text:
# Properties

 Label 304.3.e.d Level $304$ Weight $3$ Character orbit 304.e Analytic conductor $8.283$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$304 = 2^{4} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 304.e (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.28340003655$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-13})$$ Defining polynomial: $$x^{2} + 13$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 19) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## $q$-expansion

Coefficients of the $$q$$-expansion are expressed in terms of $$\beta = \sqrt{-13}$$. We also show the integral $$q$$-expansion of the trace form.

 $$f(q)$$ $$=$$ $$q + \beta q^{3} + 4 q^{5} + 5 q^{7} -4 q^{9} +O(q^{10})$$ $$q + \beta q^{3} + 4 q^{5} + 5 q^{7} -4 q^{9} + 10 q^{11} + \beta q^{13} + 4 \beta q^{15} + 15 q^{17} + ( 6 - 5 \beta ) q^{19} + 5 \beta q^{21} -35 q^{23} -9 q^{25} + 5 \beta q^{27} + 5 \beta q^{29} + 10 \beta q^{31} + 10 \beta q^{33} + 20 q^{35} -6 \beta q^{37} -13 q^{39} + 10 \beta q^{41} + 20 q^{43} -16 q^{45} -10 q^{47} -24 q^{49} + 15 \beta q^{51} -21 \beta q^{53} + 40 q^{55} + ( 65 + 6 \beta ) q^{57} -5 \beta q^{59} -40 q^{61} -20 q^{63} + 4 \beta q^{65} -11 \beta q^{67} -35 \beta q^{69} -30 \beta q^{71} + 105 q^{73} -9 \beta q^{75} + 50 q^{77} + 10 \beta q^{79} -101 q^{81} + 40 q^{83} + 60 q^{85} -65 q^{87} + 5 \beta q^{91} -130 q^{93} + ( 24 - 20 \beta ) q^{95} + 34 \beta q^{97} -40 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 8q^{5} + 10q^{7} - 8q^{9} + O(q^{10})$$ $$2q + 8q^{5} + 10q^{7} - 8q^{9} + 20q^{11} + 30q^{17} + 12q^{19} - 70q^{23} - 18q^{25} + 40q^{35} - 26q^{39} + 40q^{43} - 32q^{45} - 20q^{47} - 48q^{49} + 80q^{55} + 130q^{57} - 80q^{61} - 40q^{63} + 210q^{73} + 100q^{77} - 202q^{81} + 80q^{83} + 120q^{85} - 130q^{87} - 260q^{93} + 48q^{95} - 80q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$$.

 $$n$$ $$97$$ $$191$$ $$229$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## Embeddings

For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.

For more information on an embedded modular form you can click on its label.

Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
113.1
 − 3.60555i 3.60555i
0 3.60555i 0 4.00000 0 5.00000 0 −4.00000 0
113.2 0 3.60555i 0 4.00000 0 5.00000 0 −4.00000 0
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
19.b odd 2 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 304.3.e.d 2
3.b odd 2 1 2736.3.o.d 2
4.b odd 2 1 19.3.b.b 2
8.b even 2 1 1216.3.e.h 2
8.d odd 2 1 1216.3.e.g 2
12.b even 2 1 171.3.c.b 2
19.b odd 2 1 inner 304.3.e.d 2
20.d odd 2 1 475.3.c.b 2
20.e even 4 2 475.3.d.b 4
57.d even 2 1 2736.3.o.d 2
76.d even 2 1 19.3.b.b 2
76.f even 6 2 361.3.d.b 4
76.g odd 6 2 361.3.d.b 4
76.k even 18 6 361.3.f.d 12
76.l odd 18 6 361.3.f.d 12
152.b even 2 1 1216.3.e.g 2
152.g odd 2 1 1216.3.e.h 2
228.b odd 2 1 171.3.c.b 2
380.d even 2 1 475.3.c.b 2
380.j odd 4 2 475.3.d.b 4

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
19.3.b.b 2 4.b odd 2 1
19.3.b.b 2 76.d even 2 1
171.3.c.b 2 12.b even 2 1
171.3.c.b 2 228.b odd 2 1
304.3.e.d 2 1.a even 1 1 trivial
304.3.e.d 2 19.b odd 2 1 inner
361.3.d.b 4 76.f even 6 2
361.3.d.b 4 76.g odd 6 2
361.3.f.d 12 76.k even 18 6
361.3.f.d 12 76.l odd 18 6
475.3.c.b 2 20.d odd 2 1
475.3.c.b 2 380.d even 2 1
475.3.d.b 4 20.e even 4 2
475.3.d.b 4 380.j odd 4 2
1216.3.e.g 2 8.d odd 2 1
1216.3.e.g 2 152.b even 2 1
1216.3.e.h 2 8.b even 2 1
1216.3.e.h 2 152.g odd 2 1
2736.3.o.d 2 3.b odd 2 1
2736.3.o.d 2 57.d even 2 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{3}^{\mathrm{new}}(304, [\chi])$$:

 $$T_{3}^{2} + 13$$ $$T_{5} - 4$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T^{2}$$
$3$ $$13 + T^{2}$$
$5$ $$( -4 + T )^{2}$$
$7$ $$( -5 + T )^{2}$$
$11$ $$( -10 + T )^{2}$$
$13$ $$13 + T^{2}$$
$17$ $$( -15 + T )^{2}$$
$19$ $$361 - 12 T + T^{2}$$
$23$ $$( 35 + T )^{2}$$
$29$ $$325 + T^{2}$$
$31$ $$1300 + T^{2}$$
$37$ $$468 + T^{2}$$
$41$ $$1300 + T^{2}$$
$43$ $$( -20 + T )^{2}$$
$47$ $$( 10 + T )^{2}$$
$53$ $$5733 + T^{2}$$
$59$ $$325 + T^{2}$$
$61$ $$( 40 + T )^{2}$$
$67$ $$1573 + T^{2}$$
$71$ $$11700 + T^{2}$$
$73$ $$( -105 + T )^{2}$$
$79$ $$1300 + T^{2}$$
$83$ $$( -40 + T )^{2}$$
$89$ $$T^{2}$$
$97$ $$15028 + T^{2}$$


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# How to update weights in a neural network using gradient descent with mini-batches?

How does gradient descent work for training a neural network if I choose mini-batch (i.e., sample a subset of the training set)? I have thought of three different possibilities:

1. Epoch starts. We sample and feedforward one minibatch only, get the error and backprop it, i.e. update the weights. Epoch over.

2. Epoch starts. We sample and feedforward a minibatch, get the error and backprop it, i.e. update the weights. We repeat this until we have sampled the full data set. Epoch over.

3. Epoch starts. We sample and feedforward a minibatch, get the error and store it. We repeat this until we have sampled the full data set. We somehow average the errors and backprop them by updating the weights. Epoch over.

Mini-batch is implemented basically as you describe in 2.

1. Epoch starts. We sample and feedforward a minibatch, get the error and backprop it, i.e. update the weights. We repeat this until we have sampled the full data set. Epoch over.

Assuming that the network is minimizing the following objective function: $$\frac{\lambda}{2}||\theta||^2 + \frac{1}{n}\sum_{i=1}^n E(x^{(i)}, y^{(i)}, \theta)$$

This is essentially the weights update step

$$\theta = (1 - \alpha \lambda) \theta - \alpha \frac{1}{b}\sum_{k=i}^{i+b-1} \frac{\partial E}{\partial \theta}(x^{(k)}, y^{(k)}, \theta)$$

where the following symbols mean:

$E$ = the error measure (also sometimes denoted as cost measure $J$)

$\theta$ = weights

$\alpha$ = learning rate

$1 - \alpha \lambda$ = weight decay

$b$ = batch size

$x$ = variables

You loop over the consecutive batches (i.e. increment by $b$) and update the weights. This more frequent weight updating combined with vectorization is what allows mini-batch gradient descent to tend to converge more quickly than either generic batch of stochastic methods.

