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Vector (geometric)
Title: Vector (geometric)
Subject: Normed vector space, Monoclinic crystal system, Radial, Hodograph, Crystal momentum, Motion lines, Resultant, Two-vector, Vector decomposition, Direction vector
This article is about the vectors mainly used in physics and engineering to represent directed quantities. For mathematical vectors in general, see Vector (mathematics and physics). For other uses, see vector.
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric[1] or spatial vector,[2] or—as here—simply a vector) is a geometric quantity having magnitude (or length) and direction expressed numerically as ordered list of tuples [ x , y , z ] splitting the entire quantity into its orthogonal-axis components. A vector is an object that is an input to, or output from vector functions according to vector algebra. A Euclidean vector is typically sketched as a directed line segment, or arrow, connecting an initial point A with a terminal point B,[3] and denoted by \overrightarrow{AB}. However, as an informational object, the vector is not as informative as a directed line segment (an ordered list of two points [ A , B ]), but rather expresses the displacement, or vector offset (change in location) going from A --> B. Technically, the [ x, y, z ] components of vector \overrightarrow{AB} are equal to the vector difference \overrightarrow{B} minus \overrightarrow{A}. In this way, the vector \overrightarrow{AB} considered as a numerical quantity conceals the locations of A and B, while imparting the location of point B relative to A, as if A were the coordinate origin.
Vectors play an important role in physics: velocity and acceleration of a moving object and forces acting on it are all described by vectors. Many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances (except, for example, position or displacement), their magnitude and direction can be still represented by the length and direction of an arrow. The mathematical representation of a physical vector depends on the coordinate system used to describe it. Other vector-like objects that describe physical quantities and transform in a similar way under changes of the coordinate system include pseudovectors and tensors.
It is important to distinguish Euclidean vectors from the more general concept in linear algebra of vectors as elements of a vector space. General vectors in this sense are fixed-size, ordered collections of items as in the case of Euclidean vectors, but the individual items may not be real numbers, and the normal Euclidean concepts of length, distance and angle may not be applicable. (A vector space with a definition of these concepts is called an inner product space.) In turn, both of these definitions of vector should be distinguished from the statistical concept of a random vector. The individual items in a random vector are individual real-valued random variables, and are often manipulated using the same sort of mathematical vector and matrix operations that apply to the other types of vectors, but otherwise usually behave more like collections of individual values. Concepts of length, distance and angle do not normally apply to these vectors, either; rather, what links the values together is the potential correlations among them.
The word "vector" originates from the Latin vehere meaning "to carry". It was first used by 18th century astronomers investigating planet rotation around the Sun.[4]
2.1 Examples in one dimension
2.2 In physics and engineering
2.3 In Cartesian space
2.4 Euclidean and affine vectors
2.5 Generalizations
3 Representations
3.1 Decomposition
4 Basic properties
4.1 Equality
4.2 Addition and subtraction
4.3 Scalar multiplication
4.4 Length
4.5 Dot product
4.6 Cross product
4.7 Scalar triple product
4.8 Multiple Cartesian bases
4.9 Other dimensions
5.1 Length and units
5.2 Vector-valued functions
5.3 Position, velocity and acceleration
5.4 Force, energy, work
6 Vectors as directional derivatives
7 Vectors, pseudovectors, and transformations
The concept of vector, as we know it today, evolved gradually over a period of more than 200 years. About a dozen people made significant contributions.[5] The immediate predecessor of vectors were quaternions, devised by William Rowan Hamilton in 1843 as a generalization of complex numbers. Initially, his search was for a formalism to enable the analysis of three-dimensional space in the same way that complex numbers had enabled analysis of two-dimensional space, but he arrived at a four-dimensional system. In 1846 Hamilton divided his quaternions into the sum of real and imaginary parts that he respectively called "scalar" and "vector":
The algebraically imaginary part, being geometrically constructed by a straight line, or radius vector, which has, in general, for each determined quaternion, a determined length and determined direction in space, may be called the vector part, or simply the vector of the quaternion.[6]
Several other mathematicians developed vector-like systems around the same time as Hamilton including Giusto Bellavitis, Augustin Cauchy, Hermann Grassmann, August Möbius, Comte de Saint-Venant, and Matthew O'Brien. Grassmann's 1840 work Theorie der Ebbe und Flut (Theory of the Ebb and Flow) was the first system of spatial analysis similar to today's system and had ideas corresponding to the cross product, scalar product and vector differentiation. Grassmann's work was largely neglected until the 1870s.[5]
Peter Guthrie Tait carried the quaternion standard after Hamilton. His 1867 Elementary Treatise of Quaternions included extensive treatment of the nabla or del operator ∇.
In 1878 Elements of Dynamic was published by William Kingdon Clifford. Clifford simplified the quaternion study by isolating the dot product and cross product of two vectors from the complete quaternion product. This approach made vector calculations available to engineers and others working in three dimensions and skeptical of the fourth.
Josiah Willard Gibbs, who was exposed to quaternions through James Clerk Maxwell's Treatise on Electricity and Magnetism, separated off their vector part for independent treatment. The first half of Gibbs's Elements of Vector Analysis, published in 1881, presents what is essentially the modern system of vector analysis.[5] In 1901 Edwin Bidwell Wilson published Vector Analysis, adapted from Gibb's lectures, and banishing any mention of quaternions in the development of vector calculus.
In physics and engineering, a vector is typically regarded as a geometric entity characterized by a magnitude and a direction. It is formally defined as a directed line segment, or arrow, in a Euclidean space.[7] In pure mathematics, a vector is defined more generally as any element of a vector space. In this context, vectors are abstract entities which may or may not be characterized by a magnitude and a direction. This generalized definition implies that the above mentioned geometric entities are a special kind of vectors, as they are elements of a special kind of vector space called Euclidean space.
This article is about vectors strictly defined as arrows in Euclidean space. When it becomes necessary to distinguish these special vectors from vectors as defined in pure mathematics, they are sometimes referred to as geometric, spatial, or Euclidean vectors.
Being an arrow, a Euclidean vector possesses a definite initial point and terminal point. A vector with fixed initial and terminal point is called a bound vector. When only the magnitude and direction of the vector matter, then the particular initial point is of no importance, and the vector is called a free vector. Thus two arrows \overrightarrow{AB} and \overrightarrow{A'B'} in space represent the same free vector if they have the same magnitude and direction: that is, they are equivalent if the quadrilateral ABB′A′ is a parallelogram. If the Euclidean space is equipped with a choice of origin, then a free vector is equivalent to the bound vector of the same magnitude and direction whose initial point is the origin.
The term vector also has generalizations to higher dimensions and to more formal approaches with much wider applications.
Examples in one dimension
Since the physicist's concept of force has a direction and a magnitude, it may be seen as a vector. As an example, consider a rightward force F of 15 newtons. If the positive axis is also directed rightward, then F is represented by the vector 15 N, and if positive points leftward, then the vector for F is −15 N. In either case, the magnitude of the vector is 15 N. Likewise, the vector representation of a displacement Δs of 4 meters to the right would be 4 m or −4 m, and its magnitude would be 4 m regardless.
In physics and engineering
Vectors are fundamental in the physical sciences. They can be used to represent any quantity that has magnitude, has direction, and which adheres to the rules of vector addition. An example is velocity, the magnitude of which is speed. For example, the velocity 5 meters per second upward could be represented by the vector (0,5) (in 2 dimensions with the positive y axis as 'up'). Another quantity represented by a vector is force, since it has a magnitude and direction and follows the rules of vector addition. Vectors also describe many other physical quantities, such as linear displacement, displacement, linear acceleration, angular acceleration, linear momentum, and angular momentum. Other physical vectors, such as the electric and magnetic field, are represented as a system of vectors at each point of a physical space; that is, a vector field. Examples of quantities that have magnitude and direction but fail to follow the rules of vector addition: Angular displacement and electric current. Consequently, these are not vectors.
In Cartesian space
In the Cartesian coordinate system, the simplest type of vector is a point vector (or position vector). It represents the displacement going from the origin O = (0,0,0) out to the point P = (x,y,z), and is equivalent numerically to point P's Cartesian coordinates (x,y,z). Point vectors are the starting point in vector geometry, i.e., other vector concepts assume point vectors as foundational objects.
What is the motion going in space from point A to point B? A 2-point vector is a convenient way to quantify spatial movement. This vector can be conceptualized by first assigning A as the initial point, and B as the terminal point. For instance, consider points A = (1,0,0) and B = (0,1,0). The vector \overrightarrow{AB} is drawn as an arrow connecting the point x=1 on the x-axis to the point y=1 on the y-axis. The meaning of vector \overrightarrow{AB} is the change in position, or motion, implied in moving from A --> B. The order of the two points is critical....moving from B --> A is a completely opposite movement, and thus a different vector quantity.
What numerics does vector \overrightarrow{AB} take on? Following the same example, the value of \overrightarrow{AB} is obtained by vector subtraction:
\overrightarrow{AB} ← \overrightarrow{B} - \overrightarrow{A}
(-1, 1, 0) ← (0,1,0) - (1,0,0)
This result can be interpreted to mean, starting at A, to get to point B go:
-1 along the x-axis
1 along the y-axis
0 along the z-axis
This motion vector was obtained numerically by doing vector subtraction \overrightarrow{B} - \overrightarrow{A}. It is sometimes useful to interpret vector \overrightarrow{AB} as location of B relative to A (the Cartesian coordinates B would take on if A were to become the new origin).
Using this logic, if you are a traveller and begin at location A, and your movement away from A is vector quantity \overrightarrow{AB} , where do you end up? You end up at location B, because \overrightarrow{AB} is the precise movement that takes you from A --> B. Numerically, a movement is modeled by vector addition:
\overrightarrow{B} ← \overrightarrow{A} + \overrightarrow{AB}
(0,1,0) ← (1,0,0) + (-1, 1, 0)
This same basic approach to representing motion can be extended to multi-point excursions through space. Consider this example: You are an airplane pilot, and take off from city A = (10, 20, 0), then fly to city B = (12, 15, 0), then fly to city C = (-3, -4, 0).
What motion vector do you fly to take you from C back to where you started at A? What motion gets you from C --> A? Call this quantity \overrightarrow{CA}, and calculate it taking the vector difference \overrightarrow{A} - \overrightarrow{C}. The motion you want is (13, 24, 0).
Now, suppose you take off from A, but only know the motion vectors you flew, not the absolute locations where you landed. You should be able to figure out where you are located nonetheless. The first flight segment was vector \overrightarrow{AD} = (16, -10, 0) landing at unknown location D. The second segment was vector \overrightarrow{DE} = (-8, 22, 0) landing at unknown location E. What is the location of city E? Successive motions can be lumped into a combined motion by vector addition. You want the Cartesian coordinates of E (its vector displacement from the origin), so you numerically combine all the motions that you would need to take starting at the origin to arrive to E by adding up the vector segments:
(10, 20, 0) = \overrightarrow{A} motion from origin to city A
+ (16, -10, 0) = \overrightarrow{AD} motion from city A to city D
+ (-8, 22, 0) = \overrightarrow{DE} motion from city D to city E
(18, 32, 0) = \overrightarrow{E} motion from origin to city E
This style of aggregating successive known motions from a known starting point to estimate one's current spatial location is called dead reckoning. It was the technique used by the great ocean explorers to navigate between continents. An estimate of each day's travel was logged based on the day's heading and speed, and the motions were added together as demonstrated here.
Vectors may also be used to represent directions in space, supplanting the use of slope and angles, to great advantage in 3D geometry. Their strength is the ability to obtain directions in space directly from pairs of Cartesian points, without resorting to angles and trigonometry.
Vector math is at the core of modern spatial software apps, including 3D animation, computer vision, robotics, GPS navigation, CAD, and protein modeling. The gradual ascendance of vector math representations over their scalar antecedents (e.g. slope, angle, trigonometric functions) is in part due to their ability to scale up naturally going from 2D --> 3D --> nD applications. The other major factor has been the advent of software-based computation since the 1960s, where vector representations impose fewer exceptions when writing algorithms compared to their scalar predecessors.
Euclidean and affine vectors
In the geometrical and physical settings, sometimes it is possible to associate, in a natural way, a length or magnitude and a direction to vectors. In turn, the notion of direction is strictly associated with the notion of an angle between two vectors. When the length of vectors is defined, it is possible to also define a dot product — a scalar-valued product of two vectors — which gives a convenient algebraic characterization of both length (the square root of the dot product of a vector by itself) and angle (a function of the dot product between any two non-zero vectors). In three dimensions, it is further possible to define a cross product which supplies an algebraic characterization of the area and orientation in space of the parallelogram defined by two vectors (used as sides of the parallelogram).
However, it is not always possible or desirable to define the length of a vector in a natural way. This more general type of spatial vector is the subject of vector spaces (for bound vectors) and affine spaces (for free vectors). An important example is Minkowski space that is important to our understanding of special relativity, where there is a generalization of length that permits non-zero vectors to have zero length. Other physical examples come from thermodynamics, where many of the quantities of interest can be considered vectors in a space with no notion of length or angle.[8]
Generalizations
In physics, as well as mathematics, a vector is often identified with a tuple, or list of numbers, which depend on some auxiliary coordinate system or reference frame. When the coordinates are transformed, for example by rotation or stretching, then the components of the vector also transform. The vector itself has not changed, but the reference frame has, so the components of the vector (or measurements taken with respect to the reference frame) must change to compensate. The vector is called covariant or contravariant depending on how the transformation of the vector's components is related to the transformation of coordinates. In general, contravariant vectors are "regular vectors" with units of distance (such as a displacement) or distance times some other unit (such as velocity or acceleration); covariant vectors, on the other hand, have units of one-over-distance such as gradient. If you change units (a special case of a change of coordinates) from meters to milimeters, a scale factor of 1/1000, a displacement of 1 m becomes 1000 mm–a contravariant change in numerical value. In contrast, a gradient of 1 K/m becomes 0.001 K/mm–a covariant change in value. See covariance and contravariance of vectors. Tensors are another type of quantity that behave in this way; in fact a vector is a special type of tensor.
In pure mathematics, a vector is any element of a vector space over some field and is often represented as a coordinate vector. The vectors described in this article are a very special case of this general definition because they are contravariant with respect to the ambient space. Contravariance captures the physical intuition behind the idea that a vector has "magnitude and direction".
Vectors are usually denoted in lowercase boldface, as a or lowercase italic boldface, as a. (Uppercase letters are typically used to represent matrices.) Other conventions include \vec{a} or a, especially in handwriting. Alternatively, some use a tilde (~) or a wavy underline drawn beneath the symbol, e.g. \underset{^\sim}a, which is a convention for indicating boldface type. If the vector represents a directed distance or displacement from a point A to a point B (see figure), it can also be denoted as \overrightarrow{AB} or AB. Especially in literature in German it was common to represent vectors with small fraktur letters as \mathfrak{a}.
Vectors are usually shown in graphs or other diagrams as arrows (directed line segments), as illustrated in the figure. Here the point A is called the origin, tail, base, or initial point; point B is called the head, tip, endpoint, terminal point or final point. The length of the arrow is proportional to the vector's magnitude, while the direction in which the arrow points indicates the vector's direction.
On a two-dimensional diagram, sometimes a vector perpendicular to the plane of the diagram is desired. These vectors are commonly shown as small circles. A circle with a dot at its centre (Unicode U+2299 ⊙) indicates a vector pointing out of the front of the diagram, toward the viewer. A circle with a cross inscribed in it (Unicode U+2297 ⊗) indicates a vector pointing into and behind the diagram. These can be thought of as viewing the tip of an arrow head on and viewing the flights of an arrow from the back.
In order to calculate with vectors, the graphical representation may be too cumbersome. Vectors in an n-dimensional Euclidean space can be represented as coordinate vectors in a Cartesian coordinate system. The endpoint of a vector can be identified with an ordered list of n real numbers (n-tuple). These numbers are the coordinates of the endpoint of the vector, with respect to a given Cartesian coordinate system, and are typically called the scalar components (or scalar projections) of the vector on the axes of the coordinate system.
As an example in two dimensions (see figure), the vector from the origin O = (0,0) to the point A = (2,3) is simply written as
\mathbf{a} = (2,3).
The notion that the tail of the vector coincides with the origin is implicit and easily understood. Thus, the more explicit notation \overrightarrow{OA} is usually not deemed necessary and very rarely used.
In three dimensional Euclidean space (or R3), vectors are identified with triples of scalar components:
\mathbf{a} = (a_1, a_2, a_3).
also written
\mathbf{a} = (a_\text{x}, a_\text{y}, a_\text{z}).
This can be generalised to n-dimensional Euclidean space (or Rn).
\mathbf{a} = (a_1, a_2, a_3, \cdots, a_{n-1}, a_n).
These numbers are often arranged into a column vector or row vector, particularly when dealing with matrices, as follows:
\mathbf{a} = \begin{bmatrix}
a_1\\
\mathbf{a} = [ a_1\ a_2\ a_3 ].
Another way to represent a vector in n-dimensions is to introduce the standard basis vectors. For instance, in three dimensions, there are three of them:
{\mathbf e}_1 = (1,0,0),\ {\mathbf e}_2 = (0,1,0),\ {\mathbf e}_3 = (0,0,1).
These have the intuitive interpretation as vectors of unit length pointing up the x, y, and z axis of a Cartesian coordinate system, respectively. In terms of these, any vector a in R3 can be expressed in the form:
\mathbf{a} = (a_1,a_2,a_3) = a_1(1,0,0) + a_2(0,1,0) + a_3(0,0,1), \
\mathbf{a} = \mathbf{a}_1 + \mathbf{a}_2 + \mathbf{a}_3 = a_1{\mathbf e}_1 + a_2{\mathbf e}_2 + a_3{\mathbf e}_3,
where a1, a2, a3 are called the vector components (or vector projections) of a on the basis vectors or, equivalently, on the corresponding Cartesian axes x, y, and z (see figure), while a1, a2, a3 are the respective scalar components (or scalar projections).
In introductory physics textbooks, the standard basis vectors are often instead denoted \mathbf{i},\mathbf{j},\mathbf{k} (or \mathbf{\hat{x}}, \mathbf{\hat{y}}, \mathbf{\hat{z}}, in which the hat symbol ^ typically denotes unit vectors). In this case, the scalar and vector components are denoted respectively ax, ay, az, and ax, ay, az (note the difference in boldface). Thus,
\mathbf{a} = \mathbf{a}_\text{x} + \mathbf{a}_\text{y} + \mathbf{a}_\text{z} = a_\text{x}{\mathbf i} + a_\text{y}{\mathbf j} + a_\text{z}{\mathbf k}.
The notation ei is compatible with the index notation and the summation convention commonly used in higher level mathematics, physics, and engineering.
