content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Power Series
May 10th 2010, 08:16 PM #1
Super Member
Joined
Feb 2008
Posts
535
Power Series
Find the power series expansion about the given point of the function:
z^3 + 6z^2 - 4z -3 about z0 = 1
Can someone show how to do this...
Thanks in advance
Is...
$f(z) = z^{3} + 6 z^{2} - ... | 5 | [
-0.1103515625,
-0.011962890625,
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0.109375,
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0.0084228515625,
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0.017822265625,
0.046875,
-0.032958984375,
0.03271484375,
-0.02392578125,
0.0390625,
0.0079345703125,
-0.048828125,
-0.02294921875,
-0.04541015625,
-0.05859375,
0.... | 43,000 | 43000 | |
Attack on CRT-RSA
up vote 8 down vote favorite
The survey paper of Prof. Dan Boneh entitled "Twenty years of attacks on the RSA cryptosystem" mentioned that (Page 5) one can attack CRT-RSA in square root of decryption exponent. However no
argument is given. I know this comes from man-in-the-middle attack. However I ca... | 4 | [
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0.078125,
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0.052734375,
0.0012054443359375,
-0.03125,
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-0.056396484375,
0... | 43,001 | 43001 | |
lowest rate refinance
Chapter 4
Managing Interest Rate Risk:
Gap and Earnings Sensitivity
Asset and liability
management
The phrase, asset – liability
management has generally; however,
come to refer to managing interest
rate risk
Interest rate risk
… unexpected ... | 4 | [
0.0498046875,
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0.04736328125,
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0.042724609375,
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-0.005889892578125,
-0.030029296875,
-0.01904296875,
0.0012969970703125,
-0.055175781... | 43,002 | 43002 | |
find all numbers c that satisfy the conclusion of the Mean Value Theorem.
f(x)=e^(-3x) interval=[0,3] - Homework Help - eNotes.com
find all numbers c that satisfy the conclusion of the Mean Value Theorem.
f(x)=e^(-3x) interval=[0,3]
The question is Find c such that `f'(c)=(f(3)-f(0))/3=(e^-3-1)/3`
`f'(x)=-3(e^(... | 5 | [
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0.06787109375,
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0.076171875,
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0.0245361328125,
0.027587890625,
-0.095703125,
-0.1220703125,
-0.02282714843... | 43,003 | 43003 | |
Math Help
December 27th 2009, 08:22 PM #1
Senior Member
Joined
Jul 2009
From
Singapore
Posts
338
Expansions
$f(x)=\frac{2x}{(x+1)^2(x^2+1)}=\frac{1}{x^2+1}-\frac{1}{(x+1)^2}$
Find the seires expansion of $\log \left[ \frac{f(x)}{2x}\right]$ up to $[x^4]$
$\log\left[\frac{f(x)}{2x}\right]=\... | 5 | [
0.06201171875,
0.0235595703125,
0.07666015625,
0.0537109375,
0.0693359375,
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0.0361328125,
0.04052734375,
0.023193359375,
0.072265625,
-0.03173828125,
-0.00102996826171875,
0.058349609375,
-0.05615234375,
0.0322265625,
-0.0277099609375,
0.0583496... | 43,004 | 43004 | |
6. Power and sample size
The power of an experiment is the probability that it can detect a treatment effect, if it is present.
The six factors listed here are intimately linked so that if we know five of them we can estimate the sixth one.
• Power
• Sample size,
• Inter-individual variability,
• The magnitud... | 5 | [
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0.06591796875,
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-0.0019989013671875,
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0.05126953125,
0.068359375,
0.00164794921875... | 43,005 | 43005 | |
Proof by mathematical induction of a recursion equation
September 28th 2009, 05:56 PM #1
Newbie
Joined
Sep 2009
Posts
4
Proof by mathematical induction of a recursion equation
The recursion equation for the problem:
A "codeword" from alphabet {0,1,2,3} is said to be "legitimate" if it contains an ev... | 5 | [
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0.0228271484375,
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... | 43,006 | 43006 | |
Line bundles on fibrations
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
Let $f:Y \to X$ be a flat morphism with positive dimensional fibers. Is it always true that line bundles that are trivial along each fiber are of t... | 5 | [
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Which differential equations allow for a variational formulation?