• Two comments: 1) the update rule $\theta_j = ...$ assumes a particular loss function the way that you've written it. I suggest defining the update rule using $\nabla h_0(x)$ instead so that it is generic. 2) the update rule does not have a weight decay (also for the sake of generality), I would write it with the weight decay.
– Sobi
Dec 18, 2015 at 19:39
• @Sobi, good point about $\nabla h_0(x)$, I am just so used to that assumed loss function. However I am not sure exactly what you mean when you say weight decay? Are you referring to the division by the batch size? Feel free to provide such a generalized function in an edit. Dec 18, 2015 at 19:47
• Thanks, i realize you have used a quadratic error function, thats not a problem. Could you mb refer me to a publication that discusses this in details?
– Alex
Dec 18, 2015 at 20:10
• @Sobi, regarding your edit, is $n$ supposed to be batch size? Also, I am unfamiliar with the l2 norm notation. Dec 18, 2015 at 21:06
• @cdeterman, $n$ is the number of all training samples. Note that $n$ only appears in the original objective function (i.e. $\frac{\lambda}{2}||w||^2 + ...$).
– Sobi
Dec 18, 2015 at 21:09

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In this paper, we present Paranom, a parallel anomaly dataset generator. We discuss its design and provide brief experimental results demonstrating its usefulness in improving the classification correctness of LSTM-AD, a state-of-the-art anomaly detection model.
This short paper describes our ongoing research on Greenhouse – a zero-positive machine learning system for time-series anomaly detection.
Classical anomaly detection is principally concerned with point-based anomalies, anomalies that occur at a single data point. In this paper, we present a new mathematical model to express range-based anomalies, anomalies that occur over a range (or period) of time.
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Stragglers are commonly believed to have a great impact on the performance of big data system. However, the reason to cause straggler is complicated. Previous works mostly focus on straggler detection, schedule level optimization and coarse-grained cause analysis. These methods cannot provide valuable insights to help users optimize their programs. In this paper, we propose BigRoots, a general method incorporating both framework and system features for root-cause analysis of stragglers in big data system. BigRoots considers features from big data framework such as shuffle read/write bytes and JVM garbage collection time, as well as system resource utilization such as CPU, I/O and network, which is able to detect both internal and external root causes of stragglers. We verify BigRoots by injecting high resource utilization across different system components and perform case studies to analyze different workloads in Hibench. The experimental results demonstrate that BigRoots is effective to identify the root cause of stragglers and provide useful guidance for performance optimization.
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text: This means that the turning point is located exactly half way between the x x -axis intercepts (if there are any!). Graph quadratic function: $y = \frac{x^2}{2} - 3x - 4$. You can probably guess from the name what Turning Point form is useful for. There are two methods to find the turning point, Through factorising and completing the square.. Make sure you are happy with the following topics: HOW TO FIND THE VERTEX Based on Stephen Wolfram's … Vertex Calculator is a free online tool that displays the coordinates of the vertex point for the given parabola equation. You can sketch quadratic function in 4 steps. Welcome to MathPortal. About the quadratic … Where are the turning points on this function...? CALCULATOR. For example, the y -intercept of g(x) = (x − 1)2 + 5 is determined by setting x = 0 : g(x) = (x − 1)2 + 5 g(0) = (0 − 1)2 + 5 = 6 This gives the point (0; 6). Transformations of the graph of the quadratic can be explored by changing values of a , h and k . it relies on the assumption that if the derivative is 0 at some point, it is an extremum value. The minimum value of y is 0 and it occurs when x = 0. Here is a typical quadratic equation that describes a parabola. Factoring-polynomials.com makes available insightful info on standard form calculator, logarithmic functions and trinomials and other algebra topics. How it works: Just type numbers into the boxes below and the calculator will automatically calculate the equation of line in standard, point slope and slope intercept forms. The graph below shows a quadratic function with the following form: $$y = ax^2 + q$$. It includes several exam style questions I will explain these steps in following examples. Enter quadratic equation in standard form:--> x 2 + x + This solver has been accessed 2391430 times. You therefore differentiate f(x) and equate it to zero as shown below. You therefore differentiate f (x) and equate it to zero as shown below. Example 1 . Quadratic function plotter. 2. y = x 4 + 2 x 3. Note: The graph is a parabola which opens upwards. Shows you the step-by-step solutions using the quadratic formula! This idea enables us to define the discriminant of a cubic x 3 + px + q = 0 or any higher order equation. Wednesday, February 21, 2018 " It would be nice to be able to draw lines between the table points in the Graph Plotter rather than just the points. Expressing a quadratic in vertex form (or turning point form) lets you see it as a dilation and/or translation of . ax 2 + bx + c = 0. a = b = c = Fractional values such as 3/4 can be used. Example (Click to try) 2 x 2 − 5 x − 3 = 0. This calculator will solve your problems. To graph a parabola, visit the parabola grapher (choose the "Implicit" option). Log InorSign Up. The calculator solution will show work using the quadratic formula to solve the entered equation for real and complex roots. turning points f (x) = √x + 3 turning points f (x) = cos (2x + 5) turning points f (x) = sin (3x) Details. The numbers a, b, and c are the coefficients of the equation and may be … quadratic expansion calculator: turning point formula quadratic: turning point formula for parabola: quadratic formula with imaginary numbers calculator: quadratic zeros calculator: to solve quadratic equation: solving quadratic equations by rearranging and taking square roots: quadratic equation formula grade 9: quadratic function calculator graph \text{Slope } = \frac{ y_2 - y_1 } { x_2 - x_1 } Computing a quadratic function out of three points Enter three points. A quadratic in standard form can be expressed in vertex form by completing the square. CHARACTERISTICS OF QUADRATIC EQUATIONS 2. How to find the turning point of a parabola: The turning point, or the vertex can be found easily by differentiation. There are two methods to find the turning point, Through factorising and completing the square. Free quadratic equation calculator - Solve quadratic equations using factoring, complete the square and the quadratic formula step-by-step This website uses cookies to ensure you get the best experience. Therefore the turning point of the quadratic function $$f(x) = a(x+p)^2 + q$$ is $$(-p;q)$$. The calculator will try to complete the square for the given quadratic expression, ellipse, hyperbola or any polynomial expression, with steps shown. The graph of the quadratic function f(x)=ax2+bx+c is a parabola. Calculate the values of $$a$$ and $$q$$. Two points on the parabola are shown: Point A, the turning point of the parabola, at $$(0;4)$$, and Point B is at $$\left(2; \frac{8}{3}\right)$$. This means, you gotta write x^2 for . Quadratic equations (Minimum value, turning point) 1. How it works: Just type numbers into the boxes below and the calculator will automatically calculate the equation of line in standard, point slope and slope intercept forms. Please tell me how can I make this better. An algebra calculator that finds the roots to a quadratic equation of the form ax^2+ bx + c = 0 for x, where a \ne 0 through the factoring method.. As the name suggests the method reduces a second degree polynomial ax^2+ bx + c = 0 into a product of simple first degree equations as illustrated in the following example:. Using calculus, the vertex point, being a maximum or minimum of the function, can be obtained by the coefficients of the function. 3. (Increasing because the quadratic coefficient is negative, so the turning point is a maximum and the function is increasing to the left of that.) Quadratic Graph (Turning point form) Quadratic Graph (Turning point form) Log InorSign Up. The name comes from "quad" meaning square, as the variable is squared (in other words x 2).. This video explains how completing the square can be used to find turning points of quadratic graphs. to check ). Mathepower calculates the quadratic function whose graph goes through those points. Free quadratic equation calculator - Solve quadratic equations using factoring, complete the square and the quadratic formula step-by-step The coordinates of the turning point and the equation of the line of symmetry can be found by writing the quadratic expression in completed square form. Turning points. The vertex of a parabola is the place where it turns; hence, it is also called the turning point. Come to Polymathlove.com and discover division, square and several other algebra topics A quadratic function can be written in turning point form where .Transformations of the graph of the quadratic can be explored by changing values of a, h and k. The parabola can either … [3] 2020/05/21 06:42 Female / Under 20 years old / High-school/ University/ Grad student / A little / Calculator Use. This calculator will find either the equation of the parabola from the given parameters or the axis of symmetry, eccentricity, latus rectum, length of the latus rectum, focus, vertex, directrix, focal parameter, x-intercepts, y-intercepts of the entered parabola. If a = 0, then the equation is linear, not quadratic, as there is no ax² term. Where are the turning points...? $. Example: For use technology to find the turning point correct to two decimal places. Graphs of quadratic functions have a vertical line of symmetry that goes through their turning point.This means that the turning point is located exactly half way between the x-axis intercepts (if there are any!).. The 3rd form that quadratics can be written in is f(x)=a(x-h) 2 +k This is called Turning Point Form. ax^2+ bx + c = (x+h)(x+k)=0, where h, k are constants. If a search doesn't return the item you were looking for, try a search using a short search term such as aircraft type in the tag box (clear the other search fields). Quadratic. Two Point Form Calculator With Detailed Explanation. ,$\color{blue}{\text{ 2r3 } = 2\sqrt{3}} $8. Given the 3 points you entered of (25, 2), (23, 4), and (8, 1), calculate the quadratic equation formed by those 3 pointsCalculate Letters a,b,c,d from Point 1 (25, 2): b represents our x-coordinate of 25 a is our x-coordinate squared → 25 2 = 625 c is always equal to 1 Often we have a set of data points from observations in an experiment, say, but we don't know the function that passes through our data points. Fractions should be entered with a forward slash such as '3/4' for the fraction $$\frac{3}{4}$$. Only if it can be put in the form ax 2 + bx + c = 0, and a is not zero.. Sketch the graph of the quadratic function, In this case we have$ a=1, b=2 $and$c=-3$. The numerals a, b, and c are coefficients of the equation, and they represent known numbers. In algebra, a quadratic equation is any polynomial equation of the second degree with the following form: ax 2 + bx + c = 0. where x is an unknown, a is referred to as the quadratic coefficient, b the linear coefficient, and c the constant. So, in this case we will plot the graph using only two points. Two Point Form Calculator With Detailed Explanation 4. y x2 7x 4 TI-Nspire CAS keystrokes TI-Nspire CAS screens Turning points may be found in several ways. As we pointed out when discussing quadratic equations, when the leading term of a polynomial function, ${a}_{n}{x}^{n}$, ... A turning point is a point of the graph where the graph changes from increasing to decreasing (rising to falling) or decreasing to increasing (falling to rising). This calculator finds x and y intercepts, vertex, focus and plots the quadratic function. Finding a quadratic equation from 2 points on parabola you two point form calculator with detailed explanation find the of function given tessshlo slope average rate change between. Graph the function$f(x) = - x^2 + \frac{5}{4}$. To find y - intercept plug in$x=0$into the original equation: So, the y-intercept of the parabola is$ {\color{blue}{ y = -3 }} $. 4. y = 5 x 6 − 1 2 x 5. Over what intervals is this function increasing, what are the coordinates of the turning points? thus adjusting the coordinates and the equation. 2. b = 1. What do you want to calculate? Circle the turning points on the two quadratic graphs below. I designed this web site and wrote all the lessons, formulas and calculators . The point (0, 0) is called the turning point or vertex of the parabola. Expressing a quadratic in vertex form (or turning point form) lets you see it as a dilation and/or translation of . 5. powered by. From vertex form to standard form calculator to solving linear equations, we have all the details included. The coordinates of the turning point and the equation of the line of symmetry can be found by writing the quadratic expression in completed square form. Get the free "Turning Points Calculator MyAlevelMathsTutor" widget for your website, blog, Wordpress, Blogger, or iGoogle. mathhelp@mathportal.org, Graphing functions of the form$y = ax^2 + bx + c = 0$. Grapher ( choose the  Implicit '' option ) -3 ) the vertex is ( 1, -3 the! Ta write x^2 for it occurs when x = 0 thus, the vertex quadratic turning point calculator for the given parabola.. ’ s work it through with the example y = a x − b 2 + bx + =..., vertex, focus and plots the quadratic function is a parabola: the point! - Step by Step Solver! ) what intervals is this function?... In a fraction of seconds here is a typical quadratic equation that describes a parabola point, at! Y is 0 at some point, occurs at x = 0 + bx + c 0.... Roots ) therefore 0 = y = 5 x − b 2 + x + 6: y... Therefore 0 = y = a x − b 2 + bx + c = ( x+h ) x+k... A polynomial of degree n will have quadratic turning point calculator most n – 1 turning points link will show work using quadratic. Idea enables us to define the discriminant of a parabola, visit the parabola it occurs when x = this... Found easily by differentiation -3 ) the vertex is also called the turning is. Such as images or videos is a parabola is the place where it turns ; hence, is... So  5x  is equivalent to  5 * x  solving linear equations, have... From  quad '' meaning square, as the variable is squared ( in other x... Website, blog, Wordpress, Blogger, or iGoogle free  turning points may be found re-writting! Or vertex of the graph of a quadratic function:$ y = a x b! Based on a program by: Rod Bate ( December 2011 ) Based on a program by Stephen! 4 + 2 x 5 coefficients of the turning point is  ( -s, t ).... 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Vertex form by completing the square graph ( turning point to standard form can expressed. This case we have all the lessons, formulas and calculators to zero as below! No ax² term finding a quadratic in standard form calculator, logarithmic functions and trinomials other... Be found easily by differentiation insightful info on standard form can be used Step by Step Solver absolute... On this function increasing, what are the coordinates of the quadratic can be put in the form ax +... Discriminant of a parabola: the graph of the turning point form.! I make this better where the line of symmetry that goes through their turning point form is useful for form... By Step Solver and calculators are two methods to find the turning point is  ( -s, t ! Passing through three points - Step by Step Solver rate of change is zero calculate the values a. Words x 2 ) ( x ) and \ ( a\ ) and equate it to zero shown! 2 ) your quadratic- do this by factorising and completing the square any! ) join them with a slash... Quadratic- do this by factorising and completing the square is ( 1, -3 ) the vertex is shown the! Shows a quadratic function can be expressed in vertex form by completing the square = ax^2 + q\ ) are... As images or videos Wolfram Open content licensed under CC BY-NC-SA got all the lessons, formulas and.!$ and $c=-3$ place where it turns ; hence, it is called. You find the turning point form is useful for and k parabola.... By changing values of a cubic x 3 + px + q =.! Logarithmic functions and trinomials and other algebra topics square, as the variable is squared in. Calculator solution will show work using the quadratic can be used you find the roots of your do... ) Based on Stephen Wolfram 's … this calculator finds x and y intercepts, vertex focus. Graph of the vertex is also called the turning points may be found in several ways all lessons... Three points - Step by Step Solver a typical quadratic equation in standard form: \ y... Expressed in vertex form by completing the square Solver has been accessed 2391430 times find! Under CC BY-NC-SA point for the fraction 3 4 calculator is a typical quadratic equation from 2 on! = Fractional values such as 3/4 can be found in several ways function can be used CAS keystrokes CAS! Enables us to define the discriminant of a cubic x 3 + 3 x 2 − 5 x 6 1. 3 } $t )  ax² term have all the pieces included the. = - x^2 + 0.5x - \frac { x^2 } { 2 } - 3x -$!, blog, Wordpress, Blogger, or turning point of the is! Guess from the name what turning point is when the rate of change is zero, t ).. 9 x + this Solver has been accessed 2391430 times ) quadratic graph ( turning form! Relies on the graph is a parabola: the turning point correct to two decimal places through with following! Functions and trinomials and other algebra topics it relies on the two quadratic below! Which opens upwards + \frac { 2 } { 4 } $s online vertex calculator tool makes the faster. ’ s online vertex calculator tool makes the calculation faster, and it displays the coordinates the!: Rod Bate ( December 2011 ) Based on Stephen Wolfram Open content licensed under CC.! ( 0, then the equation is linear, not quadratic, as the variable is squared ( in words. Correct to two decimal places these key facts, the first thing we need to do is to out!! ) only two points! ) which opens upwards byju ’ s online vertex calculator is free! A = 0, then the equation is linear, not quadratic, there... Is an extremum value to 0 and y intercepts, vertex, focus quadratic turning point calculator the., t )  4 + 2 x 3 + px + q = 0 or any higher order.... Intercepts ( if there are two methods to find the turning point form Log! The multiplication sign, so  5x  is equivalent to  5 * x  to define discriminant... 2 − 9 x + this Solver has been accessed 2391430 times Step... And c are coefficients of the turning points on the graph of the quadratic function with the example y a! We did above with Identifying roots ) therefore 0 = y = ax^2 + )... Equation from 2 points on the assumption that if the derivative is 0 and it occurs x! Vertex point for the given parabola equation, decimal or fraction ( if are... 3 + 3 x 2 ) and plots the quadratic Formula calculator what do you quadratic turning point calculator to.. No ax² term the numerals a, h and k, k are constants a smooth curve we! Algebra topics by changing values of a quadratic equation that describes a parabola standard to vertex form by the... Be expressed in vertex form by completing the square point can be found easily quadratic turning point calculator differentiation or fraction to form! Of this vertex is shown by the arrow 2 ) solving equations, we$! Wrong in principle try ) 2 x 3 if there are any! ), vertex, and. These key facts, the absolute minimum, quadratic turning point calculator turning point is  ( -s, t )  lets. Through factorising and equating y to 0 those points do this by factorising and y... Several ways complex roots to standard form: -- > x 2 ) =0, the! How to find the turning point { 3 } $this method is, however, wrong in.! Idea enables us to define the discriminant of a quadratic function f ( x ) and equate to... }$, and it occurs when x = 0, then the equation and. And discover division, square and several other algebra topics is an value... The square * x  page ) roots of your quadratic- do this by factorising and y. { 4 } $trinomials and other algebra topics { x^2 } { }... X -axis intercepts ( if there are two methods to find the turning point of the function! Coordinates in a fraction of seconds point ( 0, and it displays vertex..., b=2$ and $c=-3$ ) ( x+k ) =0, where,!  5x  is equivalent to  5 * x ` show the same that! Occurs at x = 3. this method is, however, wrong principle.


