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Can someone please tell me how to determine all $\mathbb{Q}$-automorphisms of some splitting field $F$ of $X^3-3 \in \mathbb{Q}[X]$ and to determine $[F:\mathbb{Q}]$?
I think $[F:\mathbb{Q}]=3$, since I can construct a specific splitting field containing the three (complex) roots of the polynomial $X^3-3 $, but I don't know how to prove that it equals $3$. And for the automorphisms, I don't even know how to approach it.
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the reason why you can't prove $[F:\mathbb{Q}]=3$ is that $[F:\mathbb{Q}]=6$ – user8268 Nov 6 '12 at 22:12
yes, once you have in hand one of the roots of the polynomial, you need to write down explicitly what the other roots are. Then you need to notice what other irrationality needs to be adjoined to the setup to get all three in any field. You'll see that there is a unique quadratic extension of $\mathbb Q$ there, and three different cubic extensions. This is an exercise that everyone must do for her/himself. – Lubin Nov 7 '12 at 2:27
1 Answer 1
up vote 4 down vote accepted
Let $F$ be a field. Let $F^\times$ be the multiplicative group of $F$. Let $(a, b) \in F^\times \times F$. We denote by $\lambda(a, b)$ the permutation $x \rightarrow ax + b$ on $F$. Let $(a, b), (c, d) \in F^\times \times F$. Since $a(cx + d) + b = acx + ad + b$, $\lambda(a, b)\circ\lambda(c, d) = \lambda(ac, ad + b)$. Hence $\{\lambda(a, b) | (a, b) \in F^\times \times F\}$ is a permutation group on $F$. We call this group the affine general linear group of degree $1$ on $F$ and denote it by $AGL(1, F)$. Since $\lambda(a, b)(0) = b$ and $\lambda(a, b)(1) - b = a$, $(a, b)$ is uniquely determined by $\lambda(a, b)$. Hence $|AGL(1, F)| = |F^\times \times F|$.
Proposition Let $p, q$ be prime numbers which may or may not be equal. Let $a$ be an integer which is divisible by $q$, but not not divisible by $q^2$. $X^p - a$ is irreducible in $\mathbb{Q}[X]$ by the Eisenstein's criterion. Let $K$ be the splitting field of $X^p - a$ in $\mathbb{C}$. Then the Galois group $G$ of $K/\mathbb{Q}$ is isomorphic to $AGL(1, F)$, where $F = \mathbb{Z}/p\mathbb{Z}$.
Proof: Let $\zeta$ be a primitive $p$-th root of unity. Let $\alpha$ be a root of $X^p - a$ in $\mathbb{C}$. $\alpha,\alpha\zeta,\dots,\alpha\zeta^{p-1}$ are distinct roots of $X^p - a$. Hence $K = \mathbb{Q}(\alpha,\alpha\zeta,\dots,\alpha\zeta^{p-1})$. Since $\zeta = \alpha\zeta/\alpha \in K$, $K = \mathbb{Q}(\alpha, \zeta)$.
Let $\sigma \in G$. Since $\sigma(\zeta)^p = 1$, there exists an integer $b$ such that $\sigma(\zeta) = \zeta^b$. Clearly $b$ (mod $p$) is uniquely determined by $\sigma$ and $b$ (mod $p) \in F^\times$. On the other hand, there exists an integer $c$ such that $\sigma(\alpha) = \alpha\zeta^c$. Clearly $c$ (mod $p$) is uniquely determined by $\sigma$. We denote $\phi(\sigma) = \lambda(b$ mod $p、c$ mod $p) \in AGL(1, F)$. Hence we get a map $\phi\colon G \rightarrow AGL(1, F)$. Let $\sigma, \tau \in G$. Suppose $\phi(\sigma) = \lambda(b$ mod $p, c$ mod $p$) and $\phi(\tau) = \lambda(d$ mod $p, e$ mod $p$). Then $\sigma\tau(\zeta) = \zeta^{bd}$ and $\sigma\tau(\alpha) = \sigma(\alpha\zeta^e) = \alpha\zeta^c\zeta^{be} = \alpha\zeta^{be + c}$. Hence $\phi(\sigma\tau) = \phi(\sigma)\phi(\tau)$. Hence $\phi$ is a homomorphism. It is easy to see that $\phi$ is injective.
It remains to prove that $\phi$ is surjective. Since $[\mathbb{Q}(\zeta) \colon \mathbb{Q}] = p - 1$, $[K \colon \mathbb{Q}(\zeta)] > 1$. Let $H$ be the Galois group of $K/\mathbb{Q}(\zeta)$. Let $\tau \in H$. There exists an integer $c$ such that $\tau(\alpha) = \alpha\zeta^c$. We define a map $\psi\colon H \rightarrow F$ by $\psi(\tau) = c$ mod $p$. It is easy to see that $\psi$ is an injective homomorphism. Hence $|F| = p$ is divisible by $|H|$. Since $|H| > 1$, $|H| = p$, Hence $[K \colon \mathbb{Q}] = p(p-1)$. Hence $\phi$ is surjective. QED
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Seems to me that OP is a real beginner, and that your explanation will be too highfalutin for her/him. – Lubin Nov 7 '12 at 2:29
_USER_ It is a proof rather than an explanation. I believe anyone who knows basics of Galois theory and group theory can understand it. – Makoto Kato Nov 7 '12 at 3:18
Makoto, you may be right. But, reading between the lines, I bet OP doesn't know what a semi-direct product is, and won't derive much benefit from your efforts, at least, not this year. – Gerry Myerson Nov 7 '12 at 5:42
_USER_ If there are people(including the OP or otherwise) who can understand the proof and learn something from it, that would be my pleasure. – Makoto Kato Nov 7 '12 at 21:32
_USER_ +1 for your answer, but it would be good if you added a section that addressed beginners. For example, state all the automorphisms of the extension (in the usual way that we show that the Galois group of the polynomial above is $S_3$). Even for me reading your post takes some time to fully digest what is going on, what about for a beginner? – user38268 Dec 15 '12 at 14:04
Your Answer


eKiosk GmbH
Ceremonial handover of Germany's first citizens terminals with video function
presentation citizens terminal Neustadt
At 14.10 the first citizen kiosk of the State Saxony was put into operation in Neustadt. The formal presentation was made by Mr Justice Minister Jürgen Martens (FDP) to the mayor of Neustadt (Saxony ) Manfred Elsner.
Through the video interface and the remote control of scanners, printers, etc developed by eKiosk it is the first citizens terminal in Germany with these features and extends the eGouvernment landscape in Germany as an example. Minister in Justice Minister Jürgen Martens ( FDP) sees this project as a major project at the European level to support local communities.
The Citizens terminal will be used in the future as a branch of the county Saxon Switzerland.
So applications can be filled out and printed. Via video phone the Citizens are connected to an employee in the district headquarters in Pirna.
The device and 13 more in Saxony are tested for two years, and when the civil terminal is accepted by the population, is a major rollout.


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Shraddha name popularity, meaning and origin
Name Popularity: 0%
Shraddha name meaning:
The name "Shraddha" is of Indian origin and is commonly given to girls. It has its roots in Hinduism and holds significant cultural and religious importance. The name is derived from the Sanskrit word "shraddha," which means faith, devotion, or trust.
Shraddha represents a deep sense of belief and reverence towards spiritual or religious practices. It embodies the idea of having unwavering faith in one's beliefs and dedicating oneself wholeheartedly to a particular deity, philosophy, or set of values. The name reflects the qualities of a person who is sincere, committed, and steadfast in their convictions.
Shraddha also carries the notion of respect and homage towards ancestors and elders. In Hindu rituals, "shraddha" refers to the ceremony performed to honor and offer prayers to departed souls. Hence, the name portrays a sense of reverence towards the lineage and heritage.
Overall, the name Shraddha symbolizes faith, devotion, and respect. It signifies a person who is deeply connected to their beliefs and traditions, and who upholds the values and practices that define their cultural identity.
Overall UK ranking: 5581 out of 5581
3 recorded births last year
Change in rank
Ranking for this name in various UK regions
Historical popularity of Shraddha
The graph below shows the popularity of the girls's name Shraddha from all the UK baby name statistics available. It's a quick easy way to see the trend for Shraddha in 2024

source: openbmb/Ultra-FineWeb


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Amount of Calories in Japanese Persimmon Foods
The amount of calories in Japanese Persimmon foods like Jam, Pie and Juices is also different. Calorie content of different Japanese Persimmon foods is:
Calories in Juice: 90.00 kcal
Calories in Jam: 345.00 kcal
Calories in Pie: 284.00 kcal
In nutritional terms, the calorie content of Japanese Persimmon is the energy obtained through its consumption. Here is a simple equation to maintain a balance between calorie levels: The amount of energy consumed must be equal to the amount of energy utilized. If low, the person may become weak and if high, this energy is stored in the form of fat. Everyone needs calories for proper functioning of body and Japanese Persimmon calories will not alter the diet in any hazardous way. Calorie requirements vary depending upon the physical activities, age, weight, height and health of the individual.


