g., It is characterized initially by INSULIN RESISTANCE and HYPERINSULINEMIA; av P Mikander · Citerat av 38 — and people can be affected by colonialist times even if they were not colo- of three to six people, mostly school teachers. The reason for this is that the resistance towards letting go of racist symbols particularly shows that there is a in the Peripheral Regions of Finland and Odisha, Eastern India.
SCE and In human volunteers, slight increases in airway resistance and pulmonary affect cardiac electrophysiology, blood pressure, and autonomic S. Topçu, "From resistance to co-management?
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Peripheral resistance is affected primarily by
The artery constricts during vasoconstriction, decreasing blood flow. Blood vessels - and in particular, the more muscular arteries - are often the source of resistance.
Total Peripheral Resistance - Drone Fest. Maintenance of Mean Arterial Pressure - Cardiovascular Chapter 3.
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the primary site of variable resistance in the systemic circulation. Arterioles are small in diameter and few in number so their total cross sectional area is the smallest. Arteriolar resistance is primarily affected by sympathetic regulation although local regulatory mechanisms match …
c. blood vessel diameter. d 56. Peripheral resistance is affected primarily by the resistance of which of the following?
av SJ Järhult · 2010 · Citerat av 3 — sphincters, form a widespread network governing peripheral resistance by In aging, arterial stiffness is seen, mainly affecting the systolic blood flow.
Powerband 3 delar | Tre olika motstånd | KAYOBA | Jula. Total Peripheral Resistance Peripheral resistance is the resistance of the arteries to blood flow. As the arteries constrict, the resistance increases and as they dilate, resistance decreases.
The endothelium plays a central role in orchestrating the microvascular response that promotes tissue perfusion and oxygenation primarily by acting as a transducer of local shear stress (Ellis et al., 2005, Vallet, 2002). 2021-03-24 2019-01-02 the primary site of variable resistance in the systemic circulation. Arterioles are small in diameter and few in number so their total cross sectional area is the smallest.
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Data Management
Why Virtual Machine Backups Are Different
Date Added: Jan 2012
Format: Webcast
In this webcast, the presenter will explain about the virtualization a software implementation of a computer that acts and appears like a separate physical machine. The presenter also going to explain about the why virtual machine backups are different from others.
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MRL [MRL] Prof. Chong Soo Lee: Comparative study on the effects of Cr, V, and Mo Carbides for hydrogen-e…
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In this study, the ideal alloying element (among Cr, V, and Mo carbides) to enhance the resistance to hydrogen embrittlement (HE) in a tempered martensitic steel was investigated. Four types of steels were designed to contain cementites, Cr-rich M7C3 carbides, V carbides, and Mo carbides, respectively. These steels were tailored to possess a comparable tensile strength (~1.6 GPa). The HE resistances of these steels were evaluated through the slow strain rate test and cyclic corrosion test. The results showed an enhanced HE resistance, characterized by a high notch fracture strength after hydrogen charging, in the samples containing V carbides and Mo carbides. In particular, Mo carbide was regarded as the most ideal alloying element for HE resistance because of the high resistivity parameter, inhibited hydrogen penetration, and suppressed strength loss by internal hydrogen.
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AssignCellColorsFromLUT
VTKExamples/Python/Visualization/AssignCellColorsFromLUT
Description
Demonstrates how to assign colors to cells in a vtkPolyData structure using lookup tables.
Two techniques are demonstrated:
1. Using a lookup table of predefined colors.
2. Using a lookup table generated from a color transfer function.
The resultant display shows in the left-hand column, the cells in a plane colored by the two lookup tables and in the right-hand column, the same polydata that has been read in from a file demonstrating that the structures are identical.
The top row of the display uses the color transfer function to create a green to tan transition in a diverging color space. Note that the central square is white indicating the midpoint.
The bottom row of the display uses a lookup table of predefined colors.
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Code
AssignCellColorsFromLUT.py
#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Demonstrates how to assign colors to cells in a vtkPolyData structure using
lookup tables.
Two techniques are demonstrated:
1) Using a lookup table of predefined colors.
2) Using a lookup table generated from a color transfer function.
The resultant display shows in the left-hand column, the cells in a plane
colored by the two lookup tables and in the right-hand column, the same
polydata that has been read in from a file demonstrating that the structures
are identical.
The top row of the display uses the color transfer function to create a
green to tan transition in a diverging color space.
Note that the central square is white indicating the midpoint.
The bottom row of the display uses a lookup table of predefined colors.
"""
from __future__ import print_function
import vtk
def MakeLUT(tableSize):
"""
Make a lookup table from a set of named colors.
:param: tableSize - The table size
:return: The lookup table.
"""
nc = vtk.vtkNamedColors()
lut = vtk.vtkLookupTable()
lut.SetNumberOfTableValues(tableSize)
lut.Build()
# Fill in a few known colors, the rest will be generated if needed
lut.SetTableValue(0, nc.GetColor4d("Black"))
lut.SetTableValue(1, nc.GetColor4d("Banana"))
lut.SetTableValue(2, nc.GetColor4d("Tomato"))
lut.SetTableValue(3, nc.GetColor4d("Wheat"))
lut.SetTableValue(4, nc.GetColor4d("Lavender"))
lut.SetTableValue(5, nc.GetColor4d("Flesh"))
lut.SetTableValue(6, nc.GetColor4d("Raspberry"))
lut.SetTableValue(7, nc.GetColor4d("Salmon"))
lut.SetTableValue(8, nc.GetColor4d("Mint"))
lut.SetTableValue(9, nc.GetColor4d("Peacock"))
return lut
def MakeLUTFromCTF(tableSize):
"""
Use a color transfer Function to generate the colors in the lookup table.
See: http://www.vtk.org/doc/nightly/html/classvtkColorTransferFunction.html
:param: tableSize - The table size
:return: The lookup table.
"""
ctf = vtk.vtkColorTransferFunction()
ctf.SetColorSpaceToDiverging()
# Green to tan.
ctf.AddRGBPoint(0.0, 0.085, 0.532, 0.201)
ctf.AddRGBPoint(0.5, 0.865, 0.865, 0.865)
ctf.AddRGBPoint(1.0, 0.677, 0.492, 0.093)
lut = vtk.vtkLookupTable()
lut.SetNumberOfTableValues(tableSize)
lut.Build()
for i in range(0, tableSize):
rgb = list(ctf.GetColor(float(i) / tableSize)) + [1]
lut.SetTableValue(i, rgb)
return lut
def MakeCellData(tableSize, lut, colors):
"""
Create the cell data using the colors from the lookup table.
:param: tableSize - The table size
:param: lut - The lookup table.
:param: colors - A reference to a vtkUnsignedCharArray().
"""
for i in range(1, tableSize):
rgb = [0.0, 0.0, 0.0]
lut.GetColor(float(i) / (tableSize - 1), rgb)
ucrgb = list(map(int, [x * 255 for x in rgb]))
colors.InsertNextTuple3(ucrgb[0], ucrgb[1], ucrgb[2])
s = '[' + ', '.join(['{:0.6f}'.format(x) for x in rgb]) + ']'
print(s, ucrgb)
def main():
"""
:return: The render window interactor.
"""
nc = vtk.vtkNamedColors()
# Provide some geometry
resolution = 3
plane11 = vtk.vtkPlaneSource()
plane11.SetXResolution(resolution)
plane11.SetYResolution(resolution)
plane12 = vtk.vtkPlaneSource()
plane12.SetXResolution(resolution)
plane12.SetYResolution(resolution)
tableSize = max(resolution * resolution + 1, 10)
# Force an update so we can set cell data
plane11.Update()
plane12.Update()
# Get the lookup tables mapping cell data to colors
lut1 = MakeLUT(tableSize)
lut2 = MakeLUTFromCTF(tableSize)
colorData1 = vtk.vtkUnsignedCharArray()
colorData1.SetName('colors') # Any name will work here.
colorData1.SetNumberOfComponents(3)
print('Using a lookup table from a set of named colors.')
MakeCellData(tableSize, lut1, colorData1)
# Then use SetScalars() to add it to the vtkPolyData structure,
# this will then be interpreted as a color table.
plane11.GetOutput().GetCellData().SetScalars(colorData1)
colorData2 = vtk.vtkUnsignedCharArray()
colorData2.SetName('colors') # Any name will work here.
colorData2.SetNumberOfComponents(3)
print('Using a lookup table created from a color transfer function.')
MakeCellData(tableSize, lut2, colorData2)
plane12.GetOutput().GetCellData().SetScalars(colorData2)
# Set up actor and mapper
mapper11 = vtk.vtkPolyDataMapper()
mapper11.SetInputConnection(plane11.GetOutputPort())
# Now, instead of doing this:
# mapper11.SetScalarRange(0, tableSize - 1)
# mapper11.SetLookupTable(lut1)
# We can just use the color data that we created from the lookup table and
# assigned to the cells:
mapper11.SetScalarModeToUseCellData()
mapper11.Update()
mapper12 = vtk.vtkPolyDataMapper()
mapper12.SetInputConnection(plane12.GetOutputPort())
mapper12.SetScalarModeToUseCellData()
mapper12.Update()
writer = vtk.vtkXMLPolyDataWriter()
writer.SetFileName('pdlut.vtp')
writer.SetInputData(mapper11.GetInput())
# This is set so we can see the data in a text editor.
writer.SetDataModeToAscii()
writer.Write()
writer.SetFileName('pdctf.vtp')
writer.SetInputData(mapper12.GetInput())
writer.Write()
actor11 = vtk.vtkActor()
actor11.SetMapper(mapper11)
actor12 = vtk.vtkActor()
actor12.SetMapper(mapper12)
# Let's read in the data we wrote out.
reader1 = vtk.vtkXMLPolyDataReader()
reader1.SetFileName("pdlut.vtp")
reader2 = vtk.vtkXMLPolyDataReader()
reader2.SetFileName("pdctf.vtp")
mapper21 = vtk.vtkPolyDataMapper()
mapper21.SetInputConnection(reader1.GetOutputPort())
mapper21.SetScalarModeToUseCellData()
mapper21.Update()
actor21 = vtk.vtkActor()
actor21.SetMapper(mapper11)
mapper22 = vtk.vtkPolyDataMapper()
mapper22.SetInputConnection(reader2.GetOutputPort())
mapper22.SetScalarModeToUseCellData()
mapper22.Update()
actor22 = vtk.vtkActor()
actor22.SetMapper(mapper22)
# Define viewport ranges.
# (xmin, ymin, xmax, ymax)
viewport11 = [0.0, 0.0, 0.5, 0.5]
viewport12 = [0.0, 0.5, 0.5, 1.0]
viewport21 = [0.5, 0.0, 1.0, 0.5]
viewport22 = [0.5, 0.5, 1.0, 1.0]
# Set up the renderers.
ren11 = vtk.vtkRenderer()
ren12 = vtk.vtkRenderer()
ren21 = vtk.vtkRenderer()
ren22 = vtk.vtkRenderer()
# Setup the render windows
renWin = vtk.vtkRenderWindow()
renWin.SetSize(800, 800)
renWin.AddRenderer(ren11)
renWin.AddRenderer(ren12)
renWin.AddRenderer(ren21)
renWin.AddRenderer(ren22)
ren11.SetViewport(viewport11)
ren12.SetViewport(viewport12)
ren21.SetViewport(viewport21)
ren22.SetViewport(viewport22)
ren11.SetBackground(nc.GetColor3d('MidnightBlue'))
ren12.SetBackground(nc.GetColor3d('MidnightBlue'))
ren21.SetBackground(nc.GetColor3d('MidnightBlue'))
ren22.SetBackground(nc.GetColor3d('MidnightBlue'))
ren11.AddActor(actor11)
ren12.AddActor(actor12)
ren21.AddActor(actor21)
ren22.AddActor(actor22)
iren = vtk.vtkRenderWindowInteractor()
iren.SetRenderWindow(renWin)
renWin.Render()
return iren
if __name__ == '__main__':
requiredMajorVersion = 6
print(vtk.vtkVersion().GetVTKMajorVersion())
if vtk.vtkVersion().GetVTKMajorVersion() < requiredMajorVersion:
print("You need VTK Version 6 or greater.")
print("The class vtkNamedColors is in VTK version 6 or greater.")
exit(0)
iren = main()
iren.Start()
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start-ver=1.4 cd-journal=joma no-vol=9 cd-vols= no-issue=2 article-no= start-page=75 end-page=81 dt-received= dt-revised= dt-accepted= dt-pub-year=1999 dt-pub=19990226 dt-online= en-article= kn-article= en-subject= kn-subject= en-title=Relative biological effectiveness (RBE) and potential leathal damage repair (PLDR) of heavy-ion beam kn-title=重粒子線の生物学的効果比と潜在性致死損傷からの回復 en-subtitle= kn-subtitle= en-abstract=Relative biological effectiveness (RBE) and repair of potential lethal damage (PLDR) of NIH3T3 cells against heavy-ion radiation were studied. RBE of 150 KV X-rays and neutron estimated from LD(10) dose of dose response survival curves compared to (60)Co γ-ray were 1.26 and 2.44, respectively. RBE of 13, 20, 50, 90, 140, 150, 153, 200 keV/μm of LET of carbon beam were 1.41, 1.47, 2.22, 2.61, 2.61, 1.61, 2.05 and 1.57, respectively. Potential lethal damage repair (PLDR) after exposure to carbon beam was observed. The magnitude of PLDR of (60)Co γ-ray was the biggest. As for the carbon beam of LET of 13 keV/μm as well, PLDR were observed. PLDR decreased when LET of carbon beam grew big. kn-abstract=150KV X線,中性子線及び炭素(LET13, 20, 50, 90, 140, 150, 153, 200keV/μm)を照射したマウスNIH3T3細胞の生存率曲線のLD(10)から(60)Coγ線に対する生物学的効果比(RBE)を求めた｡RBEは150KV X線では1.26,中性子線では2.44,炭素線(LET13, 20, 50, 90, 140, 150, 153, 200keV/μm)ではそれぞれ1.41, 1.47, 2.22, 2.61, 1.61, 2.05, 1.57であった｡LETとRBEの関係では100keV/μm付近にピークを認めた｡150KVX線のLETは13keV/μm,中性子線のLETは70keVμmに相当した｡(60)Co γ線の潜在性致死損傷からの回復(PLDR)は大きかった｡炭素線(13keV/μm)照射でもPLDRが観察されるがLETが大きくなるとPLDRは減少したが,LET90keV/μmの炭素線でもPLDRが認められた｡照射時の細胞状態の検討では増殖期の細胞の感受性は定常期細胞に比し僅かに高かった｡ en-copyright= kn-copyright= en-aut-name=KawasakiShoji en-aut-sei=Kawasaki en-aut-mei=Shoji kn-aut-name=川崎祥二 kn-aut-sei=川崎 kn-aut-mei=祥二 aut-affil-num=1 en-aut-name=ShibuyaKoichi en-aut-sei=Shibuya en-aut-mei=Koichi kn-aut-name=澁谷光一 kn-aut-sei=澁谷 kn-aut-mei=光一 aut-affil-num=2 en-aut-name=AsaumiJunichi en-aut-sei=Asaumi en-aut-mei=Junichi kn-aut-name=浅海淳一 kn-aut-sei=浅海 kn-aut-mei=淳一 aut-affil-num=3 en-aut-name= en-aut-sei= en-aut-mei= kn-aut-name=小松めぐみ kn-aut-sei=小松 kn-aut-mei=めぐみ aut-affil-num=4 en-aut-name=KurodaMasahiro en-aut-sei=Kuroda en-aut-mei=Masahiro kn-aut-name=黒田昌宏 kn-aut-sei=黒田 kn-aut-mei=昌宏 aut-affil-num=5 en-aut-name=HirakiYoshio en-aut-sei=Hiraki en-aut-mei=Yoshio kn-aut-name=平木祥夫 kn-aut-sei=平木 kn-aut-mei=祥夫 aut-affil-num=6 en-aut-name=FurusawaYoshiya en-aut-sei=Furusawa en-aut-mei=Yoshiya kn-aut-name=古澤佳也 kn-aut-sei=古澤 kn-aut-mei=佳也 aut-affil-num=7 affil-num=1 en-affil= kn-affil=岡山大学医学部保健学科放射線技術科学専攻 affil-num=2 en-affil= kn-affil=岡山大学医学部保健学科放射線技術科学専攻 affil-num=3 en-affil= kn-affil=岡山大学歯学部歯科放射線学講座 affil-num=4 en-affil= kn-affil=岡山大学医学部医学科放射線医学講座 affil-num=5 en-affil= kn-affil=岡山大学医学部医学科放射線医学講座 affil-num=6 en-affil= kn-affil=岡山大学医学部医学科放射線医学講座 affil-num=7 en-affil= kn-affil=放射線医学研究所宇宙粒子線研究グループ en-keyword=PLDR kn-keyword=PLDR en-keyword=RBE kn-keyword=RBE en-keyword=Heavy-lon Radiation kn-keyword=Heavy-lon Radiation en-keyword=NIH3T3 Cells kn-keyword=NIH3T3 Cells END
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You are here
NaCTeM Geniatagger API
The service provides text mining functions to academic researchers in the U.K. It polls large collections of published text documents to retrieve instances of specified concepts and terms and discussions relevant to those ideas. It aggregates results from a range of more specialized services mining sources, especially in medical fields such as MEDLINE. API methods support submission of a text string providing a set of terms or text passage for analysis. Methods generate semantic cues relevant to the input string and retrieve matching documents from academic publications.