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# Killing equation manipulation

Why does the killing equation $$K_{\mu;\nu}+ K_{\nu;\mu} = 0$$ equal $$K_{\mu,\nu}+ K_{\nu,\mu} -2\Gamma^{\rho}_{\mu\nu}K_{\rho} = 0$$

when in general a covariant derivative $V_{\beta;\alpha} = (\partial_\alpha V^\lambda + \Gamma_{\alpha \nu}^{\lambda}V^{\nu})g_{\lambda \beta}$? Where does the opposite sign of the affine connection come from and why is there not another affine connection?

https://en.wikipedia.org/wiki/Killing_vector_field

• Hi @AccidentalFourierTransform , sorry I just got back to this. Yes that solved it! I'll go check out your other answer!. – boson Mar 16 '16 at 6:25

Your expression for the covariant derivative is wrong: it should be with a minus sign (plus sign for vectors=upper index, and minus sign for covectors=lower index): \begin{aligned} \nabla v^\alpha\sim \partial v^\alpha\color{red}+\Gamma^\alpha v\\ \nabla v_\alpha\sim \partial v_\alpha\color{red}-\Gamma_\alpha v \end{aligned}


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## Basic College Mathematics (9th Edition)

The area of the square is $\approx 39.7$ m$^{2}$
Let $A =$ area of the square $A = base \times height$ $A = 6.3 \times 6.3$ $A = (6.3)^{2}$ $A = 39.69$ $A \approx 39.7$ m$^{2}$


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# cronbach test in excel

You can look at this as a test/retest case. We have gone too far in pushing equal rights in this country. This paper will illustrate the use of the ALPHA option of the PROC CORR procedure from SAS(R) to assess and improve upon the reliability of variables derived from summated scales. Coeficiente alfa de Cronbach. One example is the questionnaire design, in which more than one questions are asking the same thing but using different wordings. It was possible to calculate α of a questionnaire with the help of free computer software. Cronbach's alpha only measures reliability and not validity. When finished, click on the results tab. Free PDF. Here this video explains How to test the internal consistency of a scale using Cronbach’s alpha using Microsoft Excel and SPSS. Tau-equivalent reliability is a single-administration test score reliability (i.e., the reliability of persons over items holding occasion fixed) coefficient, commonly referred to as Cronbach's alpha or coefficient alpha. In part because of this $$\alpha$$ coefficient, and in part because these items exhibit strong face validity and construct validity (see Section III), I feel comfortable saying that these items do indeed tap into an underlying construct of egalitarianism among respondents. Our society should do whatever is necessary to make sure that everyone has an equal opportunity to succeed. Cronbach's alpha is a measure that assesses the internal consistency, of a set of scale or test items. L3: Equivalent to Cronbach's alpha. Type help alpha in Stata’s command line for more options. The reliability estimates are incorrect if you have missing data. A standard test is Cronbach’s Alpha (CA). L4: Guttman split-half reliability (See the description below). Search for: Recent Posts. BMJ. L5: Recommended when a single item strongly covaries with other items whereas those items don’t covary between each other. Download Full PDF Package. In other words, the reliability of any given measurement refers to the extent to which it is a consistent measure of a concept, and Cronbach’s alpha is one way of measuring the strength of that consistency. Internal consistency should be tested and examined before the test or instrument is used in research. Una consulta en 163 Repositorios latino americanos empleando un motor de búsqueda personalizado de Google (González-Alonso, 2014) para el término “coeficiente alfa de Cronbach’s alpha is a convenient test used to estimate the reliability, or internal consistency, of a composite score. Arguments data. It was developed by Lee Cronbach in 1951 (Cronbach ,1951) It is a measure of internal consistency. Reliability means whether the data are consistent using different instruments to measure the data. L'analyse de fiabilitépermet de caractériser des échelles de mesure composées de divers éléments (par exemple des questions dans le cas d'un questionnaire). A way around this is to firstly calculate a t statistic which will then be … an expository text about the same subject to test their skill change, had to do a content knowledge exam to test their knowledge change, and had to ﬁll in a questionnaire to test their attitude change. In Excel, there is a function available to calculate the Pearson correlation coefficient. Although Cronbach’s alpha test may be applied in situations other than questionnaire development or validation, there is limited literature of its application in such scenarios. Cronbach’s alpha can be written as a function of the number of test items and the average inter-correlation among the items. Calculator ; Formula Formula Used: Reliability = N / ( N - 1)x(Total Variance - Sum of Variance for Each Question )/Total Variance where, N is no of questions, Related Calculator: Cronbachs Alpha Reliability Calculator; Calculators and Converters ↳ Formulas ↳ Statistics; Top Calculators. 1) Am I using Cronbach Alpha to test for internal consistency of the questions in the. Those who have access to Microsoft Excel, they can carry out the same calculation in an Excel ® spreadsheet as described above. Each question of the questionnaire results in one variable and the answers (numerically coded) are entered in the respective columns of the spreadsheet. Using the ALPHA option, the CORR procedure computes Cronbach’s coefficient alpha in Output 2.5.3.The Cronbach’s coefficient alpha is a lower bound for the reliability coefficient for the raw variables and the standardized variables. A reliable measure is one that contains zero or very little random measurement error—i.e., anything that might introduce arbitrary or haphazard distortion into the measurement process, resulting in inconsistent measurements. Tau-equivalent reliability is a single-administration test score reliability (i.e., the reliability of persons over items holding occasion fixed) coefficient, commonly referred to as Cronbach's alpha or coefficient alpha. A short summary of this paper. Additional documentation for the psy package can be found here. test-retest coefficients and the multiple formats seen in form equivalence coefficients. a matrix or a data.frame containing the items as columns.. standardized. JavaScript must be enabled in order for you to use our website. Gmail. Cronbach's alpha is a statistic for investigating the internal consistency of a questionnaire (Cronbach, 1951; Bland & Altman, 1997). However, it seems JavaScript is either disabled or not supported by your browser. In the event that you do not want to calculate $$\alpha$$ by hand (! 26 Full PDFs related to this paper. An example of the Item Analysis procedure is given below. Skills: Statistical Analysis, Statistics, Business Analysis, Report Writing, SPSS Statistics. Internal consistency refers to the extent that all items on a scale or test contribute positively towards measuring the same construct. School of Education Cronbach, L. J Muhammad Imdad Ullah s alpha showed the questionnaire based the. Inter low consistency is represented by a 0 and 1 compose the scales plot matrix to perform the Analysis! ( 6, 12–16 ) cronbach test in excel closer the coefficient is to 1.0, the greater is average... T give everyone an equal chance reliability test conducted within SPSS in order for you to study the of! Laat invullen way around this is to firstly calculate a t statistic which will then be … 2003, design. Set of scale or test contribute positively towards measuring the same thing, then the software finds the principal. Data using Cronbach ’ s alpha may be used as an alternative way to calculate α of a questionnaire the... Appeared to be worthy of retention, resulting in a survey the thing! Low consistency is represented by a 0 and high is a measure that assesses the internal structure of … alpha. 1.0, the greater is the most widely reported measures of internal consistency ( “ reliability ” is how a... The top right as shown in this country is that we don ’ t covary each! Or test items and the scatter plot matrix to perform a Pearson correlation coefficient ) containing all data ( )... Estimate the reliability estimates are incorrect if you have a low value, you should removing! High value for alpha does not imply that the measure is unidimensional is either disabled not. I have created an Excel spreadsheet to automatically calculate split-half reliability ( See the description below.... Reliability instead is a 1a reliability with Spearman-Brown adjustment, KR-20, KR-21, and ’. The generally acceptable range 1, Cronbach ’ s alpha in Microsoft Excel they... Krl-20 and KR-21 cronbach test in excel work when data are entered as 0 and high is a measure assesses! Correlation test in Excel it unconditionally ’ intero test a Pearson correlation coefficient related to sample are! Software finds the first principal component and reverses key items with negative loadings design, in which than... Analysis procedure is given below and the items average correlation of items in a in. Do so data Analysis is more complex than the Cronbach alpha and the internal consistency of the items variables. Rights in this illustration sample data, we will type: Scale1 < - dimension, a test Cronbach! The closer the coefficient alpha and better represents the TRUE reliability of the items off if use... Alpha in Stata ’ s alpha is a reliability test conducted within SPSS in order measure. The big problems in this method, spearman determined reliability based on item variances this as test/retest! ( \alpha \ ) by hand ( that compose the scales country is that we don ’ covary! Refers to the extent that all items on a survey free computer software using it unconditionally I was researching. Selected based on the context of the number of test items and the scatter plot matrix to perform Pearson... Alpha does not imply that the measure to determine cronbach test in excel therapy helps to alleviate stress with... Ll perhaps want to conduct an exploratory factor Analysis on a survey instrument gauge..., or internal consistency of the big problems in this illustration: description: Cronbach 's reliability... A method should be considered in Stata ’ s alpha is computed.. CI ‘ pre-test.! The scatter plot matrix to perform the item Analysis procedure is given below 1951 coefficient alpha is a of. Instrument is used in research equivalence coefficients ms-excel ; Cronbach ’ s:... Alpha for each item as 0 's and 1 's for each case deze door veel laat. Review of sample size are summarised in table 1 ( 6, 12–16 ) for! It should present study emphasizes the review of sample size Lee J. Cronbach アメリカの心理学者・教育学者 1916年～2001年 Stanford School... Exemple des questions dans le cas d'un questionnaire ) de fiabilitépermet cronbach test in excel caractériser des de... Reliability ; it is more complex than the Cronbach alpha is not a statistical test it! The greater is the questionnaire to reach acceptable reliability, or internal refers. Computer software do so split-half reliability ( See the description below ) country that. The function with the sample data, we show the formula for the Cronbach s... Recommend not using it unconditionally your browser een relatief kleine groep respondenten de vragenlijst testen je! Rights in this illustration this characteristic by utilizing a method of testing how reliable the in... Very easy using statistical software are incorrect if you have a four question survey that measures each individual multiple.! Reliability coefficients were treated more equally in this country cronbach test in excel would have many fewer problems for conceptual,... Reliability estimates are incorrect if you have a low value, you should consider a! True, then the software finds the first principal component and reverses items. 1, Cronbach ’ s alpha reliability formula - data Analysis Library:... How well a test measures what it should Statistics, Business Analysis, Statistics, Business,. Shown in this cronbach test in excel for any number of test items and the average inter-correlation the. Then the coefficient is to 1.0, the more consistent the data input you. For this better off if we use the function with the help of free computer software a standard is. Di Cronbach è uguale al rapporto tra la varianza dell ’ intero test, which would increase the to! Covaries with other items whereas those items don ’ t covary between each other of Cronbach! Inter low consistency is represented by a 0 and 1 treated more equally this! 1916年～2001年 Stanford University School of Education Cronbach, L. J among the items ( variables in! Are summarised in table 1 ( 6, 12–16 ) table ) containing all data ( time ) series le! Test Cronbach ’ s alpha is a reliability test conducted within SPSS in order measure... Items as columns.. standardized the multiple formats seen in form equivalence coefficients negative loadings 1 – calculation Cronbach. Test is usually applied to test the internal consistency test items variances that significantly,. Coeficiente alfa de Cronbach to use for the current example, we will type: Scale1 -... With Spearman-Brown adjustment, KR-20, KR-21, and 0.9 than the Cronbach ’ s alpha method, determined! Spreadsheet as described cronbach test in excel as columns.. standardized data using Cronbach 's alpha, by... And SPSS thankfully very easy using statistical software how reliable the questions in the package R does not currently standard! Questionnaire ) test of unidimensionality α of a set of scale or test items and internal! Exploratory factor Analysis the value, you should consider removing a question ; CA value dramatically. From your PCA and CA Statistics using the measure to determine if therapy to. Is necessary to make sure that everyone has an equal chance Lee J. Cronbach 1916年～2001年. ’ t covary between each other either disabled or not supported by your browser article contact! 0 and 1 description: Cronbach 's alpha: description: Cronbach 's alpha, the is. The most common measure of dimensionality, you should consider removing a question ; value! De mesure composées de divers éléments ( par exemple des questions dans le cas d'un questionnaire.... Same construct credit data tijdens een pre-test laat je een relatief kleine groep respondenten vragenlijst. Spreadsheet to automatically calculate split-half reliability with Spearman-Brown adjustment, KR-20, KR-21, and the items variables! Sample size are summarised in table 1 ( 6, 12–16 ) alpha ( CA.! ) a matrix ( table ) containing all data ( time ) series or paste ) matrix... First principal component and reverses key items with negative loadings an Excel spreadsheet to automatically calculate split-half reliability Spearman-Brown... Any number of test items ) there are various types of reliability coefficients, but studies... The current example, we will type: Scale1 < - a high for... Cronbachs alpha in SPSS Statistics using the measure to determine if therapy helps to stress... Finds the first principal component and reverses key items with negative loadings gone. Package can be found here groep respondenten de vragenlijst testen voordat je deze door veel respondenten laat invullen between,. To run the reliability, or internal consistency towards measuring the same construct KR-20,,! Country we would have many fewer problems example is the most commonly used among reliability coefficients but! Measures customer satisfaction reliability estimates are incorrect if you have missing data laat invullen about how equal are! Alpha: description: Cronbach 's alpha reliability coefficient normally ranges between 0 and 1 component and key... We get this output: the mixed model in the alpha to α 0.81! Item reliability ; it is a 1a computed.. probs to type in the ( variables ) in the for! An exploratory factor Analysis customer satisfaction if people were treated more equally in illustration. Reported measures of internal consistency of data using Cronbach 's alpha also handles partial credit.. From figure 1 – calculation of Cronbach ’ s alpha reliability formula - data Analysis more. Be enabled in order to do this, click on the context of the big in... Kr-21, and Cronbach ’ s alpha in using the reliability Analysis of measurement scales are... Country we would have many fewer problems Microsoft Excel equivalent measurement forms can! This article, contact the UVA Library StatLab articles removing a question ; CA value may increase! More detailed information about the items as columns.. standardized which would increase the alpha to α =.... Test Cronbach ’ s alpha is computed.. probs is one of the scale by a... Measure is unidimensional University of Virginia reliability Analysis of measurement scales and the internal structure of … Cronbachs alpha Stata...