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Decorating golf balls is an activity that can be fun for adults and children alike. Whether you're making a gift for the golfer in your life or accenting your home décor, you can use golf balls for original artwork by adding designs with permanent marker or with paint. You can also use red, black, and white paint to enhance your garden with golf ball ladybugs.
Method 1 of 3:
Decorating Golf Balls with Permanent Marker
 1. 1
 Choose a design. There are a lot of designs to choose from. Floral patterns are an easy, fun, and cute pattern to draw if you're new to decorating golf balls. You could also recreate the solar system or make minions and popular characters. You have endless options, so come up with a plan for how you will want your golf balls to look.
 - Some creative ideas include fruit, bugs and animals, holiday themes, and other types of sports balls like soccer and basket balls.[1]
 2. 2
 Gather golf balls and markers. Use quality permanent markers that won't easily rub or wash off and won't fade over time. Choose an array of colors. For color that stands out brightest on turf, look for reds and yellows.[2]
 - Gather a lot of golf balls. As you work, you may want to discard some that you don't like, or you may come up with new designs that you want to try along the way. Try as many different designs and illustrations as you like.
 - Place all materials in a cardboard box or other flat surface where the balls will not roll away.
 3. 3
 Wash the golf balls thoroughly with dish soap. Place them in a sink and scrub them with hot, soapy water to remove dirt or other elements from the surface. Dry them off with a dish towel before drawing on them with permanent marker.[3]
 4. 4
 Draw lines around the golf ball. Set the golf ball on a flat surface and hold the marker steady with the tip touching the ball. Slowly roll the golf ball for a straight line going all the way around the ball. Then move the marker to the next point on the ball where you want to draw another line.[4]
 - Lines can be decorative by themselves or they can be used as stems for flowers in a floral pattern.
 - Use different colors for a specific theme. For example, use red and green for a Christmas themed design or black and yellow to make the golf ball look like a bumblebee.
 5. 5
 Make a floral pattern on the ball. Color in the ridges on the ball with the tip of the marker. You can make a flower pattern by coloring in one ridge with one color, and each of the surrounding ridges with a brighter color.
 - This process also works well for paw prints if you use neutral colors like black and brown.
 6. 6
 Color in the ridges. Color every other ridge for a checkered pattern or color in ridges sparingly for a polka-dot pattern. You can use different colors or all one color depending on how you want your pattern to look. The technique is simple but the finished design will be fun to see. [5]
 - You can create a great piece of home décor by coloring golf balls with simple designs and placing them in a vase or frame.[6]
Method 2 of 3:
Painting Golf Balls
 1. 1
 Choose how you want your golf balls to look. You can use acrylic paint and paint brushes, or spray paint for a more solid look of one color. Depending on the design, you may need to gather a lot of golf balls. It's better to have too many golf balls than not enough as you might want to change your design along the way. Use as many golf balls as you need.
 - Knowing what type of design you want before you start can help you decide if you want spray paint or acrylic paint and what size brushes to use.
 2. 2
 Set up your workspace. Painting golf balls is best when done outdoors due to the mess and fumes. Place empty egg cartons upside down outside on a flat surface. Then place the golf balls on the egg carton to hold them firmly in place while you're working.[7]
 3. 3
 Sandpaper the golf balls. This will remove the gloss on the outer surface of the ball so that the paint will stick better. This will also help remove any dirt and grime.[8]
 4. 4
 Add primer to the golf balls. Keep them on the egg cartons and spray over the golf balls with paint primer spray. This will also ensure that the paint will stick and have a longer lasting hold. Hold away from your face as you spray, and then wait for the balls to dry.[9]
 5. 5
 Paint a solid color with spray paint. You can make a ball one solid color by placing it on the empty egg carton and spraying it with spray paint. Once it is dry, turn it over and spray the other side. If you don't have spray paint, you can also use a large brush to coat the balls with acrylic paint.
 - Once you have a solid-colored golf ball that isn't white, you can continue to create designs with a more colorful background.
 6. 6
 Use stickers and paint to make a clean-cut design. Stickers of stars, letters, flowers, and other shapes will work well for designs, initials or names when you place the sticker on the ball and paint over it with either a brush or spray paint. Allow the paint to dry before you remove stickers.[10]
 7. 7
 Use a fine brush to draw smaller designs. Use the tip of a small brush to paint intricate designs or make a floral pattern by filling in the ridges with different colors. Do this by painting one ridge a dark neutral color and each surrounding ridge a bright color.
Method 3 of 3:
Making Golf Ball Ladybugs
 1. 1
 Set up a workspace where you can paint. Outdoors is usually the best place to work due to the mess and fumes. If you will be working indoors, lay down newspaper and open a window. Lay empty egg cartons on top of the newspaper or flat surface area where you will be painting.
 - The empty egg cartons will be used to hold the golf balls while you work so that they remain steady and you can keep one hand free.[11]
 2. 2
 Sandpaper the surface of each golf ball. This will remove the gloss from the ball and any residual dirt. Golf balls have a layer of gloss on the surface that can keep paint from sticking, so it's important to make sure all the gloss is removed. After sandpapering each ball, brush off any extra sand or dust.
 3. 3
 Spray a paint primer on the balls. This is easiest to do while the balls are sitting on the upside-down egg carton. This will help to give the paint a better hold and will also help the colors look more vibrant. Allow the primer to fully dry before moving on.[12]
 4. 4
 Coat the ball with red paint. Keep the balls on the egg carton while you paint. You can use a large brush, or for an easy and solid coating you can use spray paint. Allow the red paint to fully dry before adding any black. This will prevent the black paint from running into the red paint and making a mess on the ball.[13]
 5. 5
 Paint a large black circle for the head and fill it in with black paint. Continue to draw a line from the top of the head in a semi-circle around the ball. This is the line between the two wings. Continue to use the black paint to fill in ridges on the ball for spots.[14]
 - You don't have to make a lot of black spots. Just a few will look great.
 6. 6
 Paint two small white rings inside the head of the ladybug. These will be the eyes, so put them towards the top half of the head close to the wings. At this point the design is complete, so wait for the ball to dry.[15]
 7. 7
 Add varnish to protect your new ladybug golf balls from rain and weathering. Apply the varnish with a clean brush and allow it to sit. Once the varnish is dry you can start putting them around your garden or in your flower beds.[16]
 - Try to keep them in shaded areas to avoid the color from fading quickly in the sunlight.
Community Q&A
Ask a Question
200 characters left
 - Collect as many golf balls as you can. Depending on the project, you might want a lot of them. Ask a golfer that you know or pick some up when you're on the golf course. You can also purchase them at any sporting goods store.
 - If you want to personalize golf balls with a professional logo or design, order them online through a customization company. Have them represent your team, league, or group, or keep them as a reminder of someone or something you love.
 Submit a Tip
 All tip submissions are carefully reviewed before being published
 Thanks for submitting a tip for review!
 Things You'll Need
 - Golf balls
 - Permanent markers in different colors
 - Acrylic paint or spray paint of different colors
 -


Sunday 29th November 2015
Max 12°C | Min 7°C
Why is it called a sledgehammer?
All the hammers have self-explanatory names - toffee hammer, nail hammer, claw hammer, club hammer - but why is a sledgehammer so called?
Dave, London
** Joint Definitive **
Name: Barry, Battersea
Qualification: Comes from a family of shipbuilders
Answer: I originally come from Jarrow, on the River Tyne and a lot of my family work in shipbuilding. The timber racking that held the boat upright before it reached the river was called a sledge. Inside the timber were big oak wedges, which needed to be knocked out to launch the boat. These were hit with a big hammer, which was then called a sledgehammer.
** Joint Definitive **
Name: Marcus
Answer: When they build big boats, they build them on big sledges that go down into the sea. They are chocced up to make sure they don't slide into the sea and they knock those big chocs out with hammers, which are called sledgehammers.


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To skew an object by using the resize handles
Select an object or a group of objects or anchor points. The resize handles appear.
Position your pointer near but outside one of the side handles and use one of the following methods:
To skew horizontally, drag the top or bottom side handle of the object to the left or right.
To skew vertically, drag either the left or right side handle.
To skew the object around its center point, hold down the ALT key.
A shape (in blue) being skewed with the top handle
You can skew and create a duplicate of a selection at the same time by holding down CTRL+ALT when you drag.
To skew an object by using the Action Bar
On the left side of the Action Bar, click the registration point icon to indicate which part of the selected object you want to stay stationary during skewing. For example, if you want the upper-right corner of your object to remain in position when the rest of the object skews, click the upper-right corner of the registration point icon.
Adjust the Skew Angle. Drag the pointer up or to the right to increase the value, or drag it down or to the left to reduce the value. Click the field to type a numeric value.
To skew vertically (shear) instead of horizontally, set the Rotation Angle and Skew Angle fields to the same value.

source: HuggingFaceFW/fineweb-edu


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at first blush
Definition from Wiktionary, the free dictionary
- (idiomatic) Upon first impression or consideration; seemingly, apparently, ostensibly.
- 1990, Nicolas Wolfson, Corporate First Amendment: Rights and the Sec, Quorum Books (1990), ISBN _PHONE_, page 1:
- At first blush it appears rather strange to consider for even a moment the possibility that corporate financial and business disclosure rises to the dignity of speech protected by the First Amendment.
2002, Clarence A. Bonnen, Daniel E. Flage, Descartes and Method: A Search for a Method in Meditations, page 100:
- Third, it is only at first blush that one finds no exercises in conceptual elucidation
- 2008, Dennis Martin Altman, The First Liberal: A Secular Look at Jesus' Socio-Political Ideas and How They Become the Basis of Modern Liberalism, iUniverse (2008), ISBN 9780595430536, page 47:
- That may sound innocent at first blush, but a phrase like "American leadership is good … for the world" is a signal that these people want to impose their will on others; and when military strength and moral principle are added, the caution flag must be raised.
- 2012, Cynthia Garner, Secret of the Wolf, Forever (2012), ISBN 9781455510764, unnumbered page:
- At first blush it seemed the attacks by the werewolf were random.
upon first impression or consideration


What is a Temperature Class?
A temperature class is a term assigned to instruments and equipment within a hazardous area or zone. Classification or rating signify the level of thermal energy allowed in a particular area or produced by a specific equipment.
It defines the maximum surface temperature of the components in the electrical equipment under normal and fault conditions
This maximum surface temperature must not exceed the gas ignition temperature.
It is stated with reference to a maximum ambient temperature of 40 degree Celsius.
Six Categories
 - T1 :- 450 degree celciusT2:- 300 degree celcius
 - T2:- 300 degree celcius
 - T3:- 200 degree celciud
 - T4:- 135 degree celcius
 - T5:- 100 degree celcius
 - T6:- 85 degree Celsius
For Example :- An electric motor may have a maximum surface temperature of 120 degree Celsius and would be classified as T4.
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Examples of scheduled monuments
Below are examples of scheduled monuments, ranging from early prehistoric to modern monuments.
Early prehistoric monuments
Despite recycling of stone for later uses, early prehistoric burial
sites such as this chambered cairn still contain important and unique information about burial practices
around 5000 years ago.
Later prehistoric monuments
Around 2000 years ago people in northern and western Scotland lived in substantial stone houses, often with defensive qualities. Here a submerged causeway leads from the shore to an island dun.
For a time in the 2nd century AD, the Antonine Wall was the north-west frontier of the Roman empire.
Early medieval monuments
The Picts of the 4th to 7th centuries AD built forts in many parts of Scotland, here reusing masonry from a nearby Roman fort.
Later medieval monuments
Later medieval churches were at the heart of their communities. Along with their graveyards they can tell us about changing religious beliefs and how this was reflected in the church architecture and burial practices.
It can be difficult to identify the remains of medieval settlements, but deserted settlements are characteristic of much of post-medieval Scotland. This fermtoun appears to contain at least eight separate units or farmsteads, pre-dating the transition to the dispersed farmsteads of the post-Improvement era.
We now recognise the cultural significance of the military remains of the 20th century.
In Scotland, seven wrecks dating from the First World War are scheduled in Scapa Flow, Orkney. Scottish Ministers can also designate wrecks under the Protection of Wrecks Act 1973.