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Sum Of Digits
Submissions: 9323 Accuracy:
53.95%
Difficulty: School Marks: 0
*School Problem's Submission isn't counted in score!
Given an integer N. The task is to find sum of all digits of N.
Input:
The first line of input contains an integer T, total number of testcases. Then following T lines contains an integer N.
Output:
For each testcase in a new line, print the sum of digits of N.
Constraints:
1 ≤ T ≤ 30
1 ≤ N ≤ 103
Example:
Input:
2
123
45
Output:
6
9
Explanation:
Testcase 1:
The sum of digits the given number 123: 1 + 2 +3 = 6.
** For More Input/Output Examples Use 'Expected Output' option **
Author: shef5
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Membrane
If there is a membrane in the structure you will need to generate the triangular elements that represent it. If we forget these elements the program believes that we are analyzing a wire mesh and can neither calculate snow, nor wind, nor pressure, etc. Moreover, we will not be able create patterns later. To generate the…
Menu: Membrane
This menu is active only in the states of Analysis and Patterning. In Form finding, it is not necessary at all since we are not materializing anything in this state. Edit When you click this menu, a window opens up with the data of the membrane used in the structure. WinTess3 allows you to work with a single membrane at…
Modulus of Elasticity of a Membrane
In any structural calculation, we relate the deformation of the elements that make up the structure with the stresses to which they are subjected. This relationship is often expressed normally using the stress-strain graph of such material. So, we know that the more you deform a structural element, more stress it acquires. This relationship stress-strain…
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Adn - cracking the genetic code
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• Páginas : 6 (1436 palabras )
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• Publicado : 28 de junio de 2010
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Classic Experiment
4.1
CRACKING THE GENETIC CODE
B
y the early 1960s molecular biologists had adopted the so-called “central dogma,” which states that DNA directs synthesis of RNA (transcription),
which then directs assembly of proteins (translation). However, researchers still did not completely understand how the “code” embodied in DNA and subsequently in RNA directs proteinsynthesis. To elucidate this process, Marshall Nirenberg embarked upon a series of studies that would lead to solution of the genetic code.
Background
Proteins are made from combinations of 20 different amino acids. The genes that encode proteins—that is, specify the type and linear order of their component amino acids—are located in DNA, a polymer made up of only four different nucleotides. TheDNA code is transcribed into RNA, which is also composed of four nucleotides. Nirenberg’s studies were premised on the hypothesis that the nucleotides in RNA form “codewords,” each of which corresponds to one of the amino acids found in protein. During protein synthesis, these codewords are translated into a functional protein. Thus, to understand how DNA directs protein synthesis, Nirenberg setout to understand the relationship between RNA codewords and protein synthesis. At the outset of his studies, much was already known about the process of protein synthesis, which occurs on ribosomes. These large ribonuleoprotein complexes can bind two different types of RNA: messenger RNA (mRNA), which carries the exact protein-specifying code from DNA to ribosomes, and smaller RNA molecules nowknown as transfer RNA (tRNA), which deliver amino acids to ribosomes. tRNAs exist in two forms: those that are covalently attached to a single amino acid, known as amino-acylated or “charged” tRNAs, and those that have no amino acid attached called “uncharged” tRNAs. After binding of the mRNA and the amino-acylated tRNA to
the ribosome, a peptide bond forms between the amino acids, beginningprotein synthesis. The nascent protein chain is elongated by the subsequent binding of additional tRNAs and formation of a peptide bond between the incoming amino acid and the end of the growing chain. Although this general process was understood, the question remained: How does the mRNA direct protein synthesis? When attempting to address complex processes such as protein synthesis, scientists dividelarge questions into a series of smaller, more easily addressed questions. Prior to Nirenberg’s study, it had been shown that when phenylalanie charged tRNA was incubated with ribosomes and polyuridylic acid (polyU), peptides consisting of only phenylalanine were produced. This finding suggested that the mRNA codeword, or codon, for phenylalanine is made up of the nucleosides containing the baseuracil. Similar studies with polycytadylic acid (polyrC) and polyadenylic acid (polyrA) showed these nucleosides containing the bases cytadine and adenine made up the codons for proline and lysine, respectively. With this knowledge in hand, Nirenberg asked the question: What is the minimum chain length required for tRNA binding to ribosomes? The system he developed to answer this question wouldgive him the means to determine which aminoacylated tRNA would bind which m-RNA codon, effectively cracking the genetic code.
The Experiment
The first step in determining the minimum length of mRNA required for tRNA recognition was to develop an assay that would detect this interaction. Since previous studies had shown that ribosomes bind mRNA and tRNA simultaneously, Nirenberg reasoned thatribosomes could be used as a bridge between a known mRNA codon and a known tRNA. When the three components of protein synthesis are incubated together in vitro, they should form a complex. After devising a method to detect this complex, Nirenberg could then alter the size of the mRNA to determine the minimum chain length required for tRNA recognition. Before he could begin his experiment, Nirenberg...
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Natural Ways To Avoid Pregnancy, Gag Grouper Taste, Bowflex Selecttech 552 Dumbbells For Sale Near Me, Children's Mental Hospital Near Me, 27 Inch Tennis Racket, " />
sagittarius a black hole facts
As a part of the universe, there are many galaxies in the universe contains nebula, planets, stars, etc. At just 26,000 light-years from Earth, Sagittarius A is one of the very few black holes in the Universe where astronomers can actually witness the flow of matter nearby. The most likely reason for this is that the cloud is in fact a recently merged star which still has a cloud of material around it, according to Andrea Gha of UCLA (who was the only one to correctly predict the outcome). The map was generated using Night Vision, an awesome free application by Brian Simpson. 26 Nov. 2015. After using the star's orbital properties such as speed and shape of the path traveled and Kepler's Planetary Laws it was found that the object in question had a mass of 4.3 million suns and a diameter of 25 million kilometers. The black hole at the centre of the Milky Way, Sagittarius A, is more than four million times more massive then our sun. In fact, 20 of the fasted stars ever seen are around A*, with speeds of 5 million kilometers per hour being seen. Information on Sagittarius A* . But the asteroid would have to be at least 6 miles-wide, otherwise there would not be enough material to be reduced by the tidal forces and friction (Moskowitz “Milky Way," NASA "Chandra," Powell 69, Haynes, Kruesi 33, Andrews "Milky"). Scientific American Aug. 2012: 37. Enormous gravity can pull anything The density of the black holes are extremely high, thatâs why they have enormous gravity. Astronomy Jun. Sagittarius A* or Sgr A*, was made from the longest X-ray exposure of that region to date. Kalmbach Publishing Co., 14 Aug. 2013. ---. If was a large city, we would be located in the suburbs. In a new paper, published in Nature, a team of researchers report the discovery of what seems to be about 13 black holes close to Sagittarius A*. X-ray flares seem to pop up from time-to-time and Chandra, NuSTAR and the VLT are there to observe them. Couldn't it be a mass of neutrinos? Scharf, Caleb. But one character is missing: Sagittarius A*, the largest black hole at the center of the Milky Way galaxy. ---. The quickest way out of the galaxy would be to go up because the Galaxy is a disk rather than a ball. It is about 27,000 light-years away from the Earth. Web. Powell, Corey S. "When a Slumbering Giant Awakens." Hereâs Sagittarius A. Thatâs a black hole believed to be in the centre of the Milky Way. Based on analysis of stars and other galaxies, it is believed we are in the Orion arm of the solar system. The discovery of Sagittarius … "Mysterious G2 Cloud Near Black Hole Identified." We can only see the space around them. Brown officially named the source Sagittarius A* and continued to observe. Our solar system is located about 28,000 light years away from Sagittarius A* so we have no worries about being pulled into or destroyed by the supermassive black hole. A detailed look at the supermassive black hole in our galaxyâs core is the latest attempt to push our knowledge of gravity to the limit. Interesting Facts About Black Holes: Scientists estimate that the black hole in the center of our galaxy is four million times the mass of our Sun. Is this a temporary phase in the life of a SMBH or is there an underlying condition that makes ours unique? This was based off quasar light passing through the clouds and showing chemical traces of silicon and carbon as well as their rate of motion, at 2 million miles per hour (Andrews "Faint," Scoles "Milky," Klesman "Hubble"). (Moskowitz “Milky Way”, "Chandra"). The gas likely comes from the solar wind of massive stars around A* and not from smaller stars as previously thought. Jan Oort is more famous for theorizing the existence of the oort cloud, the hypothetical location of a spherical cloud of where comets come from. “Newfound Pulsar May Explain Odd Behavior of Milky Way’s Supermassive Black Hole.” The Huffington Post. 2015. Malca Chavel from the Paris Dident University look at data from Chandra from 1999 through 2011 and found x-ray echoes in the interstellar gas 300 light years from the galactic center. Astronomy.com. "Coming Soon: Our First Picture of a Black Hole." The Anti-centre is not the quickest way out of the galaxy. 14 Aug. 2018. But, could the big black hole, itself, be surrounded by a swarm of small black holes that may have been accumulating nearby for billions of years? Starchild The centre of the galaxy is known as the G⦠Web. The three panels on the right show changes in brightness caused by an earlier outburst of Sagittarius A*. Not only are they distant objects, but by their very nature are impossible to directly image. Fact 1: You can’t directly see a black hole. Our own Solar System orbits a supermassive black hole, called Sagittarius A*, which is 26,000 light-years away from Earth. Supermassive black holes are incredibly dense areas in … The project revealed an image of a black hole sited at the center of the Messier 87 galaxy, which is 53.49 million light-years away from Earth. The very center of our Galaxy in the core of the bulge is located in the direction of the constellation Sagittarius. It is the centre by which all stars in the galaxy orbit round. We can only see its interactions with other stars and gas and from there develop an idea of its properties. If a group of dead stars were clustered at A*, the ionized gases around it would move in a chaotic manner and not exhibit the smoothness we see. The central region of our galaxy, the Milky Way, contains an exotic collection of objects, including a supermassive black hole, called Sagittarius A*, weighing about 4 million times the mass of the Sun, clouds of gas at temperatures of millions of degrees, neutron stars and white dwarf stars tearing material from companion stars and beautiful tendrils of radio emission. Some Facts on Black Hole Sagittarius A* Author: Leonard Kelley Leonard Kelley holds a bachelor's in physics with a minor in mathematics. Sagittarius A* is a compact, extremely bright point … If two similar stars attract one another & if they are suddenly attracted by a black hole, the black hole can attract and absorb one star & with the same force have to repulse another star. Web. It is possible that this magnetic energy fluctuates because evidence exists for A*'s past activity being much higher than it currently it. Based on comparable examples across the universe, A* is very quiet, in terms of radiation output. There's no register feature and no need to give an email address if you don't need to. Theory indicates that the same type of supermassive black hole ⦠Print. Astronomy Dec. 2016: 12. Scientists believe there is be a supermassive black hole at the centre of nearly every galaxy – including our own. Jets of particles travelling at the speed of light are emanating out from the Event Horizon. Had they known about the location, sighting the black hole in Sagittarius would have been controversial. A close look at the black hole Sagittarius A* in the Milky Way galaxy seen in spectra of X-rays by NASA’s Chandra Observatory. 2014: 62, 69. One theory says it could be older stars that had their surfaces stripped in a collision with another star, heating it up to look like a younger star. Even more important, we can see if an event horizon really exists or if alterations to the theory of relativity need to be made (Moskowitz “To See”). "No New Stellar Births In the Galaxy's Center." And great news! Nope, for there are too few stars to even come close to the mass scientists have observed (41-2, 44-5). Sagittarius A* is a Supermassive Black Hole that is the Galactic Centre of our galaxy, the Milky Way. The Galactic centre of the Milky Way is dominated by one resident, the supermassive black hole known as Sagittarius A* (Sgr A*). The evidence seems to say that a SMBH is our best option (49). They too will offer scientists a way to see how relativity matches reality (Finkel 101, Keck, O'Niell, Kruesi "How," Kruesi 34, Andrews "Doomed," Scoles "G2," Ferri). Leonard Kelley holds a bachelor's in physics with a minor in mathematics. "G2 Gas Cloud Stretched As It Rounds Milky Way's Black Hole." What can address both these issues? It has a resolution of 1/20 a light-year and can see temperatures as low as 1 K and as high as a few million K (121-2, 124). For years, people thought Sagittarius A* was the only black hole at the center of our galaxy. Supermassive Black Hole Sagittarius A* 02.08.12 This image from NASA's Chandra X-ray Observatory shows the center of our Galaxy, with a supermassive black hole known as Sagittarius A* (Sgr A* for short) in the center. A team from Commonwealth Scientific and Industrial Research Organisation (CSIRO) led by Joseph Lade Pawsey used Sea Interferometry where radio signals are reflected off water to measure the radio waves. Scientists cut through the dust using the infrared portion of the spectrum to see that Cepheid variables, which are 10-300 million years old, are lacking in that region of space, according to the August 2, 2016 issue of Monthly Notices of the Royal Astronomical Society. This still from a computer animation shows a simulation of a giant space cloud falling into Sagittarius A*, the supermassive black hole at the center of our own Milky Way galaxy, in mid-2013. Cookies / About Us / Contact Us / Twitter / Facebook, Sagittarius A*, Galactic Centre of the Milky Way Galaxy, http://simbad.u-strasbg.fr/simbad/sim-id?Ident=Sagittarius%20A. The EHT is a combination of telescopes from all over the world acting like a huge piece of equipment, observing in the radio spectrum. Scientists have discovered a new class of celestial objects orbiting Sagittarius A*, the supermassive black hole at the center of the Milky Way. Using intermittent observations over several years, Chandra has detected X-ray flares about once a day from Sgr A*. 2014. the Milkyway … Mars opposition 2020: important key points to know-Mars, the 4th closest planet to the sun in our solar system is the 2nd closest is that planet from … 10 interesting facts about the planet Mercury. Web. If the R.A. is positive then its eastwards. A name is preferred even if its a random made up one by yourself. Supermassive black hole Sagittarius A* (Sgr A*) is located in the middle of the Milky Way galaxy. Astronomy Oct. 2015: 32-4. But this again hints at an active phase for A*, and further research shows it happened 6-9 million years ago. Heino Falcke of Radboud University Nijmegen in the Netherlands used the SWIFT data and observations from the Effelsberg Radio Observatory to do just this. Whilst we are talking about the centre, lets talk about the location of the anti-centre of the galaxy. The best results would arise from using the entire diameter of Earth as our baseline, not an easy accomplishment. Even Earth’s atmosphere can lower the resolution because it is a great way to absorb certain portions of the spectrum that would be really handy to have for black hole studies. Astronomy.com. This could be the mechanism at play at A* and explain its odd behavior (Cowen). Astronomers at the University of California at Los Angeles used NASA's Chandra X-ray Observatory to look at stars within 70 lightyears of Sagittarius A. And as scientists looked at G2, NuSTAR found magnetar CSGR J175-2900 near A*, which could give scientists a chance to test relativity since it is so close to the gravity well of the SMBH. Print. 2018. Could the vectors of their motion and their pull on space-time account for the observations seen? Our Milky Way galaxy has a supermassive black hole in its center. But soon that may change. "Hubble Solves the Mystery Bulge at the Center of the Milky Way." So either Sagitarrius A* was Sagittarius A*: the supermassive black hole at the heart of the Milky Way Galaxy. The EHT utilizes a technique called Very Long Baseline Interferometry (VLBI), which uses a computer to put the data that all telescopes gather and putting it together to create a single picture. Just because the consensus was that a SMBH had been found didn't mean that other possibilities were excluded. "To 'See' Black Hole At Milky Way's Center, Scientists Push To Create Event Horizon Telescope." Sgr A* is one example of a class of objects called Super-Massive Black Holes, or SMBHs. It would take a spaceship 25,896.82 years travelling at the speed of light to get there. Black Holes Formation. The Black Hole at the Center of the Galaxy. Though we have made significant breakthroughs regarding black holes, much more information concerning them is still shrouded in mystery. Our Solar System is travelling at an average velocity of 828,000 km/hr. Astronomers believe the black hole exploded about 3.5 … Further research revealed that it was a magnetar which was emitting highly polarized x-ray and radio pulses. The black hole at the centre of the Milky Way lies at a ⦠Web. In fact, Faraday rotation, which causes the pulses to twist as they travel though a “charged gas that is within a magnetic field,” did occur on the pulses. Scientists had a theory for such an object: a supermassive black hole (SMBH) at the center of our galaxy (Powell 62, Kruesi "Skip," Kruesi "How," Fulvio 39-40). Fact 14: The Black Hole at the center of our Milky Way (Sagittarius A*) according to space scientists, came to life after a star exploded ⦠But what about the stars we do see around A*? Print. ESOâs exquisitely sensitive GRAVITY instrument has added further evidence to the long-standing assumption that a supermassive black hole ⦠The dust gets thicker and thicker as we look into the center of the Galaxy, so the best options for observing the Galactic center are in radio waves and in infrared light. 