For more details on this topic, see Basis (linear algebra).
As explained above a vector is often described by a set of vector components that add up to form the given vector. Typically, these components are the projections of the vector on a set of mutually perpendicular reference axes (basis vectors). The vector is said to be decomposed or resolved with respect to that set.
However, the decomposition of a vector into components is not unique, because it depends on the choice of the axes on which the vector is projected.
Moreover, the use of Cartesian unit vectors such as \mathbf{\hat{x}}, \mathbf{\hat{y}}, \mathbf{\hat{z}} as a basis in which to represent a vector is not mandated. Vectors can also be expressed in terms of the unit vectors of a cylindrical coordinate system (\boldsymbol{\hat{\rho}}, \boldsymbol{\hat{\phi}}, \mathbf{\hat{z}}) or spherical coordinate system (\mathbf{\hat{r}}, \boldsymbol{\hat{\theta}}, \boldsymbol{\hat{\phi}}). The latter two choices are more convenient for solving problems which possess cylindrical or spherical symmetry respectively.
The choice of a coordinate system doesn't affect the properties of a vector or its behaviour under transformations.
A vector can be also decomposed with respect to "non-fixed" axes which change their orientation as a function of time or space. For example, a vector in three-dimensional space can be decomposed with respect to two axes, respectively normal, and tangent to a surface (see figure). Moreover, the radial and tangential components of a vector relate to the radius of rotation of an object. The former is parallel to the radius and the latter is orthogonal to it.[9]
In these cases, each of the components may be in turn decomposed with respect to a fixed coordinate system or basis set (e.g., a global coordinate system, or inertial reference frame).
The following section uses the Cartesian coordinate system with basis vectors
{\mathbf e}_1 = (1,0,0),\ {\mathbf e}_2 = (0,1,0),\ {\mathbf e}_3 = (0,0,1)
and assumes that all vectors have the origin as a common base point. A vector a will be written as
{\mathbf a} = a_1{\mathbf e}_1 + a_2{\mathbf e}_2 + a_3{\mathbf e}_3.
Two vectors are said to be equal if they have the same magnitude and direction. Equivalently they will be equal if their coordinates are equal. So two vectors
{\mathbf a} = a_1{\mathbf e}_1 + a_2{\mathbf e}_2 + a_3{\mathbf e}_3
{\mathbf b} = b_1{\mathbf e}_1 + b_2{\mathbf e}_2 + b_3{\mathbf e}_3
are equal if
a_1 = b_1,\quad a_2=b_2,\quad a_3=b_3.\,
For more details on this topic, see Vector space.
Assume now that a and b are not necessarily equal vectors, but that they may have different magnitudes and directions. The sum of a and b is
\mathbf{a}+\mathbf{b}
=(a_1+b_1)\mathbf{e}_1 +(a_2+b_2)\mathbf{e}_2 +(a_3+b_3)\mathbf{e}_3.
The addition may be represented graphically by placing the tail of the arrow b at the head of the arrow a, and then drawing an arrow from the tail of a to the head of b. The new arrow drawn represents the vector a + b, as illustrated below:
This addition method is sometimes called the parallelogram rule because a and b form the sides of a parallelogram and a + b is one of the diagonals. If a and b are bound vectors that have the same base point, this point will also be the base point of a + b. One can check geometrically that a + b = b + a and (a + b) + c = a + (b + c).
The difference of a and b is
\mathbf{a}-\mathbf{b}
=(a_1-b_1)\mathbf{e}_1 +(a_2-b_2)\mathbf{e}_2 +(a_3-b_3)\mathbf{e}_3.
Subtraction of two vectors can be geometrically defined as follows: to subtract b from a, place the tails of a and b at the same point, and then draw an arrow from the head of b to the head of a. This new arrow represents the vector a − b, as illustrated below:
Subtraction of two vectors may also be performed by adding the opposite of the second vector to the first vector, that is, a − b = a + (−b).
Main article: Scalar multiplication
A vector may also be multiplied, or re-scaled, by a real number r. In the context of conventional vector algebra, these real numbers are often called scalars (from scale) to distinguish them from vectors. The operation of multiplying a vector by a scalar is called scalar multiplication. The resulting vector is
r\mathbf{a}=(ra_1)\mathbf{e}_1
+(ra_2)\mathbf{e}_2 +(ra_3)\mathbf{e}_3.
Intuitively, multiplying by a scalar r stretches a vector out by a factor of r. Geometrically, this can be visualized (at least in the case when r is an integer) as placing r copies of the vector in a line where the endpoint of one vector is the initial point of the next vector.
If r is negative, then the vector changes direction: it flips around by an angle of 180°. Two examples (r = −1 and r = 2) are given below:
Scalar multiplication is distributive over vector addition in the following sense: r(a + b) = ra + rb for all vectors a and b and all scalars r. One can also show that a − b = a + (−1)b.
The length or magnitude or norm of the vector a is denoted by ‖a‖ or, less commonly, |a|, which is not to be confused with the absolute value (a scalar "norm").
The length of the vector a can be computed with the Euclidean norm
\left\|\mathbf{a}\right\|=\sqrt.
Unit vector
Main article: Unit vector
A unit vector is any vector with a length of one; normally unit vectors are used simply to indicate direction. A vector of arbitrary length can be divided by its length to create a unit vector. This is known as normalizing a vector. A unit vector is often indicated with a hat as in â.
To normalize a vector a = [a1, a2, a3], scale the vector by the reciprocal of its length ||a||. That is:
\mathbf{\hat{a}} = \frac{\mathbf{a}}{\left\|\mathbf{a}\right\|} = \frac{a_1}{\left\|\mathbf{a}\right\|}\mathbf{e}_1 + \frac{a_2}{\left\|\mathbf{a}\right\|}\mathbf{e}_2 + \frac{a_3}{\left\|\mathbf{a}\right\|}\mathbf{e}_3
Null vector
Main article: Null vector
The null vector (or zero vector) is the vector with length zero. Written out in coordinates, the vector is (0,0,0), and it is commonly denoted \vec{0}, or 0, or simply 0. Unlike any other vector it has an arbitrary or indeterminate direction, and cannot be normalized (that is, there is no unit vector which is a multiple of the null vector). The sum of the null vector with any vector a is a (that is, 0+a=a).
Main article: dot product
The dot product of two vectors a and b (sometimes called the inner product, or, since its result is a scalar, the scalar product) is denoted by a ∙ b and is defined as:
\mathbf{a}\cdot\mathbf{b}
=\left\|\mathbf{a}\right\|\left\|\mathbf{b}\right\|\cos\theta
where θ is the measure of the angle between a and b (see trigonometric function for an explanation of cosine). Geometrically, this means that a and b are drawn with a common start point and then the length of a is multiplied with the length of that component of b that points in the same direction as a.
The dot product can also be defined as the sum of the products of the components of each vector as
\mathbf{a} \cdot \mathbf{b} = a_1 b_1 + a_2 b_2 + a_3 b_3.
Main article: Cross product
The cross product (also called the vector product or outer product) is only meaningful in three or seven dimensions. The cross product differs from the dot product primarily in that the result of the cross product of two vectors is a vector. The cross product, denoted a × b, is a vector perpendicular to both a and b and is defined as
\mathbf{a}\times\mathbf{b}
=\left\|\mathbf{a}\right\|\left\|\mathbf{b}\right\|\sin(\theta)\,\mathbf{n}
where θ is the measure of the angle between a and b, and n is a unit vector perpendicular to both a and b which completes a right-handed system. The right-handedness constraint is necessary because there exist two unit vectors that are perpendicular to both a and b, namely, n and (–n).
The cross product a × b is defined so that a, b, and a × b also becomes a right-handed system (but note that a and b are not necessarily orthogonal). This is the right-hand rule.
The length of a × b can be interpreted as the area of the parallelogram having a and b as sides.
The cross product can be written as
{\mathbf a}\times{\mathbf b} = (a_2 b_3 - a_3 b_2) {\mathbf e}_1 + (a_3 b_1 - a_1 b_3) {\mathbf e}_2 + (a_1 b_2 - a_2 b_1) {\mathbf e}_3.
For arbitrary choices of spatial orientation (that is, allowing for left-handed as well as right-handed coordinate systems) the cross product of two vectors is a pseudovector instead of a vector (see below).
Scalar triple product
Main article: Scalar triple product
The scalar triple product (also called the box product or mixed triple product) is not really a new operator, but a way of applying the other two multiplication operators to three vectors. The scalar triple product is sometimes denoted by (a b c) and defined as:
(\mathbf{a}\ \mathbf{b}\ \mathbf{c})
=\mathbf{a}\cdot(\mathbf{b}\times\mathbf{c}).
It has three primary uses. First, the absolute value of the box product is the volume of the parallelepiped which has edges that are defined by the three vectors. Second, the scalar triple product is zero if and only if the three vectors are linearly dependent, which can be easily proved by considering that in order for the three vectors to not make a volume, they must all lie in the same plane. Third, the box product is positive if and only if the three vectors a, b and c are right-handed.
In components (with respect to a right-handed orthonormal basis), if the three vectors are thought of as rows (or columns, but in the same order), the scalar triple product is simply the determinant of the 3-by-3 matrix having the three vectors as rows
(\mathbf{a}\ \mathbf{b}\ \mathbf{c})=\left|\begin{pmatrix}
a_1 & a_2 & a_3 \\
b_1 & b_2 & b_3 \\
c_1 & c_2 & c_3 \\
\end{pmatrix}\right|
The scalar triple product is linear in all three entries and anti-symmetric in the following sense:
(\mathbf{a}\ \mathbf{b}\ \mathbf{c}) = (\mathbf{c}\ \mathbf{a}\ \mathbf{b}) = (\mathbf{b}\ \mathbf{c}\ \mathbf{a})=
-(\mathbf{a}\ \mathbf{c}\ \mathbf{b}) = -(\mathbf{b}\ \mathbf{a}\ \mathbf{c}) = -(\mathbf{c}\ \mathbf{b}\ \mathbf{a}).
Multiple Cartesian bases
All examples thus far have dealt with vectors expressed in terms of the same basis, namely, e1, e2, e3. However, a vector can be expressed in terms of any number of different bases that are not necessarily aligned with each other, and still remain the same vector. For example, using the vector a from above,
\mathbf{a} = a_1\mathbf{e}_1 + a_2\mathbf{e}_2 + a_3\mathbf{e}_3 = u\mathbf{n}_1 + v\mathbf{n}_2 + w\mathbf{n}_3
where n1, n2, n3 form another orthonormal basis not aligned with e1, e2, e3. The values of u, v, and w are such that the resulting vector sum is exactly a.
It is not uncommon to encounter vectors known in terms of different bases (for example, one basis fixed to the Earth and a second basis fixed to a moving vehicle). In order to perform many of the operations defined above, it is necessary to know the vectors in terms of the same basis. One simple way to express a vector known in one basis in terms of another uses column matrices that represent the vector in each basis along with a third matrix containing the information that relates the two bases. For example, in order to find the values of u, v, and w that define a in the n1, n2, n3 basis, a matrix multiplication may be employed in the form
\begin{bmatrix} u \\ v \\ w \\ \end{bmatrix} = \begin{bmatrix} c_{11} & c_{12} & c_{13} \\ c_{21} & c_{22} & c_{23} \\ c_{31} & c_{32} & c_{33} \end{bmatrix} \begin{bmatrix} a_1 \\ a_2 \\ a_3 \end{bmatrix}
where each matrix element cjk is the direction cosine relating nj to ek.[10] The term direction cosine refers to the cosine of the angle between two unit vectors, which is also equal to their dot product.[10]
By referring collectively to e1, e2, e3 as the e basis and to n1, n2, n3 as the n basis, the matrix containing all the cjk is known as the "transformation matrix from e to n", or the "rotation matrix from e to n" (because it can be imagined as the "rotation" of a vector from one basis to another), or the "direction cosine matrix from e to n"[10] (because it contains direction cosines).
The properties of a rotation matrix are such that its inverse is equal to its transpose. This means that the "rotation matrix from e to n" is the transpose of "rotation matrix from n to e".
By applying several matrix multiplications in succession, any vector can be expressed in any basis so long as the set of direction cosines is known relating the successive bases.[10]
With the exception of the cross and triple products, the above formulae generalise to two dimensions and higher dimensions. For example, addition generalises to two dimensions as
(a_1{\mathbf e}_1 + a_2{\mathbf e}_2)+(b_1{\mathbf e}_1 + b_2{\mathbf e}_2) = (a_1+b_1){\mathbf e}_1 + (a_2+b_2){\mathbf e}_2
and in four dimensions as
\begin{align}(a_1{\mathbf e}_1 + a_2{\mathbf e}_2 + a_3{\mathbf e}_3 + a_4{\mathbf e}_4) &+ (b_1{\mathbf e}_1 + b_2{\mathbf e}_2 + b_3{\mathbf e}_3 + b_4{\mathbf e}_4) =\\
(a_1+b_1){\mathbf e}_1 + (a_2+b_2){\mathbf e}_2 &+ (a_3+b_3){\mathbf e}_3 + (a_4+b_4){\mathbf e}_4.\end{align}
The cross product does not readily generalise to other dimensions, though the closely related exterior product does, whose result is a bivector. In two dimensions this is simply a pseudoscalar
(a_1{\mathbf e}_1 + a_2{\mathbf e}_2)\wedge(b_1{\mathbf e}_1 + b_2{\mathbf e}_2) = (a_1 b_2 - a_2 b_1)\mathbf{e}_1 \mathbf{e}_2.
A seven-dimensional cross product is similar to the cross product in that its result is a vector orthogonal to the two arguments; there is however no natural way of selecting one of the possible such products.
Vectors have many uses in physics and other sciences.
Length and units
In abstract vector spaces, the length of the arrow depends on a dimensionless scale. If it represents, for example, a force, the "scale" is of physical dimension length/force. Thus there is typically consistency in scale among quantities of the same dimension, but otherwise scale ratios may vary; for example, if "1 newton" and "5 m" are both represented with an arrow of 2 cm, the scales are 1:250 and 1 m:50 N respectively. Equal length of vectors of different dimension has no particular significance unless there is some proportionality constant inherent in the system that the diagram represents. Also length of a unit vector (of dimension length, not length/force, etc.) has no coordinate-system-invariant significance.
Vector-valued functions
Main article: Vector-valued function
Often in areas of physics and mathematics, a vector evolves in time, meaning that it depends on a time parameter t. For instance, if r represents the position vector of a particle, then r(t) gives a parametric representation of the trajectory of the particle. Vector-valued functions can be differentiated and integrated by differentiating or integrating the components of the vector, and many of the familiar rules from calculus continue to hold for the derivative and integral of vector-valued functions.
Position, velocity and acceleration
The position of a point x = (x1, x2, x3) in three-dimensional space can be represented as a position vector whose base point is the origin
{\mathbf x} = x_1 {\mathbf e}_1 + x_2{\mathbf e}_2 + x_3{\mathbf e}_3.
The position vector has dimensions of length.
Given two points x = (x1, x2, x3), y = (y1, y2, y3) their displacement is a vector
{\mathbf y}-{\mathbf x}=(y_1-x_1){\mathbf e}_1 + (y_2-x_2){\mathbf e}_2 + (y_3-x_3){\mathbf e}_3.
which specifies the position of y relative to x. The length of this vector gives the straight line distance from x to y. Displacement has the dimensions of length.
The velocity v of a point or particle is a vector, its length gives the speed. For constant velocity the position at time t will be
{\mathbf x}_t= t {\mathbf v} + {\mathbf x}_0,
where x0 is the position at time t=0. Velocity is the time derivative of position. Its dimensions are length/time.
Acceleration a of a point is vector which is the time derivative of velocity. Its dimensions are length/time2.
Force, energy, work
Force is a vector with dimensions of mass×length/time2 and Newton's second law is the scalar multiplication
{\mathbf F} = m{\mathbf a}
Work is the dot product of force and displacement
E = {\mathbf F} \cdot ({\mathbf x}_2 - {\mathbf x}_1).
Vectors as directional derivatives
A vector may also be defined as a directional derivative: consider a function f(x^\alpha) and a curve x^\alpha (\tau). Then the directional derivative of f is a scalar defined as
\frac{df}{d\tau} = \sum_{\alpha=1}^n \frac{dx^\alpha}{d\tau}\frac{\partial f}{\partial x^\alpha}.
where the index \alpha is summed over the appropriate number of dimensions (for example, from 1 to 3 in 3-dimensional Euclidean space, from 0 to 3 in 4-dimensional spacetime, etc.). Then consider a vector tangent to x^\alpha (\tau):
t^\alpha = \frac{dx^\alpha}{d\tau}.
The directional derivative can be rewritten in differential form (without a given function f) as
\frac{d}{d\tau} = \sum_\alpha t^\alpha\frac{\partial}{\partial x^\alpha}.
Therefore any directional derivative can be identified with a corresponding vector, and any vector can be identified with a corresponding directional derivative. A vector can therefore be defined precisely as
\mathbf{a} \equiv a^\alpha \frac{\partial}{\partial x^\alpha}.
Vectors, pseudovectors, and transformations
An alternative characterization of Euclidean vectors, especially in physics, describes them as lists of quantities which behave in a certain way under a coordinate transformation. A contravariant vector is required to have components that "transform like the coordinates" under changes of coordinates such as rotation and dilation. The vector itself does not change under these operations; instead, the components of the vector make a change that cancels the change in the spatial axes, in the same way that co-ordinates change. In other words, if the reference axes were rotated in one direction, the component representation of the vector would rotate in exactly the opposite way. Similarly, if the reference axes were stretched in one direction, the components of the vector, like the co-ordinates, would reduce in an exactly compensating way. Mathematically, if the coordinate system undergoes a transformation described by an invertible matrix M, so that a coordinate vector x is transformed to x′ = Mx, then a contravariant vector v must be similarly transformed via v′ = Mv. This important requirement is what distinguishes a contravariant vector from any other triple of physically meaningful quantities. For example, if v consists of the x, y, and z-components of velocity, then v is a contravariant vector: if the coordinates of space are stretched, rotated, or twisted, then the components of the velocity transform in the same way. On the other hand, for instance, a triple consisting of the length, width, and height of a rectangular box could make up the three components of an abstract vector, but this vector would not be contravariant, since rotating the box does not change the box's length, width, and height. Examples of contravariant vectors include displacement, velocity, electric field, momentum, force, and acceleration.
In the language of differential geometry, the requirement that the components of a vector transform according to the same matrix of the coordinate transition is equivalent to defining a contravariant vector to be a tensor of contravariant rank one. Alternatively, a contravariant vector is defined to be a tangent vector, and the rules for transforming a contravariant vector follow from the chain rule.
Some vectors transform like contravariant vectors, except that when they are reflected through a mirror, they flip and gain a minus sign. A transformation that switches right-handedness to left-handedness and vice versa like a mirror does is said to change the orientation of space. A vector which gains a minus sign when the orientation of space changes is called a pseudovector or an axial vector. Ordinary vectors are sometimes called true vectors or polar vectors to distinguish them from pseudovectors. Pseudovectors occur most frequently as the cross product of two ordinary vectors.
One example of a pseudovector is angular velocity. Driving in a car, and looking forward, each of the wheels has an angular velocity vector pointing to the left. If the world is reflected in a mirror which switches the left and right side of the car, the reflection of this angular velocity vector points to the right, but the actual angular velocity vector of the wheel still points to the left, corresponding to the minus sign. Other examples of pseudovectors include magnetic field, torque, or more generally any cross product of two (true) vectors.
This distinction between vectors and pseudovectors is often ignored, but it becomes important in studying symmetry properties. See parity (physics).
Affine space, which distinguishes between vectors and points
Array data structure or Vector (Computer Science)
Banach space
Clifford algebra
Covariance and contravariance of vectors
Four-vector, a non-Euclidean vector in Minkowski space (i.e. four-dimensional spacetime), important in relativity
Function space
Grassmann's Ausdehnungslehre
Hilbert space
Normal vector
Pseudovector
Tangential and normal components (of a vector)
Vector bundle
Vector calculus
Vector notation
Mathematical treatments
Physical treatments
Commons has media related to Vectors.
The Wikibook Waves has a page on the topic of: Vectors
PDF)
applied mathematics)
Addition of forces (vectors) Java Applet
French tutorials on vectors and their application to video games
Topics related to linear algebra
Vector space
Vector projection
Linear span
Linear map
Linear projection
Linear independence
Linear combination
Column space
Row space
Dual space
Orthogonality
Eigenvalues and eigenvectors
Least squares regressions
Inner product space
Gram–Schmidt process
Matrix decomposition
Cramer's rule
Invertible matrix
Gaussian elimination
Transformation matrix
Block matrix
Numerical linear algebra
Numerical stability
Sparse matrix
Comparison of linear algebra libraries
Comparison of numerical analysis software
Normed vector space
Functional analysis, Mathematics, Norm (mathematics), Linear algebra, Topology
Monoclinic crystal system
Crystallography, Crystal system, Crystal, Orbifold, Chemical polarity
Radius, Radius (bone), Geometric term of location, Vector (geometric), Radiate
Hodograph
Physics, Astronomy, Aviation, Meteorology, Wind