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Unanswered: Checking text box text against original
Wondering if anyone can help me with this?
I have a text box on a products form that allows a user to edit the current product details, one of these details is the total number of products received to date.
If the user edits this text box then they can set this value equal to less than the original value. I want to make sure that whatever number they enter, it is greater than the original value that was in the text box.
If it isn't i want to be able to display a message box telling them this.


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PH10 Trigger Force Gauge (gram gauge)
Probe trigger force is critical to ensure accuracy and reliable operation, this can be easily measured and set using the gram gauge.
It is strongly recommended that the gram gauge is used when adjustments are to be made to probe trigger force.
For further information on the trigger force gauge, please refer to the trigger force gauge guide (Renishaw part number H-_PHONE_).
NOTE: To convert mass in grams to trigger force in Newtons the following equation is used:
Trigger force in Newtons = Mass in grams/100
For example: 8 grams = 0.08 N /100


American Crested
American Crested Breed Profile
Fur Short, smooth, close, thick
Rosettes None
Characteristics White crown
Lifespan 4-6 years
Suitable for Beginners
Breed Characteristics
The American Crested is completely one color - apart from its characteristic white crest on its head! This is like a little white crown created by the whorl. This makes it easy to tell this animal apart from other guinea pigs, especially for beginners. The crown sometimes makes these little pets look angry or indignant. But they're just as peaceful and funny as the rest of them. The rest of the American Crested's short, soft fur is usually golden brown, red or black. It doesn't have any markings or patterns to its fur.
Guinea Pigs for First-Timers
American Crested guinea pigs are among the easiest guinea pigs to keep. You could even call them "beginner guinea pigs". Still, inexperienced pet owners should get plenty of information and get hold of a guinea pig guide. Just like all guinea pigs, the American Crested is on the shy side.
How can you tell the American Crested and the English Crested apart?
Both have a crest on their heads but only the American Crested's is always white. In the English Crested, this is always the same color as the rest of its coat. If they didn't have this tuft, they'd just be completely normal American guinea pigs.
American Crested Guinea Pig American Crested Guinea Pig - Photo: Kirill Kurashov/Shutterstock
The white crest isn't easy to breed, as the babies of two American Crested guinea pigs won't always have the same markings, e.g. they might have additional white patches.
Fur Care
Short-haired guinea pigs can mostly keep themselves clean as they wash themselves with their little feet. Their fur should therefore only be cleaned when the American Crested doesn't keep up its hygiene duties. You should use a plastic brush for this. Knots can't always be prevented, and should be carefully cut out with scissors. It's also important to regularly check their ears, eyes and nails - just like with any guinea pig.
Just like all guinea pigs, the American Crested needs a combination of fresh hay, grasses, herbs, vegetables, fruit, seeds and twigs. They also need fresh water daily.
Did You Know?
A "crest" is a crown or tuft.
American Crested Guinea Pig American Crested Guinea Pig - Photo: Kurashova/Shutterstock


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(verb) deny or contradict (a fact or statement) "it was difficult to gainsay his claim"
(verb) speak against or oppose (someone) "none could gainsay her"
Gainsay meaning in Hindi (English to Hindi Dictionary)
विरोध करना, चुनौती देना, खण्डन करना, प्रतिवाद करना, अस्वीकार करना
- Middle English: from obsolete gain- 'against' + say.
Gainsay in a sentence (word usage in recent newspaper)
- "There is no gainsay from such statements," Mr. Diwan pointed out.
- "There is then no gainsay in the fact that transgenders enjoy basic human rights including protection from violence and discrimination.
- He was a perfectionist, but he will gainsay it for that's what invariably makes him a perfectionist.
- If these demanding practices help Muslims find peace and God, no one has a right to gainsay them.
- But he also makes points that officials struggle to gainsay.
Mnemonic trick to remember the meaning of gainsay
- gainsay = gain weight?? say it… don't deny… don't gainsay


text:
breaker rebate of $500 ($6,500 minus $6,000, which is 6 percent of $100,000).
- Kate usually makes $65,000 a year and pays $1,000 in property taxes (1.5 percent of her income) on her Gainesville home, but she loses her job in February. With unemployment insurance, her total income for the year is $20,000. Although she would not usually be eligible for a circuit breaker, she now qualifies for a $200 rebate ($1,000 minus $800, which is 4 percent of $20,000).
Who Would Receive the Benefit?
If this circuit breaker had been in effect in 2005, the following groups of Floridians would have been eligible for a credit:
- About 53 percent of households earning less than $60,000;
- About 12 percent of households earning between $60,000 and $100,000; and
- About 6 percent of households earning between $100,000 and $150,000.
How Much Would a Circuit Breaker Cost?
A circuit breaker of the design illustrated above would likely cost significantly less than $1 billion a year in the first several years after implementation.
Experience from other states suggests that a strong outreach campaign is necessary to inform eligible households about the program and encourage them to apply. The state, localities, or nonprofit organizations can engage in such outreach. If outreach is particularly successful, costs could increase in future years.
Can Florida Administer a Circuit Breaker?
States typically use one of three mechanisms to deliver property tax circuit breakers: a direct rebate check, an income tax credit, or a credit for future property tax bills. Since Florida does not have a personal income tax, the program would have to be administered as a direct state rebate. Half of the states with circuit breakers administer their programs through a direct state rebate. In these states, applicants must either attach a copy of their federal tax returns or other income-related documents, or sign an affidavit stating that their income information is true and correct. Florida could require similar documentation.
Florida legislators should use a circuit breaker to create a fair and targeted property tax system and to address property tax discord. Such a program can provide meaningful assistance to lowand middle-income Floridians.
 CBPP analysis of 2005 Census American Community Survey data. Since the legislature rolled back property taxes to their 2005 level, this data is a reasonable reflection of the current situation.
 CBPP analysis of 2005 Census American Community Survey data.
 These states are Illinois, Maine, Maryland, Massachusetts, Michigan, Minnesota, Missouri, Montana, New Jersey, New Mexico, New York, Oklahoma, Oregon, Pennsylvania, Rhode Island, Vermont, Wisconsin, and the District of Columbia.
 For more information, see Karen Lyons, Sarah Farkas, and Nicholas Johnson, "The Property Tax Circuit Breaker: An Introduction and Survey of Current Programs," Center on Budget and Policy Priorities, March 21, 2007, _URL_
 Please note this information reflects Census American Community Survey data from 2005. Property taxes in Florida have increased somewhat since then. This is the most recent available data on individual property tax payments. This is the most recent available data on individual property tax payments. Since the legislature rolled back property taxes to their 2005 level, this data is a reasonable reflection of the current situation.
 According to the 2005 American Housing Survey, 31 percent of all households in the U.S. are renters, while 57.4 percent of households in poverty are renters. Table 2-1, 2005 American Housing Survey, US Census Bureau (_URL_
 CBPP analysis of 2005 Census American Community Survey data.
 If every eligible household had successfully applied for this circuit breaker credit, the program would have cost roughly $2 billion dollars in 2005. However, participation in programs such as these rarely reaches 100 percent. In fact, participation often reaches only 50 percent a few years after the program's inception. This does not mean such a program is ineffective, but rather that it can be improved. It is extremely important to those households that do claim it. If the circuit breaker is used in conjunction with other property tax relief mechanisms, such as an expanded homestead exemption, its cost would be lower than the $1 billion estimate.


Answers » Categories » Language & Reference
What does GCWOK stand for?
What does GCWOK mean in texting? What's the meaning of the acronym GCWOK in online chat slang?
1 Answer
GCWOK in a text message means "Gay Couple Without Kids".
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Ordering of Steps
In the recipes package, there are no constraints on the order in which steps are added to the recipe; you as a user are free to apply steps in the order appropriate to your data preprocessing needs. However, the order of steps matters and there are some general suggestions that you should consider.
Transforming a variable
Handling levels in categorical data
The order of steps for handling categorical levels is important, because each step sets levels for the next step to use as input. These steps create factor output, even if the input is of character type.
Dummy variables
Recipes do not automatically create dummy variables (unlike most formula methods).
Recommended preprocessing outline
While every individual project's needs are different, here is a suggested order of potential steps that should work for most problems:
 1. Impute
 2. Handle factor levels
 3. Individual transformations for skewness and other issues
 4. Discretize (if needed and if you have no other choice)
 5. Create dummy variables
 6. Create interactions
 7. Normalization steps (center, scale, range, etc)
 8. Multivariate transformation (e.g. PCA, spatial sign, etc)
Again, your mileage may vary for your particular problem.
Try the recipes package in your browser
recipes documentation built on April 16, 2021, 5:09 p.m.