up vote 23 down vote favorite
16
Many ODE's and PDE's arising in nature have a variational formulation. An example of what I mean is the following. Classical motions are solutions $q(t)$ to Lagrange's equation $$ \frac{d}{dt}\frac{\
partial L(q,\dot q)}... | 4 | [
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-0.0... | 43,008 | 43008 | |
inverse laplace transform
How to show that $L^{-1} [\frac{6}{(s^2+2s+2)^2}]=3\exp(-t)sin(t)-3t\exp(-t)cos(t)$ where $L^{-1}[F(s)] = f(t)$ is the inverse laplace ? Ty
$\mathcal{L}\{3e^{-t}\sin t-3e^{-t}\cos t\}=3\mathcal{L}\{e^{-t}\sin t\}-3\mathcal{L}\{e^{-t}\cos t\}$ . Now use $\mathcal{L}\{e^{-at}\sin bt\}=\frac{b}{... | 5 | [
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0.0166015625,... | 43,009 | 43009 | |
Survey Respondents Flip Coins
Associated Topics || Dr. Math Home || Search Dr. Math
Survey Respondents Flip Coins
... | 4 | [
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Pulling Pushing and Grouping for Image Segmentation
Pulling, Pushing and Grouping for Image
Segmentation
Guoping Qiu1 and Kin-Man Lam2
1
School of Computer Scienc... | 4 | [
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twisting function
Context
Cohomology
Special and general types
Special notions
Variants
Operations
Theorems
Contents
Idea
The notion of twisting functions is an explicit simplicial formula for a cocycle with values in a simplicial group. The twisted product induced from the twisting function is an explicit sim... | 4 | [
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0.018... | 43,012 | 43012 | |
Infinite sequences and series?
June 1st 2011, 01:58 PM #1
Senior Member
Joined
Dec 2010
From
CPT
Posts
302
Infinite sequences and series?
Find the limit as n approaches infinity
1. (n^3-2)/(n^2)
(n^3/n^2) -2/n^2)/ (n^2/n^2)
(n-2/n^2) I am not sure how to proceed now
2. (7-2n)/(5n)... | 4 | [
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0.00518798828125,
0.0556640625,
... | 43,013 | 43013 | |
Benchmark of Femlab_ Fluent and Ansys
B ENCHMARK OF F EMLAB , F LUENT
AND A NSYS
O LIVIER V ERDIER
Preprints in Mathematical Sciences
2004:6
CENTRUM SCIENTIARUM MATHEMATICARUM
Centre for Mathematical Sc... | 4 | [
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-0... | 43,014 | 43014 | |
[SOLVED] Help sovling a simple equation
February 15th 2008, 04:19 PM #1
brenoink
Guest
[SOLVED] Help sovling a simple equation
sin(theta)(V2) - (V1)(d1) = (d2)cos(theta)
I need to solve this for theta.
I wasn't sure where to put this, so I put it here as it seems most general.
This isn't for a clas... | 5 | [
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0.13... | 43,015 | 43015 | |
Curve
Math::PlanePath::SierpinskiCurve -- Sierpinski curve
use Math::PlanePath::SierpinskiCurve;
my $path = Math::PlanePath::SierpinskiCurve->new (arms => 2);
my ($x, $y) = $path->n_to_xy (123);
This is an integer version of the self-similar curve by Waclaw Sierpinski traversing the plane by right triangles. The d... | 5 | [
0.004425048828125,
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0.0322265625,
-0.050048828125,
0.01171875,
-0.140625,
-0.061279296... | 43,016 | 43016 | |
or
Lesson κδ': A Theorem from the Optics
What seems obvious is not always true
The mathematical theory of perspective was well-developed in ancient times, when it was known as Optics. The theory was lost, then rediscovered in the renaissance by Alberti and others. Euclid's
Optics, a treatise on elementary perspective... | 4 | [
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-0.08154296875,
0.005584716796875,
0.05... | 43,017 | 43017 | |
Computing Permutations with Partial Duplicates
up vote 0 down vote favorite
1
I am looking for a way to compute the number of $K$ permutations of a multiset with $N*D$ elements where each group has exactly $D$ equal elements (and typically $D < N$ ).