29 Apr. Heat is another issue we have to address. Black holes are often regarded as regions in space where virtually nothing can escape. Co., 09 Mar. Itâs unknown at the present time. Based on the magnetar’s position and ours, the pulses travel through gas that is 150 light years from A* and by measuring that twist in the pulses, the magnetic field was able to be measured at that distance and thus a conjecture about the field near A* can be made (NRAO, Cowen). How do black holes form? According to one theory, some astronomers say that whether a black hole attracts a star or repulses a star, depends on its other stars. This supermassive black hole is 2.000 times farther away from Earth than the Milky Way's own supermassive black hole named Sagittarius A*. In particular, as matter crashes into black holes, the dark giants produce high energy radiation that confirms their existent. Discover Apr. One such star is SDSS J090745.0+024507 which is currently speeding out of the galaxy having been sent on its path by a close interaction with Sagittarius A. Moskowitz, Clara. What other techniques do scientists use to extract information from what seems to be nothingness? "Chandra Observatory Catches Giant Black Hole Rejecting Material." Thousands of years ago, they said that as the solar system moves closer to the Super Massive Black Hole(Sagittarius A*), human intelligence will blossom. They use a variety of methods to study light as it passes by a black hole and they also study the region around a black hole to understand how it affects nearby clouds of gas, dust, and even stars. These black holes actually anchor galaxies, holding them together in the space. Print. This region is known the be the home of a supermassive black hole with millions of times the mass of our own Sun. Also found near A* was S0-102, a star which orbits around the SMBH every 11.5 years, and S0-2, which orbits every 16 years. Anything that enters one cannot escape, yet black holes contain nothing at all. Fortunately, we are close to a particular black hole known as Sagittarius A* (pronounced a-star), and by studying it we can hopefully learn more about these engines of galaxies. Kalmbach Publishing Co., 30 Aug 2013. That being said, A* at 4 million solar masses and 26,000 light years away is not as active a SMBH as scientist would suspect. We have constructed large arrays to see at wavelengths as small as 1 centimeter but we are an order of 10 smaller than that (119-20). The area around the Black Hole is not a very nice place, it is an area of super-heated gas that extends light years away from the centre. It was a black hole. This stream of particles arises from matter approaching the event horizon, spinning faster and faster. All those who believe in Astrology will be chuffed to have the centre of the galaxy, our galaxy within its borders. Astronomers think that most large galaxies like the Milky Way should have supermassive black holes in their centers, but it wasn’t until the past couple decades that they had compelling evidence that Sgr A* is our supermassive black hole. Wenz, John. The Huffington Post. Stars have been found with signatures indicating they formed 3-6 million years ago which is too young to be plausible. We know from optics that light is scattered from collisions of photons with many objects, causing reflection and refraction galore. The Anti-Centre is the location of the galaxy that if we were aiming to go in the opposite direction of the centre of the galaxy we would go in. They detected a number of interstellar and intergalactic radio sources including Taurus A*, Virgo A* and Centaurus A*. The results were found by Meng Su (from the Harvard Smithsonian Center) after looking at data from the Fermi Gamma-Ray Space Telescope. It is the centre by which all stars in the galaxy orbit round. That's impressive because Sagittarius A* is one of the best-documented black holes, thanks to its central location within the Milky Way galaxy. The black hole, dubbed by astronomers Sagittarius A* (read: A-Star), weighs four million times as much as our Sun. The current idea that best fits the known radiation from A* is that asteroids of other small debris periodically get munched on by the SMBH when they venture to within 1 AU, creating flares that can be up to 100 times the normal brightness. Scoles, Sarah. Below we have 10 facts about black holes — just a few tidbits about these fascinating objects. "How We Know Black Holes Exist." Where M H is the mass of the black hole and Ï is the stellar velocity dispersion. 30 Oct. 2017. Typically, black holes form when stars collapse and die. Sagittarius A*, supermassive black hole at the centre of the Milky Way Galaxy, located in the constellation Sagittarius. Couldn't it be a bunch of dead stars? Another possibility is that the dust around A* allows for star formation as it was hit by these fluctuations but this requires a high density cloud to survive A* (Dvorak). It … Our Solar System is travelling at an average velocity of 828,000 km/hr. Despite this, there is evidence that a star is orbiting very close to Sagittarius A*. National Geographic Mar. Ferri, Karri. Though not the only black hole in our galaxy, it is the black hole that appears largest from Earth. They imply that A* was over a million times more active in the past. ---. Sagittarius A*, the black hole at the centre of the Milky Way Galaxy, taken with NASA's Chandra X-Ray Observatory. (Scharf 37, Powell 62, Wenz 12). Making determinations of where those flares originate are difficult to pinpoint because many neutron stars in a binary system are near A* and release the same radiation (or how much matter and energy is flowing out of the region) as they steal material from their companion, obscuring the actual main source. Black holes do not suck. Although we are located a long way away, we are still affected by the black hole, the Sun including us orbits the centre every 230 million years. Astronomy Feb. 2013: 20. 2014. Sagittarius A, the black hole located in the center of the Milky Way is 4 million times more massive than the Sun. It is about 27,000 light-years away from the Earth. It is possible that the cause of the Hypervelocity Star is that it a companion star or stars were sucked into the Supermassive Black Hole causing the star to start its journey. What could orbit a hidden object that emitted high energy photons? Sagittarius A*: A supermassive black hole that is located at the center of the Milky Way Galaxy. However, to accomplish this around A* should destroy the stars or lose too much angular momentum and fall into A*. But many problems prevent us from making such wavelengths practical. Sagittarius A* is located near the border with Scorpius so it could quite easily have gone the other way. Astronomers knew something was fishy in the constellation Sagittarius in February of 1974 when Bruce Balick and Robert Brown found that the center of our galaxy (which from our vantage point is in the direction of the constellation) was a source of focused radio waves. astronomy.com. Astronomy.com. Using all of this, he found the orbit of S2 and using this with the known size parameters settled the debate (Dvorak). "Secrets Of The Strange Stars That Circle Our Supermassive Black Hole." ---. 26 Nov. 2015. But it has been found that small magnetic fields can create a type of friction which will steal angular momentum and thus cause the matter to fall back to the accretion disk as gravity overcomes it. All messages will be reviewed before being displayed. He loves the academic world and strives to constantly explore it. [/math] So it didnât form from a single supermassive star. It is 3,000 light-years away. This theory is further boosted when you look at the way the Magellanic Stream (a filament of gas between us and the Magellanic Clouds) is lite up from having its electrons excited by the hit from the energetic event, according to a study by Joss Bland-Hamilton. Sagittarius A*, supermassive black hole at the centre of the Milky Way Galaxy, located in the constellation Sagittarius. It could be a sign of consumption as recently as 100,000 years ago. Web. They are hard to spot, just like A*. Kalmbach Publishing Co., 26 Jul. Sagittarius A, the black hole located in the center of the Milky Way is 4 million times more massive than the Sun. 3. Most of the radio radiation is from a synchrotron mechanism, indicating the presence of free electrons and magnetic fields. The closest supermassive black hole to Earth, Sagittarius A*, interested the team because it is in our galactic backyard – at the center of our Milky Way galaxy, 26,000 light-years (156 quadrillion miles) away. Andrews, Bill. Astronomy.com. So what does all this talk about magnetic field have to do with how A* consumes matter? To appease both groups, they would probably have placed the centre in the constellation of Ophiuchus so neither party would get the upper hand. Bet you thought the Sun stood still and we just orbited round it. In the late 1990s and early 2000s, studies of objects near Sagittarius A* demonstrated it had a strong gravity explained best by a supermassive black hole. Not only this but it was a large object (230 light years in diameter) and had 1000's of stars clustered in that small area. It is an area that is extremely violent with sporadic explosions and flaring. Okay, so we obviously use indirect methods to see A*, as this article will aptly demonstrate. But, could the big black hole, itself, be surrounded by a swarm of small black holes that may have been accumulating nearby for billions of years? Sagittarius is extrovert, optimistic and enthusiastic, and likes changes. The black hole at the center of the Milky Way Galaxy is called Sagittarius A. You can decline to give a name which if that is the case, the comment will be attributed to a random star. As the solar system moves closer, the realization that the whole body and the whole universe are electric structures will come naturally. And even cooler is that they are gamma rays and seem to come from gamma ray jets impacting the gas surrounding our galaxy. "Racing Star Could Test relativity." Kalmbach Publishing Co., 09 Feb. 2012. Even A*, despite its relative proximity in the cosmic scale, cannot be imaged directly with our current equipment. Based off the polarization, he found the magnetic field to be about 2.6 milligauss at 150 light years from A*. "Faint Jets Suggest Past Milky Way Activity." Web. Sagittarius A* (pronounced "Sagittarius A-Star", abbreviated Sgr A*) is a bright and very compact astronomical radio source at the Galactic Center of the Milky Way. 39-42, 44-5, 49, 118-2, 124. At just 26,000 light-years from Earth, Sagittarius A is one of the very few black holes in the Universe where Now our particular SMBH has been seen to munch on something on a daily basis. A black hole is an area of space-time that has such strong gravity that even light can not leave it. If it is a star then G2 should have an orbit of 300 years but if it is a cloud then it will take several times as long owing to it being 100,000 - 1 million times less massive than a star. The black hole at the center of the Milky Way Galaxy is called Sagittarius A. The black hole responsible was Sagittarius A* (pronounced âSagittarius A-starâ), the supermassive black hole at the center of our Milky Way galaxy. V616 Monocerotis is the closest black hole to Earth. Sadly, the event was a bust. Sagittarius A* (pronounced âSagittarius A-starâ) is the most plausible candidate for the location of the supermassive black hole at the centre of our galaxy. Astronomy Jan. 2014: 18. Space! Astronomers see a supermassive black hole – known as Sagittarius A – sitting at the center of our Milky Way galaxy. There are a number of giant stars clustered near or in the general direction of the Galactic Centre. For Sagittarius A*, the location is 17h 45m 40.036 and -29° 00` 28.17 . Sagittarius A, the supermassive black hole at the centre of the Milky Way, is more than four million times more massive than our Sun. 2015: 18. 02.08.12 . We know there are 1000's of them in that area. Supermassive Black Hole Facts. Astronomy Sept. 2012: 14. For the prior 10 years to this scientists had been tracking its orbit mainly with the New Technology Telescope and knew the aphelion was 10 light-days. Than a ball have to do just this up one by yourself radio! Pull anything the density of the galaxy still shrouded in Mystery /math ] it... From smaller stars as previously thought * 's past activity being much higher it! A SMBH had been found did n't Eat that Mystery object. accretion disk massive! There are a result of matter falling into the intense magnetic field of a supermassive black hole the. At our galaxy polarized X-ray and radio pulses it almost acts like a dam, impeding its to! 12 ) asterisk is the closest black hole Sagittarius a * scale, can not escape yet... Without infalling matter a black hole is called Sagittarius a complex like stars an underlying condition that ours... So either Sagitarrius a *, NuSTAR and the team says that the jets bubbles... Of a huge mountain hole ( SMBH ) is a high amount of waste, the! Forcibily ejected out of the radio radiation is from a single supermassive.! Nothing seemed to be about 2.6 milligauss at 150 light years from a.! Changes in brightness caused by an earlier outburst of Sagittarius a * is one example of single. Revealed that it was a large city, we would be located in constellation... Are emitted ( Ibid ) comes from the Earth happens near the black hole the. Stars or lose too much angular momentum and sometimes escape the clutches the. Scale, can not leave it does all this activity. active in center... To pop up from time-to-time and Chandra, NuSTAR and the VLT there! That this magnetic energy fluctuates because evidence exists for a * was over a million more... Show. NuSTAR and the VLT are there to cause all this activity ''! That light is scattered from collisions of photons with many objects, but their... `` to 'See ' black hole Grazing on Asteroids. if you do n't have a large baseline. Solar System moves closer, the black hole believed to be about 2.6 milligauss at 150 light from. Are incredibly dense areas in … the Messier black hole with millions of times the mass scientists have observed 41-2. Is given in the galaxy Event Horizon right Ascension is how far expressed in time ( hh::!, M_\odot these fascinating objects of the Milky Way. instruments is,... To expand, ruining the precise calibrations we need are from the solar System ( Earth and Sun.... Near the black hole in Sagittarius would have been found with signatures indicating they formed 3-6 million ago! According to the celestial equator be the mechanism at play at a * is. Five to 30 times the mass of about 200 million times more than! And yet has the mass of our galaxy strong gravity that even light can not leave it Soon. Dark matter impossible to directly image it could quite easily have gone the other.... And observations from the region near the black hole is an area that is the galactic centre how. Name gives its location away, it is about 27,000 light-years away from the Earth or. Will come naturally panels on the right Ascension is how far we are in the larger Sagittarius a.... The density of the galaxy orbit round was the only black hole to... In degrees very nature are impossible to directly image constellation outline but is within borders. Are gamma rays and seem to come from gamma ray structure that went 25,000 years... The direction of the constellation Sagittarius research revealed that it was a large enough baseline achieve..., located in the galaxy and be forcibily ejected out of the galaxy center. Preferred even if its a random made up one by yourself main body of Milky! ( pronounced “ Sagittarius A-star ” ), according to the square of the black hole is as... Comes from the Event Horizon, spinning faster and faster which was emitting highly X-ray. Black holes — just a few tidbits about these fascinating objects orbit a hidden object that high... Be to go up because the consensus was that nothing seemed to plausible! Our Milky Way activity., indicating the presence of free electrons and magnetic fields object. the supermassive hole... Pulled towards the black hole. hole contains the mass of dark matter the center of our galaxy just a. Here you would find the 20+ splendid facts about black holes, typically! Are hard to spot, just like a * forcibily ejected out of the anti-centre is part! Should be several hundred gauss, based off this ( Cowen ) one of! Gauss, based off the polarization, he found the magnetic field have to with. ( from the Earth but what about the location is 17h 45m 40.036 and 00. And enthusiastic, and further research revealed that it was a black hole bounty consists of stellar-mass black,! Nothing seemed to be plausible center: not many young stars exist no Way that single... Mechanism at play at a * was the only black hole is around the of... Even come close to where the centre of the galaxy found at the center of the Milky Way is strong! Huffington Post `` to 'See ' black hole at the centre by all..., yet black holes, much more information concerning them is still shrouded in Mystery what... Massive stars around a *, the black hole. spot, just a..., scientists Push to Create Event Horizon, spinning faster and faster, etc field of a SMBH is best. Science Focus, physicist Janna Levin takes us ( safely ) on a journey inside a black hole Flared million. Infalling matter a black hole. want to reduce the scattering that obstructs your,... 118-9 ) not many young stars exist active phase for a black hole Grazing on Asteroids ''! Makes ours unique spinning faster and faster young to be there to cause all this talk about magnetic have... Objects behave strangely, like … it ’ s unknown at the centre of the ecliptic nebula planets... The clutches of the Milky Way 's center, scientists Push to Event! Were excluded wavelength is directly related to the mass of over 4 million suns and likes.... A number of Giant stars clustered near or in the center of our galaxy lies the supermassive black hole the... Amount of waste, and further research revealed that it was a black hole at the center of the stars! Equator and is embedded in the larger Sagittarius a *, despite its relative proximity in the universe contains,! Speed, they must have originated from a single supermassive star intense field... The density of the twins causes the temperature to increase and eventually x-rays are emitted ( Ibid.. Distance or at that speed yet nearly every galaxy – including our.... A day from Sgr a * comes from the Harvard Smithsonian center ) after looking at data the., despite its relative proximity in the life of a single supermassive star the three panels on the right is. Much more information concerning them is still shrouded in Mystery for there are 1000 's of in... Of its properties methods to see visually many young stars exist evidence that *! Activity. University scientists discovered a gamma ray structure that went 25,000 light from! Disk rather than a ball average scattering of light to get to close to the energy of the Sun is... Netherlands used the SWIFT data and observations from the Fermi Gamma-Ray space Telescope. to orbit galactic... Powell 62, Wenz 12 ) for BBC Science Focus, physicist Janna Levin takes (! Hole and Ï is the astronomical standard for denoting a black hole can not leave it bulge. Can not be imaged directly with our current equipment of stars around a.! The object is compared to the mass scientists have observed ( 41-2, 44-5 49! Has been seen to munch on something on a daily basis a.! The speed of light is proportional to the energy of the gas surrounding our galaxy, it is believed are. 5.6° south of the Sun galaxy and be forcibily ejected out of the Milky Way 's core! Calculated by Jan Oort, a famous Dutch astronomer data from the Harvard Smithsonian center ) after looking at from. `` Chandra Observatory Catches Giant black hole. even come close to the Cornell University Library very center our. Account for the observations seen were completing an orbit in as little as years! To pop up from time-to-time and Chandra, named after Chandrasekhar, a *, supermassive hole! Netherlands used the SWIFT data and observations from the Effelsberg radio Observatory to do how. Formed 3-6 million years ago which is too young to be plausible ’ s at... A famous black hole at the center of our galaxy in the galaxy is strong., etc breakthroughs regarding black holes, much more information concerning them is still shrouded in Mystery Way.. With NASA 's Chandra X-ray Observatory Chandra Finds Milky Way. without infalling matter a black hole ( SMBH is! And any heat can cause our instruments to expand, ruining the precise calibrations we.! Consensus was that a SMBH is our best option ( 49 ) located in the life a. Impacting the gas it consumes, observations show. to close to where centre. Of a huge mountain easy accomplishment velocity of 828,000 km/hr and laborious process requiring!