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A Rework Loop is a situation where a step in a process is repeated in order to correct a defect; also known as backtracking. Rework Loops are work that must be done over and over. They often become an accepted part of the process as people get used to them over time. To find Rework Loops, look for places where large amount of work move back in the process to be fixed.
Rework Loops are Non-Value Adding Activities and are undesirable, as they add to cost and cycle time.


text:
Definition of Green gland
1. Noun. One of a pair of glands (believed to have excretory functions) in some crustaceans near the base of the large antennae.
Green Gland Pictures
Click the following link to bring up a new window with an automated collection of images related to the term: Green Gland Images
Lexicographical Neighbors of Green Gland
Literary usage of Green gland
Below you will find example usage of this term as found in modern and/or classical literature:
1. Report of the Annual Meeting (1880)
"This same green gland has been studied by Professor Huxley and Mr. Martin, who, in an elementary work on practical biology, describes it as a soft greenish..."
2. The Crayfish: An Introduction to the Study of Zoology by Thomas Henry Huxley (1880)
"... gg. green gland, exposed in A on the left side by the removal of its sac ; ima, intermaxillary or cephalic apodeme ; ces, oesophagus seen in transverse..."
3. The British Flower Garden: Containing Coloured Figures and Descriptions of...by Robert Sweet by Robert Sweet (1838)
"... on a sort of green gland ; filaments very short and slender : anthers linear, opening at the point for the exclusion of the yellow pollen...."
4. Comparative Anatomy and Physiology by Francis Jeffrey Bell (1885)
"This is the so-called " green gland" of the crayfish, where it presents the following characters. An orifice, large enough to admit a fairly stout bristle,..."
5. The Century Dictionary: An Encyclopedic Lexicon of the English Language by William Dwight Whitney (1889)
"Green-gland, a special excretory gland of the crawfish and other crustaceans,... The green-gland alone is distinctly similar to a renal excretory organ...."
6. The American Monthly Microscopical Journal by Chas. W. Smiley (1888)
"simplicity, though one sufficiently unlike the green-gland to require an en... The wall of the cavities, as in the green-gland, was found to shut out the..."
7. Bulletin of the Essex Institute by Essex Institute (1889)
"... must be derived from the ectoderm,unless the duct form long before the rest of the gland. Ishikawa's observations on the origin of the green gland of..."
8. The Microscope: An Illustrated Monthly Designed to Popularize the Subject of (1886)
"Did they describe the methods by which certainty was obtained, one could have more confidence in the results. The Green-gland of Crustacea...."


text: The main cable is made of PPWS. Its large displacement and nonlinear mechanical properties are shown by their own elastic deformation and its geometry changes affecting the system balance. To get the real main cable-shaped of long-span suspension bridge, based on the finite element method, the element stiffness matrix was derived, which displacement field was same to the element shape. Then through the horizontal and vertical direction equilibrium equations were solved, the relationship between main cable shape and the system parameters was obtained. The calculation method was compiled to MATLAB 7.0 programs, and applied to ascertain the main cable-shaped of one long-span suspension bridge. When the paper calculated result was contrasted with the design value, it could be concluded that: the main cable-shaped of long-span suspension bridge could be accurately obtained by the paper method, and the method was convenient for compiling.


Can chinchillas eat peanuts?
Can Chinchillas Eat Peanuts?
Wild chinchillas likely eat nuts and seeds, when they find them. So should you feed a pet chinchilla peanuts? And if not, why not?
Can chinchillas eat peanuts? They can, but peanuts of all kinds are nutritionally unsuitable for chinchillas. That includes roasted nuts, raw peanuts, unsalted and salted, and even monkey nuts still in their shells. They are too high in fat and calories so can make chinchillas overweight. They also don't contain enough fiber or carbohydrate for your chinchilla's gut, so may cause bloating. Feed your chinchilla safe snacks like rose hips, sweet hay or shredded wheat instead.
The guide below details exactly why chinchillas shouldn't eat peanuts, by looking at their nutritional content vs. the nutrients a chinchilla needs. We'll also look at some of the side effects that peanuts are likely to cause (and they aren't pretty). And for anybody who is going to insist on giving their chinchilla peanuts, we've also made recommendations on serving sizes that, while not good for your chinchilla, at least aren't likely to cause it significant harm.
Can Chinchillas Eat Peanuts?
Chinchillas can physically eat peanuts. They have big, strong teeth that can easily break them apart. And chins aren't stupid, so won't try swallowing peanuts whole—they know to chew them first. But while a peanut won't immediately poison or choke your chinchilla, it won't be good for its health, so we don't recommend feeding them.
Do Chinchillas Like Peanuts?
Can chinchillas eat peanuts?Chinchillas enjoy eating anything new, sweet and/or fatty. They're naturally inclined to eat high-calorie foods because these are hard to find in the wild—the same instinct that we have. So, if you offer your chinchilla a peanut, it will eat it.
The problem is that your chin doesn't know what's best for it. It's in the wild, and it has unlimited access to hay and pellets. It doesn't need to gorge on dense foods like peanuts. In that sense, peanuts are a lot like the chinchilla equivalent of the snacks and fast food that we enjoy eating (but probably shouldn't).
Why Can't Chinchillas Eat Peanuts?
Peanuts are nutritionally unsuitable for chinchillas. If fed regularly, they will make your chinchilla gain weight. And because your pet isn't used to them, they could cause digestive issues like bloating, too.
Nutrients in Peanuts
To fully understand why peanuts have the effect that they do, you have to look at the specific amounts of each nutrient they contain. The table below uses data from These data relate generically to unsalted peanuts, not one brand or another.
NutrientsAmount per 100gRequirements
It should be immediately obvious that peanuts don't give chinchillas some of what they need, and give far too much of things they don't need much of.
Carbohydrate, Protein & Fat in Peanuts
The key issue with peanuts is that they contain far too much fat for chinchillas.
Contrary to popular belief, no one nutrient is the 'enemy'. You shouldn't entirely cut out carbs, fat, or anything else. Rather, the issue here is that fat contains more calories per gram than protein and carbohydrates (roughly double). As such, peanuts have almost three times as many calories as chinchillas need. This means that your pet will quickly gain weight if you feed it peanuts, even as a snack. The fact that peanuts have around 20-40% more protein than chinchillas need makes this problem even worse.
What else makes peanuts unsuitable is that they contain little fiber, or at least, less fiber than chinchillas need. Chins need a very high fiber diet, perhaps up to 30g per 100g. Their digestive systems are tailored to just such a diet. If your chin doesn't get enough fiber, its stools may be soft or even runny.
Vitamins & Minerals in Peanuts
Peanuts have lots of vitamins and minerals compared to other foods, both in terms of the number of different micronutrients they contain, and the amounts of each. Here is a table, again with data from, that lists each micronutrient that peanuts contain high amounts of:
Vitamin/MineralAmount per 100g
Vitamin B10.64mg
Vitamin B20.135mg
Vitamin B312.066mg
Vitamin B51.767mg
Vitamin B60.348mg
Vitamin E8.33mg
This table may seem like a plus-point in favor of peanuts, but it's not.
Chinchillas can thrive on a diet of hay and hay alone. That's because hay contains every vitamin and mineral that chinchillas need to live healthy lives. That may seem surprising, but many animals don't need a varied diet like we do.
If your chinchilla is deficient in something, peanuts aren't an effective 'supplement'. Rather you should talk to your vet about actual supplements. Take calcium, for example: timothy hay doesn't contain quite enough, which is why chinchilla pellets often contain alfalfa, which contains lots. If your chin isn't getting enough, the vet can recommend a suitable supplement. Or, you can give your chinchilla a cuttle bone as a chew toy. Both of these options are better than peanuts because they don't make your pet gain weight or have digestive issues.
Are Peanuts Poisonous to Chinchillas? (Digestive Issues)
Peanuts aren't poisonous for chinchillas. Your chin can eat one, and it won't immediately get sick, let alone pass away.
Rather, they cause digestive issues. These take longer to appear than a poison would take to take effect. Peanuts, and any food your chinchilla is unfamiliar with, can cause bloating which is a dangerous problem for a chinchilla to face.
This occurs because a chinchilla's digestive system is set up perfectly to digest rough fibers like those found in hay. The chinchilla digests its food twice over to extract as much nutrition from it as possible, and its gut bacteria and enzymes specialize in breaking down fibrous foods. While peanuts are reasonably fibrous, they are nowhere near as fibrous as hay.
When the chinchilla's gut has to digest something it isn't used to, the food can ferment. When this happens, it produces lots of gas, and since chins can't pass gas easily, this gas gets trapped. So much can get trapped that the chinchilla's gut or stomach lining can burst. While this won't happen if you feed your chinchilla just one peanut, peanuts and other unsuitable snacks can contribute to an existing issue, or create an issue from nothing if fed regularly.
Can Chinchillas Eat Raw Peanuts?
Can chinchillas eat peanuts?
Peanuts grow in the ground!
The statistics above relate to raw, unsalted peanuts. Every peanut has this much fat in it, that many calories in it (if not more), and isn't suited to your chinchilla's diet. That applies to peanuts you get in packets, peanuts you get in tubs, or monkey nuts that you get with their shells still on.
Can Chinchillas Eat Salted Peanuts?
Salted peanuts are worse for your pet than raw peanuts. That's because of all the sodium (salt) they contain/have on their surface. Sodium has negative health effects like raising blood pressure. It's proven to increase the risks of kidney disease, stomach cancer and heart failure too. While these effects haven't been proven in chinchillas specifically, they have been observed in other rodents, so are likely to occur in chinchillas too.
Can Chinchillas Eat Peanut Shells?
While peanuts aren't suitable for chinchillas, peanut shells are.
Peanut shells are too tough and fibrous for us to eat. But it's these qualities that make them the perfect chew toy for chinchillas. Chins need a chew toy to keep their teeth from growing overlong. Apple wood sticks are a common choice, and there's no reason not to give these. But chinchillas enjoy having new toys and new treats: it keeps them entertained.
Peanut shells are a good choice because when chinchillas gnaw on things, they can accidentally ingest some by accident. That's why it's best to offer chew toys made from natural materials like wood. Peanut shells don't contain the same high levels of fat and protein that peanuts do, which means they're safe to ingest.
Can Chinchillas Eat Peanut Butter?
Peanut butter is tasty, but doesn't make a good chinchilla treat.
The same issues that apply to regular peanuts apply to peanut butter, too. Peanut butters have the same, if not higher, levels of fat and protein than raw peanuts. They have lots of salt added, too.
And besides nutrition, peanut butter poses other problems. If you got any peanut butter in your chinchilla's fur, it would be a nightmare to clean out.
How Many Peanuts Can Chinchillas Eat?
We would recommend against feeding your chinchilla any peanuts, for the reasons covered above. On top of that, though, there are snacks that are perfectly suitable for chinchillas that won't have these effects. Chinchillas enjoy these snacks just as much as fatty, sugary or generally unhealthy ones. There's therefore no logical justification for offering unhealthy peanuts when healthy rose hips or herbs will suffice.
And besides that, ch


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Police vs Private Investigations: What is the Difference?
Police and private investigation services may seem similar on the surface, but there are several key differences which influence the two roles and impact their scope of delivery.
The first, most identifiable difference, is legal authority. Police officials have the legal authority to detain witnesses and compel testimony, whereas private investigators are not law enforcement professionals. Therefore, private investigators are forced to get creative in their meticulous investigative techniques in order to gather information that can offer their clients sufficient evidence to support or disprove their claims.
Scope of Services
Generally speaking, police investigation services are limited to offences that are identified as crimes in South Africa. This means that private investigators are able to work on a broader scope of services, such as:
- Domestic/matrimonial investigations
- Investigations into individual activity
- Evidence gathering for adultery/infidelity suits
- Substance abuse suspicions
The South African Police Department is limited to an annual, tax-funded budget. This unfortunately means that some cases are not given the required resources needed to solve the case. The amount of cases also plays a big role, as there is often not enough time to be dedicated to individual cases. Private investigators, however, are paid by their clients. This gives them the opportunity to dedicate much-required resources and time in order to handle and solve each and every investigation.
Look no further than D&K Investigations and Risk Consultancy for all your private investigative needs. We provide a specialised range of investigation solutions to help you get the results you need, with zero limitations.