9 Apr - 77 min - Uploaded by Your Zouk TV Abonnez-vous: nayari-return.com Retrouvez le meilleur de nos artistes dans notre playlist. 13 May - 6 min - Uploaded by hatianmuzik Daan Junior:Supporter les artistes acheter l'album. Complete your Daan Junior record collection. Discover Daan Junior's full discography. Shop new and used Vinyl 2 Appearances · 1 Albums · 1 Compilations.
Listen to albums and songs from Daan Junior. Join Napster and Daan Junior · On avance (Live) by Daan Junior Daan Junior · J'ai soif de toi by Daan Junior. View Daan Junior profile, informations, Albums and News; Gender: Male; Solo; Genre: Varietes; Manager: Unknown; Albums (4) Album J'ai soif de toi. 17 May Stream Daan Junior - J'ai Peur [Album A Cause De Toi ] by Marc-Arthur Quarante-Sept from desktop or your mobile device.
Video: Daan Junior Interview: A Cause de Toi new album + New Band + Live interview with Daan Junior talking about his latest studio album " A Cause de Toi . Daan Junior Get 3 months of Unlimited for $ to listen to this album plus tens of millions Buy CD Album $ Includes FREE MP3 version of this album. Is there another man in konpa music more mysterious than Daan Junior? "Oh, Daan Junior," they sigh. The record J'ai Soif de Toi, my second album. DAAN JUNIOR'Slatest and greatest Cd with hit songs like A Cause de Toi, One Love, Wapfem nan Pa Normal" Haitian CD Smooth Kompa Love Mizik Album. DAAN JUNIOR - LIVE - IN CONCERT REZLITA ALBUM "Ladaan invit FABIOLA SHYNE" HAITIAN MUSIC CD. DAAN JUNIOR live in concert Cd performing their .