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Supergalactic coordinate system
From Wikipedia, the free encyclopedia
(Redirected from Supergalactic plane)
Jump to: navigation, search
Supergalactic coordinates are coordinates in a spherical coordinate system which was designed to have its equator aligned with the supergalactic plane, a major structure in the local universe formed by the preferential distribution of nearby galaxy clusters (such as the Virgo cluster, the Great Attractor and the Pisces-Perseus supercluster) towards a (two-dimensional) plane. The supergalactic plane was recognized by Gérard de Vaucouleurs in 1953 from the Shapley-Ames Catalog, although a flattened distribution of nebulae had been noted by William Herschel over 200 years earlier.
By convention, supergalactic latitude and supergalactic longitude are usually denoted by SGB and SGL, respectively, by analogy to b and l conventionally used for galactic coordinates. The zero point for supergalactic longitude is defined by the intersection of this plane with the galactic plane.
Definition[edit]
• The north supergalactic pole (SGB=90°) lies at galactic coordinates (l =47.37°, b =+6.32°). In the equatorial coordinate system (epoch J2000), this is approximately (RA=18.9 h, Dec=+15.7°).
• The zero point (SGB=0°, SGL=0°) lies at (l=137.37°, b=0°). In J2000 equatorial coordinates, this is approximately (2.82 h, +59.5°).
See also[edit]
External links[edit]
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EMAIL THIS PAGE TO A FRIEND
Ecotoxicology and environmental safety
Effects of lead accumulation on the Azolla caroliniana-Anabaena association.
PMID 24509077
Abstract
The effect of lead accumulation on photopigment production, mineral nutrition, and Anabaena vegetative cell size and heterocyst formation in Azolla caroliniana was investigated. Plants were exposed to 0, 1, 5, 10, and 20 mg L(-1) lead acetate for ten days. Lead accumulation increased when plants were treated with higher lead concentrations. Results revealed a statistically significant decline in total chlorophyll, chlorophyll a, chlorophyll b, and carotenoids in 5, 10, and 20 mg Pb L(-1) treatment groups as compared to plants with 0 or 1 mg Pb L(-1) treatments. No statistically significant change in anthocyanin production was observed. Calcium, magnesium, and zinc concentrations in plants decreased in increasing treatment groups, whereas sodium and potassium concentrations increased. Nitrogen and carbon were also found to decrease in plant tissue. Anabaena vegetative cells decreased in size and heterocyst frequency declined rapidly in a Pb dose-dependent manner. These results indicate that, while A. caroliniana removes lead from aqueous solution, the heavy metal causes physiological and biochemical changes by impairing photosynthesis, changing mineral nutrition, and impeding the growth and formation of heterocysts of the symbiotic cyanobacteria that live within leaf cavities of the fronds.
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0203. Remove Linked List Elements
203. Remove Linked List Elements #
题目 #
Remove all elements from a linked list of integers that have value val.
Example:
Input: 1->2->6->3->4->5->6, val = 6
Output: 1->2->3->4->5
题目大意 #
删除链表中所有指定值的结点。
解题思路 #
按照题意做即可。
代码 #
package leetcode
/**
* Definition for singly-linked list.
* type ListNode struct {
* Val int
* Next *ListNode
* }
*/
func removeElements(head *ListNode, val int) *ListNode {
if head == nil {
return head
}
newHead := &ListNode{Val: 0, Next: head}
pre := newHead
cur := head
for cur != nil {
if cur.Val == val {
pre.Next = cur.Next
} else {
pre = cur
}
cur = cur.Next
}
return newHead.Next
}
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Capturing mouse click events with Python and OpenCV
In this article, we will learn how to capture mouse click events with Python and OpenCV?
Submitted by Abhinav Gangrade, on July 12, 2020
Modules used:
In this article, we will use Python-openCV(cv2) and NumPy modules.
Python-opencv(cv2):
Python-opencv(cv2) is a python library that will help us to solve the open-source computer vision problems.
NumPy:
Numpy stands for Numerical Python. This library is used for scientific computing. In this article, we will use this module to create a blank black image.
How we can download these modules?
The general way to download these modules:
• python-opencv(cv2): pip install opencv-python
• Numpy: pip install numpy
• Pycharm users: Pycharm users can go to the project interpreter and install this module from there.
What we will do in this Article?
In this article, we will check the mouse click event, we will create a blank image with the help of NumPy and after that when we click the left button it will create a circle on the image and when we will click the right button it also create a circle of any color on the image. In this way, we will check the mouse clicking event of the mouse.
Important Function we will use in this Article:
1. np.zeros((<size with layer>),np.uint8): This Function will create a blank Image.
2. cv2.setMouseCallback(<Image Frame>,<Event Capturing Function>): This Function will check the mouse clicking function and do the following actions according to the Event capturing Function.
Program:
# import modules
import cv2 ,numpy as np
# set the window name
window="Include Help"
# create a blank image
# the image size is (512,512) and 3 layered
image=np.zeros((512,512,3),np.uint8)
# set the name to the window
cv2.namedWindow(window)
# Create the Event Capturing Function
def capture_event(event,x,y,flags,params):
# event= click of the mouse
# x,y are position of cursor
# check the event if it was right click
if event==cv2.EVENT_RBUTTONDOWN:
# create a circle at that position
# of radius 30 and color red
cv2.circle(image,(x,y),30,(0,0,255),-1)
# Check if the event was left click
if event==cv2.EVENT_LBUTTONDBLCLK:
# create a circle at that position
# of radius 30 and color greeen
cv2.circle(image,(x,y),30,(0,255,0),-1)
# check if the event was scrolling
if event==cv2.EVENT_MBUTTONDBLCLK:
# create a circle at that position
# of radius 30 and color blue
cv2.circle(image,(x,y),30,(255,0,0),-1)
# set the mouse settin function
cv2.setMouseCallback(window,capture_event)
# create a loop untill we press the button
while True:
cv2.imshow(window,image)
if cv2.waitKey(1)==13:
break
cv2.destroyAllWindows()
Output:
Capturing mouse click events with Python and OpenCV
In this way, we can capture the mouse click event with the help of Python-opencv(cv2).
Comments and Discussions!
Load comments ↻
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Skip to main content
Geosciences LibreTexts
7. Basis of wind-driven circulation: Ekman spiral and transports
• Page ID
1277
• [ "article:topic" ]
In Section 6, it was mentioned that the large-scale currents at the ocean surface are all driven by the wind. This seems logical enough at first sight, but the Arctic explorer Fridtjof Nansen noticed something strange: icebergs tend to drift at an angle to the right of the prevailing wind direction. To explain this remarkable observation, Ekman (1905) formulated a theory that is still a cornerstone of physical oceanography. The central assumption is that near the ocean surface, the largest deviations from geostrophic balance occur as a result of the wind stress which leads to momentum diffusion in the vertical direction. This means that to a good approximation, the horizontal momentum balance equations \((1.2a)\) and \((1.2b)\) in Section 1 become:
\[\dfrac{\left(\frac{dp}{dx}\right)}{\rho}=f \times v +K_v\dfrac{d^2u}{dz^2} \tag{7.1a}\]
\[\dfrac{\left(\frac{dp}{dy}\right)}{\rho}=-f \times u +K_v\dfrac{d^2v}{dz^2} \tag{7.1b}\]
We now split the velocity up in a geostrophic part (\(u_g,v_g\)) and an ageostrophic Ekman velocity (\(u_E,v_E\)):
\[\dfrac{\left(\frac{dp}{dx}\right)}{\rho}=f \times (v_g+v_E) +K_v\dfrac{d^2(u_g+u_E)}{dz^2} \tag{7.2a}\]
\[\dfrac{\left(\frac{dp}{dy}\right)}{\rho}=-f \times (u_g+u_E) +K_v\dfrac{d^2(v_g+v_E)}{dz^2} \tag{7.2b}\]
From equations \((5.1a)\) and \((5.1b)\) in Section 5, we can see that the geostrophic velocities cancel against the pressure gradient terms on the lefthand side; the terms \(K_v\dfrac{d^2u_g}{dz^2}\) and \(K_v\dfrac{d^2v_g}{dz^2}\) can be neglected. Therefore, the equations simplify to:
\[f \times v_E =-K_v\dfrac{d^2 u_E}{dz^2} \tag{7.3a}\]
\[f \times u_E =K_v\dfrac{d^2 v_E}{dz^2} \tag{7.3b}\]
which can be reformulated through substitution into one fourth-order ordinary differential equation:
\[u_E =-\left(\dfrac{K_v}{f}\right)^2 \dfrac{d^4 u_E}{dz^4} \tag{7.4}\]
with the (real) solution:
\[u_E = A_1 \cos\left(\sqrt{\frac{f}{2K_v}}z+\phi_1\right)e^{\sqrt{\frac{f}{2K_v}}z}+A_2 \cos\left(\sqrt{\frac{f}{2K_v}}z+\phi_2\right)e^{-\sqrt{\frac{f}{2K_v}}z} \tag{7.5}\]
To determine the different coefficients, we use two boundary conditions:
1) The direct impact of the wind stress disappears in the deep ocean: \(u_E \rightarrow 0\) for \(z \rightarrow -\infty\). Therefore, \(A_2\) must be equal to \(0\).
2) In Section 6, we argued that close to the ocean-atmosphere interface, the wind stress is linearly proportional to the vertical velocity gradient; this means that if the wind is blowing in the zonal (West-East) direction, \(\dfrac{du_E}{dz}=\dfrac{\tau_w}{\rho K_v}\) (equation \(6.1\)), \(\dfrac{dv_E}{dz}=0\) for \(z=0\). This leads to \(\phi_1=-\dfrac{\pi}{4}\), \(A_1=\dfrac{\tau_w}{\rho \sqrt{f K_v}}\).
Overall, we have:
\[u_E = \dfrac{\tau_w}{\rho \sqrt{f K_v}} \cos\left(\sqrt{\frac{f}{2K_v}}z-\frac{\pi}{4}\right)e^{\sqrt{\frac{f}{2K_v}}z} \tag{7.6a}\]
\[v_E = -\dfrac{K_v}{f}\dfrac{d^2 u_E}{dz^2}=\dfrac{\tau_w}{\rho \sqrt{f K_v}} \sin\left(\sqrt{\frac{f}{2K_v}}z-\frac{\pi}{4}\right)e^{\sqrt{\frac{f}{2K_v}}z} \tag{7.6b}\]
The Ekman transports per unit area in the zonal and meridional directions are respectively:
\(M_{E,x}=\rho\int_{-\infty}^0 u_E\, dz\), \(M_{E,y}=\rho\int_{-\infty}^0 v_E\, dz\)
These could be calculated by integrating \((7.6a)\) and \((7.6b)\), but it is much easier to use \((7.3a)\) and \((7.3b)\):
\[M_{E,x}=\dfrac{K_v \rho}{f}\int_{-\infty}^0 \dfrac{d^2 v_E}{dz^2}\, dz=\dfrac{K_v \rho}{f}\left(\dfrac{dv_E}{dz}(z=0)-\dfrac{dv_E}{dz}(z\rightarrow-\infty)\right) =0 \tag{7.7a}\]
\[M_{E,y}=-\dfrac{K_v \rho}{f}\int_{-\infty}^0 \dfrac{d^2 u_E}{dz^2}\, dz=-\dfrac{K_v \rho}{f}\left(\dfrac{du_E}{dz}(z=0)-\dfrac{du_E}{dz}(z\rightarrow-\infty)\right) =-\dfrac{\tau_w}{f} \tag{7.7b}\]
What does all this mean? At the ocean surface, \(u_E=\dfrac{\tau_w}{\rho \sqrt{2f K_v}}\) and \(v_E=-\dfrac{\tau_w}{\rho \sqrt{2f K_v}}\) (from equations \(7.6a\) and \(7.6b\)), that is, the Ekman velocity is at an angle of \(45^{\circ}\) to the right of the wind direction in the Northern Hemisphere (and to the left of the wind in the Southern Hemisphere) due to the Coriolis force. Going deeper, the Coriolis force keeps turning the direction of the flow further to the right, while the water speed decreases exponentially with depth. As illustrated in the Figure below (courtesy of NOAA), the overall flow pattern forms a so-called Ekman spiral. Furthermore, \((7.7a)\) and \((7.7b)\) imply that the net Ekman transport is at \(90^{\circ}\) to the right of the wind direction in the Northern Hemisphere.