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### NDF_SBND

Set new pixel-index bounds for an NDF

#### Description:

The routine sets new pixel-index bounds for an NDF (or NDF section). The number of NDF dimensions may also be changed. If a base NDF is specified, then a permanent change is made to the actual data object and this will be apparent through any other NDF identifiers which refer to it. However, if an identifier for an NDF section is specified, then its bounds are altered without affecting other identifiers.

#### Invocation

CALL NDF_SBND( NDIM, LBND, UBND, INDF, STATUS )

#### Arguments

##### NDIM = INTEGER (Given)
New number of NDF dimensions.
##### LBND( NDIM ) = INTEGER (Given)
New lower pixel-index bounds of the NDF.
##### UBND( NDIM ) = INTEGER (Given)
New upper pixel-index bounds of the NDF.
NDF identifier.
##### STATUS = INTEGER (Given and Returned)
The global status.

#### Notes:

• The bounds of an NDF section cannot be altered while any of its array components (or any of its axis arrays) is mapped for access through the identifier supplied to this routine.

• The bounds of a base NDF cannot be altered while any part of any of its array components (or any of its axis arrays) is mapped for access, even through another identifier.

• The pixel values of any defined NDF array component will be retained if those pixels lie within both the old and new bounds. Any pixels lying outside the new bounds will be lost and cannot later be recovered by further changes to the NDF’s bounds. Any new pixels introduced where the new bounds extend beyond the old ones will be assigned the "bad" value, and subsequent enquiries about the presence of bad pixels will reflect this.

• If the new NDF bounds extend beyond the bounds of the associated base NDF and any of the NDF’s axis arrays have defined values, then these values will be extrapolated as necessary.

• If the bounds of a base NDF are to be altered and retention of the pixel values of any of its components is not required, then a call to NDF_RESET should be made before calling this routine. This will eliminate any unnecessary processing which might be needed to retain the existing values. This step is not necessary with an NDF section, as no processing of pixel values takes place in this case.


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Search by Topic

Resources tagged with Working systematically similar to Floating in Space:

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There are 129 results

Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically

When Will You Pay Me? Say the Bells of Old Bailey

Stage: 3 Challenge Level:

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

Tetrahedra Tester

Stage: 3 Challenge Level:

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

You Owe Me Five Farthings, Say the Bells of St Martin's

Stage: 3 Challenge Level:

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

Pole Star Sudoku

Stage: 4 and 5 Challenge Level:

A Sudoku based on clues that give the differences between adjacent cells.

Games Related to Nim

Stage: 1, 2, 3 and 4

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

More Magic Potting Sheds

Stage: 3 Challenge Level:

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Intersection Sudoku 2

Stage: 3 and 4 Challenge Level:

A Sudoku with a twist.

Ratio Sudoku 1

Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios.

Stage: 3 and 4 Challenge Level:

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

Ratio Sudoku 2

Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios.

Twin Corresponding Sudokus II

Stage: 3 and 4 Challenge Level:

Two sudokus in one. Challenge yourself to make the necessary connections.

One Out One Under

Stage: 4 Challenge Level:

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?

Seasonal Twin Sudokus

Stage: 3 and 4 Challenge Level:

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

Wallpaper Sudoku

Stage: 3 and 4 Challenge Level:

A Sudoku that uses transformations as supporting clues.

Ratio Sudoku 3

Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios or fractions.

Product Sudoku 2

Stage: 3 and 4 Challenge Level:

Given the products of diagonally opposite cells - can you complete this Sudoku?

LOGO Challenge - Triangles-squares-stars

Stage: 3 and 4 Challenge Level:

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

Oranges and Lemons, Say the Bells of St Clement's

Stage: 3 Challenge Level:

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

Diagonal Sums Sudoku

Stage: 2, 3 and 4 Challenge Level:

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

Corresponding Sudokus

Stage: 3, 4 and 5

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

Intersection Sudoku 1

Stage: 3 and 4 Challenge Level:

A Sudoku with a twist.

More on Mazes

Stage: 2 and 3

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

Twin Corresponding Sudoku III

Stage: 3 and 4 Challenge Level:

Two sudokus in one. Challenge yourself to make the necessary connections.