This notice provides details of expected Treasury Bond issuance by the Australian Office of Financial Management (AOFM) on behalf of the Australian Government during the 2007-08 financial year (1 July 2007 to 30 June 2008).
In the 2007-08 financial year, Treasury Bond issuance is expected to total $5.1 billion. This consists of $2.1 billion of issuance into the existing April 2012 bond line (bringing the volume on issue for this bond line up to $5 billion) and $3.0 billion of issuance of a new May 2021 Treasury Bond.
One further tender is planned for the 2006-07 financial year. It will be for the issue of $300 million of the April 2012 Treasury Bond on 22 May 2007.
Treasury Bond issuance is undertaken with the objective of maintaining liquid and efficient Treasury Bond and Treasury Bond futures markets. The volume and timing of Treasury Bond issuance accordingly takes account of the need to have an appropriate range of Treasury Bonds available for inclusion in the bond baskets for Treasury Bond futures contracts.
It should be noted that all the details in respect of Treasury Bond tenders provided above are indicative only and the AOFM reserves the right to amend any of these details at any time. Tenders will be confirmed at midday on the day prior to a scheduled tender.


text:
package controllers

import play.api._
import play.api.mvc._
import play.api.libs.json._
import scala.concurrent.Future
import reactivemongo.api._
import play.modules.reactivemongo.MongoController
import play.modules.reactivemongo.json.collection.JSONCollection
import reactivemongo.bson.BSONObjectID

object Tasks extends Controller with MongoController {

	def collection: JSONCollection = db.collection[JSONCollection]("tasks")

	import play.api.data.Form
	import models._
	import models.JsonFormats._

	def newTask = Action(parse.json) { request =>
		request.body.validate[Task].map { task =>
			val objectId = BSONObjectID.generate
			val taskWithId = Json.obj("_id" -> objectId.stringify, "title" -> task.title, "text" -> task.text)
			val futureResult = collection.insert(taskWithId)
			Async {
				futureResult.map(_ => Ok(Json.obj("id" -> objectId.stringify)))
			}
		}.recoverTotal { error =>
			BadRequest(Json.obj("res" -> "KO") ++ Json.obj("error" -> JsError.toFlatJson(error)))
		}
	}

	def getAll = Action {
		Async {
			val cursor: Cursor[JsValue] = collection.find(Json.obj()).cursor[JsValue]
			val futureTaskList: Future[List[JsValue]] = cursor.toList

			futureTaskList.map { tasks =>
				Ok(Json.toJson(tasks))
			}
		}
	}

	def remove(taskId: String) = Action {
		Async {
			val futureResult = collection.remove(Json.obj("_id" -> taskId))
			futureResult.map(_ => Ok)
		}
	}