I've got an application that actually generates these unique permut... | 5 | [
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0.039794921875,
-0.05859375,
0.006378173828125,
0.0732421875,
0.055908203125,
0.064453125,... | 43,018 | 43018 | |
Volume 5,
Volume 5, Issue 6, June 1964
•
View Description Hide Description
The procedure proposed by I. E. Segal for the quantization of nonlinear problems of field theory is here applied to the one‐dimensional oscillator. It is shown that for the linear oscillator
Segal's procedure is equivalent to t... | 4 | [
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0.00473022460937... | 43,019 | 43019 | |
Finding Two Orthogonal Vectors in R3
Date: 12/15/2003 at 21:03:14
From: Emerson
Subject: Find two non zero vectors in R3 ..........
I'm supposed to find two non-zero vectors in R3 that are orthogonal,
but I'm pretty confused about the whole idea. Can you explain it to me?
Date: 12/25/2003 at 20:15:46
From: Doctor... | 4 | [
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Binary Matrix Multiplication
Feb 3, 2014
Binary Matrix Multiplication
I put this code together as part of my CS 238 class (Discrete Math 2). In our current exploration (project), we need to analyze binary (zero-one) matrices for certain properties. One of these
properties is transitive. The easiest way to test if a b... | 4 | [
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0.072265625,
-0.00384521484375... | 43,021 | 43021 | |
Dickson-Hardy-Littlewood theorems
From Polymath1Wiki
(Difference between revisions)
Teorth m (fix typo)
( Newer edit →
Talk
... | 4 | [
0.026611328125,
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-... | 43,022 | 43022 | |
Math Forum Discussions
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Topic: Testing differences on a normal sample pair
Replie... | 5 | [
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0.046875,
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0.060791015625,
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0.01251220703125,
-... | 43,023 | 43023 | |
Existence of positive solutions for fourth-order semipositone multi-point boundary value problems with a sign-changing nonlinear term
Abstract
In this article, some new sufficient conditions are obtained by making use of fixed point index theory in cone and constructing some available integral operators together with ... | 5 | [
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0.02734375,
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probability of girls sit together/ seperated
July 6th 2014, 07:51 AM #1
Member
Joined
Apr 2014
From
canada
Posts
136
probability of girls sit together/ seperated
Ten Students sit in a row. Find the probability of 6 boys and 4 girls can be arranged if (i) all girls are side by side?
(ii) all girls... | 4 | [
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0.0249023437... | 43,025 | 43025 | |
Derivation using Logical Laws
August 3rd 2011, 06:10 AM
demode
Derivation using Logical Laws
Let A be the statement form $(eg p \to (q \leftrightarrow r))$. Find a statement form B in "relaxed" disjunctive normal form which is logically equivalent to A. Then Show that $A \approx B$ (i.e.
derive B from A usin... | 5 | [
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0.010559082031... | 43,026 | 43026 | |
antiderivative.
I think I can read it correctly. In latex (when it works again) $\int_{0}{1} \sqrt{9+4t^2}dx$. In easier to read type: int sqrt(9+4t^2)dt, evaluated from 0 to 1. Before I do this, have you studied
trig substitution, because if you haven't this might be slightly difficult to get at first?
i know some tr... | 4 | [
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0.0234... | 43,027 | 43027 | |
A new formula for Apery's constant and other zeta(2n+1)?
11 Jun
A new formula for Apery’s constant and other zeta(2n+1)?
I. Introduction
In Identities Inspired from Ramanujan’s Notebooks, Simon Plouffe recounts how, based on Ramanujan’s,
\begin{aligned}\sum_{k=1}^\infty \frac{\coth(\pi k)}{k^3} = \frac{7}{180}\pi^3... | 4 | [
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0.0025177001953125,
-0.041015625,
-0.03564453125,
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-0.007934570312... | 43,028 | 43028 | |
quare
Statistics::ChiSquare - How well-distributed is your data?
use Statistics::ChiSquare;
print chisquare(@array_of_numbers);
Statistics::ChiSquare is available at a CPAN site near you.
Suppose you flip a coin 100 times, and it turns up heads 70 times. Is the coin fair?
Suppose you roll a die 100 times, ... | 5 | [
-0.037841796875,
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-0.0... | 43,029 | 43029 | |
How do photons travel by Miles Mathis
return to homepage
return to updates
HOW DO PHOTONS TRAVEL?
by Miles Mathis
milesmathis.com
email... | 4 | [
-0.03125,
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The Magnetized Universe - M. Giovannini
5.3. Physical scales in the evolution of magnetic fields
When MHD is discussed in curved spce-times, the evolution of the geometry reflects in the time evolution of the physical scales of the problem.