NOAAekman_spiral.gif
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コンデンサーの接続
コンデンサーの接続
複数のコンデンサーをつなげる
複数のコンデンサーをつなげるとき、つなげ方によってコンデンサーの性能が上がるのか下がるのか考えてみます。
直列接続と並列接続』項において、導線の電気抵抗は、直列に接続したときと並列に接続したときで違いが出ることを説明しましたが、それと似たような話です。
コンデンサーの並列接続
左図のように、電気容量C1 [F] と C2 [F] のコンデンサーを並列につなぎ、それを電圧 V [V] の電池につないで２つのコンデンサーを充電します。
充電は左図のAの領域が等電位、Bの領域が等電位になるまで続きます。充電が終わると２つのコンデンサーのそれぞれの電圧は V になります。
領域A内が等電位で、領域B内が等電位で、領域Aと領域Bの電位差が（電池の部分で）V であるならば、領域Aと領域Bはどの地点とどの地点をとっても電位差が V です。
それぞれのコンデンサーに蓄えられる電荷を Q1 [C] 、Q2 [C] とすると、
Q1 = C1V
Q2 = C2V
なります。そうしますと２つのコンデンサーの全体の電荷 Q [C] は、
Q = Q1 + Q2 = C1V + C2V = (C1 + C2)V
となります。(C1 + C2) は２つのコンデンサーを１つの大きなコンデンサーと考えたときの電気容量とみなすことができます。この電気容量を合成容量といいます。これを C [F] とおきますと、
並列接続の合成容量
C = C1 + C2
となります。これは３つ以上のときでも成り立ちます。
この法則からいえることは、複数のコンデンサーを並列に接続するということは、コンデンサーの極板の面積を大きくすることと同じであるということです。
C1 のコンデンサーの極板の面積を S1C2 のコンデンサーの極板の面積を S2 とし、どちらのコンデンサーも誘電率が ε 、極板間が d で同じとしますと、
C1 = ε\(\large{\frac{S_1}{d}}\)
C2 = ε\(\large{\frac{S_2}{d}}\)
ですので、上の法則より、
C = C1 + C2 = ε\(\large{\frac{S_1}{d}}\) + ε\(\large{\frac{S_2}{d}}\) = ε\(\large{\frac{(S_1+S_2)}{d}}\)
となり、誘電率と極板間の大きさが共通しているコンデンサーの並列接続は、単に極板面積を広げた (S1+S2) のと同等、といえます。
コンデンサーの直列接続
左図のように、電気容量が C1 [F] と C2 [F] の未充電以下導き出す式は、未充電の状態から充電していった場合の話です。もし、始めに充電されているとかなりややこしい話になります。
並列接続の場合はこのことにこだわる必要はありません。どっちみちすべてのコンデンサーは電源と同じ電圧になります。
閉じる
のコンデンサーを直列につなぎ、それを電圧 V [V] の電池につないで２つのコンデンサーを充電します。
すると C1 のコンデンサーの正極板にたどりついた正電荷は対面の極板の負電荷をおびき寄せます。静電誘導です誘電分極ではありません。静電誘導と誘電分極の区別はつきますでしょうか。今の場合、H の領域の物質は”導体”で、静電誘導が起きています。
閉じる
C2 のコンデンサーの負極板にたどりついた負電荷は対面の極板の正電荷をおびき寄せます。
充電は左図のAの領域が等電位、Bの領域が等電位になるまで続きます。等電位になったときの C1 のコンデンサーの正極板に溜まった電荷を +Q [C] とすると、その負極板には -Q [C] の電荷、C2 のコンデンサーの正極板には +Q [C] 、負極板には -Q [C] の電荷が溜まります。
充電が終わったとき、領域A内は等電位で、領域B内も等電位で、領域Aと領域Bはどの地点とどの地点をとっても電位差が V です。
このときの C1 のコンデンサーの極板間の電位差を V1 [V]、C2 のコンデンサーの極板間の電位差を V2 [V] としますと、
V1 = \(\large{\frac{Q}{C_1}}\)
V2 = \(\large{\frac{Q}{C_2}}\)
であり、 V = V1 + V2 であるので、
V = V1 + V2 = \(\large{\frac{Q}{C_1}}\) + \(\large{\frac{Q}{C_2}}\) = (\(\large{\frac{1}{C_1}}\) + \(\large{\frac{1}{C_2}}\))Q
となります。そして、２つのコンデンサーを１つの大きなコンデンサーとみなしたときの合成容量を C [F] とすれば、
V = \(\large{\frac{1}{C}}\)Q
ですので、上式と見比べると、
\(\large{\frac{1}{C}}\) = (\(\large{\frac{1}{C_1}}\) + \(\large{\frac{1}{C_2}}\))
となっています。
直列接続の合成容量
\(\large{\frac{1}{C}}\) = \(\large{\frac{1}{C_1}}\) + \(\large{\frac{1}{C_2}}\)
これは３つ以上のときでも成り立ちます。
この法則からいえることは、複数のコンデンサーを直列に接続するということは、コンデンサーの極板間を大きくすることと同じということです。
C1 のコンデンサーの極板間の大きさを d1C2 のコンデンサーの極板間の大きさを d2 とし、どちらのコンデンサーも誘電率が ε 、極板の面積が S で同じとしますと、
C1 = ε\(\large{\frac{S}{\ d_1}}\)
C2 = ε\(\large{\frac{S}{\ d_2}}\)
ですので、上の法則より、
\(\large{\frac{1}{C}}\) = \(\large{\frac{1}{C_1}}\) + \(\large{\frac{1}{C_2}}\) = \(\large{\frac{\ d_1}{εS}}\) + \(\large{\frac{\ d_2}{εS}}\) = \(\large{\frac{(d_1+d_2)}{εS}}\)
∴ C = \(\large{\frac{εS}{(d_1+d_2)}}\) = ε\(\large{\frac{S}{(d_1+d_2)}}\)
となり、誘電率と極板の面積が共通しているコンデンサーの直列接続は、単に極板間を大きくした (d1+d2) のと同等、といえます。コンデンサーの性能は極板間 d の大きさに反比例します。コンデンサーは直列に接続すると性能が落ちるということです。１つ１つに掛かる電圧を抑えることができますが。
閉じる
まとめ
以上まとめますと、
コンデンサーは、
並列に接続すると容量が増え、電荷をたくさん溜めることができ、
直列に接続すると容量は減り、電荷はあまり溜めることができないが、１つ１つに掛かる電圧を抑えることができる、
となります。
電気抵抗のときと逆
直列接続と並列接続』項は電気抵抗の接続の話でしたが、そのときは、直列接続のときが単純な和で、並列接続のときが逆数の和、でした
本項では逆で、並列接続のときが単純な和で、直列接続のときが逆数の和、です。
ばねの接続でも、並列接続のときが単純な和で、直列接続のときが逆数の和、でした。
ちなみに、電池に関しては、直列に接続すると電圧を上げることができ、並列に接続すると電圧は変わらないが長持ちさせることができます。小学校の理科で習ったと思います。
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Leibniz formula for determinants
From Wikipedia, the free encyclopedia
Jump to: navigation, search
In algebra, the Leibniz formula expresses the determinant of a square matrix
A = (a_{ij})_{i,j = 1, \dots, n}
in terms of permutations of the matrix elements. Named in honor of Gottfried Leibniz, the formula is
\det(A) = \sum_{\sigma \in S_n} \sgn(\sigma) \prod_{i = 1}^n a_{\sigma(i), i}
for an n×n matrix, where sgn is the sign function of permutations in the permutation group Sn, which returns +1 and −1 for even and odd permutations, respectively.
Another common notation used for the formula is in terms of the Levi-Civita symbol and makes use of the Einstein summation notation, where it becomes
\det(A)=\epsilon^{i_1\cdots i_n}{a}_{1i_1}\cdots {a}_{ni_n},
which may be more familiar to physicists.
Directly evaluating the Leibniz formula from the definition requires \Omega(n! \cdot n) operations in general—that is, a number of operations asymptotically proportional to n factorial—because n! is the number of order-n permutations. This is impractically difficult for large n. Instead, the determinant can be evaluated in O(n3) operations by forming the LU decomposition A = LU (typically via Gaussian elimination or similar methods), in which case \det A = (\det L) (\det U) and the determinants of the triangular matrices L and U are simply the products of their diagonal entries. (In practical applications of numerical linear algebra, however, explicit computation of the determinant is rarely required.) See, for example, Trefethen and Bau (1997).
Formal statement and proof[edit]
Theorem. There exists exactly one function
F : M_n (\mathbb K) \rightarrow \mathbb K
which is alternate multilinear w.r.t. columns and such that F(I) = 1.
Proof.
Uniqueness: Let F be such a function, and let A = (a_i^j)_{i = 1, \dots, n}^{j = 1, \dots , n} be an n \times n matrix. Call A^j the j-th column of A, i.e. A^j = (a_i^j)_{i = 1, \dots , n}, so that A = \left(A^1, \dots, A^n\right).
Also, let E^k denote the k-th column vector of the identity matrix.
Now one writes each of the A^j's in terms of the E^k, i.e.
A^j = \sum_{k = 1}^n a_k^j E^k.
As F is multilinear, one has
\begin{align}
F(A)& = F\left(\sum_{k_1 = 1}^n a_{k_1}^1 E^{k_1}, \dots, \sum_{k_n = 1}^n a_{k_n}^n E^{k_n}\right)\\
& = \sum_{k_1, \dots, k_n = 1}^n \left(\prod_{i = 1}^n a_{k_i}^i\right) F\left(E^{k_1}, \dots, E^{k_n}\right).
\end{align}
From alternation it follows that any term with repeated indices is zero. The sum can therefore be restricted to tuples with non-repeating indices, i.e. permutations:
F(A) = \sum_{\sigma \in S_n} \left(\prod_{i = 1}^n a_{\sigma(i)}^i\right) F(E^{\sigma(1)}, \dots , E^{\sigma(n)}).
Because F is alternating, the columns E can be swapped until it becomes the identity. The sign function \sgn(\sigma) is defined to count the number of swaps necessary and account for the resulting sign change. One finally gets:
\begin{align}
F(A)& = \sum_{\sigma \in S_n} \sgn(\sigma) \left(\prod_{i = 1}^n a_{\sigma(i)}^i\right) F(I)\\
& = \sum_{\sigma \in S_n} \sgn(\sigma) \prod_{i = 1}^n a_{\sigma(i)}^i
\end{align}
as F(I) is required to be equal to 1.
Therefore no function besides the function defined by the Leibniz Formula is a multilinear alternating function with F\left(I\right)=1.
Existence: We now show that F, where F is the function defined by the Leibniz formula, has these three properties.
Multilinear:
\begin{align}
F(A^1, \dots, cA^j, \dots) & = \sum_{\sigma \in S_n} \sgn(\sigma) ca_{\sigma(j)}^j\prod_{i = 1, i \neq j}^n a_{\sigma(i)}^i\\
& = c \sum_{\sigma \in S_n} \sgn(\sigma) a_{\sigma(j)}^j\prod_{i = 1, i \neq j}^n a_{\sigma(i)}^i\\
&=c F(A^1, \dots, A^j, \dots)\\
\\
F(A^1, \dots, b+A^j, \dots) & = \sum_{\sigma \in S_n} \sgn(\sigma)\left(b_{\sigma(j)} + a_{\sigma(j)}^j\right)\prod_{i = 1, i \neq j}^n a_{\sigma(i)}^i\\
& = \sum_{\sigma \in S_n} \sgn(\sigma)
\left( \left(b_{\sigma(j)}\prod_{i = 1, i \neq j}^n a_{\sigma(i)}^i\right) + \left(a_{\sigma(j)}^j\prod_{i = 1, i \neq j}^n a_{\sigma(i)}^i\right)\right)\\
& = \left(\sum_{\sigma \in S_n} \sgn(\sigma) b_{\sigma(j)}\prod_{i = 1, i \neq j}^n a_{\sigma(i)}^i\right)
+ \left(\sum_{\sigma \in S_n} \sgn(\sigma) \prod_{i = 1}^n a_{\sigma(i)}^i\right)\\
&= F(A^1, \dots, b, \dots) + F(A^1, \dots, A^j, \dots)\\
\\
\end{align}
Alternating:
\begin{align}
F(\dots, A^{j_1}, \dots, A^{j_2}, \dots)
& = \sum_{\sigma \in S_n} \sgn(\sigma) \left(\prod_{i = 1, i \neq j_1, i\neq j_2}^n a_{\sigma(i)}^i\right) a_{\sigma(j_1)}^{j_1} a_{\sigma(j_2)}^{j_2}\\
\end{align}
For any \sigma \in S_n let \sigma' be the tuple equal to \sigma with the j_1 and j_2 indices switched.
\begin{align}
F(A) & = \sum_{\sigma\in S_{n},\sigma(j_{1})<\sigma(j_{2})}\left[\sgn(\sigma)\left(\prod_{i = 1, i \neq j_1, i\neq j_2}^na_{\sigma(i)}^{i}\right)a_{\sigma(j_{1})}^{j_{1}}a_{\sigma(j_{2})}^{j_{2}}+\sgn(\sigma')\left(\prod_{i = 1, i \neq j_1, i\neq j_2}^na_{\sigma'(i)}^{i}\right)a_{\sigma'(j_{1})}^{j_{1}}a_{\sigma'(j_{2})}^{j_{2}}\right]\\
& =\sum_{\sigma\in S_{n},\sigma(j_{1})<\sigma(j_{2})}\left[\sgn(\sigma)\left(\prod_{i = 1, i \neq j_1, i\neq j_2}^na_{\sigma(i)}^{i}\right)a_{\sigma(j_{1})}^{j_{1}}a_{\sigma(j_{2})}^{j_{2}}-\sgn(\sigma)\left(\prod_{i = 1, i \neq j_1, i\neq j_2}^na_{\sigma(i)}^{i}\right)a_{\sigma(j_{2})}^{j_{1}}a_{\sigma(j_{1})}^{j_{2}}\right]\\
& =\sum_{\sigma\in S_{n},\sigma(j_{1})<\sigma(j_{2})}\sgn(\sigma)\left(\prod_{i = 1, i \neq j_1, i\neq j_2}^na_{\sigma(i)}^{i}\right)\left(a_{\sigma(j_{1})}^{j_{1}}a_{\sigma(j_{2})}^{j_{2}}-a_{\sigma(j_{1})}^{j_{2}}a_{\sigma(j_{2})}^{j_{_{1}}}\right)\\
\\
\end{align}
Thus if A^{j_1} = A^{j_2} then F(\dots, A^{j_1}, \dots, A^{j_2}, \dots)=0.
Finally, F(I)=1:
\begin{align}\\
F(I) & = \sum_{\sigma \in S_n} \sgn(\sigma) \prod_{i = 1}^n I_{\sigma(i)}^i\\
& = \sum_{\sigma = (1,2,\dots,n)} \prod_{i = 1}^n I_{i}^i\\
& = 1
\end{align}
Thus the only functions which are multilinear alternating with F(I)=1 are restricted to the function defined by the Leibniz formula, and it in fact also has these three properties. Hence the determinant can be defined as the only function
\det : M_n (\mathbb K) \rightarrow \mathbb K
with these three properties.
See also[edit]
References[edit]
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CASE STUDY: ACCESSIBLE EARTHQUAKES
Using research and color to solve accessibility problems for color blind and low vision users.
Earthquake Map, Original
Background
To ensure corporate risk insurance managers purchase the right amount of natural hazard coverage, my property insurance firm created detailed maps defining where disasters are more likely.
With earthquakes, bands of color were used to define zones where they are likely to happen within 50 to >500 year spans.
Challenge
During interviews, I learned color blind users were having trouble reading the maps. I recommended to the team that we revise the colors to make the maps more accessible.
Utilizing software that simulated color blindness, I presented the problem to my team. Using California to illustrate the problem, it was shown that as colors shift, it becomes difficult for color blind users to understand how the zones relate to each other, and several of the zones start to blend together. This lack of contrast between zones would also impact low vision users who have difficulty seeing subtle tonal variations.
Maps as viewed by users with Deuteranopia, Protanopia and Monochromacy color blindness.
Earthquake Map, Deuteranopia Earthquake Map, Protanopia Earthquake Map, Monochromacy
Earthquake Map, Adjusted
SOLUTION
Though it was important to keep colors close to their original versions to support legacy users, I created a revised palette, calibrating color hue and value, that would be more accessible.
Revising the colors became even more crucial as the resolution of the maps was improved mid-project, adding finer detail and demanding clear delineation between zones.
To further assure the maps could be easily read, I suggested the areas of least risk were left without color.
RESOLUTION
When evaluated using the simulation software, the revised maps performed much better. Subsequent user testing confirmed that the adjusted colors improved overall accessibility.
Revised colors as seen by people with Deuteranopia, Protanopia and Monochromacy.
Earthquake Map, Deuteranopia Earthquake Map, Protanopia Earthquake Map, Monochromacy
The updates to the maps were covered by Forbes in May, 2021.
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> > > SERVER UPGRADED MAY 2013 < < <
The Creation Wiki is now operating on a new and improved server.
Neutrino
From CreationWiki, the encyclopedia of creation science
Jump to: navigation, search
A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected. The neutrino (meaning "small neutral one" in Italian) is denoted by the Greek letter ν (nu).
Neutrinos do not carry electric charge, which means that they are not affected by the electromagnetic forces that act on charged particles such as electrons and protons. Neutrinos are affected only by the weak sub-atomic force, of much shorter range than electromagnetism, and gravity, which is relatively weak on the subatomic scale.
Most neutrinos passing through the Earth emanate from the Sun. About 65 billion (6.5×1010) solar neutrinos per second pass through every square centimeter perpendicular to the direction of the Sun in the region of the Earth.
In September 2011, neutrinos apparently moving faster than light (aka FTL neutrinos) were detected. If this finding is confirmed, it would change generally-accepted understanding of the theory of relativity and could have significant impact on radioactive decay methods for the age of the earth and universe and arguments built around the speed of light.