}

redpajama_set_name: RedPajamaGithub


text:
Britain's biggest current account provider hikes overdrafts rates for some to 49.9%: Lloyds Bank next to reveal changes
UK families' confidence about their finances slumps to its lowest level in nearly a year as Brexit fears hit
A study by research group IHS Markit found there is gloom about the future
Its index of household confidence was 43.4, down from 44.7 in January
Perceptions of job security fell for the fourth month in a row
Families' confidence about their finances has slumped to its lowest level in nearly a year, a major survey has revealed
Families' confidence about their finances has slumped to its lowest level in nearly a year, a major survey has revealed.
The study by research group IHS Markit found there is deepening gloom about the future amid political turmoil over Brexit.
Its index of household confidence – where anything over 50 means consumers think their finances are improving and anything below means they think things are getting worse – was 43.4 this month, down from 44.7 in January.
Meanwhile, workers are more worried they might be made redundant.
Perceptions of job security fell for the fourth month in a row, to their lowest since January 2018.
Recent disappointing figures from the Office for National Statistics also showed the economy grew by only 0.2 per cent in the last three months of 2018.
Joe Hayes, an economist at IHS Markit, said: 'The impact on confidence caused by Brexit uncertainty continues to pose a notable risk to the domestic economy, also highlighted by job security perceptions becoming increasingly negative.'
UK families' confidence about their finances slumps to its lowest level in nearly a year

redpajama_set_name: RedPajamaCommonCrawl


text:
[coffee] COFFEE TIME!
Coffee is the second most traded product in the world after petroleum. World wide coffee production tips the scales at about 6 million metric tonnes.
It takes five years for a coffee tree to reach maturity. The average yield from one tree is the equivalent of one roasted pound of coffee.
People who buy coffee primarily at drive through windows on their way to work will spend as much as 45 hours a year waiting in line.
Of the various botanical species of coffee trees in the world, only two are extensively cultivated commercially; Arabica and Robusta.
The average person who buys coffee outside the office to consume at work will spend the equivalent value of a round trip plane ticket to Florida every year.
The first coffee house in Europe opened in Venice in 1683, while coffee was available in Europe as early as 1608, mostly for the rich.
The expression "a cup of Joe" to denote coffee, was first coined during WWII, when American servicemen (G.I. Joe) were identified as big coffee drinkers.
The largest coffee-producing nation, Brazil, is responsible for 30 to 40 % of total world output.
In the late 1800's, Chase and Sanborn put out a flier on how to read the coffee grounds at the bottom of the cup (like a fortune teller).
Coffee cherries usually contain two "beans", except for the single bean peaberry anomaly. Cherries with three beans are deemed to be a sign of good luck.
A Belgian living in Guatemala invented the first instant coffee in 1906 and later immigrated to the United States. His name, ironically enough, was George Washington.


KIEV, Ukraine (AP) — Straight after a third successive Champions League title was secured, Cristiano Ronaldo was talking about Real Madrid in the past tense.
Real's biggest star hinted he was unsure he'd stay with the club. Its best player in the Champions League final, Gareth Bale, looks more likely to be departing.
"In the next few days I'll give the fans an answer because they are the ones who have always been by my side," Ronaldo said. "It was very beautiful to be with Madrid."
Keeping up the cryptic tone, he added: "The future of any player is not important. We made history."
After soaring to score a magnificent bicycle kick for Madrid's second goal, Bale brought his fans back down to earth with his announcement that he'll discuss his future with his agent this summer.
The Welshman was a substitute in four of seven Champions League games this season, including his super-sub display in the final.
Real coach Zinedine Zidane responded very differently to the two players' comments.
On Ronaldo, Zidane was clear Sunday: "He will stay with us at Real Madrid," and predicted the Portuguese star's tone would soon change. "Perhaps in three or four days' time he might say something else."
On Bale, Zidane was circumspect.
"It's a little bit of a complicated situation but everyone has their own interests, their own future to think about," he said. "It's true some players deserve more playing time on the pitch but this is a decision that has to be made by the manager."
Where Bale could go is less clear.
Tottenham is widely reported to have a buy-back option as part of Bale's 2013 transfer to Real, but seems highly unlikely to be able to afford his wage bill. Other destinations are unclear, though Manchester United has been reported in British media as a possible destination.
If he goes back to England this summer, Bale would leave Madrid with a curiously lopsided record of four Champions League titles yet only one in La Liga.
Ronaldo has the same number of Champions League wins and two Spanish titles but his performances have been era-defining in a way Bale's are not.
Even more so than the Welsh player, Ronaldo's future is likely to be determined by the very small number of clubs capable of affording his demands — supposing he actually wants to leave Madrid — and the 33-year-old has never indicated any desire to take a pay cut for the sake of pastures new.
Both would leave Madrid with a rich store of memories. Bale has his moments of genius like Saturday's goal, but is increasingly a super-sub, a player who falls short of the crushingly consistent brilliance of Ronaldo.


Isabel Marant Wants to Cast Older Girls but "Can't"
Paris-based designer, Isabel Marant, is the quintessential Parisian woman. She has taken the fashion industry by storm with her embroidered jackets and easy-chic wares, not to mention her footwear. You may recall that she started the wedge sneaker trend. She sat down with the Guardian recently to talk about her H&M collection, which crashed the fast fashion retailer's website before selling out almost instantaneously. She said she used "exactly the same fabric" for a particular skirt that she uses for her own collection. She also took on the topic of underage models, saying: "Sometimes we give an image of life that will never exist, using models who are 15 and pretending they are 35 or 40, and when you are 35 or 40 you want to look like this when you will never be able to. So there's a bit of a disconnect."
While the designer isn't shy about speaking up about the average age of models that walk during Fashion Week, don't get your hopes up about seeing real girls on the Isabel Marant runway anytime soon. The designer says, "I can't – most of the girls [the agencies send] are 15 years old. I try to use girls who have personality. When they walk in a room, I'll think: 'Ah! There's something to this girl.' It's more a way of moving or being that means something to me."
While I'm not exactly buying that she "can't" cast younger girls, in Marant's defense, she isn't casting the youngest of the young (a la Marc Jacobs circa February 2012). Aymeline Valade, Joan Smalls, Magda Frackowiak (pictured above), Abbey Lee, Anja Rubik, Nadja Bender (also pictured above) and Arizona Muse - all Isabel Marant favorites - are actually "older girls" in the industry. Because in fashion, 22 is old. While I am not holding my breathe for new faces to be 19 or 20 years old, designers addressing the issue is promising, right?