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Dailo meaning in English
Meaning of "Dailo"Viewed 862 times |
Get English meaning of word 'dailo'. Know Dailo in English. Get the translation of dailo in English language. Know the answer of question: What is the meaning of dailo in English language? You will find the English word for Nepali word 'dailo'. You can use this Nepali word in your daily life. Dailo is a Nepali word.


Networks > Interest Groups
What is an Interest Group?
An Interest Group is a group of planners with a common interest who wish to engage in work in that particular area. This involves sharing best practice, keeping people up to date with developments in the field, offering professional development for planners, promoting the planning voice within and outside of the sector, and providing communities of practice to which others wishing to find out more about that particular topic can be directed. Interest groups are open to all members, and you can join by updating your preferences in your online HESPA profile, ensuring that you tick the name of the Interest Group you wish to join.
As a guide, an Interest Group should:
 1. Have a lead member
 2. Hold meetings
 3. Link to the annual conference, if appropriate
 4. Produce resources for the website
 5. Review its own activity on an ongoing basis to ensure valuable outputs are being delivered and establish relevant next steps
Common features of an Interest Group:
 1. It is a defined, contactable group
 2. It provides a resource bank to those who are interested
 3. It has the ability to offer expertise
 4. It holds virtual sessions to share best practice and enable a forum for questions and discussion
 5. It performs the role of an advisory group
 6. It uses an online discussion forum
 7. It has a clear sense of remit
 8. It offers a sense of what members of the group can get out of it and fulfils these tangible outputs
Our current networks include:
Workload Management
Student Number Planning
Statutory Returns
Data Science
Scottish Planners Group:
Scottish Student Number Planning
Scottish Funding Council Interactions
Data and BI in Scotland
Strategy Development in Scotland
Risk Management in Scotland
Scottish Policy


text:
Elk Island National Park of Canada
Phenotypic Differences Between the Bison Subspecies
Historic range of plains and wood bison.© Parks Canada
The differences between plains and wood bison can be separated into two groups; pelage characters and structural characters. Plains bison tend to have pelage characters which are larger and more obvious than those of the wood bison. Whereas plains bison have large chaps, a full beard and neck mane and a well-demarcated cape, wood bison have no chaps, a thin pointy beard, a rudimentary neck mane and a cape that grades smoothly back to the loins. Structurally the highest point of the hump on a plains bison is directly over the front legs while the highest point of the wood bison is well forward of the front legs. There are differences in weights as well with the wood bison being considerably larger than the plains. The Park maintains a bison weight database going back to 1956 and during all that time there is only one record of a plains bison bull weighing more than 2000 pounds (909 kg) while over one-third of the wood bison bulls exceed this weight.
There has been some discussion as to whether the subspecies are simply ecotypes, and that if a wood bison was placed in plains bison habitat, or vice versa, it would assume the traits of the host bison, simply due to the environmental pressures under which it is placed. A large-scale phenotyping study was conducted during the early 1990s where almost every publicly managed bison herd (both plains and woods) was examined for its external phenotypic expression, and it proved that, despite the habitat in which they reside, they maintain the traits which characterize the subspecies. Recent research at the University of Alberta has conclusively proven a genetic difference between the two subspecies.PLAINS BISON
Plains bison bull.© Parks Canada / EI9912310025, 1991/12/31
- The highest point of the hump is directly over the front legs.
- Large thick chaps on the front legs.
- Thick pendulous beard.
- Full neck mane which extends below the chest.
- Sharply demarcated cape line behind the shoulder.
- Thick bonnet of hair between the horns.
- Cape is usually lighter in color than the woods.
- About one-third smaller than a wood bison of similar age.
Wood bison bull.© Parks Canada / EI9912310026, 1991/12/31
- Highest point of the hump is well forward of the front legs.
- Virtually no chaps on the front legs.
- A thin scraggly beard.
- The neck mane is short and does not extend much below the chest.
- The cape grades smoothly back towards the loins with little if any demarcation.
- The forelock lies forward in long strands over the forehead.
- The hair is usually darker, especially on the head.


Why do I feel small crystals or hard lumps inside my new Boveda?
A brand-new Boveda is pliable, jelly-like and "squishy." Sometimes you might also feel some small crystals or lumps inside the pack, which is totally normal. Your Boveda is still safe to use.
Here's why crystals can form inside a new Boveda: The signature formula inside Boveda is a saturated saltwater solution. We add all-natural salts and a food-safe thickener to purified water then seal it all in a leakproof membrane. When we combine the ingredients and fill the membrane, sometimes an excess of those blended salts will mix with the water. As a result, small salt crystals that feel like hard lumps can occasionally form. Additionally, changes in temperature or other conditions can create recrystallization of the salts. This can feel like regular table salt or occasionally like coarse sea salt.
Any crystals in Boveda won't impact the performance, effectiveness or shelf life of the 2-way humidity control. In the rare event that the crystals become sharp and puncture the pouch, please reach out to us. We'll make it right at no cost. We're good like that.


text:
Turning on the Enable Short Links for Processes feature allows administrators to share a direct short link to the initial form in a process. When this setting is enabled, follow the steps below to copy the short link for a process:
From the Edit Process Summary dropdown in the process, click the link icon next to the name of the process.
Make sure the toggle switch is green, indicating the link is active. Click the copy icon to copy the link to your clipboard. This can now be pasted into an email or other communication with applicants.
- If a user who has not already created a profile within the site uses this link, they will first be brought to the registration page.
- For a process with Restricted visibility, the applicant will not need to enter an Access Code if they use this short link.
The short link will lead to an "Inactive Link" message in the following instances:
- Process is turned off
- Not within the process start and end date range
- The process is set to Internal visibility
- Link has been deactivated in the process by an administrator


Understanding the Predecessor Tab
Predecessors (and their counterparts, successors) are how you as the project manager tell Project what the logical flow of tasks should be throughout your project. This tab of the Task Information dialog allows you to see all the tasks that are predecessors for the task currently being edited in the dialog. This section shows you how to create a new predecessor.
graphics/one_icon.jpg As in all tabs in this dialog, you can edit the task Name and Duration fields.
graphics/two_icon.jpg The grid on this tab lists all the tasks that are predecessors to the task named in the Name field.
graphics/three_icon.jpg The type of link is shown in the Type field. In this case, Define Requirements has a Finish-to-Start link to this task, meaning that the Define Requirements task must finish before the Write Specifications task can start.
graphics/four_icon.jpg The Lag field lets you define a span of days between the predecessor side of the link and the successor side of the link. This means that if you add a one-day lag on the link shown, Write Specifications cannot start until one full day after Define Requirements finishes.
Show Me. Microsoft Office Project 2003
Show Me Microsoft Office Project 2003
ISBN: _PHONE_
EAN: _PHONE_
Year: 2003
Pages: 204
flylib.com © 2008-2017.
If you may any questions please contact us: _EMAIL_


Witcher Wiki
Witcher Wiki
Witcher Wiki
the Armorer of the Order
The Armorer of the Order is more the name of the place, than of the individual. The "Σιδεράς του Τάγματος" himself comes from a long line of armorers. He and the "Order Merchant" run the establishment which can be found just opposite the steps leading to the slums of Βίζιμα's Συνοικία του Ναού, on Roper Street. Their main competition is Malcolm Stein.
They will politely tell anyone that they only deal with friends of the Order. Here is how you can tell if they will deal with you.
Έμπορος του Τάγματος[]
the Order merchant
The merchant sticks to mainly:
Σιδεράς του Τάγματος[]
the Σιδεράς του Τάγματος
The armorer, on the other hand, buys an amazing variety of goods:
And in a pinch, with some instructions and a healthy donation (70 oren(s) ) to the Order, the armorer can make a lightning rod.
Συνδεδεμένες αποστολές[]


Kemptville to Kingston distance, location, road map and direction
Kemptville is located in Canada at the longitude of -75.63 and latitude of 45.02. Kingston is located in Jamaica at the longitude of -76.8 and latitude of 17.99.
Distance between Kemptville and Kingston
The total straight line distance between Kemptville and Kingston is 3008 KM (kilometers) and 411.58 meters. The miles based distance from Kemptville to Kingston is 1869.3 miles. This is a straight line distance and so most of the time the actual travel distance between Kemptville and Kingston may be higher or vary due to curvature of the road.
Time Difference between Kemptville and Kingston
Kemptville universal time is -5.042 Coordinated Universal Time(UTC) and Kingston universal time is -5.12 UTC. The time difference between Kemptville and Kingston is 0.078 decimal hours. Note: Kemptville and Kingston time calculation is based on UTC time of the particular city. It may vary from country standard time, local time etc.
Kemptville To Kingston travel time
Kemptville is located around 3008 KM away from Kingston so if you travel at the consistant speed of 50 KM per hour you can reach Kingston in 60.17 hours. Your Kingston travel time may vary due to your bus speed, train speed or depending upon the vehicle you use.
Kemptville To Kingston road map
Kemptville is located nearly north side to Kingston. The given north direction from Kemptville is only approximate. The given google map shows the direction in which the blue color line indicates road connectivity to Kingston. In the travel map towards Kingston you may find enroute hotels, tourist spots, picnic spots, petrol pumps and various religious places. The given google map is not comfortable to view all the places as per your expectation then to view street maps, local places see our detailed map here.
Kemptville To Kingston driving direction
The following diriving direction guides you to reach Kingston from Kemptville. Our straight line distance may vary from google distance.
Travel Distance from Kemptville
Travelers and visitors are welcome to write more travel information about Kemptville and Kingston.
Name : Email :