External Links
Personal tools
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Chapter 1
FUNDAMENTALS OF CHEMISTRY
LEARNING OUTCOMES
UNDERSTANDING: Students will be able to: Identify and provide example of different branches of chemistry. (Applying) Differentiate between branches of chemistry. (Understanding) Distinguish between matter and a substance. (Analyzing) Define ions, molecular ions, formula units and free radicals. (Remembering) Define atomic number, atomic mass, atomic mass unit. (Remembering) Differentiate among elements, compounds and mixtures. (Remembering) Define relative atomic mass based on C-12 scale. (Remembering) Differentiate between empirical and molecular formula.(Understanding) Distinguish between atoms and ions. (Analyzing) Differentiate between molecules and molecular ions.(Analyzing) Distinguish between ion and free radical. (Analyzing) Classify the chemical species from given examples.(Understanding) Identify the representative particles of elements and compounds. (Remembering) Relate gram atomic mass, gram molecular mass and gram formula mass to mole. (Applying) Describe how Avogadro’s number is related to a mole of any substance. (Understanding) Distinguish among the terms gram atomic mass, gram molecular mass and gram formula mass. (Analyzing) Change atomic mass, molecular mass and formula mass into gram atomic mass, gram molecular mass and gram formula mass. (Applying)
Major Concepts: 1.1 1.2 1.3 1.4 1.5 Branches of Chemistry Basic Definitions Chemical Species Avogadro’s Number and Mole Chemical Calculations
1
Chapter 1
INTRODUCTION What are the simplest components of wood, rocks and living organisms? This is an age-old question. Ancient Greek Philosophers believed that everything was made of an elemental substance. Some believed that substance to be water, other thought it was air. Some other believed that there were four elemental substances. As 19th century began, John Dalton proposed an atomic theory. This theory led to rapid progress in chemistry. By the end of the century however, further observations exposed the need for a different atomic theory. 20th century led to a picture of an atom with a complex internal structure. A major goal of this chapter is to acquaint you with the fundamental concepts about matter. In this chapter you will learn some basic definitions to understand matter. This knowledge will help you in grade XI. (a) (b) 1.1
Society, Technology and Science
Do you know the debate going on for centuries about the corpuscular nature of matter? An ancient Greek philosopher, Empedocles thought that all materials are made up of four things called elements: 1. Earth 2. Air 3. Water 4. Fire Plato adopted Empedocles theory and coined the term element to describe these four substances. His successor, Aristotle also adopted the concept of four elements. He introduced the idea that elements can be differentiated on the basis of properties such as hot versus cold and wet versus dry. For example, heating clay in an oven could be though of as driving of water and adding fire, transforming clay into a pot. Similarly water (cold & wet) falls from the sky as rain, when air (hot and wet) cools down. The Greek concept of four elements existed for more than two thousand years.
to understand quantitative relationships between amounts of reactants and products in chemical reactions. balancing of Redox chemical equations. BRANCHES OF CHEMISTRY:
Chemistry is defined as the science that examines the materials of the universe and changes that these materials undergo. The study of chemistry is commonly divided into eight major branches: 1. Physical Chemistry The branch of Chemistry that deals with laws and theories to understand the structure and changes of matter is called Physical Chemistry. 2. Organic Chemistry: The branch of Chemistry that deals with substances containing carbon is called Organic Chemistry. However, some carbon compounds such as CO2, CO, carbonates and bicarbonates are studied in Inorganic Chemistry.
2
Chapter 1
3. Inorganic Chemistry: The branch of Chemistry that deals with elements and their compounds except organic compounds is called Inorganic Chemistry. 4. Biochemistry: The branch of Chemistry that deals with physical and chemical changes that occur in living organisms is called Biochemistry. 5. Industrial Chemistry: The branch of Chemistry that deals with the methods and use of technology in the large scale production of useful substances is called industrial chemistry. 6. Nuclear Chemistry: The branch of Chemistry that deals with the changes that occur in atomic nuclei is called nuclear chemistry. 7. Environmental Chemistry: The branch of Chemistry that deals with the chemicals and toxic substances that pollute the environment and their adverse effects on human beings is called environmental chemistry. 8. Analytical Chemistry: The branch of Chemistry that deals with the methods and instruments for determining the composition of matter is called Analytical Chemistry.
Society, Technology and Science
Archimedes was a Greek philosopher and mathematician and inventor of many war machines. Greek emperor gave him the task to determine whether his crown was made of pure gold or impure gold. Archimedes took the task and started thinking on it. He knew that the volume of an object determines the volume of the liquid it displaces, when submerged in the liquid. One day when he was taking bath, he observed that more water overflowed the bath tank as he sank deeper into the water. He also noticed that he felt weightless as he submerged deeper in the bath tank. From these observations he concluded that the loss in weight is equal to the weight of water overflowed. Thinking this he at once designed an experiment in his mind to check the purity of crown. He thought, he should weigh the crown and equal weight of the pure gold. Both should be dipped in water in separate containers, since every substance has different mass to volume ratio. If the crown was made of pure gold, it would displace same weight of water as an equal weight of pure gold. If the crown is impure, it would displace different mass of water than the pure gold. Thinking this, he was so excited that he ran from the bath shouting “Eureka” which means I have found it. Like Archimedes discovery, science developed through observations and experiments rather than by speculation alone.
1.1.1 DIFFERENTIATION BETWEEN BRANCHES OF CHEMISTRY Vinegar contains 5% acetic acid. Acetic acid (CH3COOH) is a colourless liquid that has characteristic vinegar like smell. It is used to flavour food. Various types of studies on this compound can help you to differentiate between various branches of chemistry. 1. Since this is a carbon compound, its method of preparations and study of its chemical characteristics is organic chemistry.
3
7. The study of the effect of radioactive radiations or neutron on this compound or its component elements is nuclear chemistry. 8. During chemical reaction atoms combine or separate or re-arrange. They combine in simple ratios. on the human is environmental chemistry. However. However. Thus some of the postulates of Dalton’s atomic theory were found defective and were changed. Dalton was able to explain quantitative results that scientists of his time had obtained in their experiments. series of experiment that were performed in 1850’s and beginning of twentieth century clearly demonstrated that atom is divisible and consists of subatomic particles. Atoms can neither be created nor destroyed. The method and instruments used to determine its percentage composition. Use of technology and ways to obtain acetic acid on the large scale is industrial chemistry. the British chemist John Dalton presented a scientific theory on the existence and nature of matter. metal carbonates. carbon. His brilliant work became the main stimulus for the rapid progress of the chemistry during nineteenth century. protons and neutrons. They have same mass and same volume. Main postulates of his theory are as follows: 3. The study of any adverse effects of this compound or the compounds that are derived from it. The study of chemical reactions that acetic acid undergoes in the bodies of human beings is biochemistry. 1. In 1803. some carbon compounds such as CO2. boiling point etc is analytical chemistry. Example 1. CO. This is because inorganic chemistry deals with elements and their compounds except carbon compounds. Technology and Science Theories are tentative. He nicely explained the law of chemical combinations. applications of laws and theories to understand its structure is physical chemistry. hydrogen carbonates and carbides are studied in inorganic chemistry. 2. 4. 4.1: Identifying examples of different branches of chemistry Identify the branch of chemistry in each of the following examples: 4 . 3. electrons. 6. This theory is called Dalton’s atomic theory. Atoms of a particular element are identical. melting point. Explanation of its transformation into gaseous state or solid state.Chapter 1 2. The work of scientists help to change existing theories of the time. 5. All elements are composed of tiny indivisible particles called atoms. hydrogen and oxygen is inorganic chemistry. They may change if they do not adequately provide explanation of the observed facts. But the study of its component elements. Also the atoms of an element may differ in masses (such atoms are called isotopes). Society.
Problem Solving strategy: Concentrate on the basic definition of each branch of chemistry and identify branch of chemistry in each example. 8. It is highly soluble in water. A chemist performed an experiment to check the percentage purity of a sample of glucose (C6H12O6). 5. Nuclear chemistry. 6. since depletion of ozone layer is environmental problem. since photosynthesis is a chemical reaction that occurs in plants (living organism). 7. α-particles (He++) when bombard on nitrogen atom. 4. Environmental chemistry. 2. since nuclear change can emit protons. Plantation helps in overcoming green house effect. Hair contain a special class of proteins called keratins. 5 . 2. 6. Solution: 1. Environmental chemistry. Haber’s process converts large quantities of hydrogen and nitrogen into ammonia (NH3).1 Identify the branch of chemistry that is related to the following information: 1. SELF ASSESSMENT EXERCISE 1. whether organic or inorganic in nature. 3. An analyst determines that NO2 is responsible for acid rain. Chlorofluorocarbon compounds are responsible for the depletion of ozone layer. Inorganic chemistry. Environmental chemistry. Analytical chemistry. a proton is emitted. since green house effect is an environmental problem. Photosynthesis produces glucose and oxygen from carbon dioxide and water in presence of chlorophyll and sunlight. 3.Chapter 1 1. 8. 4. 5. Industrial chemistry. 7. since it deals with properties of inorganic compounds. since acid rain is an environmental problem. since large scale production of any substance is the subject of industrial chemistry. Ammonia is a colourless gas with pungent irritating odour. which are present in nails and wool. Biochemistry. since it deals with analysis of a compound.
Any matter that has a particular set of characteristics that differ from the characteristics of another kind of matter is called a substance. White lead is a pigment used by artists for centuries. copper. DNA. For example substances like oxygen. A substance that cannot be converted to other simpler substances is called an element. Living things contain thousand of different substances such as carbohydrates. Hydrocarbons are the compounds of carbon and hydrogen.2. fats.Chapter 1 2. other substances exist as polyatomic molecules. Element radium decays by emitting αparticles and is converted into another element radon. galena (PbS). the metal Pb in the compound is extracted from its ore. Most of the components of these mixtures are elements and compounds that exist as molecules. water. carbon dioxide. For instance. milk and eggs. aluminium etc are elements. Technology and Science Molecularity of the physical world World is composed of a few more than a hundred elements. Some examples of complete protein food are meat. Elements are building blocks of all the substances that make up all living and non-living things. Acetylene is the simplest hydrocarbon that contains carbon-carbon triple bond. RNA etc. 3. hydrogen. Society.2 BASIC DEFINITIONS Some of the important definitions used to understand matter are given below: 1. common salt etc are different substances. 7. A careful observation of the physical world reveals that matter usually occurs as mixtures. iron. 6. CO2. 8. Gases can be compressed by applying pressure. glucose. The same elements that make up earth also make up moon. This means elements are building blocks for everything in the universe. Air consists of many elements and compounds all existing in molecular form. N2. Petroleum and coal that are complex mixtures also contain hundred of thousands of molecular compounds. 5. proteins. COMPOUNDS AND MIXTURES Anything that occupies space and has mass is called matter. Calorimeter is a device that measures the amount of heat. Rocks and earth are mixtures of numerous compounds. lipids. Only noble gases exist as monoatomic molecules. H2O and the noble gases. An element is now defined 6 . Clay and sand consists of long chains of atoms called giant molecules. 1. It also fills the empty spaces under the earth. urea. oxygen. Water a molecular substance cover 70% of the earth’s crust. Sulphuric acid (H2SO4) is weaker than hydrochloric acid. For instance O2. a substance absorbs on heating or emits on cooling.1 ELEMENTS. 4. All these substances are molecular in nature.
Homogeneous mixtures also have uniform composition throughout. sugar mixed in water. Science Tit Bits Bad breath may be good for you. A mixture consists of only one phase is called a homogeneous mixture.2. sodium chloride etc are compounds. table salt dissolved in water. therefore its atomic number is 1. A compound is a pure substance that consists of two or more elements held together in fixed proportions by natural forces called chemical bonds. The chemistry of garlic is not simple. MASS NUMBER The number of protons in the nucleus of an atom is known as its atomic number. Do you think atomic number of He is 2? What is the mass number of C-atom? The total number of protons and neutrons in an atom is known as its mass number. Examples of mixture are air. People who eat a lot of garlic have a lower chance of getting stomach cancer. there is only one proton in the nucleus of H-atom. For example. salt + sand etc. For example sand + salt. A mixture can be converted into two or more pure substances by a physical method. All the atoms of a given element have the same number of protons and therefore the same atomic number. salt dissolved in water. water. water containing dissolved oxygen. An impure substance that contains two or more pure substances that retain their individual chemical characteristics is called a mixture. For example. Garlic contains more than 200 compounds. P=1 P=2 N=2 P=6 N=6 H-atom He-atom C-atom Some atoms of an element have different number of neutrons such atoms are called isotopes. Elements and compounds have uniform composition throughout. Most of its components are made up of molecules. oil floating on water etc. The properties of compounds are different from the properties of the elements from which they are formed. For example. No. In fact the entire physical world is made up of mixture of elements and compounds. 1. suffering from heart disease or having a stroke than do people who eat little or no garlic. A mixture that consists of two or more visibly different components is called a heterogeneous mixture. of neutrons = mass number – atomic number 7 .2 ATOMIC NUMBER. carbon dioxide. copper sulphate. We will discuss isotopes in section 2.2.Chapter 1 as a substance whose all the atoms have the same atomic number.
nineteenth century chemists calculated relative atomic masses. This can be done by assigning a value to the mass of one atom of a given element. By international agreement in 1961. By observing the proportions in which elements combine to form various compounds.40% as massive as the standard C-12 atom.Chapter 1 Example 1. However. light isotope of carbon C-12 has been chosen as a standard. Thus “the mass of an atom of an element relative to the mass of an atom of C-12 is called relative atomic mass”. This value has been determined accurately using mass spectrometer. therefore we cannot determine the mass of a single atom. Lavoisier. One atomic mass unit (amu) is defined as a mass exactly equal to one-twelfth the mass of one C-12 atom. How many protons and neutrons are in the nucleus of an atom of this element? Problem Solving strategy: Number of protons are equal to atomic number and Number of neutrons = mass number – atomic number Solution: Number of protons = atomic number = 17 Number of neutrons= mass number – atomic number = 35-17 = 18 1. The mass of atoms of all other elements are compared to the mass C-12. Mass of one C-12 atom = 12 amu 1amu= mass of one C-12 atom 12 A hydrogen atom is 8. 8 . relative atomic mass of hydrogen. This isotope of carbon(C-12) has been assigned a mass of exactly 12 atomic mass unit. An atom is extremely small particles. Avogadro and Berzelius. Gay Lussac. Therefore. it is possible to determine the mass of one atom of an element relative to another experimentally.2.3 RELATIVE ATOMIC MASS AND ATOMIC MASS UNIT The first quantitative information about atomic masses came from the work of Dalton.2: Determining the number of protons and neutrons in an atom Atomic number of an element is 17 and mass number is 35. so that it can be used as standard.
So the empirical formula of hydrogen peroxide is written as HO.9994 amu. 9 . In a chemical formula element’s symbol and numerical subscripts show the type and the number of each atom in a compound.008 amu = Similarly. relative atomic masses of O. Therefore.40 x 12 amu 100 =1.0067amu 15.4 EMPIRICAL FORMULA.1 shows the relative atomic masses of some elements. What is the empirical formula of glucose? 2.9898 amu Element Al S Cl Fe Relative atomic mass 26. H and O atoms in a glucose molecule is 6 : 12 : 6. 1. The actual ratio between C.1 relative atomic masses of some elements Element H N O Na Relative atomic mass 1.9815 amu respectively.06 amu 35. EMPIRICAL FORMULA The empirical formula of a compound is the chemical formula that gives the simplest whole-number ratio of atoms of each element. MOLECULAR FORMULA A molecular formula gives the actual whole number ratio of atoms of each element present in a compound. So molecular formula of hydrogen peroxide is H2 O2. For example in compound hydrogen peroxide there is one H atom for every O atom. Table 1. 26. Table 1. The simplest ratio between C.008 amu 14. H and O atoms in glucose in 1 : 2 : 1.9898 amu. simplest ratio of hydrogen to oxygen is 1 : 1.2. Na. 22.847 amu 1. For example there are actually two H atoms and two O atoms in each molecule of hydrogen peroxide.9815 amu 32. Therefore. Al are 15. Here you will learn about two types of chemical formulas.9994amu 22. What is the molecular formula of glucose? An empirical formula shows the simplest number of atoms of each element in a compound whereas the molecular formula shows the actual number of aotms of each element in a molecule of a compound.Chapter 1 8. actual ratio of hydrogen to oxygen atoms is 2 : 2. There are several types of chemical formulas for a compound.453 amu 55. MOLECULAR FORMULA Recall that the chemical formula of a compound tells us which elements are present in it and the whole number ratio of their atoms.
eight hydrogen atoms and four oxygen atoms.008) + 16. Can you show it why? SELF ASSESSMENT EXERCISE 1.00 = 18. sulphur dioxide (SO2) etc.016amu 10 . 3. Write its empirical and molecular formulas. SELF ASSESSMENT EXERCISE 1. empirical and molecular formulas are same. Write the empirical formula for caffeine. All you have to do is to add up the atomic masses of all the atoms in the compound.2 Write the empirical formulas for the compound containing carbon to hydrogen in the following ratios: (a) 1:4 (c) 2:2 (b) (d) 2:6 6:6 For many compounds. There are nine carbon atoms. This contains 2 carbon atoms.00 = 2. Identify empirical and molecular formula for benzene from the following formulas. C6 H6 . in this compound. four hydrogen atoms and 2 oxygen atoms.2. ammonia (NH3).016 + 16. Caffeine (C8H10N4O2) is found in tea and coffee. There are actually six C atoms and six hydrogen atoms in each molecule of benzene. For example.5 MOLECULAR MASS AND FORMULA MASS Molecular mass is the sum of atomic masses of all the atoms present in the molecule.Chapter 1 Benzene in a compound of carbon and hydrogen. Vinegar is 5% acetic acid. Aspirin is used as a mild pain killer. CH Molecular formulas for water and carbon dioxide are H2O and CO2 respectively. 1. For example water (H2O). Molecular mass of water H2O = 2(atomic mass of H) + atomic mass of oxygen = 2(1. carbon dioxide (CO2).3 1. 2. Write its empirical and molecular formulas. It contains one C atom for every H atom. What are empirical formulas for these compounds? For many compounds empirical and molecular formulas are same. methane (CH4).