text:
The Houston Midtown Chapter of The Society for Financial Awareness Presents MONEY MATTERS with Christopher Hensley (Retirement)
Money Matters Episode 182- How To Spend Wisely in Retirement W/ Dr. Wade Pfau
How much can you spend in retirement? Naturally, this is an essential question for those approaching this important life transition. Essentially, if you wish to retire one day, you are increasingly responsible for figuring out how to save during your working years and convert your savings into sustainable income for an ever-lengthening number of retirement years. The nature of risk also changes in retirement, as the lifestyle of retirees become more vulnerable to the impacts of market volatility, unknown longevity, and spending shocks. Retirees have one opportunity to build a successful plan. It is not an easy task, but it is manageable.
On today's show we talked with Author Dr. Wade Pfau about his new book How to Spend Money Wisely in Retirement.
Dr. Wade D. Pfau, CFA®, is a Professor of Retirement Income in the PhD in Financial and Retirement Planning program at The American College of Financial Services. He is also a contributor to the The College's Retirement Income Certified Professional® (RICP®) designation program curriculum.
Dr. Pfau is a co-editor of the Journal of Personal Finance. He has spoken at the national conferences of organizations for financial professionals such as the CFA Institute, FPA, NAPFA, AICPA-PFP, and AFS. He also publishes frequently in a wide variety of academic and practitioner research journals. He hosts the Retirement Researcher blog, and is a monthly columnist for Advisor Perspectives, a RetireMentor for MarketWatch, a contributor to Forbes, and an Expert Panelist for The Wall Street Journal. His research has been discussed in outlets that include print editions of The Economist, The New York Times, The Wall Street Journal, and Money Magazine.
To learn more about Wade visit:
www.retirementresearcher.com
#WadePfau
Category:Retirement -- posted at: 2:11pm PST
Money Matters Episode 175- Making Smart Money Choices for Military Service Members W/ Michael Meese
For years the Military Retirement has stayed the same with no changes. In 2018, we will see a massive change to retirement benefits for service members in the armed forces.
On today's show we talked with retired brigadier general and current COO of the American Armed Forces Mutual Aid Association (AAFMAA), Michael Meese. Mike discussed important finance tips for military members, spouses and their families. We discussed budgeting, insurance, retirement benefits, mortgages, deployments and relocations. Additionally, we had a deep dive into the upcoming major changes to the military retirement system including why its changing and what service members need to know to prepare themselves.
Mike joined AAFMAA as Chief Operating Officer in 2013. He retired from the United States Army as a Brigadier General having concluded his 32 year career as the Professor and Head of the Department of Social Sciences at the U.S. Military Academy.
At West Point, he taught economics and national security courses and was the Director of the Economics program. He has written numerous articles and two books: the Armed Forces Guide to Personal Financial Planning and American National Security. He has served in a variety of strategic political-military positions including deployments to Afghanistan, Iraq, and Bosnia for a total of 31 months and was the Executive Director of the Secretary of the Army's Transition Team in 2005 and the co-director of the Department of Defense Panel on Commercialization. He is a graduate of the National War College, U.S. Military Academy, and earned his Ph.D., MPA and an M.A. from Princeton University.
To learn more about Michael visit:
www.AAFMAA.com
Here is a short piece on the upcoming changes for the military retirement system I did for American Business Television:
http://www.americanbusinesstv.com/2017/07/03/christopher-hensley-on-the-national-defense-authorization-act/
#AAFMAA
Category:Retirement -- posted at: 8:42am PST
Money Matters Episode 163-The Encore Curve: Retire With a Life Plan That Excites You W/ Andy Raub
Today's retirement looks nothing like your parents' experience. Our longer life expectancy and increasing intellectual capital have transformed our notion of the golden years. Often we're just not ready for a life without work. We fear outliving our money and our meaning. We want to stay productive (whatever that means to us personally) well into the future and for baby boomers and the following generations, that future is closer than we think. No matter your definition of financial confidence, with the right tools and approach, you can create the retirement of your dreams: your memorable encore. The Encore Curve examines two crucial questions: Now what am I going to do? and will I have enough money?
Andy Raub has helped countless individuals plan for their retirement and manage their investments. As an early Baby Boomer, he understands the fears most retirees now face, which prompted him to write a book to help them reset their life goals and reorganize their money so they can live with renewed purpose.
To learn more about Andy Raub visit:
http://www.ameripriseadvisors.com/andy.raub/
Personal Finance Cheat Sheet Article:
#EncoreCurve
Thu, 20 October 2016
Money Matters Episode 150- Get Whats Yours for Medicare W/ Philip Moeller
We spoke with New York Times bestselling author Philip Moeller on his newest book Get Whats Yours for Medicare. We also discussed the current election and what a Trump or Clinton presidency means to the Social Security and Medicare system.
A coauthor of the New York Times bestselling guide to Social Security Get What's Yours authors an essential companion to explain Medicare, the nation's other major benefit for older Americans. Learn how to maximize your health coverage and save money.
Social Security provides the bulk of most retirees' income and Medicare guarantees them affordable health insurance. But few people know what Medicare covers and what it doesn't, what it costs, and when to sign up. Nor do they understand which parts of Medicare are provided by the government and how these work with private insurance plans—Medicare Advantage, drug insurance, and Medicare supplement insurance.
Do you understand Medicare's parts A, B, C, D? Which Part D drug plan is right and how do you decide? Which is better, Medigap or Medicare Advantage? What do you do if Medicare denies payment for a procedure that your doctor says you need? How do you navigate the appeals process for denied claims? If you're still working or have a retiree health plan, how do those benefits work with Medicare? Do you know about the annual enrollment period for Medicare, or about lifetime penalties for late enrollment, or any number of other key Medicare rules?
Health costs are the biggest unknown expense for older Americans, who are turning sixty-five at the rate of 10,000 a day. Understanding and navigating Medicare is the best way to save health care dollars and use them wisely. In Get What's Yours for Medicare, retirement expert Philip Moeller explains how to understand all these important choices and make the right decisions for your health and wealth now—and for the future.
To learn more about Phil Moeller visit:
www.GetWhatsYours.org
http://www.fa-mag.com/news/on-it-s-80th-anniversary–advisors-consider-social-security-s-impact–future-22784.html?section=3
#PhilMoeller
Direct download: MMEPISODE150.mp3
Category:Retirement -- posted at: 12:22pm PST
Money Matters Episode 131- Rightsizing Your Retirement W/ Jeff Christakos CFP
One of the key challenges of managing your finances during retirement is determining how much you can spend without depleting your nest egg. What do you do if you retire and the market goes south shortly after?
Friday we were joined by Jeffrey Christakos, CPA/PFS, CFP, CLU, AIF. We discussed rightsizing your life for retirement and what to do in the event of a market downturn when you retire.
To learn more about Jeff visit:
www.westfieldwealth.com
To learn more about Houston Money Week 2016 visit:
You can keep up to date with the ACA changes at :
www.houstonfirstfinancialgroup.com then click health insurance
or to compare different plans in Texas, check subsidies and enroll go to my site at:
https://www.healthsherpa.com/?_agent_id=christopher-hensley
http://www.cheatsheet.com/…/how-schools-can-improve-their-…/
http://www.fa-mag.com/…/advisors-stay-the-course-amid-monda…
http://www.fa-mag.com/…/on-it-s-80th-anniversary–advisors-…
#KPFTHOUSTON #JEFFCHRISTAKOS
Direct download: Money_Matters_Episode_131.mp3
Category:Retirement -- posted at: 10:23am PST
Money Matters Episode 126- I'm Retired Now What W/ Kyle Sadler
Ah, retirement—you've anticipated this life stage for years, but now that it's finally here, you're not quite sure what to do with it.
Presenting 99 fresh ideas to keep you active and engaged, I'm Retired…Now What? is more than just a list of things to do. Written by a financial advisor who has worked with retirees for more than sixteen years, this guide helps you see your continued value and recognize the importance of living this new phase well.
We were joined on the show by author Kyle Sadler. Inventor and former owner of the nationally known website BarterOnly.com, Kyle A. Sadler, AIF, CRC, is the president of Precept Wealth Management, an investment advisory firm based on Christian fundamentals and values. He holds a business administration BS in accounting from Sam Houston State University, has more than twenty years of experience working in the financial industry, and is the author of two long-running retirement seminars and a corporate training program for financial advisors.
To learn more about Kyle visit:
www.afteruretire.com
www.houstonfrstfinancialgroup.com then click health insurance
http://www.fa-mag.com/…/on-it-s-80th-anniversary--advisors-…
#KPFTHOUSTON #
Money Matters Episode 124- Juggling Work and Caregiving W/ Amy Goyer
Approximately 19% of the population is caring for an adult relative (sibling, grown child, parent, neighbor) who is dealing with long term medical issues such as cancer, stroke, Alzheimers, dementia, or catastrophic injuries. Caregiving impacts people emotionally, physically and economically. Last year Americans worked millions of hours without compensation, care that would have cost $470 BILLION (the value of Walmart's annual sales, and more than the US annual Medicare budget). The pressures of caring for relatives without compensation can also impair the ability of a caregiver to hold down a "day job". Then add on huge medical expenses that can drive families into poverty and bankruptcy.
More on Amy Goyer, Author, Speaker, Consultant As AARP's Family Expert, I provide expertise on a variety of family issues - from grandparenting to family caregiving, parenting and other family relationships, multigenerational living, family history and just about anything that pertains to families! Right now the most important role I'm playing in life is that of primary caregiver for my parents who are 85 and 88.
To learn more about Amy visit:
http://blog.aarp.org/author/amygoyer/
#KPFTHOUSTON #AmyGoyer
Direct download: Money_Matters_126_Mixdown_1.mp3
Money Matters Episode 79- Americans Flunk Retirement Income Readiness, Now What? W/ Jamie Hopkins
Retirement income literacy is of essential importance to the financial security of retired Americans. With limited or no ability to earn additional money through work, this group must know how much they need to accumulate by the time they retire and know how to manage their money during retirement.
Further, retirement income literacy will become more important as the number of people entering
retirement with defined benefit plan guaranteed lifetime income decreases, life expectancy at age 65
increases, and Social Security income decreases due to increases in the age of entitlement for full
benefits. In addition, the increases in Medicare premium taken out of Social Security retirement
benefits each year will likely be higher than the cost of living adjustments to Social Security.
We were joined today by Associate Professor of Taxation, Associate Director of the New York Life Center for Retirement Incomeand Larry R. Pike Chair in Insurance & Investments for the American College, Jamie Hopkins.
To find out more about the American College visit the website at:
www.theamericancollege.edu
Also mentioned on the show today:
Forbes Article about new MYRA by Jamie Hopkins
#kpft #theamerican college #forbes
Direct download: Money_Matters_Episod_79.mp3
Fri, 14 November 2014
Money Matters Episode 75- After 50 It's Up to Us W/ George Schofield
By 2015, 77 million Americans will be 50 to 69 years old! As the first generation to be so long-lived, we face the challenge of taking personal responsibility for the quality of our extended lives. Well be log-term pioneers, making the second part of our lives as rich and rewarding as the first, if not more so. But aging isn't the point. The point is lifelong development- our ability to live skillfully each day with the opportunities, choices, and changes that will happen inside and outside of our plans; it's knowing what we'll have to be great at beyond fifty to lead vigorous, creative lives in our eighties and nineties.
We were joined today by author George H. Schofield, PH.D. We discussed life after 50 and the revolution in planning and retirement.
To find out more about George visit his website at:
www.georgeschofield.com
For the book click here:
After 50 It's Up to Us - Developing the Skills and Agility We'll Need
Direct download: MoneyMatterEpisode75.mp3
Money Matters Episode 56- Total Compensation -Federal Employee Benefits W/ Brian Kuhn CFP
The U.S. Department of Labor Statistics in 2010 reported that approximately two million people work for the United States federal government, not including those employees by the postal service or military. The United States government is by far our country's largest employer and provides extensive employee benefits.
Our guest today was Author and CFP Brian Kuhn. We discussed the ins and outs of the Federal Employee Benefits.
Brian Kuhn is a family wealth advisor with Planning Solutions Group, LLC. With 13 years in the financial planning field, he works with families and individuals, with a specific focus on government employees, in the area of retirement planning, wealth preservation, and insurance protection.
To learn more about Brian you can visit his website at:
www.psgclarity.com
Or his book at:
Total Compensation: A Practical Guide to Federal Employee Benefits
Direct download: Money_Matters_Episode56.mp3
Money Matters Episode 55- Inside Social Security W/ Gordon Sherman
For many Social Security might be the only form of income they have when it comes time to retire. Almost every day we see headlines in the news telling us that Social Security is being depleted. Is Social Security in trouble? If so what does this mean to us?
Our guest today, former regional commisioner of the Social Security Department, Gordon Sherman.
Gordon Sherman is retired from 43-years of service to the military and federal government. During the last 23 years of his career, he was the southeast regional commissioner of the Social Security Administration. Mr. Sherman's many banking affiliations over the years included board positions for Citizens & Southern Bank of Gwinnett County, East Metro Division of Citizens & Southern Bank of Atlanta, The Enterprise Bank of Dunwoody, Georgia, Fidelity National Bank, Fidelity Southern and Regions Bank of Atlanta where he served as board chairman. The National Public Service Award, Ewell T. Bartlett Humanity in Government Award, three Presidential Executive Awards and a Making The King Holiday Award are among the many accolades Sherman has received. He earned a B.S. from Auburn University, a J.D., LL.M. and an honorary LL.D. from Woodrow Wilson College of Law and is a graduate of the Senior Governmental Managers Program, Harvard University, the U.S. Army Command and General Staff College and the Industrial College of the Armed Forces.
To contact Gordon Sherman you can email him at gordosherman@aol.com
Direct download: MoneyMattersEpisode55.mp3
Money Matters Episode 42- The Couple's Retirement Puzzle W/ Roberta K. Taylor
Are you and your partner on the same page when it comes to retirement planning? Or…are you like millions of couples avoiding these critical conversations?
• If, When and How to Retire: Twice The Husband, Half the Income
• Let's Talk About Money: Finances Without Fighting
• Changing Roles and Identity: I Don't Do Windows!
• Time Together, Time Apart: I Love You and I Need My Space
• Health and Wellness: Will Medicare Pay for the Spa?
Enhance your communication skills, make decisions together and develop your shared vision for the second half of life.
You can find learn more about Roberta by visiting :
http://www.pathmaking.com/
or order a copy of the book here:
The Couple's Retirement Puzzle
You can listen live by going to www.kpft.org and clicking on the HD3 tab. You can also listen to this episode and others by podcast at:
Money Matters Episode 31 - The Power of Choice - Personal Responsibilty and Financial Choices W/ Jeff Kanaly
On this weeks show we answered the question how does one make good financial decisions in a world dominated by risk and uncertainty. We discussed the book The Power of Choice which is dedicated to the idea that each of us has a choice to better our lives, empower ourselves and reach our goals.
We were joined by author Jeff Kanaly.
Jeff is Vice Chairman of Kanaly Trust and serves on the organization's board of directors. He has been with the company for over 35 years and concentrates on corporate strategic planning. An important focus for Jeff is ensuring that the high quality of service Kanaly Trust was founded on continues to be the central focus of the organization. He specializes in serving multi-generational families due to his depth of experience in high level, intricate estate and financial planning practices.
A graduate of the University of Texas at Austin, Jeff holds a Bachelor of Business Administration degree in Finance. He is a CERTIFIED FINANCIAL PLANNERTM practitioner and a Certified Trust and Financial Advisor (CTFA). He is a member of the Financial Planning Association (FPA), the Houston Chapter of the FPA, the Houston Estate and Financial Forum (HEFF), and the Association of Trust Organizations (ATO).
Jeff has served on many public and professional committees. He is a past national board member of the Financial Planning Association (FPA) and previously served on its Tax Sub-committee. He was involved in the merger of the Institute of Certified Financial Planners (ICFP) and the International Association of Financial Planners (IAFP) that formed the FPA. He was responsible for the coordination of the FPA's Pro-bono Program, has served on the ICFP board and on its Practice Management Committee. He is past president of the Association of Independent Trust Companies (AITCO now ATO), and previously served on its board of directors as treasurer. He is also a past chairman and president of the Houston Society ICFP. Jeff also serves on the Investment Committee at Kanaly Trust.
Jeff has served on the board of directors of the American Heart Association in Northwest Harris County and on the board of Applause Theatre. He is actively involved with the National MS Society, South Central Chapter as Chair of the Houston Leadership Council and was instrumental in launching the MS Entrepreneurs Program which helps those affected by MS at a grass-roots level. In addition, Jeff was recently selected as the Investment Committee liaison for the South Central Region of the MS Society.
Jeff's comments have appeared in such publications as Robb Report Worth, the Houston Business Journal and Financial Planning.
To find out more click below the:
Choice of A Lifetime
Kanaly Trust
Direct download: MM31.mp3
Money Matters Episode 30 - Be Prepared to Go the Distance with Retirement W/ Guest Ellen Rogin CPA, CFP
Whether you've been training for years for your retirement or you are a newbie, moving toward your goals, taking the right actions and following a plan will help you to cross the finish line feeling great and it will inspire those around you to do the same!
· How preparing for retirement is like preparing for a marathon – and the 6 training fundamentals that apply to both goals
· Why some people are great with money and others struggle
· My 5-step system for reducing stress around your finances
On this episode we are joined by author and speaker Ellen Rogin.
A CPA, Certified Financial Planner™ and Abundance Activist® - Ellen is a nationally known expert on living a life of success and prosperity.
A financial advisor chock full of "left-brain" credentials (MBA, CPA, Certified Financial Planner™), she also walks on the "right" side, balancing values, big picture ideas, and meditation with all her professional training. Ellen is as comfortable talking about the power of compound interest as she is the power of belief. Ellen shares this fresh approach in her book "Great with Money: 6 Steps to Lifetime Success and Prosperity."
Ellen is a frequent speaker to the financial profession, sharing her experiences and expertise at building successful client relationships and growing a successful practice. She is a regular contributor to Horsesmouth®, a support service for financial advisors and is a host of Horsesmouth Advisor Radio.
For more than 20 years, Ellen has been a financial advisor in Northfield, Illinois, and serves on the Board of Directors for Metropolitan Capital Bank in Chicago.
She co-authored the books:
Great with Money: 6 Steps to Lifetime Success & Prosperity
Breakthrough!
Inspirational Strategies for an Audaciously Authentic Life