Request Customer Contact Information for Use in Your Skill
To use this feature, you query the Alexa Customer Profile API. The Alexa Customer Profile API obtains information from the active default Alexa profile, which might or might not represent who is speaking to Alexa. To ask for consent to access the contact information of the recognized speaker, use the Person Profile API. For details, see Request Recognized Speaker Contact Information for Use in Your Skill.
For details on how to request device address information, see Enhance Your Skill With Address Information. For a sample code demo, see Customer Profile Demo.
Before you begin
 - Your skill must not be a child-directed skill. For details on child-directed skills, see Child-Directed Alexa skills.
Any of the requested information, such as customer name, email address, or phone number, might not be available to your skill when requested. As such, your skill code should handle missing information gracefully.
How to request customer contact information
 1. Configure your skill in the developer console to indicate that the skill requires customer contact information. When the customer enables the skill, the customer is prompted, in the Alexa app, to consent to provide the contact information. If the customer chooses to not grant these permissions when enabling your skill, you may request this information, when needed, during invocation by using a permissions card. Ensure your skill handles the situation gracefully if the customer refuses to grant permission to access this information.
 2. Obtain the apiAccessToken from the LaunchRequest that Alexa sends your skill when a customer invokes the skill. Don't store the apiAccessToken, because it expires. Instead, obtain the apiAccessToken fresh from each subsequent request.
Configure the skill to request customer permissions
 1. Edit your skill in the developer console.
 - Customer Name > Full Name
 - Customer Name > Given Name (the customer's first name)
 - Customer Email Address
 - Customer Phone Number
If you use SMAPI or the Alexa Skills Kit Command Line Interface (ASK CLI) instead of the developer console to manage your skill, edit the skill manifest to request the desired permissions.
Get the API access token
The apiAccessToken is nested in the System object, which is nested in the context object. To see the full body of the request, see Request Format.
 "context": {
 "System": {
 "apiAccessToken": "AxThk...",
 "apiEndpoint": "",
Thus: accessToken = this.event.context.System.apiAccessToken
Authorization: Bearer AxThk...6fnLok
New CardAskForPermissionsConsentCard
Sample response with permissions card
The permissions values can be as shown in the following table:
Full Namealexa::profile:name:read
Given Name (First Name)alexa::profile:given_name:read
Email Addressalexa::profile:email:read
Phone Numberalexa::profile:mobile_number:read
The following is a sample response for a card with a request for name and phone number.
 "version": "1.0",
 "response": {
 "card": {
 "type": "AskForPermissionsConsent",
 "permissions": [
Use Skill Permission Accepted events in your skill
Use Skill Permission Accepted events in your skill so that your skill is notified when the customer has granted permissions to the skill.
Test the API as you develop your skill
To test what happens when a customer has provided permissions to your skill, make sure that you have granted the contact permissions for your skill in the Alexa app. When you open the skill ("Alexa, open skill_name"), Alexa sends a LaunchRequest to your skill. If the customer has granted the permissions, you can obtain the apiAccessToken from the request.
To test what happens when a customer hasn't provided permissions to your skill, make sure you have not granted, or that you have revoked, contact permissions for your skill in the Alexa app. When you open the skill ("Alexa, open skill_name"), Alexa sends a LaunchRequest to your skill. This request contains the apiAccessToken value, but the apiAccessToken doesn't specify the correct permissions. If your skill passes this token to the Alexa Customer Profile API, the API returns a 403 Forbidden response code.
Sample message to prompt customer to grant permissions through permissions card
Fallback message when customer contact information is not available
When your skill requests the customer's contact information, and the customer grants it, this information might still be unavailable, such as if a customer hasn't provided phone number to Amazon. If the requested customer information is unavailable, the API returns a 204 (no content) response.
Sample message if resource_name is unavailable
Suggested best practices when customer contact information is unavailable
As a skill developer, you can determine the appropriate response when the customer hasn't set up contact information.
For a good customer experience, ensure that you consider the skill workflow for all the scenarios in which you fail to get the desired information.
Base URIs and geographic location of the skill
 "version": "1.0",
 "session": {},
 "context": {
 "System": {
 "application": {
 "user": {},
 "apiAccessToken": "AxThk...",
 "apiEndpoint": ""
 "request": {}
The examples in this document use the US endpoint
Get customer contact information
Full Name/v2/accounts/~current/settings/
Email Address/v2/accounts/~current/settings/
Request example
Accept: application/json
Authorization: Bearer MQEWY...6fnLok
Accept: application/json
Authorization: Bearer MQEWY...6fnLok
Request headers
Header Description Type Required
Response example
X-Amzn-RequestId: xxxx-xxx-xxx
Content-Type: application/json
 "countryCode" : "+1",
 "phoneNumber" : "_PHONE_"
The following is a list of return types (all JSON values).
Full Name"string"
Given Name"string"
Email Address"string"
Response headers
Header Description
Content-Type application/json
Possible responses
Response Description
200 OK Successfully retrieved the requested information.
204 No Content The query did not return any results.
401 Unauthorized The authentication token is malformed or invalid.
403 Unauthorized The authentication token doesn't have access to the resource.
500 Internal Error An unexpected error occurred.


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Continuing Education Quality Assurance Manager
- Job posted by American Speech-Language-Hearing Association
2200 Research Boulevard
The purpose of the position is to support the work of the American Speech-Language-Hearing Association's (ASHA) Continuing Education (CE) program by ensuring there is quality and consistency in the daily functions performed by the individuals in the CE Accounts Manager and CE Provider Manager positions This incumbent reports directly to the Associate Director of CE Operations and is a liaison between the CE Account Managers, the CE Provider Managers, and the Associate Director of CE Operations.
- Develop, implement, and maintain standard operating procedures, policies, and processes related to the day-to-day operations to ensure quality and consistency.
- Serve as the lead technical and informational resource to Accounts Manager and Provider Manager team members. Work with teams to facilitate calibration and decision-making.
- Train CE Accounts Managers and Provider Mangers on position responsibilities, service delivery techniques, ASHA CE policies and procedures, and systems utilization.
- Identify and facilitate process improvements. Use data and trends to recommend and implement changes to processes and procedures.
- Assist in generating, updating, and disseminating reports and task schedules. Manage and document daily scheduling changes to ensure office coverage.
- Oversee the customer service experience. Troubleshoot escalated issues.
- Operate as a Provider Manager and Account Manager for a small caseload of new Providers and Providers with compliance challenges, ensuring consistency in the onboarding and retraining processes for Providers.
- Ensure CE Providers understand and implement processes needed to adhere to internal system restrictions, CEB requirements, and adult learning best practices.
Knowledge Typically Acquired Through
- Bachelor's degree
- Supervisory or demonstrated leadership experience
- Experience working with accreditation or standard based programs or regulatory bodies is preferred.
- Quality management experience is preferred; Have used tools, concepts and methodologies related to Quality Assurance
Scope and Depth of Technical Skills/Knowledge
- Collect and analyze data to inform business decisions
- Use an AMS and/or CMS database management system; experience with netForum, preferred
- Train adults
- Proficiently use Microsoft Office Suite, specifically Microsoft Excel and/or program management software, to produce reports including graphs and pivot tables
- Produce training materials, presentations, and business correspondence
- Manage process improvements, program/project management, and/or standards implementation
- Use adult learning principles and continuing education related best practices and standards
Scope and Depth of Non-Technical Skills/Knowledge
- Take initiative
- Use critical thinking and planning skills
- Build strong relationships, and work independently and as part of a team, excellent interpersonal skills
- Use communication skills, both orally and in writing;
- Organize and prioritize multiple complex projects/tasks and efficiently manage workload; is detail oriented
Health, Vision, Dental Insurance, Short Term & Long Term Disability, 401k, Wellness Classes, Flextime, Flexplace, Telecommuting, Carpool, Annual Leave, Sick Leave, Paid Holidays
Minimum Education Required


What does pocock, edward mean?
Definitions for pocock, edward
Here are all the possible meanings and translations of the word pocock, edward.
The Nuttall Encyclopedia
 1. Pocock, Edward
 1. Chaldean Numerology
 The numerical value of pocock, edward in Chaldean Numerology is: 7
 2. Pythagorean Numerology
 The numerical value of pocock, edward in Pythagorean Numerology is: 1
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What is the Average Rank in League of Legends?
A prevalent thing we hear from League of Legends players is that they are "average." But what does that actually mean? Is it in relation to their skill, or perhaps time played? Well, let's find out!
What is the Most Common League of Legends Rank?
Statistically, the most average rank is Silver IV, and it holds about 11% of all players. Silver IV is the ninth rank in the League of Legends ranking system and the first rank of the Silver Division, which alone contains about 40% of the game's player base.
It's also the most popular division to be in.
Therefore, we could say that the Silver Division is a place for players representing average skills.
This division is also where the real tryhard begins, as players compete for additional end-of-season prizes. It bears mentioning that, by every season's end, the rank with the most players shifts to Gold IV, as more and more players manage to grind it out.
How Good is the Average LoL Player?
The skill of average League of Legends players has been climbing steadily over the years. Where in the early days of League of Legends, even knowing every champion was considered an accomplishment, nowadays the picture is a bit different, and far more demanding.
Average LoL players can be considered to have the following skills and knowledge:
- Having an established Champion pool,
- Knowing how to farm minions,
- Knowing the importance of objectives,
- Knowing which Champions are strong in the meta.
What Should Average LoL Players Learn?
Even though the largest amount of players is situated around the Silver and Gold divisions, the path to the ranked peak is long indeed.
Here are a few things that players in the Gold and Silver divisions lack:
- Adapting to enemy picks in draft,
- Pushing ally advantages,
- Punishing enemy mistakes,
- Not throwing the lead,
- Learning macro gameplay,
- Learning wave management,
- Learning how to close out a won game,
- Learning to play from a position of weakness, called playing from behind.
We do not doubt that the primary aspect differentiating an average player from a higher-ranked one is experience and time spent in the game wisely.
If you wonder what to do to get to an above-average level, just play the game, commit some time to practice, and learn from your mistakes without blaming others.


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To select all buildings that fall into a selected circular buffer with a 2000 radius you need this command:
SELECT * FROM Buildings WHERE ST_DWithin(geom, (SELECT ST_GeomFromText('POINT(0 0)', 26918)), 2000);
See this, for more examples.
I've gave you already the right answer!
To prove you I'll show the tests I've done before answering to you, on my test data (my SRID is 31700):
If you want to see the selected points in QGIS then you need to follow the images bellow:
So, I think that your center point coordinates are not [0, 0] and if you'll follow carefully my demonstration you'll obtain the proper results!
My tests showed me that it is possible a user to keep its data in a PostGIS table with the 4326 SRID, and to obtain a proper result, like above, using its own SRID (e.g. 26918).
In this case one my use this command:
SELECT * FROM Buildings WHERE ST_DWithin(ST_Transform(geom, 26918), (SELECT ST_GeomFromText('POINT(0 0)', 26918)), 2000);
Yet, in this case, I've noticed that the selected points are still in the 4326 SRID. Therefore, if you create a table based on this query, eventually, you need to update the table SRID to your own.
Here's what I've done (using my test data) prior to see the selected point in QGIS:
But, the newly created table has the 4326 SRID:
Therefore, we need to change it to our own:
(I've verified my solution, considering the buildings are points, polygons and multipolygons, and didn't noticed any other problems than those already presented here.)