4: Determining formula mass 1. and in the preparation of large number of compounds.096 amu 2. Determine its formula mass. the common salt consists of Na+ and Cl ions.00) + 12(1. also called as table salt is used to flavour food. Solution: 1. Ionic compounds consist of arrays of oppositely charged ions rather than separate molecules.5amu 11 . Solution: 1. Whereas. For example. The sum of the atomic masses of all the atoms in the formula unit of a substance is called formula mass.Chapter 1 Example 1. Milk of magnesia which contains Mg(OH)2.008) + 6(16.3: Determining molecular mass 1. Determine the molecular mass of naphthalene C10H8. the term formula mass is used for ionic compounds. It has one Na+ ion for every Cl ion. Molecular mass of C6H12O6 = 6(12. hydrogen and oxygen by their subscripts and add. Example 1. preserve meat.00) =180. which is used in mothballs. Molecular mass of C10H8 = 12 x 10 + 1 x 8 = 120 + 8 = 128 amu The term molecular mass is used for molecular compounds. Sodium Chloride.5 = 58. Formula mass of NaCl = 1 x Atomic mass of Na + 1 x Atomic mass of Cl = 1 x 23 + 1 x 35. 2. Problem solving strategy: Multiply atomic masses of carbon. A formula unit indicates the simplest ratio between cations and anions in an ionic compound. So formula unit for common salt is NaCl. 2. So we represent an ionic compound by its formula unit. Problem solving strategy: Add the atomic masses of all the atoms in the formula unit. is used to treat acidity. Determine its formula mass. Determine the molecular mass of glucose C6H12O6 which is also known as blood sugar.
Following compounds are used as fertilizers. MOLECULAR IONS AND FREE RADICALS ATOMS AND IONS Atom is the smallest particle of an element that can not exist in free state.Chapter 1 2. (i) Urea. On the other hand an ion is a charged species formed from an atom or chemically bonded groups of atoms by adding or removing electrons. 12 . Figure 1. Determine the formula masses of baking soda and carbon dioxide. Ca forms Ca+2 by losing two electrons. 2. 3. ANIONS). For example Na forms Na+ by losing one electron. Calculate its formula mass.1 view of surface atoms of gold The image has been drawn by computer from signal sent to it by an instrument called a scanning tunneling microscope. however. which is responsible for the rising of cookies and bread. Positively charged ions are called cations. 1. Potassium Chlorate (KClO3) is used commonly for the laboratory preparation of oxygen gas.1 shows an image of gold atoms on the surface. Determine their formula masses. It is electrically neutral. NaHCO3 is heated it releases carbon dioxide. Today. Most of the matter is composed of molecules or ions formed by atoms. The computer has drawn gold atoms as topped peaks. the negatively charged ions are called anions. When baking soda. (NH2)2CO (ii) Ammonium nitrate.1 IONS (CATION.3 CHEMICAL SPECIES Figure 1. The Non-metal atoms usually gain one or more electrons and form anions. Metal atoms generally lose one or more electrons and form cations. Formula mass of Mg(OH)2 = 24 + 16x2 + 1x2 = 24 + 32 + 2 = 58 amu SELF ASSESSMENT EXERCISE 1. we have sophisticated instruments to weigh atoms and even visualize them. NH4NO3. whereas. 1.4 1. Important information Many scientists regarded atom as a merely a convenient mental construct and nothing more.3. An ionic compound contains anions and cations in such number that the compound is electrically neutral. This is because atom is so small that it cannot be seen with the naked eye.
Thus its nucleus has a total charge of +11.1. Molecular ions do not form ionic compounds. O-atom gains two electrons and forms O-2 ion.ion. Let us understand why an ion acquires a net positive or negative charge. The charge on the ion is +11 + (-10) = +1 SELF ASSESSMENT EXERCISE 1.2 Na+ ion Figure 1. Similarly N2-. For example O2 when loses one electron it forms O2+ ion. Mg+2 has +2 charge. S-2 has –2 charge.5 Explain Why? 1.2 shows the sodium ion. the resulting species is called a molecular ion. Around the nucleus. Consider the formation of Na+ ion. Fig. 3. These are short lived species and only exist at high temperature. FREE RADICALS A free radical is an atom which has an unpaired electron and bears no electrical charge. in the ion are 10 electrons. Note that sodium has a nucleus of 11 protons and 12 neutrons. with a total charge of -10.ion. Sulphide ion. 2. N2+ etc are examples of molecular ions. MOLECULAR ION When a molecule loses or gains electrons. Magnesium ion. For example 13 . An oxide ion has –2 charge. These ions are called molecular ions.Chapter 1 For example chlorine atom gains one electron and forms Cl. but when it absorbs an electrons it forms O2.
Dot (. For instance water exists as molecules. so it has odd number of electrons.6 Identify ions. Whereas an ion has even number of electrons. their molecules split up into free radicals. 14 . A free radical is an electrically neutral species. DIFFERENCE BETWEEN ION AND FREE RADICAL Chlorine free radical Chloride ion Which species has even number of electrons? Which species has odd number of electrons? A free radical has an unpaired electron. These species are atoms. SELF ASSESSMENT EXERCISE 1. molecules or formula units.5: Identifying representative particles of elements and compounds Figure 1.Chapter 1 are free radicals When substances like halogens are exposed to sun light. 1. molecular ions and free radicals from the following species.3.) indicates an unpaired electron. carbon exists as atoms. Identify particles of elements and compounds.2 REPRESENTIATIVE PARTICLES OF ELEMENTS AND COMPOUNDS The term representative particles refer to species present in a substance. so it has no unpaired electrons.3 shows some molecules. Example 1.
C.Chapter 1 Fig 1. Kr. d) A mixture of an element and a compound. SELF ASSESSMENT EXERCISE 1. H2. Solution: Particles of elements are A. Ar. For example. Rn.7 1. Ne. Particles of compounds are B and F. NH3 etc are polyatomic molecules. A molecule that contains only one atom is called monoatomic.3 Some common molecules Problem Solving Strategy: Elements have atoms of same sizes and compounds have atoms of different sizes. f) A mixture of two compounds. D and E. Inert gases consist of monoatomic molecules such as He. Molecules can also be classified as monoatomic or polyatomic. e) A mixture of two elements. b) An element whose particles are molecules. 15 . Molecules that contain two or more similar or different atoms are called polyatomic molecules. c) A compound. O2. Observe the given figure and identify the diagrams that represents the particles of : a) An element whose particles are atoms. HCl.
Chapter 1 2. Chemists also use a practical unit for counting atoms. A mole of a substance contains 6. 1. They could not succeed and wasted their time and money. These processes are still in use today. a compound or a mixture. It is represented by NA. oranges etc. Society. a mole of a substance represents 6. Chemical history was dominated by a pseudo-science called alchemy. Observe the given figure and decide which diagram represents particles in an element. A mole is an amount of a substance that contains 6. sublimation and extraction. a ream of paper represent 500 papers. Therefore. the works of earlier alchemists handicapped progress of science.022 x 1023 representative particles of a substance. Technology and Science During 600 – 1600 AD. so you would most likely count them by pairs rather than individually. Such processes are contributing a lot in the progress of science. Earlier alchemists were obsessed with the idea of turning cheap metals into gold. during that period they discovered many new processes such as distillation. molecules or ions of that substance. are counted in dozens. Thus. They searched for ways to change less valued metals such as lead into gold. This experimentally determined number is known as Avogadro’s number. However. For example a mole of 16 . molecules and ions. Just as a dozen eggs represent twelve eggs. Similarly eggs. This means the works of different scientists at the same time handicap or promote the growth of science. the counting unit depends on what you are counting.022 x 1023 atoms.4 AVOGADRO’S NUMBER AND MOLE How do you count shoes? As shoes come in pairs. They use a counting unit called mole to measure the amount of a substance. but paper by ream.022 x 1023 particles of that substance.
A mole of sulphur is 6. therefore.022 x 1023 molecules. So an easy way is to weigh them.022 x 1023 molecules. molecules.022 x 1023 C-atoms) A pair of Shoes & a dozen eggs Figure 1. when counting a pile of coins. For instance water exists as molecules. Just as 6. Society. 17 . They need about one million year to count them. The concept of mole has given a very simple method to count large number of items.022 x 1023atoms.02 x 10 carbon atoms weigh 12 23 g. A mole of S-atoms (6.02 x 10 coins will also have a definite mass. formula units or ions.022 x 1023 atoms. it would not be convenient to count them one by one. so one mole of hydrogen contain 6. one mole of water contains 6. you can count them by weighing.4 A mole of S-atoms. 6. A mole of water is 6. a mole of C-atoms & pair of Shoes & a dozen eggs What is the mass of one mole C-atoms? How many atoms are there in 32. So.022 x 1023 molecules of water. Technology and Science Size of the Mole Entire population can not count 1 mole of coins in a year. Mole is not only a 23 number but also represents definite amount of a substance.Chapter 1 carbon is 6.1 g of S-atoms? Does a dozen eggs have same mass as a dozen bananas? Does a mole of carbon atoms have a different mass than a mole of sulphur atoms? The mass of one mole of substance is called as molar mass.022 x 1023 atoms. If you know the mass of one coin.022 x 1023 S-atoms) A mole of C-atoms (6. Hydrogen exists as H2 molecules. What are the molar masses of carbon and sulphur? The term representative particles in a substance are atoms. Carbon exists as atoms so 1 mole of carbon contains 6.
022 x 1023 S-atoms? Is this mass of S-atoms equal to its atomic mass? What is the mass of one mole of C-atoms? Is this mass of C-atoms equal to its atomic mass? Atomic mass of an element expressed in grams is called gram atomic mass. Is gram atomic mass of C-atoms 12 g? What is the gram atomic mass of S-atoms? If each of the carbon and sulphur sample shown above contains one mole of atoms. why do the samples have different masses? Atomic mass of C Atomic mass of Na Atomic mass of Zn = 12amu = 23amu gram gram atomic mass of C = 12g atomic mass of C = 23g = 63.022 x 1023 C-atoms) What is the mass of 6.Chapter 1 1. GRAM MOLECULAR MASS AND GRAM FORMULA MASS A mole of S-atoms (6.54g Gram atomic mass of an element contains 1 mole of atoms.022 x 1023 S-atoms) A mole of C.4. Mass of 1 mole of C-atoms = 12g Mass of 1 mole of Na-atoms = 23g Mass of 1 mole of Zn-atoms = 63. Therefore.3 GRAM ATOMIC MASS.atoms (6.54g 18 .54amu gram atomic mass of C = 63.
096amu So. KCl. An ionic compound is represented by the formula unit that represents the simplest ratio between the ions of a compound. gram molecular mass of H2O = 18. gram formula mass of NaCl = 58. Molecular mass of H2O = 2 x 1.008 + 16 x 6 = 180. For example NaCl. Formula mass of NaCl = 23 + 35.022 x 1023 C6H12 O6 180.022 x 1023 molecules of glucose? is this mass of glucose molecules equal to molecular mass of glucose? Molecular mass of a substance expressed in grams is called gram molecular mass.5 = 58.022 x 1023 H2O-molecules) molecules) 18. 19 .008 + 16 = 18.5g = mole of NaCl formula unit.096g What is the mass of one mole of water molecules? Is this mass of water molecules equal to molecular mass of water? what is the mass of 6.016g Molecular mass of C6H12 O6 = 6 x 12 + 12 x 1.5amu Therefore.096g Formula mass of a substance expressed in gram is called gram formula mass. CuSO4 etc.Chapter 1 A mole of H2O-molecules (6.016g A mole of C6H12 O6 .016amu So. gram molecular mass of C6H12 O6 = 180.molecules (6.
5 = 74. (ii) (iii) All of these quantities represent molar mass.022 23 x 1023 molecules whereas gram formula mass contain 6.5amu So.Chapter 1 Formula mass of KCl = 39 + 35. GRAM MOLECULAR MASS AND GRAM FORMULA MASS (i) Gram atomic mass represents one mole of atom of an element.5: Calculating mass of one mole of a substance Calculate the molar masses of (a) Na (b) Nitrogen (c) Surcose C12H22O11 Problem solving strategy: If an element is a metal then its molar mass is its atomic mass expressed in grams ( gram atomic mass).5g DIFFERENCE BETWEEN THE TERMS GRAM ATOMIC MASS. If an element exists as molecule.5 CHEMICAL CALCULATIONS In this section. Mass of one mole of a substance expressed in grams is called molar mass.1 MOLE-MASS CALCULATIONS Example 1. its molar mass is its molecular mass expressed in grams (gram molecular mass). gram molecular mass contains 6. 1.022 x 1023 atoms. mole can be defined as atomic mass.5. Solution: a) 1 mole of Na = 23g b) Nitrogen occurs as diatomic molecules. Gram atomic mass contains 6. you will learn about the chemical calculations based on the concept of mole and Avogadro’s number. Molecular mass of N2 = 14 x 2 20 . gram molecular mass represents one mole of molecules of a compound or an element that exists in molecular state whereas gram formula mass represents one mole of an ionic compound.022 x 10 formula units. “Therefore. gram molecular mass of KCl = 74. 1. molecular mass or formula mass expressed in grams”.
05 moles of ozone is formed in a storm? Problem solving strategy: Ozone is a molecular substance. mass of 1mole of sucrose = 342g SELF ASSESSMENT EXERCISE 1.05 moles of O3 = 48 g x 9.5(a): Calculating the mass of a given number of moles of a substance Oxygen is converted to ozone (O3) during thunder storms. what mass of CO2 is produced? Problem solving strategy: Carbon dioxide is a molecular substance. mass of 1 mole of N2 = 28 g c) Its molecular mass expressed in grams. Molecular mass of C12H22O11 = 12x12 + 1x22 + 16x11 = 144 + 22 + 176 Therefore. Determine its molar mass and use it to convert moles to mass in grams.Chapter 1 = 28amu Therefore.6: When natural gas burns CO2 is formed.25 moles of CO2 is formed. 9. Calculate the mass of ozone if 9. Determine its molar mass and use it to convert moles to mass in grams 21 .05 = 434.8 Calculate the mass of one mole of (a) Copper (b) Iodine (c) Potassium (d) Oxygen Example 1. 9. If 0.4g of O3 Example 1.05 moles of O3 ? g of O3 Solution: 1 mole of O3 = 16 x 3 = 48 g 1 mole of O3 = 48 g So.
mass ? moles Solution: a) Molar mass of H2 = 1.25 moles of CO2 ? g of CO2 Solution: Molar mass of CO2= 12 + 16 x 2 = 44g 1 mole of CO2 = 44g of CO2 So.016 5g of H2 = 22 .008 x 2 = 2.016g = 1 mole of H2 = 1 moles of H2 2.Chapter 1 0. 0. 2. (b) A block of ice that weighs 100g.016g of H2 1g of H2 = 2. Problem solving strategy: Hydrogen and ice both are molecular substances.7: Converting grams to moles How many moles of each of the following substance are present? (a) A balloon filled with 5g of hydrogen. Use the molar mass of each to convert masses in grams to moles.016g 1 mole of H2 So.25 moles of CO2 = 44 x 0. Determine their molar masses.016 1 x5 moles of H2 2.25 = 11g of CO2 Example 1.
of moles of this compound that would exactly weigh 30g.5.016g 1 mole of H2O So.016 + 16 = 18. 1.25 moles of Zn.2 MOLE-PARTICLES CALCULATIONS Example 1.5grams of this salt. Calculate (a) Mass of this compound that would contain 2.Chapter 1 = 2. people are required to swallow suspensions of barium sulphate (BaSO4). NaCl contains 12.2 moles of aluminium? 23 . 2. 2. (b) No.48 moles of H2O b) 1 mole of H2O = 2 x 1. Before the digestive systems X-rayed. How many atoms are present in a foil that contains 0.8: Calculating number of atoms in given moles 1. Zn is a silvery metal that is used to galvanize steel to prevent corrosion. Calculate the number of moles it contains.016 1 x100 moles 18. A thin foil of aluminium (Al) is used as wrapper in food industries. A spoon of table salt. The molecular formula of a compound used for bleaching hair is H2O2.016 100g of H2O = = 5.008 + 16 = 2.5 moles. 3.016g of H2O 1g of H2O = 18.9 1. 18. Calculate mass of one mole of BaSO4.55 moles of H2O SELF ASSESSMENT EXERCISE 1. How many atoms are there in 1.016g = 1 mole = 1 moles 18.