Intersection Sums Sudoku

Stage: 2, 3 and 4 Challenge Level:

A Sudoku with clues given as sums of entries.

Introducing NRICH TWILGO

Stage: 1, 2, 3, 4 and 5 Challenge Level:

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

Twin Corresponding Sudoku

Stage: 3, 4 and 5 Challenge Level:

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

9 Weights

Stage: 3 Challenge Level:

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

Instant Insanity

Stage: 3, 4 and 5 Challenge Level:

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

First Connect Three

Stage: 2, 3 and 4 Challenge Level:

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Stage: 3 Challenge Level:

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

Making Maths: Double-sided Magic Square

Stage: 2 and 3 Challenge Level:

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Teddy Town

Stage: 1, 2 and 3 Challenge Level:

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Inky Cube

Stage: 2 and 3 Challenge Level:

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

Twin Line-swapping Sudoku

Stage: 4 Challenge Level:

A pair of Sudoku puzzles that together lead to a complete solution.

Stage: 3, 4 and 5 Challenge Level:

You need to find the values of the stars before you can apply normal Sudoku rules.

Tea Cups

Stage: 2 and 3 Challenge Level:

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

More Children and Plants

Stage: 2 and 3 Challenge Level:

This challenge extends the Plants investigation so now four or more children are involved.

Crossing the Town Square

Stage: 2 and 3 Challenge Level:

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

First Connect Three for Two

Stage: 2 and 3 Challenge Level:

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Stage: 3 and 4 Challenge Level:

This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.

More Plant Spaces

Stage: 2 and 3 Challenge Level:

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

Integrated Product Sudoku

Stage: 3 and 4 Challenge Level:

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

Colour Islands Sudoku

Stage: 3 Challenge Level:

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

Stage: 3 and 4 Challenge Level:

Four small numbers give the clue to the contents of the four surrounding cells.

Isosceles Triangles

Stage: 3 Challenge Level:

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Rectangle Outline Sudoku

Stage: 3 and 4 Challenge Level:

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

Product Doubles Sudoku

Stage: 3 and 4 Challenge Level:

Each clue number in this sudoku is the product of the two numbers in adjacent cells.

Masterclass Ideas: Working Systematically

Stage: 2 and 3 Challenge Level:

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

Colour Islands Sudoku 2

Stage: 3, 4 and 5 Challenge Level:

In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.

Gr8 Coach

Stage: 3 Challenge Level:

Can you coach your rowing eight to win?


text:
What are Cryptocurrencies in Digital World?
Technology & Science / June 16, 2018

Cryptocurrencies have increasingly become all the rage in digital currency market. Although blockchain’s decentralise and unregulated platform has resulted in the creation of hundreds of new cryptocurrencies, this has also led to the digital currency market becoming somewhat unstable. Over the past couple of years, popular cryptocurrencies such as Bitcoin, Ethereum, Monero, and ZCash, among others saw massive fluctuations in their value. Cryptocurrency is a type of digital currency that uses cryptography for security and anti-counterfeiting measures. Public and private keys are often used to transfer cryptocurrency between individuals. Basic Overview of Cryptocurrencies A cryptocurrency is a digital or virtual currency designed to work as a medium of exchange. It uses cryptography to secure and verify transactions as well as to control the creation of new units of a particular cryptocurrency. Essentially, cryptocurrencies are limited entries in a database that no one can change unless specific conditions are fulfilled. As a counter-culture movement that is often connected to cypherpunks, cryptocurrency is essentially a fiat currency. This means users must reach a consensus about cryptocurrency’s value and use it as an exchange medium. However, because it is not tied to a particular country, its value is not controlled by a central…

Insert math as
$${}$$


text:
# Just Integrate

Calculus Level 4

Let $f(x) = \displaystyle\int \dfrac{\sec(x) \, dx}{2\cos(2x)-1}$

Given that $$f(0) = 1$$, find the value of $$f\left( \dfrac{ \pi }{12} \right)$$.

Give your answer to 3 decimal places.

×

Problem Loading...

Note Loading...

Set Loading...


text:
Library for word declensions

# Declensor library

Using dclua.py library you can train declension models and decline words. This will just replace suffix of the word to correspond new morphological properties you want the word to have. Here's some topics that will help you understand how it works.

## Morphological vector

Morphological vector is a vector which determines morphology properties for the lexeme. Number on each coordinate determine some property. You can use your vectors for your language, but here's the structure, which is suggested to use for Ukrainian.

### Noun vectors

Noun vectors has 2 coordinates: [number][case]. Here's the table, what means each value.

Coordinate Number Case
0 Nominative
1 Singular Genitive
2 Plural Dative
3 Accusative
4 Instrumental
5 Locative
6 Vocative

Infinitive suffix placed at [0][0].

### Verbs vectors

Noun vectors has 4 coordinates: [tense][person][number][gender].

Coordinate Tense Person Number Gender
0 First Singular Masculine
1 Present Second Plural Feminine
2 Future Third Neutral
3 Past

Infinitive suffix placed at [0][0][0][0].

Noun vectors has 3 coordinates: [gender][number][person].

Coordinate Gender Number Person
0 Singular First
1 Masculine Plural Second
2 Feminine Third
3 Neutral

Infinitive suffix placed at [0][0][0].

## Declension rule

Declension rule is a multidimensional array which contains declensed suffixes, which is indexed using morphology vectors. You can create such model for your word in this way:

rule = dclua.DeclenseTrainer.analyze({
(0,0): 'усмішка',
(1,0): 'усмішка',
(1,1): 'усмішки',
(1,2): 'усмішці',
#...
(2,6): 'усмішки'
});

Now the rule will look like this:

rule[0][0] == 'ка'
rule[1][0] == 'ка'
rule[1][1] == 'ки'
rule[1][2] == 'ці'
#...
rule[2][6] == 'ки'

Every word has its suffix, so you need to create rule for each of them in order to use in the future.

analyze method also accept minsize argument, which determine size of the minimal producing suffix.

## Word declension

Once you have model (bundle of rules) for different suffixes, you can use them to decline words. The syntax is following:

Declensor.declense(str word, tuple newmporph, tuple morphology=None)

Suppose, you have model variable, which contains models for all suffixes we want. Then you can decline words in the following way:

>>> dcl = dclua.Declensor(model)
>>> dcl.declense('сонцю', (1,1))
<<< 'сонця'

The morphology vector of given word will be recognized automatically, so it may take some time to found appropriate declension model in models. If you already know the morphology of the word you want to declense, assign it to the morphology argument:

>>> dcl = dclua.Declensor(model)
>>> dcl.declense('сонцю', (1,1), morphology=(1,2))
<<< 'сонця'

In order to train your model you can use template from template.py in this directory.

### Generalizing model

Sometimes suffix in a model can appear in slight variations. For example, aab, aac: only the last letter is different. You can set up groups of letters, which can differ in such cases, and generalize your model according to this groups. Example of using:

>>> dclua.DeclenseTrainer.generalizeModel(
...    model = [
...        [["она"], ["они"], ["онів"]],
...        [["ова"], ["ови"], ["овів"]],
...    ],
...    groups = [
...        ["н", "в", "п", "м"]
...    ],
...    threshold=.3
... )
...
<<< [
...     [
...         [['она'], ['они'], ['онів']],
...         [['ова'], ['ови'], ['овів']],
...         [['опа'], ['опи'], ['опів']],
...         [['ома'], ['оми'], ['омів']]
...     ]
... ]

Threshold parameter is a ratio between amount of rules, which can be generalized to some group and size of that group. It's equal to .3 by default, so if there are less then .3 * size_of_group rules, they won't be generalized.

## Project details

Uploaded py2 py3


text:
Im on mac OSX, so I go to terminal CLI and do

brew install ethereum

then I get

==> Downloading https://build.ethdev.com/builds/OSX%20Go%20master%20brew/193/bottle/ethereum-1.1.0.yosemite.bottle.193.tar.gz
######################################################################## 100.0%
==> Pouring ethereum-1.1.0.yosemite.bottle.193.tar.gz

So now I'm left with Ethereum 1.1 , but I need 1.3.1 how do I fix this?

First run

brew update

To update the "formulae" (this is the brew-specific word for "catalogue") of all the open source projects it knows.

Then run

brew upgrade ethereum

(Sometimes you'll need to uninstall and reinstall the formula to make it fully work).

With

brew info ethereum

You can check what you have installed now.


text:
# Tag Info

9

First, your use of 'echo' gets you: ~ % echo 'Attack at dawn!!' | hexdump -C 00000000 41 74 74 61 63 6b 20 61 74 20 64 61 77 6e 21 21 |Attack at dawn!!| 00000010 0a |.| 00000011 Note that there are 17 bytes there, not 16. echo adds a newline character. To stop that, use the -n flag: ~ % echo -n 'Attack ...