Looking to get your child into hockey? This program is an introduction to playing the game in a fun and positive learning environment. The program is designed for players who are either new to the game or have 1 - 2 years playing experience. Players will work with our coaches on developing and improving their on-ice fundamental skills including skating, puck control, passing, receiving and shooting through exciting drills and games. Players must be comfortable skating on their own without a parent, with the ability to stand and skate forward in a controlled manner. All lessons are one hour.
This program add-on lets new players use their skills in game situations.
This unique 3-on-3 program gives players more time with the puck so they can continue to improve their skills and apply what they've learned. This program can be an add-on for Discover Hockey or purchased as a separate product. All sessions are one hour. Please note that if you are purchasing 3 on 3 hockey in conjunction with Discover Hockey, your discount will be applied at checkout.
New to the game or have 1 - 3 years playing experience Please note: there are no spring/summer sessions for this program.
Hockey is awesome right? Well we agree, but we know that playing a variety of sports creates better athletes. And better athletes make better hockey players. So why not give your child the opportunity to stay on the ice, while also improving critical fundamental and sport skills in this hockey and multi-sport development program. Our Hockey Canada-certified coaches have developed an on-ice curriculum to help improve your child's hockey specific skills, skating and individual tactics. Then off the ice, players will get the opportunity to learn and play different sports like floorball, rugby, handball, obstacle course training and more! As if this doesn't sound cool enough, on the last day participants will get to put their skills to work by participating in a cross-ice 3-on-3 style tournament! The tournament will take place on the morning of June 22nd.
This unique 3-on-3 program gives players more time with the puck so they can continue to improve their skills and apply what they've learned.
This program is for players looking to enhance their hockey skills in a progressive manner. Whether you are returning to the game after some time off or looking to improve your skills for your adult league, our team of coaches will work with players on proper skating mechanics, puck skills (passing, shooting, and puck control) and will focus on individual and team tactics. Players can put their new skills to the test in two scrimmage style games on the 4th and 8th sessions. All sessions are one hour and fifteen minutes long.
A step between the Discover Hockey Program and the WinSport Hockey League. Come out and play 8 practices and 10 refereed games as you build on your existing hockey skills.
Looking to get ahead of the game or to get extra one-on-one instruction to really improve your skills? Look no further than WinSport Private Lessons. Whether it is learning to skate, power skating, figure skating or hockey skills sessions, you'll be matched with one of our qualified instructors who will teach and challenge you at exactly the right pace for you. Lessons can be booked in either 30 minute or 45 minute sessions.


Make someone's birthday extra special this year. Send delicious birthday wishes with a Chocol@ Happy Birthday box of Belgian chocolates and a beautiful bouquet of roses. Chocol@ pralines are uniquely designed by master chocolatier Jean-Phillipe Darcis to send an edible greeting that will never be forgotten. Intense dark, milk, and white chocolate pralines are adorned with letters spelling out your message. Each praline character has its own special filling, bursting with the indulgent flavors of hazelnut, coffee, vanilla, salted caramel, citrus, passion fruit, and more. A bouquet of nine bright pink and orange roses with fresh green accents completes this memorable birthday celebration.


The Ravenna Lady Ravens traveled to Peninsula tonight for a league contest, defeating the Woodridge Lady Bulldogs 58-25, as Woodridge hosted the first official regular season contest in their new gymnasium. The Lady Ravens force the Bulldogs into 35 turnovers, executing 23 steals, and turning those steals into easy transition baskets. Daijah Caples lead the thievery with 5 steals. Kaitlyn Rogers puts away two three-point baskets and Avery Robinson puts down three threes of her own, racing out to 12 and 11 points, respectively. Layla Foster lead the Dawgs' scoring attack with 8 points. Ravenna had 10 players net points tonight with Rogers and Robinson being the only two scorers in double-figures. The Ravens beat out the Dawgs on the boards 32-26, Ravenna paced by Lauren Calhoun's 10 boards, and Olivia Woods lead Woodridge with 6. This was the Lady Ravens' first league game of the season, netting them at .500 for the season, after Saturday's loss in Beloit. The Lady Ravens take to the court at Ravenna High School's James L. Coll Gymnasium on Saturday at 2:30pm for a non-conference tilt with the Garretsville Garfield Lady G-Men, whom will enter the contest with a 1-1 record on the season, hoping to stop the Lady Ravens' bid for their program's 500th win.


Box after box of donations are pouring in to fill the food pantry at the YMCA in Lawrence and Andover, Massachusetts, to help the displaced Merrimack Valley residents.
People can get anything from toiletries such as toothbrushes to microwavable foods so they can get through another few weeks without gas.
"We opened this on Monday and we had 100 families show up," one YMCA worker said. "We think that need will continue and possibly grow."
Now that the organization's gym has hot waters, they have opened it to the thousands of explosion victims who remain without any gas.
"We've opened our branches for showers so anyone in the community can come to our Andover or Lawrence facility and take a hot shower, get a work out in, even just relax in our lounge," a YMCA worker said.
Over at the Cor Unum Meal Center in Lawrence, workers take pride in staying open because of the emergency.
"You didn't know if it was the end of the world or what was happening," a worker said.
Volunteers said since the tragedy, they have not stopped serving breakfast or dinner. Even without gas service, they have managed to serve cold, bagged lunches to go.
"Why not? There are so many people in need," said volunteer Cynthia Johnson.


The first two weeks of preseason for the Houston Dynamo coincided with the start of preseason for the team's hybrid USL affiliate, the RGV FC Toros. Players from RGV got a closer look at how the first team prepares for the upcoming season, while Dynamo coaches had the opportunity to see up-and-coming players in a new environment. The teams faced off in a pair of scrimmages to help prepare for the start of the season, including a chance to play under the lights at BBVA Compass Stadium during the Dynamo's annual Open Practice.


text:
Maria Berry
1851 - 1935 (84 years) Has no ancestors and no descendants in our family tree.
Stephen William Fifield
Birth 1832 Micheldever, Hampshire, England
Christened 29 Apr 1832 Micheldever, Hampshire, England
Died 1897 South Stoneham, Hampshire, England
Father Henry Fifield
b. 1800, Micheldever, Hampshire, England
Mother Harriet Lock
b. 1802, East Stratton, Hampshire, England
Married 10 Nov 1825 Micheldever, Hampshire, England
Family Maria Berry
b. 1851, Winchester, Hampshire, England
Married 1877 Southampton, Hampshire, England
Jonas James Woodford
Birth 21 Feb 1843 Chelsea, London, England
Christened 15 Oct 1843 Chelsea, London, England
Died 1930 Manchester (South District), England
Family 1 Zilpha Henrietta Butcher
Married 1867 St Pancras, London, England
1. Leonard James W Woodford
2. Henrietta Louisa A Woodford
3. Lilian Grace Woodford
b. 1871, Holloway, London, England
4. Millicent Daisy Woodford
b. 1874, Islington, London, England
5. Lino Alexander Woodford
6. Helen Irene Woodford
Family 2 Maria Berry
Name Maria Berry
Born 1851 Winchester, Hampshire, England [1]
Census 3 Apr 1881 Micheldever Station, Hampshire, England [1]
Western House
Census 5 Apr 1891 Eastleigh, Hampshire, England [2]
"Trictosin", Souithampton Road
Census 2 Apr 1911 Kidderminster, Worcestershire, England [3]
"Rosedale", Somerleyton Avenue
Last Modified 9 Mar 2013
Family 1 Stephen William Fifield (ID:I22909)
d. 1897, South Stoneham, Hampshire, England (Age 65 years)
Age at Marriage She was 26 years - He was 45 years
Family 2 Jonas James Woodford (ID:I22938)
b. 21 Feb 1843, Chelsea, London, England
d. 1930, Manchester (South District), England (Age 86 years)
Age at Marriage She was 53 years - He was 60 years and 10 months
Born - 1851 - Winchester, Hampshire, England
Married - 1877 - Southampton, Hampshire, England
Western House - 3 Apr 1881 - Micheldever Station, Hampshire, England
"Trictosin", Souithampton Road - 5 Apr 1891 - Eastleigh, Hampshire, England
"Rosedale", Somerleyton Avenue - 2 Apr 1911 - Kidderminster, Worcestershire, England
Died - 1935 - Manchester (South District), England
[S8343] Census 1881 Micheldever Station, Hampshire, England RG11/1229/48/2 (Stephen Fifield), (RG11/1229/48/2).
[S8346] Census 1891 Eastleigh, Hampshire, England RG12/924/134/32 (Stephen Fyfield), (RG12/924/134/32).
[S8347] Census 1911 Kidderminster, Worcestershire, England RG14/17564/21 (James J Woodford), (RG14/17564/21).