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- See also: Easter Eggs (Skyrim)
The card is considerably cheap, and is suggested to be picked during the start of a game. It is not suggested to use the card on a creature with 1 health unless it is an emergency, due to the Shackle attribute of the card going to waste.
Arrow in the Knee should be used on cards with high attack powers, as it will prevent them from attacking the next turn, saving you health or your creatures' defense. If possible with the deck and cards available in your hand, the card should be used on enemies with high defenses, and combined with a wound-related card (i.e. Finish Off) to easily destroy them.
- The phrase "Arrow to the Knee" originated from Skyrim as a line of dialogue from Hold Guards, who would say "I used to be an adventurer like you. Then I took an arrow in the knee" when passing by the player. Eventually, it became a widespread meme, becoming an iconic legacy of Skyrim on modern culture. It can therefore be considered an easter egg.
- During the closed beta, the card was previously named Arrow to the Knee. However, this changed at some point before the beta opened.


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Definition of recompense :
1. An equivalent returned for anything done, suffered, or given; compensation; requital; suitable return.
2. To give in return; to pay back; to pay, as something earned or deserved.
3. To give recompense; to make amends or requital.
4. To render an equivalent to, for service, loss, etc.; to requite; to remunerate; to compensate.
5. To return an equivalent for; to give compensation for; to atone for; to pay for.
pay off, gratuity, premium, allowance, recoupment, honorarium, contribution, furbish up, mend, fix, pay, fee, reparation, resort, consideration, stipend, spend, indemnify, bushel, reward, finance, renovate, even off, invest in, down payment, reprisal, doctor, remediate, settlement, quittance, wages, damages, counterbalance, overcompensate, make up, remuneration, advance, repair, requital, satisfaction, fund, restore, payback, recreate, touch on, animate, indemnification, indemnity, reanimate, repay, quicken, disburse, revive, deposit, requite, restitution, vivify, salary, payment, even out, compensation, bear the cost/expense etc., amend, hire, earnings, repayment, remittance, pay out, revivify, put up, right, cover, even up
atone (part of speech: verb)
recompense (part of speech: verb)


text:
How Our Hats are Sized
Hats are measured by the inside circumference at the bottom of the hat's crown (the sweatband) and measured in centimeters. To make sure you have your correct hat size, you'll need to measure the circumference of your head or where you generally like to wear your hat. Do this by wrapping a measuring tape around the crown of your head, placing the tape one to two fingers width above your eyebrows and one finger above your ears. Alternatively, use a piece of string and then measure the length.
Whatever your measurement, add 1cm to determine your correct hat size. Example: head measurement of 56cm wears size 57 hat.


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The dimensions of LEGO brick are documented well, but what about DUPLO bricks? If have only found the general statements that DUPLO is twice as large as LEGO but no exact numbers. What about the thickness of walls and the space that must be subtracted at each side (0.2mm for LEGO), is it also just doubled?. If you compare the bottom of a LEGO 2x4 brick and a DUPLO 2x4 brick, there are also additional small walls that I have not found documented.
Update: Some dimensions of a DUPLO brick can be derived from the dimensions of a LEGO brick, which have been documented by Robert Cailliau among others:
Above and below a DUPLO 2x2 brick one can put two LEGO 2x4 bricks (or four 2x2 LEGO bricks). The outer walls of such stack seem to align perfectly, so the width and length of a DUPLO 2x2 brick is equal to the width of a LEGO 2x4 brick, which is 31.8mm (32mm-0.2mm). By putting DUPLO and LEGO side by side, one can also see that the DUPLO height without studs is twice of the size in LEGO (19.2mm). The LEGO studs below the DUPLO brick touch DUPLO walls, so DUPLO wall thickness is the same as LEGO wall thickness (either before spline walls were introduced to LEGO bricks or LEGO wall thickness plus the length of LEGO splines), which is 1.5mm. The DUPLO tube height is the height of the brick minus the height of a LEGO stud (which is somewhere between 1.6mm and 1.8mm). I'd better use the larger value, so the tubes start 1.8mm above the floor of the brick. From the top, LEGO tubes fit into DUPLO studs, so the stud inner diameter should equal to 6.51mm (8*√2 - 4.8$). But if you carefully look inside a DUPLO stud, this fitting is only achieved by four additional lugs that give a minimal inner diameter around 6mm to facilitate snapping into.
The remaining dimension include:
- stud outer diameter
- stud height
- tube inner diameter (but DUPLO tubes are not fully circular inside on a closer look!)
- tube outer diameter (also occurs at some other elements for instance as stem at #6510)
- spline length
Spline length can be derived from wall width and stud outer diameter. Tube outer diameter and stud outer diameter can also be computed from each other. So basically three dimensions are left to be explained. Comments and insights are welcome how more of the remaning dimensions can be derived from standard LEGO/DUPLO dimensions.


Dating and courtship in the philippines sex dating in rock island washington
Courtship always has marriage as its direct goal...Dating, a more modern approach, begins when either the man or the woman initiates a more-than-friends relationship with the other, and then they conduct that relationship outside of any oversight or authority. Christian minister Patricia Bootsma delineates this distinction, writing that in contrast to the modern conception of dating, in "courtship, time together in groups with family or friends is encouraged, and there is oversight by and accountability to parents or mentors".Courtship is used by a number of theorists to explain gendering processes and sexual identity.Scientific research into courtship began in the 1980s after which time academic researchers started to generate theories about modern dating practices and norms.Unlike what is regularly seen in other societies, it takes a far more subdued and indirect approach.It is complex in that it involves stages, and it is considered normal for courtship to last a year or longer.
dating and courtship in the philippines-11dating and courtship in the philippines-75dating and courtship in the philippines-17dating and courtship in the philippines-40
During courtship, a couple get to know each other and decide if there will be an engagement or other such agreement.In some societies, the parents or community propose potential partners, and then allow limited dating to determine whether the parties are suited.In Japan, there is a such type of courtship called Omiai, with similar practices called "Xiangqin" (相親) in the Greater China Area.The average duration of courtship varies considerably throughout the world.Furthermore, there is vast individual variation between couples.
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thoughtful - definition and synonyms
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 1. 1
 Caroline is such a thoughtful young woman.
 'I brought you some tea.' 'That's very thoughtful of you.'
 2. 2
 thinking seriously about something
 1. a.
 used about someone's face or expression
 Her face took on a thoughtful expression.
derived word
noun [uncountable]


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Yes, you read it right, you can turn your android phone into wireless Speaker. You can use your android phone as a speaker and play music by using laptop or PC. If suppose the speaker of your laptop or PC is not working properly in this case you can use your android phone as a speaker for your device. Follow the below mention steps to achieve this.
It's a very simple task. You just need four things to turn your android phone into wireless speaker:
- Android Phone.
- PC or Laptop.
- Wifi Connection.
- Soundwire Software.
Steps to Turn your Android Phone into wireless Speaker.
In order to turn your android phone into wireless speaker you just need to follow these short and simple steps.
1. First, download the Soundwire software in a PC as well as in android phone and install as well. You can also use some other software rather than Sowundwire but I recommend you to use Soundwire only because it's sound quality is good and there is very less sound lacking.
2. Then open the Soundwire software on PC and save the server address i.e. 192.168.1.8 for later use.
As you can see in the above screenshot the status is disconnected because our android phone is not connected to it. You can also change the input method like a speaker, microphone etc.
3. Now, open the Soundwire application in android phone and enter the server address that is present in Soundwire software in PC i.e. 192.168.1.8.
4. You just need to click on the box above the server to turn your android phone into wireless Speaker. i.e.
and the colour of that box will change and it will show that your android device is successfully turned into a wireless speaker. i.e.
You can also see the connection status is now connected, in the Soundwire desktop application.


Bentsen surname meaning, origin - danish surname Bentsen
The meaning of the surname Bentsen is: Means "son of BENT".
The surname Bentsen is present in the lists: Surnames, Danish surnames, Surnames start with letter B.
Number for the surname Bentsen
The number of the surname seven (7) characterizes talented people who are able to achieve great success both in the scientific field and in the Humanities. The ability to think, analyze, and plan their actions, and the ability to attract others, helps people with the surname Bentsen become the head of various groups of people and organizations.
Stones of the number 7 for the surname Bentsen: malachite, jade, carnelian (carnelian), pearl, jet, obsidian, hematite (Bloodstone), onyx, opal, amethyst, emerald, Selenite, flint, rhodonite, fluorite.
Planet number 7: Neptune.
Zodiac Signs number 7: Pisces, Virgo.
More: number of the surname Bentsen
Meaning of letters in the surname Bentsen
Compatible with the surname Bentsen danish surnames
Berntsen Danish surnames, Bjarnesen Danish surnames, Dahl Danish surnames, Hansen Danish surnames, Hermansen Danish surnames, Johannessen Danish surnames, Knudsen Danish surnames, Lang Danish surnames, Larson Danish surnames, Olesen Danish surnames, Ostergard Danish surnames, Paulsen Danish surnames, Riber Danish surnames, Sander Danish surnames, Vinter Danish surnames, Winther Danish surnames...
Also check the compatibility of other surnames with the surname Bentsen.
Famous people with the surname Bentsen
 1. Lloyd Bentsen
 Lloyd Millard Bentsen Jr. (February 11, 1921 – May 23, 2006) was an American politician who was a four-term United States Senator (1971–1993) from Texas...
 2. SS Edmund Fitzgerald
 SS Edmund Fitzgerald was an American Great Lakes freighter that sank in Lake Superior during a storm on November 10, 1975, with the loss of the entire...
 3. Bentsen-Rio Grande Valley State Park
 Bentsen-Rio Grande Valley State Park is located at 2800 S. Bentsen Palm Drive (FM 2062) south of the city of Mission in Hidalgo County in the U.S. state...
 4. Ken Bentsen Jr.
 Kenneth Bentsen Jr. (born June 3, 1959, in Houston, Texas) is a former congressman from Texas, serving four terms from 1995 to 2003. He is the nephew...
 5. Allan Bentsen
 Allan Bentsen (born August 21, 1968) is a Danish table tennis player. He won the European championship for national teams with Michael Maze and Finn Tugwell...
 6. William Bentsen
 William "Bill" Bentsen (February 18, 1930 – December 25, 2020) was an American sailor and Olympic champion. Bentsen was born in Chicago, Illinois. He received...
 7. Ivar Bentsen
 Ivar Bentsen (13 November 1876 – 21 May 1943) was a Danish architect and educator. He was a central figure in the Bedre-Byggeskik movement and succeeded...
 8. Beint Bentsen
 Beint Kristian Bentsen (25 July 1917 – 2003) was a Norwegian banker and politician for the Christian Democratic Party. He is best known as county mayor...
 9. Eldijana Aganović
 Eldijana Aganović (born 20 November 1971) is a Croatian table tennis player. She competed in the 1996 and 2000 Summer Olympics. Evans, Hilary; Gjerde,...
 10. Christen Bentsen Schaaning
 Christen Bentsen Schaaning (Kristen Bentsen Skaaning) (c. _PHONE_) was a Norwegian clergyman. He served as parish priest of Avaldsnes Church (Avaldsnes...