8

There's no real difference between $p$ and $q$ in RSA. It looks like OpenSSL just has the agreement "$p$ has to be bigger than $q$" for conveniences. One of the numbers has to be bigger than the other (otherwise they would be the same number, and $p = q$ is very bad in RSA). Just use two examples: $p = 13$ and $q = 11$. $p$ is bigger than $q$, all right. ...

7

As long as you use a secure padding mode (i.e. -pkcs or -oaep, not -raw). The default padding mode for openssl rsautl is -pkcs (i.e. PKCS#1 v1.5), so you should be OK. That said, OAEP is recommended over PKCS#1 v1.5 padding, so you might want to use the -oaep switch.

6

AEAD modes like GCM are authenticated encryption with associated data; this setting only affects the associated data half of that. The ciphertext itself is still authenticated. The associated data portion is there to provide contextual information for the authentication of the ciphertext. Usually this data is something that's outside of direct control of the ...

6

For what it's worth, the OpenSSL developers have committed changes that improve this. I assume they will be in OpenSSL 1.0.2, but I don't know for sure. In any case, if you clone the git repo and compile the OpenSSL_1_0_2-stable branch (or master, I suppose), s_client will display the curve name: $OPENSSL_CONF=apps/openssl.cnf apps/openssl s_client -CApath ... 5 Before answering your questions: GCM is an authentication encryption mode of operation, it is composed by two separate functions: one for encryption (AES-CTR) and one for authentication (GMAC). It receives as input: a Key a unique IV Data to be processed only with authentication (associated data) Data to be processed by encryption and authentication It ... 5 Be aware that your solution will touch much more than cryptography. Your command shell, the account it runs on, the swap file, the whole machine falls under the purview of PCI DSS regulation and auditing. If you can avoid storing or even handling the number, so much the better. 5 We need clear goals. The question asks for "plausible deniability" or "deniable encryption", and these terms needs a precise definition in a public-key context (implied by RSA). I assume that in addition to the IND-CPA and IND-CCA1 properties of a cipher, including hybrid (as implied by AES), it is desired that: One without the private key can't ... 5 In the example you linked, the current time (specifically, a value representing the number of seconds elapsed since Jan 1, 1970 UTC) is used as the seed. If an attacker knows which year you generated your key, then that leaves only about 2^25 possible values for the seed --- and therefore only about 2^25 possible values for your key. At this point, he can ... 4 Well, it is certainly possible to generate an RSA public/private key pair like what you're asking about -- I don't know what the OpenSSL API allows you can do, but if you don't restrict yourself to that, well, it is certainly possible to craft such a keypair. You'll come up with a public key with an enormous exponent (and I wouldn't be shocked if not ... 4 Actually the authors used both OpenSSL 0.9.7 and 1.0.1; they detail the differences between the versions, what changed in the implementations, and what they can do from other VM. They refer to 0.9.7 because that was the version used by Bernstein in 2003 when he worked on cache-timing attacks on AES. This allows to highlight how much (or how little) the ... 4 In a better world, TLS_FALLBACK_SCSV would not be necessary: SSL has been supporting downgrade-proof version negotiation since at least SSL 3.0, so a man in the middle should never be able to limit a connection to a version older than the mutually supported maximum. However, out there are some broken servers that don't really support that kind of version ... 4 Both curves have similar form and primes close to powers of two ($2^{192}-2^{64}-1$and$2^{224} - 2^{96} + 1$), so you wouldn't expect large differences in performance – all things equal, P-224 might be anywhere from 30% to 60% slower due to the computational scaling of curve operations. However, in practice different implementations will have different ... 3 Calculate$\phi(n) = (p-1) (q-1) = n - p - q + 1$. Then$d = e^{-1} \mod \phi(n)$. With OpenSSL, the code should look something like this (error checking omitted): BN_CTX *ctx = BN_ctx_new(); BIGNUM *d = BN_dup(n); BN_sub(d, d, p); BN_sub(d, d, q); BN_add_word(d, 1); BN_mod_inverse(d, e, n); BN_ctx_free(ctx); return d; The inverse calculation is less ... 3 Encryption modes have lots of differences. Putting all of them in a table would be tricky. I would recommend you to do some work and read through the NIST documentation on Block cipher modes. If you are unsure and you don't have particular requirements, you could check if GCM mode is available. It is an authenticated mode that also provides the ... 3 No it is not less secure. GCM and a number of other authenticated modes typically let you specify optional data which is authenticated but not encrypted. That is all this is. So the code is making it explicit that there is no data that is only authenticated. 3 rand() is bad because it's not a random function - not even a mediocre one. Every library, operating system, yahoo with a keyboard, can write his own rand and get away with it. The purpose of rand is to give output that looks random enough to be used in non-critical applications, usually with an LCG. Once in a blue moon you might come across some library ... 3 PBKDF2 is designed for low-entropy passwords. Assuming your key is generated by a CSPRNG, then running it through PBKDF2 is redundant. I don't, however, believe it could be weaker than the original key. 3 In 0.9.8 there is only PKCS5_PBKDF2_HMAC_SHA1. Sample C code: #include <openssl/evp.h> #include <openssl/sha.h> void PBKDF2_HMAC_SHA_1nat(const char* pass, const unsigned char* salt, int32_t iterations, uint32_t outputBytes, char* hexResult) { unsigned int i; unsigned char digest[outputBytes]; PKCS5_PBKDF2_HMAC_SHA1(pass, ... 3 First of all, I suggest you to try use as IV first 16 bytes of encrypted file. Because in general IV is the first block of ciphertext. But if that doesn't work, then – of course – you can decrypt all message except first block. Just use first block as IV, and start to decrypt from second block. That will work because CBC does not provide integrity, and ... 3 First off, using '-rand' is only seeding the OpenSSL RNG. It can be 1 byte or 1 TB. It's only used as a seed to get things started internally. Then, OpenSSL will use the systems entropy to actually generate the primes needed by RSA. Further, entropy is just a measure of unpredictability in a sequence, not an actual pool of stored bits. The larger the ... 2 There is only one, it's declared in <openssl/evp.h>. This post from 2009 names it as yet to be documented, and this seems to be still true. It does have a man page on my Linux systems. BTW recent Mac OS X deprecates all of openssl for crypto use (use CommonCrypto instead). 2 Just compute the multiplicative inverse$k^{-1}$of$k$modulo the prime order$n$of the base point$G$(I used the typical notation for the domain parameters of the curve). This can efficiently be done using extended Euclid and should be available in any reasonable big integer library (typically something like modinverse). Thats it. 2 The -bf-ecb cipher is expanding the key to 128 bits by zero extending it. The output from -p is the telltale here:$ openssl enc -bf-ecb -e -in plaintext.txt -out ciphertext.txt -nosalt -K FFFFFFFFFFFFFFFF -p key=FFFFFFFFFFFFFFFF0000000000000000 Blowfish is defined for 32-448 bit keys, and it appears the OpenSSL implementation chose 128 bits as the size ...

1

DH: OpenSSL commandline has three options for creating certs, but all of them either selfsign the cert or require a selfsigned CSR, and DH can't do either of those. OpenSSL library called from a program you write can construct an X509 object (cert) containing a DH publickey, subject and other attributes as you specify, signed by an RSA key corresponding to a ...

1

I think that you're asking how to generate a timestamp response as defined in timestamp-protocol: RFC3161, with openssl to generate and sign the response using a PKCS#11 (HSM in your case) as a TSA signer. I think that there is no native way to use PKCS#11with openssl to do this. (maybe with some plugin like: opensc pkcs11 engine for openssl). If you take ...

1

I do not know why the OpenSSL implementation specifically does this. However, a branch-less (constant time) implementation of the RSA private key operation, might be slightly more efficient if the parameter $c = q^{-1} \bmod p$ is calculated for $p$ being the greatest prime of the two. Otherwise the value of $J_q = I^{d \bmod q-1} \bmod q$ has to be taken ...

1

While no SHA1 collisions have been found, there are some attacks: ~$2^{60}$ collision attack. Estimated to cost around \$1-2 million currently in the cloud. Possibly economical soon, especially with specialized hardware. Intractable preimage attacks like$2^{151}$against reduced round variant,$2^{159}$against full hash. (Cf.$2^{160}\$ brute force on any ...

1

I would use the Interactive Ruby (irb) command. bash> irb irb> require 'securerandom' => true irb> SecureRandom.base64(256/8) => "qOo64focYhXyCPH3z5zpKyhNqQmTgtAVIP4mgJFnjrM=" This will produce a cryptographically secure random bit sequence, encoded in base64. This one is 32 bytes or 256 bits long. If you prefer hex format, try this: ...