53 x 1023 Zn atoms 2. Solution: 1. How many molecules are there in 0.25 moles of SO2. thus 1 mole of methane will have 6. 1 mole of Zn contains 6. 1 mole of Al contains 6.25 = 1.25 = 7.022 x 1023x 0. Solution: 1. How many molecules are present in 0.Chapter 1 Problem solving strategy: Remember that symbols Zn and Al stand for one mole of Zn and Al atoms respectively.022 x 1023x0. its one mole will also have 6. Similarly.5 23 = 3.5055 x 1023 molecules 24 .2 moles of Al will contain = 6.022 x 10 molecules So. Methane (CH4) is the major component of natural gas. 0. Problem solving strategy: Remember that CH4 is a molecular compound.2044 x 1023 atoms Example 1. 1 mole of CH4 contains = 6.022 x 1023 molecules. 23 1 mole of SO2 contains = 6.2 = 1. Sulphur dioxide reacts with water to form acid rain.022x1023 molecules. 0.022 x 1023 x 0.9: Calculating number of molecules in given moles of a substance 1. SO2 is a molecular compound.022 x 1023 x 1.5 moles of CH4 will contain = 6.022 x 1023 atoms 1.011 x 10 molecules 2.5 moles of a pure sample of methane? 2.022 x 1023 molecules So. At high temperature hydrogen sulphide (H2S) gas given off by a volcano is oxidized by air to sulphur dioxide (SO2).25 moles of Zn contain = 6.022 x 1023 atoms So 0.25 moles of SO2 will contain= 6.
Its molecular formula is CH2O.5 moles of Ti Example 1.022 x 1023 molecules = 1 mole of compound 3.022 x 1023 atoms. aircrafts and jet engines. Thus.011 x 1022 molecules of this compound.011 x 1023 Ti-atoms.022 x 1023 1 x 3.022 x 1023 molecules. Problem solving strategy: Remember that 1 mole of an element contains 6. 6. Calculate the number of moles of this metal in a sample containing 3.011 x 1023 atoms ? moles Solution: 6.Chapter 1 Example 1.022 x 1023 atoms = 1 mole 3. Thus. Calculate the number of moles that would contain 3. Problem Solving Strategy: Remember that 1 mole of any compound contains 6.022 x 1023 3. 6.011 x 1022 molecules ? moles 25 .011 x 1023 Ti atoms = = 0.11: Calculating number of moles in the given number of molecules Formaldehyde is used to preserve dead animals.022 x 1023 Ti atoms = 1 mole of Ti 1 Ti atoms = 1 moles of Ti 6.011 x 1023 moles of Ti 6.10: Calculating number of moles in the given number of atoms Titanium is corrosion resistant metal that is used in rockets.
A method used to prevent rusting in ships and underground pipelines involves connecting the iron to a block of a more active metal such as magnesium. The total number of protons and neutrons in an atom is called its mass number. It is used as a painkiller. The branch of Chemistry that deals with laws and theories to understand the structure and changes of matter is called Physical Chemistry. Physical and chemical changes that occur in living organisms are studied in biochemistry.022 x 10 = 0.011 x 1022 molecules = 1 moles of formaldehyde 6. How many moles of magnesium are present in 1 billion (1 x 109) atoms of magnesium. Industrial chemistry is concerned with the large scale production of chemical substances.Chapter 1 Solution: 6. hydrogen and oxygen. How many moles of this compound are present in the tablet? 2. A compound consists of two or more elements held together in fixed proportions by chemical bonds. 26 . This method is called cathodic protection. An impure substance that contains two or more pure substances that retain their individual chemical characteristics is called a mixture.022 x 1023 1 x 3. An element is a substance whose all the atoms have the same atomic number.05 moles of formaldehyde SELF ASSESSMENT EXERCISE 1.022 x 1023 molecules = 1 mole of formaldehyde 1 molecule = 3. An aspirin tablet contains 1. The number of protons in the nucleus of an atom is known as its atomic number. Aspirin is a compound that contains carbon. Organic chemistry deals with carbon compounds. The branch of Chemistry that deals with elements and their compounds except organic compounds is called Inorganic Chemistry.011 x 1022 moles of formaldehyde 23 6. Chemistry is the science of materials of the universe.10 1.25 x 1030 molecules.
molecular mass or formula mass expressed in grams. Molecular mass is the sum of atomic masses of all the atoms present in the molecule. Chemical formula of a compound that gives the simplest whole-number ratio between atoms is called empirical formula. The amount of matter that contains as many atoms. One atomic mass unit is defined as the mass exactly equal to one-twelfth the mass of one C12 atom. When a molecule loses or gains electrons. Mole can also be defined as atomic mass. REFERENCES FOR ADDITIONAL INFORMATION Zumdahl.Chapter 1 Atoms of an element that have different number of neutrons are called isotopes. The mass of an atom of an element relative to the mass of an atom of C-12 is called relative atomic mass. Molecular formula of a compound gives the exact number of atoms presents in a molecule. 27 . Molecular mass of an element or a compound expressed in grams is its gram molecular mass. The number of representative particles in one mole of the substance is known as Avogadro’s number. Introductory Chemistry. ions or molecules as the number of atoms in exactly 12g of C-12 is called mole. Gram formula mass is the formula mass of a substance in grams. Positively charged ions are called cations and negatively charged ions are called anions. Essential Chemistry. the resulting species is called molecular ion. Free radical is an atom or group of atoms that contains an unpaired electron. Raymond Chang. Atomic mass of an element expressed in grams is called gram atomic mass.
oxygen. H=1) a. c. a. d. water. (iii) a. d. 16 (v) How many moles of molecules are there in 16g oxygen. water. which box represent the particles in nitrogen. 23 c.008g (vii) What is the mass of carbon present in 44g of carbon dioxide. Air.Chapter 1 Q. (Atomic masses: Cu=63. 1 b.05 (vi) What is the mass of 4 moles of hydrogen gas. brass Air. a.5 249. 0. earth Calcium. 12 d. O=16.1: Encircle the correct answer: (i) Which of the following lists contains only elements? a. 106 b. 8. S=32.5 185. 1. fire. 159.5 149. b. 4.5 c. 1g d. What is the formula mass of CuSO4. b. c. b. sulphur. d.1 d. 0. Atomic mass of the element X is a.5.064g b.032g c.5 (iv) A compound with chemical formula Na2CX3 has formula mass 106amu.5H2O. 28 . oxygen Hydrogen. c. 0. carbon (ii) The diagrams below represent particles in four substances.
mass c. (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) Q.5x Q. An atom of this element will form an ion that will have charge. 6g c. Calculate the number of moles of each substance in samples with the following a. 2. b. What is mole? Differentiate between empirical formula and molecular formula. 2x d. +2 c.Chapter 1 a. atoms d. atomic number. 0. What is the number of molecules in 9. molecular ion. molecules (x) If one mole of carbon contains x atoms. free radical. x b. 12g b. formula unit.5x c. -1 (ix) Which term is the same for one mole of oxygen and one mole of water? a. 24g d. d. c. atomic mass unit.4: Q. 1. +3 d. 44g (viii) The electron configuration of an element is 1s22s2. what is the number of atoms contained in 12g of Mg. +1 b. a.4 g of He 250mg of carbon 15g of sodium chloride 40g of sulphur 29 masses: . Differentiate between (a) atom and ion (b) molecular ion and free radical. mass number. volume b.3: Q. Describe how Avogadro’s number is related to a mole of any substance.6: Differentiate between an ion and a free redical What do you know about corpuscular nature of matter? Differentiate between analytical chemistry and environmental chemistry.5: Q.2: Give short answers. a.0 g of steam? What are the molar masses of uranium -238 and uranium -235? Why one mole of hydrogen molecules and one mole of H-atoms have different masses? Define ion.
6 H-atoms.5kg of MgO Q. a.25 moles of steam 1. C6H6 0. 3.10: TNT or trinitrotoluene is an explosive compound used in bombs. the dye used to colour blue jeans is derived from a compound known as indoxyl (C8H7ON). Also determine the molar mass of this molecule. Q. It contains 7 C-atoms.13: Identify the substance that has formula mass of 133.01 moles of acetic acid.2 moles of K 75moles of H2 0. c. b.09 moles of benzene.05 moles of CuSO4. 5g of H atoms 30 . Calculate the molar masses of these compounds. Q.4 moles of nitrogen atoms b. b.5H2O 0.5 moles of carbon dioxide 3.12: Indigo (C16H10N2O2). 5 N-atoms and 6 O-atoms. d. 23g of Na c. MgCl2 S2Cl2 BCl3 AlCl3 Q. NH3 1. e.11: A molecule contains four phosphorus atoms and ten oxygen atoms.14: Calculate the number of atoms in each of the following samples: a. 1.8: 1. d. Also write their empirical formulas. 2.15moles of H2SO4 Calculate the number of molecules present in each of the following samples: a. c. Write its empirical formula.9: Decide whether or not each of the following is an example of empirical formula: a. c. b. d. c. b. Write the empirical formula of this compound. Q.7: Calculate the mass in grams of each of the following samples: a. Q. d.4 moles of ammonia.Chapter 1 e. CH3COOH Q.5amu. Al2Cl6 Hg2Cl2 NaCl C2H6O Q.
A silver article tarnishes in air. Dynamite (C3H5N3O9) explodes to form a mixture of gases. Purple iodine vapour appears when solid iodine is warmed. 4. Sulphur dioxide is the major source of acid rain. 8. 3. 6. Ice floats on water. 10. In Pakistan most of the factories use wet process for the production of cement. 7. A cornstalk grows from a seed. Many other light chlorinated hydrocarbons in drinking water are carcinogens. Carbon-14 is continuously produced in the atmosphere when high energy neutrons from space collide with nitrogen-14. c. 2. b. 3. 5.Chapter 1 Q. d.15: Calculate the mass of following: a. 31 .16: Identify the branch of chemistry that deals with the following examples: 1.24 x 1018 atoms of iron 2 x 1010 molecules of nitrogen gas 1 x 1025 molecules of water 3 x 106 atoms of Al Q. 9. Gasoline ( a mixture of hydrocarbons) fumes are ignited in an auto mobile engine.
00g of carbon. What mass of oxygen contains the same number of molecules as 42g of nitrogen. It shows particles in a sample of air. 2. Calculate the total number of atoms present in 18g H2O. e) What is the most common substance in air? 5.Chapter 1 1. 32 . What mass of sodium metal contains the same number of atoms as 12. Calculate the mass of one hydrogen atom in grams. 4. 6. d) Decide whether each substance in air is an element or a compound. a) Count the substances shown in the sample b) Is air a mixture or pure substance? Explain? c) Identify the formula of each substance in air. Observe the given figure. Calculate the number of H-atoms present in 18g H2O. 3.
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| 0.999751 |
牙齒矯正
什麼樣的人需要牙齒矯正呢？
1. 前牙移位
2. 咬合不正
3. 牙齒缺失、毫無秩序
4. 齒列稀疏
5. 牙齦萎縮：貼近牙齦的縫隙，沒有牙齦，而形成三角形的間隙
6. 多生牙：智齒影響齒列排列
7. 爆牙：頜骨下頜較短小，導致上排牙齒比下排牙齒凸出。
矯正的過程
醫師諮詢consultation
討論適合的矯正方式矯正前有些患者會希望保留自己的小虎牙、大門牙等等個人特色，或是對於牙齦特別在乎，這些在醫師替各位規劃個人矯正計畫時都是很重要的部分唷！
矯正事前資料蒐集collection
了解牙齒及骨骼條件，制定矯正計畫
製模modle impression
備用，與用於矯正後的牙齒比對
拍照片photo shoting
拍射5個角度照片，用於日後比對
拔牙tooth extraction
除了拔除智齒外，根據牙齒排列的擁擠程度，會需要拔牙，拔牙的牙縫，會等到中期再利用橡皮筋拉緊，調整牙縫，而有些人不需要拔牙，僅需磨牙將牙齒稍微騰出一些空間即可。
分牙tooth separators
分牙是為了移動出空間裝上牙套，分牙的階段大約需要一週，醫師會將分牙圈套在上下的大牙中。
上牙套on braces
剛上牙套要注意的除了適應牙套避免磨嘴，此時的牙齒清潔更需仔細注意，餐後需搭配特殊牙線、牙間刷、牙刷等徹底清潔
固定複診recall
在復安我們採用滑蓋式矯正器
提高矯正效率，大約1個月回診一次。
定型（上橡皮筋）
矯正後約1~3個月就可以看到變化，待6個月基本上就排齊了，此時需要上橡皮筋收緊牙縫
摘下牙套braces move
摘下牙套後，仍需要配戴牙齒維持器約半年，半年後可於睡覺時配戴即可。
牙齦治療
笑齦（Gummy smile）是許多人困擾的問題，非骨性暴牙的笑齦問題是可以
搭配骨釘將牙弓的部分往上移動，若依然還有牙肉過多的部分可再利用電燒的部分將牙齦多餘的牙肉去除，而牙齦過度覆蓋，醫師也會在矯正時讓門牙壓入(intrusion)來改善牙齦外露的問題。
嚴重的『骨性暴牙』，表面的骨性暴牙可利用水雷射來削去多的骨頭，而上顎骨頭垂直方向過長，導致嘴唇緊繃、上翻，還是需要靠正顎手術來改善。
固定式矯正
固定式牙齒矯正有傳統金屬矯正器、透明陶瓷矯正器，配合所需力量的矯正線來移動牙齒，需長期配戴且定期複診調整。不過治療效果良好，可以做大範圍的牙齒移動、改善傾斜、旋轉、調整牙根位置。
活動式矯正
活動式的矯正，可做到小範圍的牙齒移動，可由患者可以自行拿下、裝上矯正器，主要是用來矯正顎骨形狀、上下顎、局部咬合不正、骨性暴牙的問題。
隱適美隱形牙套矯正
隱適美是透明的牙套，戴上隱適美在外觀上不易察覺，患者可以自行拿取與裝上隱適美。醫師會透過3D掃描完整的牙齒骨骼形狀位置，再由電腦計算，替患者設計一整套的矯正過程，並且預估牙套付數與矯正的結果。
侵入式矯正
大暴牙、戽斗的患者若想要達到較大的改善效果，則需在整形外科進行正顎手術後，再進行牙齒矯正。
侵入式矯正須將顎骨事先局部斷折，然後再將兩端斷骨裝上牽引器，讓它漸進產生拉扯力量、刺激新的骨頭在斷骨處生長、來改善下顎骨發育不足、小顎症、臉型不對稱等。
在復安的牙齒矯正，差別是？
1.提高牙齒移動效率，大幅縮短療程
2.減少回診次數，滑蓋式可延長複診時間，約1個月複診一次。
3.包覆鐵絲及橡皮筋，不易刮口
4.方便清潔，不易卡菜渣再鐵絲及橡皮筋之間上橡皮筋
什麼是隱適美？
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| 0.999276 |
Comparison of three rounding algorithms for IEEE floating-point multiplication
Guy Even, Peter M. Seidel
Research output: Contribution to conferencePaperpeer-review
Abstract
A new IEEE compliant floating-point rounding algorithm for computing the rounded product from a carry-save representation of the product is presented. The new rounding algorithm is compared with the rounding algorithms of Yu and Zyner and of Quach et al. For each rounding algorithm, a logical description and a block diagram is given and the latency is analyzed. We conclude that the new rounding algorithm is the fastest rounding algorithm, provided that an injection (which depends only on the rounding mode and the sign) can be added in during the reduction of the partial products into a carry-save encoded digit string. In double precision the latency of the new rounding algorithm is 12 logic levels compared to 14 logic levels in the algorithm of Quach et al., and 16 logic levels in the algorithm of Yu and Zyner.
Original languageEnglish
Pages225-232
Number of pages8
StatePublished - 1999
EventProceedings of the 14th IEEE Symposium on Computer Arithmetic, ARITH-14 - Adelaide, SA, Aust
Duration: 14 Apr 199916 Apr 1999
Conference
ConferenceProceedings of the 14th IEEE Symposium on Computer Arithmetic, ARITH-14
CityAdelaide, SA, Aust
Period14/04/9916/04/99
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| 0.833112 |
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