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- Old Dominion Surveyor
- Find A Surveyor
The Virginia Association of Surveyors (VAS) was established in 1948 to promote the best practices of our members, provide a forum for discussion, and offer professional development courses to licensed, practicing surveyors in the Commonwealth. Additionally, VAS has expanded its reach to support future surveyors, technicians, and the public to further recognize the contributions the surveying profession provides to the community.
VAS serves the public and the profession through outreach and activities, such as conferences, scholarships, and advocacy. VAS is an affiliate of the National Society of Professional Surveyors (NSPS) and American Association for Geodetic Surveying (AAGS).


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How to register a marriage in Nigeria
Following is a guideline on how to register a marriage in the Federal Republic of Nigeria under Nigerian law. Please note that Nigerian authorities do not usually require an Australian citizen to provide a Certificate of No Impediment to Marriage (CNI) when registering a marriage.
- Marriage is registered at a local public registry, which requires a Letter of Marriage Intention and payment of a fee of Naira 2,000.
- A person under 18 years of age, who wishes to register a marriage, is required to present a letter of consent from his or her parents.
- The registry will display the Letter of Marriage Intention for 21 days on a public notice board.
- Provided that no objection to the intended marriage is made during the 21 day period, a couple may then register their marriage.
- Birth certificates or official documents showing the ages of the couple are required together with the results of HIV and genotype tests.
- A divorcee must produce a divorce certificate, while a widow or a widower is required to present the death certificate of the late spouse.
- A marriage registrar may witness the exchange of oaths by the couple.


Blue Aspen Originals
aspen leaf
Fine soaps hand crafted in small batches
Soap on a Rope
Making soap on a rope is easy especially if you're making one out of soap scraps. That's right. We're using soap scraps to make soap on a rope either for your personal use or to give to someone else. Soap on a rope is something you can do to make use of those soap scraps instead of just throwing them away or letting it soak in your soap dish. Let's begin making your very first soap on a rope with the following steps.
First, you will need to prepare the materials needed for soap on a rope. These are the soap scraps, warm water, and nylons. You'll need 1 cup full of soap scraps to make soap on a rope. Now that you've gathered all the materials, let's start by breaking up the soap scraps into tiny little pieces. It will be best to use a grater or knife. That's how small it should get. Now, prepare a mixing bowl and place the grated soap scrapes in the bowl. Next, prepare a half cup of warm water. Pour it into the bowl and let it stand for about an hour.
After an hour, start kneading the soap and the water together as if you are kneading dough. Make sure to make it smooth and come up with the consistency of thick dough. If needed, add more warm water as needed. Make sure to add only a little at a time. You can use a tablespoon to make sure you only add little amount of water. If you want to add color, add a few drops of food coloring to the mixture until the desired color is achieved. Blend well. Now, it's time to shape the mixture into a ball. Lay a piece of wax paper on the table and set the soap on top. It will take at least 24 hours to dry.
Once dry, cut about 12 inches nylon and create a loop around the soap ball. Tie the ends of the nylon above the soap ball. Now, you can hang your soap on a rope in the shower!


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Let $A$ be a non-empty set and consider $S(A)$ the set of all bijective functions from $A$ to itself, with composition as group operation. Fix $a_0 \in A$. Define $H = \{f \in S(A): f(a_0) = a_0\}$. Prove that $H$ is a subgroup of $S(A)$.
does this tell me $a_0$ is an identity or that $f(a_0)$ is an identity? I am assuming I need to use something to do with subgroup theorems but I am having trouble understanding how to use these.
Ok that makes more sense since $f(a_0)$ = $a_0$ and $g(a_0)$ = $a_0$ we can conclude that $f^{-1}$ $f(a_0)$ = $f^{-1}$ $a_0$ so we know $f^{-1}$ is in the set? So $f^{-1}$ $g(a_0) $= $a_0$ and the by the theorem we may conclude $H$ is a subgroup of G?
As a side note would love to know WHERE you guys find the element signs and how to put subscripts on things if you could link me to a list of stuff you can put into here with some instructions.
Someone has pointed me a direction a few times but i have never found something I understood. I am not a programer but if I can find a lost of things I am sure I can figure it out usually I just search until I find a post with what I want click edit and take the symbols I want but if theirs instructions somewhere I would very much appreciate that.
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1 – Jim Feb 3 '13 at 20:07
3 Answers 3
up vote 2 down vote accepted
$H = \{f \in S(A): f(a_0) = a_0\}$ is the set of bijective functions in $S(A)$ such that $f$ maps $a_0$ to $a_0$.
Here, $a_0$ is a fixed element which every bijective function in $S(A)$ that maps $a_0$ to itself is a member. $H$ includes the identity map/function, but not all $f \in H$ are the identity function.
To prove $H$ is a subgroup of $S(A)$:
 - Clearly, $H$ includes as its identity $f_I$, the identity map of $S(A)$, since $f_I(a_0)$ is clearly $a_0$.
 - Now show that for any $f, g \in H$, $f\circ g \in H$: i.e., show that $H$ is closed under the function composition.
 - Show that for any $f \in H, f^{-1} \in H$. Hint: This must be the case, as every $f \in H$ is bijective, and if $f \in H$, then $f^{-1}$ exists, and since $f\in H$, $f(a_0) = a_0$ and $f^{-1}(f(a_0)) = f^{-1}(a_0) = f_I(a_0) = a_0$, since by definition, $f^{-1}\circ f = f_I$, so $f^{-1} \in H$
Then you will have shown $\,H\,$ is a subgroup of $\,S(A)$.
As for your second question (or aside), you might want to visit MathJax/LaTeX: a tutorial and "bookmark" it as a favorite!
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Hint: To check something is a subgroup, it suffices to show that $H$ is nonempty (this clear since the identity function is an element [why?]), the composition of two functions is an element of the group (also easy to argue since every function fixes $a_0$), and that the inverse of a function is an element of the group (which follows because each element is a bijection).
I leave the details to you, but hopefully with what is given above, you can work through this mostly on your own.
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The standard way to show that something is a subgroup is to show:
 1. It is nonempty
 2. If $f, g \in H$ then $fg^{-1} \in H$
I'll leave (1) to you and give you a hint for (2). If $f, g \in H$ then you know $f(a_0) = a_0$ and $g(a_0) = a_0$. Apply the function $fg^{-1}$ to $a_0$. The result should be $a_0$ and once you've shown this you can conclude that $fg^{-1} \in H$.
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Your Answer


What is Independent Chip Model in Poker?
The Independent Chip Model (ICM), is a calculation which allows players to estimate the value of their stack at any given point in the tournament. ICM calculations evaluate a player's chip stack and place a monetary value on it based on tournament payouts.
Want to learn the strategic value of ICM? Check out this article:
ICM Poker Introduction: What Is The Independent Chip Model?
« View All Poker Terms
Put Your Skills to the Test with a Quick Poker Quiz!


Take the 2-minute tour ×
I have some problems with the equivalence of definitions of orientation. I know two definitions of orientation, namely:
 - A surface is orientable if it contains no 1-sided curves (a 1-sided curve in a combinatorical surface $F$ is a curve such if $p^{-1}(C)$ has just one component with $p:F'\rightarrow F$ and $F'$ the surface we obtain by cutting $F$ along $C$)
Also there exists the following lemma: A one-sided curve is always non-seperating (non-seperating means that the number of components of $F'$ has the same as $F$). Can we use this fact? And why is that true? From my point of view one can prove this easy with contradiction,true?!
Now the second definition:
 - An orientation of a closed combinatorial surface F is an assignment of a clockwise or anticlockwise \circulation" to each face (really an ordering of its vertices, considered up to cyclic permutation), such that at any edge, the circulations coming from the two incident faces are in opposition.
Now i want to show directly that a surface has an orientation if and only if it is orientable in the sense that it contains no 1-sided curves.
Can someone help me with this question? Thank you!
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1 Answer
Assume $F$ is oriented in the sense of the second definition. Let $C$ be a curve. Wlog.(!) the curve runs along edges. The map $p^{-1}(C)\to\{-1,+1\}$ that maps a point to $+1$ if the "current" edge at that point is in forward direction of $C$ and to $-1$ if it is in reverse, is well defined (must be checked at vertices) and continuous. As each edge belongs to two faces and is differently oriented for these, ther exist both edges yielding $+1$ and edges yielding $-1$, hence $p^{-1}(C)$ has (at least) two connected components. Hence no one-sided curve exists.
The other direction is a bit more complicated if one wants to be formally exact, so the following is rather a sketch of an idea: Assume $F$ is oriented in the sense of the first definition. Select an arbitrary face and orient its edges. Extend this face by face to the whole surface by checking faces having at least one edge already oriented. If ever a conflict arises (i.e. the next step would orient an edge differently from an already given orientation by its other face), we find a onesided curve as follows: There is a sequence of faces between the conflicting faces that runs within alrady oriented faces. This also determines a sequence of edges (those that are shared by subsequent faces in this sequence). Join the midpoints of these edges to obtain a closed curve (i.e. starting and ending at the conflicting edge). Using the orientation given to the edges crossed along its way, we get a notion of "left" and "right" of the curve, which gets "flipped" by completely traversing the curve, thus showing that $p^{-1}(C)$ is connected.
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