Hundreds of years tradition, unique and original sound and the opportunity to take it all wherever you go.
If you want to arrange events and present your guests the original Slovak tradition associated with the representation of the production of fujara, interesting information, as well as demonstrations of playing on fujara, gem our folk culture, do not hesitate to contact us with confidence.
People ask me very often how did I find my way to fujara and why I chose to produce, as my life mission. I always reply with the same answer, I didn't chose fujara it was the other way round. Fujara chose me. I made my first fujara in 1990 and I remember that moment with a smile on my face because I was very happy for every single time this fujara brought out. Many days, months even years has passed by since then and I have stayed loyal to fujara. At the end since 2003, It became not even my hobby but also my life profession. During the years I developed skills and gained experience. I have to mention that during the long years I met loads of special professionals who stayed near me on my way. It wasn't always easy way. I got loads of advices but also criticism from the people I looked up to. All the obstacles from the beginning and the occasional misunderstanding, all these things , in connection with my stubborness to go further towards fujara with excellent sound and shape, brought me here. Brought me to the meadow near the village in the west Slovakia callled Dolné Trhovište. I don´t play there my first fujara which I made myself in 1990 but I play the fujara number 1000 because the other 999 are used by people from all over the world. The range of people is from famous musicians, folklore groups as well as celebrities to the people like me. Those whom fujara secceded in charming.


text:
Q: Image source is not found in my JSP page. Getting 404 page not found in browser console I know there is some mistake I'm making but I can't figure out what it is. Please help me out.
This is my project folder structure.

I tried below -

*

*background="<%=request.getContextPath()%>/images/backgroundImage.jpg"

*background="images/backgroundImage.jpg" for body tag.

*I tried that css url also.
I'm getting same error in my browser console.

What am I doing wrong?

A: Man I will suggest you to create a folder resources under webcontent. Put all your images inside there.
Then in your jsp page map that image like
<img src="/resources/backgroundImage.jpg"" alt="View" style="width:304px;height:228px;">

redpajama_set_name: RedPajamaStackExchange


text:
AMBODE VISITS JAPAN, WOOS INVESTORS ON TRANSPORTATION, URBAN DEVELOPMENT
Nkechi Naeche March 22, 2018
Lagos State Governor, Mr. Akinwunmi Ambode (2nd right); member, House of Representatives, Japan and Chairman, Japan-AU Friendship League, Mr. Ichiro Aisawa (middle); member, House of Representatives of Japan and Deputy President, Japan-African Union Parliamentary Friendship League, Mr. Asahiko Mihara (2nd left); the Japanese Ambassador to Nigeria, Mr. Sadanobu Kusaoke (left) and Nigeria's Ambassador to Japan, Mallam Mohammed Gana Yisa (right) during the Governor's meeting with the Japan-African Union Parliamentary Friendship Committee in Tokyo, Japan, on Thursday, March 22, 2018.
Lagos State Governor, Mr. Akinwunmi Ambode on Thursday held a meeting with the Japan-African Union Parliamentary Friendship committee in Tokyo, an influential group in the Japanese parliament.
Governor Ambode said the meeting, which was attended by members of Japan House of Representatives – Hon. Ichiro Aisawa and Hon. Asahiko Mihara, was in furtherance of his quest to woo Japanese investors especially with regards to finding a comprehensive solution to the challenge of transportation in the State.
He said his presence in Japan was pursuant to his determination to achieve infrastructural renewal for Lagos State.
"As a government, the renewal of infrastructure of Lagos State is of paramount interest to us. We cannot afford to miss the train of regeneration going around the world. We must continue to seek comprehensive and holistic solution to the various challenges confronting us.
"Lagos and Tokyo share many similarities including huge populations which require a comprehensive transportation and urban management strategy to deal with. Japan is also a city Lagos should aspire to be in terms of vertical development, land space optimisation, and efficiency," the Governor said.
The meeting was also attended by the Japanese Ambassador to Nigeria, Mr. Sadanobu Kusaoke and the Nigerian Ambassador to Japan, Mallam Mohammed Gana Yisa.
During the week, the Governor also visited the headquarters of Yurikamome Incorporated, a light rail transportation facility which connects the down town Tokyo with Tokyo Waterfront City.
The light rail has and is patronized by all those who live, work and visit the facility since it opened in November 1995. It operates in just 14.5km and has 16 stations.
The light rail carries more than 45 million people yearly. It was further gathered that the Tokyo Metropolitan Government built the infrastructure, while Yurikamome Incorporated provided other necessary equipment.
gov Ambode visit to Japan
DAPCHI GIRLS' RELEASE: PDP PLUMBS THE DEPTHS OF INFAMY - FG
Tony Elumelu Foundation Selects 1,000 Entrepreneurs For 2018 Programme
Dangote feeds 30,000 IDPs in Zamfara
Buhari inaugurates Oshodi Transport Interchange, Ayinke House, 5.7km Murtala Mohammed International Airport Road, commends Ambode
Buhari Approves New Excise Duty Rates for Alcoholic Beverages, Tobacco
FEC approves dredging of Warri-Escravos seaport for N13bn
Army Kills Four Armed Herdsmen, Arrests 20 In Benue


text:
Biografia
Nel 1965 partecipa al Festival di Sanremo, venendo chiamato in extremis a sostituire Dionne Warwick quale partner straniero di Bruno Lauzi nel brano Il tuo amore, che non viene ammesso alla serata finale.

Nel 1967 pubblica Mind-Dusters, il suo album di debutto, a cui ne sono seguiti ad oggi altri 13, compresa una compilation.

Rankin è scomparso all'età di 69 anni a Los Angeles a seguito di un tumore polmonare

Discografia

Note

Collegamenti esterni

redpajama_set_name: RedPajamaWikipedia


For every one of our songs, you will be saying "oh I love this one" and you just will not be able to sit down as dance song after dance song keeps you on the floor and in the crowd of other revelling partygoers.
You can totally pick what playlists you want – take a look at our repertoire of music. There really is something for everyone! On stage for this annual event was Mark, Polly, Izzy Nick, Rob and Stu; a real winning combination!
We would love to thank Brave Souls Travel for their great video of the band at Swanage – thanks for letting us post it guys!
If you would like to chat with us about playing at your festival or carnival then please either fill in our enquiry form, or call us on 01435 408083.


I have provided links to items where I could find them, email me if you have any questions though.
Added a couple of Nate Berkus moroccan shag pillows from Target to the couch. I love how these are firm and not super soft and flimsy like most throw pillows are. I need support man!
The mother-of-pearl and gold tray is from HomeGoods and these are my first acquisitions for my design/decor library. Yes, we leave our remotes out. I have tried putting them in the boxes below the coffee table but they don't stay there long at all so I have given up. At least they are orderly now.
The center frame is new from HomeGoods. I like that it has a slightly modern texture with the ovals but is still in neutral colors.
Our bookshelves have a mix of nautical/beach and the new: faux corals are from Kohl's a while back, the marble geometric thingie is from West Elm (and is SUPER heavy), the gold dot frame is from Target, the pulleys are from the father-in-law, the old metal box was a thrift find from a friend, the metal orb is from HomeGoods and the maroon vase is from West Elm.
The stuff on this end table has been changed a million times and never felt quite right. I tried this plant there and now it feels much better, same with the whelk shells. The gold bowl is from Pottery Barn (no longer available, boo) and the coasters are from West Elm during our recent Houston shopping trip.
The biggest addition has been the Poang leather chair from Ikea. The linen and silver chevron pillow is from HomeGoods and the gray felt storage ottoman was a Target clearance rack score.
The foyer table decor has also been difficult for me but I have found that less is more here. Maybe one more small box or something on the left, maybe. The table itself was only $40 at World Market a few years ago thanks to crazy discounts and coupons and was actually used as our TV stand before I got the Pottery Barn Logan system. The white wood vase and large glass bottle are from World Market and the antler is the only deer shed I've found in the field myself. The glass vase and antler idea was inspired by this YHL post of course. Picture frame is Nate Berkus from Target, the mirror was from Joss & Main, and the floor lamp is the Sutter from Pottery Barn (thank you rewards points!). The vintage boat props underneath (next to the surround sound monstrosity -which I would like to make a cover for like Dana did here) have been collected by my father-in-law and I love them.
Follow me on Facebook and Instagram to get sneak peeks of things as I find them while out shoppin'.
Our new quartz master bathroom countertop is scheduled to be installed tomorrow morning, just in time for Friday's post!!
Getting some good pics with your new camera. :) looks nice.


what would best suit your needs?
THERAPY is a deeply introspective journey that looks at interpersonal relationships, relational history, traumas, and identifies maladaptive or destructive coping patterns. Therapy is for the individual who continues to recreate patterns in their life which gets in the way of occupational, relational and personal success. Therapy facilitates deep insight into why you are the way you are, and encourages compassionate understanding rather than criticism. It is non-judgmental, focuses on self-efficacy and works toward healing parts of yourself that have been shut-down, blocked, or overly activated do to life circumstances. Therapy helps restore balance to mental, physical, and emotional ways of being, so that you can function to your highest capabilities.
COACHING focuses more on individual progress, highlighting strengths and helps re-wire thinking patterns that keep you stuck. Coaching varies from psychotherapy in that it is more fast-paced, quicker to be action oriented, and for those who already have done work on themselves in regards to core wounds, stuckness, strengths, and weaknesses. Coaching does not address underlying mental health conditions or diagnosis that are included in the DSM-V. Coaching tends to be more short-term, highly focused, directive and externally goal oriented. It is for the perfectionist, high-achiever, and self-motivator, who is relatively high functioning in areas of life, yet is still somehow getting in their own way.