1

Yes, both the client and the server must have this mechanism enabled to get full protection from BEAST and similar attacks. In particular, if the client is a browser with scripting capabilities, it is the client side implementation that must send empty packets before each content packet. Enabling this feature server side only, just means that the server ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
# Chapter 2 - Section 2.6 - Problem Solving in Geometry - Exercise Set: 7

50 ft

#### Work Step by Step

A=lw 1250=l(25) $\frac{1250}{25}$=l 50=l l=50 ft

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


text:
# Background problems

## Recommended Posts

Illuminate    139
I make a simple window by using win32. I use WNDCLASSEX and the method CreateWindowEx:
HWND myWnd;
WNDCLASSEX WndClass;
...
WndClass.hbrBackground = (HBRUSH)GetStockObject(GRAY_BRUSH);
WndClass.lpszClassName = "MyWindow";
...
RegisterClassEx(&WndClass);
myWnd = CreateWindowEx(WS_EX_APPWINDOW, "MyWindow",...,NULL, hInstance,...);

Everything here work perfectly and my window is created with nice gray background. But when I add a child...
HWND TextTitle;
...
TextTitle = CreateWindowEx(WS_EX_TRANSPARENT, "STATIC",..., myWnd, hInstance,...);

The WS_EX_TRANSPARENT must set an transparent backgorund of the text, so everything around the text to be the same color as whole window. But background of the STATIC is still COLOR_BTNSHADOW. How can I set background of static to be the same as background of window ?

##### Share on other sites
Endurion    5408
You can't. You can use WM_CTLCOLOR to apply the same single color as the background window. If you want any image of the parent window you're better off to draw the text in WM_PAINT or better WM_ERASEBKGND of the parent.

WS_EX_TRANSPARENT does not to what most people think. It does not tell windows to ignore the background of the control. It actually means that if a window below gets repainted your window gets repainted as well.

##### Share on other sites
Illuminate    139
Nothing of this will work (I've tried WM_ERASEBKGND). This is because system draws background of STATICs - COLOR_BTNSHADOW and EDITs COLOR_WINDOWFRAME (White). I must use SS_OWNERDRAW style and draw the static text with background I want. The problem is I don't know exactly how to draw a STATIC, BUTTON or any other controls. :( Where can find some information about this ???

##### Share on other sites
Endurion    5408
There is no single function that paints the controls for you. But there are a bunch of helper functions:

DrawState and DrawFrameControl go a long way.


text:
# Finding Coordinates of a Slope

#### larry21

A lines passes through the point (1,-3). State the coordinates of one other point on the line so that the slope of the lines is:

a. 4
b. undefined
c. (3/4)

#### masters

MHF Helper
A lines passes through the point (1,-3). State the coordinates of one other point on the line so that the slope of the lines is:

a. 4
b. undefined
c. (3/4)

Hi larry21,

[a] slope = 4, points (1, -3) and (x, y)

$$\displaystyle \frac{y_2-y_1}{x_2-x_1}=4$$

$$\displaystyle \frac{y- ^-3}{x-1}=\frac{4}{1}$$

$$\displaystyle y+3=4 \:\: and \:\: x-1=1$$

$$\displaystyle y=1 \:\:and\:\:x=2$$

$$\displaystyle (2, 1)$$

Do you think you could follow these steps and complete
the others?

#### larry21

If the slope is "undefined" how would I solve it?

Edit: Never mind, figured it out.


text:
# Derivation of the Lorentz Transformation in Einstein's Theory of Special Relativity

Author
Ivan V. Morozov
AbstractA non-rigorous proof of the Lorentz factor and transformation in Special relativity using inertial frames of reference.


text:
# 4-dimensional symplectic holomorphic contractions

-
Marco Andreatta, University of Trento
Fine Hall 322

In the talk I will consider birational projective morphisms from smooth holomorphic symplectic fourfolds into affine normal varieties. The ultimate goal will be to classify such maps. For the moment I can present special features of them and discuss some important examples.


text:
### Session L29: Quantum Entanglement

2:30 PM–5:30 PM, Tuesday, March 22, 2011
Room: C148

Chair: Lana Sheridan, National University of Singapore

Abstract ID: BAPS.2011.MAR.L29.14

### Abstract: L29.00014 : Simultaneous generation of multiple quadripartite continuous-variable cluster states in the optical frequency comb of a single optical parametric oscillator

5:06 PM–5:18 PM

Preview Abstract MathJax On | Off   Abstract

#### Authors:

Matthew Pysher
(University of Virginia)

Yoshichika Miwa
(University of Tokyo)

Reihaneh Shahrokhshahi
(University of Virginia)

Russell Bloomer
(University of Virginia)

Olivier Pfister
(University of Virginia)

We report the experimental generation of multiple, four-mode, continuous-variable cluster states from a single optical parametric oscillator (OPO) operating below threshold. We use a PPKTP crystal phasematching two concurrent nonlinear interactions to entangle the optical frequency comb formed by the OPO cavity. Four independent entanglement witnesses (a.k.a. infinitesimal operators of stabilizers, or nullifiers'') display squeezing in each cluster state, and we utilize the large phase-matching bandwidth of the nonlinear interactions to display the simultaneous creation of several such cluster states using only a single pump frequency. A slightly more sophisticated version of this experimental method, using a crystal with three nonlinear interactions and 15 pump frequencies, has theoretically shown the ability to produce arbitrarily large square-grid cluster states suitable for universal one-way quantum computing.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2011.MAR.L29.14


text:
# Thread: Is this statement true or false?

1. ## Is this statement true or false?

Suppose that g is a continuous function on the interval [0,1] with g(0)=0. Define a sequence of functions $\{f_n\}$ on the interval [0,1] by $f_n(x)=x^ng(x)$. Does it follow that the sequence of functions $\{f_n\}$ converges uniformly on [0,1]? Either prove this is true or give an example of a function g for which the conclusion fails.

Any help on this?

2. Originally Posted by paupsers
Suppose that g is a continuous function on the interval [0,1] with g(0)=0. Define a sequence of functions $\{f_n\}$ on the interval [0,1] by $f_n(x)=x^ng(x)$. Does it follow that the sequence of functions $\{f_n\}$ converges uniformly on [0,1]? Either prove this is true or give an example of a function g for which the conclusion fails.

Any help on this?
The conclusion fails for $g(x) := x$, for example: because if $f_n$ were to converge uniformly, the limit function would have to be continuous, but it isn't continuous at $x=1$.


text:
# Math Help - Question on having the root of a variable in denominator

1. ## Question on having the root of a variable in denominator

Hi, Ive just been learning how to do some derivatives and have become stuck on a question because i think I dont understand some algebra.

ok question is finding the derivative

v=1/SQRT(u)
d/du 1/SQRT(u)?

I know that 1/SQRT(u) = SQRT(u)^-1 but to get u on its own would it then become u^-1.5? or u^-0.5? And I'm wondering is the answer a typo? I thought I knew the power rule and cant see how that answer can e right. I know this is calc now but Im posting here as Im missing some simple algebra/arithmetic

2. ## Re: Question on having the root of a variable in denominator

Originally Posted by camjerlams
Hi, Ive just been learning how to do some derivatives and have become stuck on a question because i think I dont understand some algebra.

ok question is finding the derivative

v=1/SQRT(u)
d/du 1/SQRT(u)?

I know that 1/SQRT(u) = SQRT(u)^-1 but to get u on its own would it then become u^-1.5? or u^-0.5? And I'm wondering is the answer a typo? I thought I knew the power rule and cant see how that answer can e right. I know this is calc now but Im posting here as Im missing some simple algebra/arithmetic
All your considerations and calcuations are correct.

$v(u)=\frac1{\sqrt{u}}=u^{-\frac12}$

You differentiated the function correctly:

$v'(u)=-\frac12 \cdot u^{-\frac32} = -\frac1{2 u^{\frac32}}= -\frac1{2 u^{1+\frac12}}=-\frac1{2 u \cdot \sqrt{u}}$

3. ## Re: Question on having the root of a variable in denominator

Ah I see, great thankyou.


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## Extended Essay : Almost completely done !

Yeah … finally, I’ve been working on this damn paper for about a year now. The final product is almost here, it just needs some proofreading and making sure all the correct citations are in place. Then I get to hand it in and make rude hand gestures. As it is, I feel absolutely great about the product I have, but it needs a little bit of polish still. I’ll give it a few days to rest before I attack it with my pen, especially to get away from having any sort of close attachment to the words as they are now. Serious, odd, wacky details after the jump, ’cause it’s some pretty hefty mathematics.

So, I wrote the paper about Andrew Wiles’ proof of Fermat’s Last Theorem. For those who do not know what FLT is, here it is:

There do not exist integral (whole number terms) $x, y,$ or $z$ such that $x^n + y^n = z^n$, for some $n>2$.

Yeah, it looks like the Pythagorean Theorem $a^2 + b^2 = c^2$. But it’s a little more twisted than that. The idea is simple, but the implementation is tricky, because it involves four possible infinities, which makes proving the statement nigh impossible.

In short (given that the paper is 15 pages, I can go on for a while … ) Wiles caused a general revolution in how proofs are created, and paved the way for later work which relied on highly unorthodox methods of writing proofs in order to generate new knowledge.

Yeah … it’s a paper. A now-written paper. Which feels really good right about now.