5.3.1. Before matter-radiation equality
From Eq. (5.32), the comoving moment... | 4 | [
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Retaining Wall Design Calculations
Retaining Wall Design Calculation Example
The cross section of a cantilever retaining wall is shown in figure 8.10.Calculate the factors of safety in regards to overturning,sliding and bearing capacity.
Solution:
From the figure ,
H’=H[1]+H[2]+H[3]=6tan10⁰+18+2.75=21.81ft , ... | 5 | [
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-... | 43,032 | 43032 | |
How can we condition on events with probability 0?
May 18th 2013, 08:44 AM #1
Member
Joined
Feb 2011
Posts
83
Thanks
2
How can we condition on events with probability 0?
We are given that the joint density of X and Y is
$f(x,y) = \begin{cases} & .5 \; \text{if } \; 0 \leq x \leq .5 \; \;\text{an... | 4 | [
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-0.0062255859375,... | 43,033 | 43033 | |
The notch shape data
Reading in and preprocessing the data
The first step is to read in the data. Assume that the original data are held in the file
notchshape.dat in the same directory as the Splus data files. In practice you will have the
data in some other directory... | 4 | [
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... | 43,034 | 43034 | |
Mix.lorenz.html
1. Lorenz, E. N. 1963. Deterministic nonperiodic flow. J. Atm. Phys. 357:130-141. The Lorenz equations are a "three mode" approximation of the partial differential equation describing convective flow
in a fluid heated from below. The equations themselves may be written as follows:
dx/dt = a... | 4 | [
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Cardinal Numbers
August 23rd 2009, 08:44 AM
adam63
Cardinal Numbers
This question has two parts - I've solved the first part, only I can't seem to find a way to solve the second part:
*Let A,B,C be sets. Prove that if B,C ⊆ A , |C|=|B|, and B∩C=http://upload.wikimedia.org/math/c/d...8d7cc238fb.png then |A-B... | 5 | [
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-0.1... | 43,036 | 43036 | |
Induced pretopologies on sSet
up vote 2 down vote favorite
1
Recall that the geometric realisation functor $| - |: sSet \to Top$ preserves products (choosing $Top = k Space$ or similar). Thus any given singleton Grothendieck pretopology on $Top$ gives rise to
a singleton pretopology on $sSet$. I have in mind three, no... | 4 | [
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Convert the Second Order Equation
February 11th 2010, 06:45 AM
Len
Convert the Second Order Equation
Convert the second order equation
$\frac{d^2y}{dt^2}=0$
into a first order system using:
$v=\frac{dy}{dt}$
Then find the general solution for $\frac{dv}{dt}$ equation then sub the solution int... | 5 | [
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0.0500488281... | 43,038 | 43038 | |
Solving for Interval [0, 2pi)
May 8th 2006, 01:06 PM #1
Newbie
Joined
Jan 2006
Posts
20
Trig Product Formula Problem
My question states: cos(3x)+cos(x)=0
I got two answer pi/2 and pi/4 but there are supposed to be more, can you show me how to get all the answers?
Thanks alot
Solving for Interval... | 4 | [
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Variance of the sum of N independent variables
January 31st 2009, 08:14 AM #1
Member
Joined
Jan 2009
Posts
83
Variance of the sum of N independent variables
Let X1,X2,...XN be independent identically distributed random variables, where N is a
non-negative integer valued random variable. Let Z = X1 + ... | 5 | [
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WattNode Pulse - Option Kh - Watt-Hours Per Pulse
WattNode Pulse - Option Kh - Watt-Hours Per Pulse
Overview
Option Kh (watt-hours per pulse or Kh Watthour Constant) specifies number of watt-hours that must accumulate for each pulse generated by the meter. Each pulse includes an ON (conducting) and OFF
period. The n... | 4 | [
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Measures....
May 1st 2007, 04:22 PM
lprox015
Measures....
Quadrilateral PQRS is a rectangle with diagonals PR and QS. If the measure of angle 1 = 18, find the measures of angles 2, 3, and 4. Explain how to get the answer please. Thanks in advance!
May 1st 2007, 06:01 PM
Jhevon
Quote:
triangle RST is... | 4 | [
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Integration by substitution
integrate[1/(x^2(x^2 +1)^0.5)] - Wolfram|Alpha I don't entirely understand the first step. Could someone elaborate? I understand the basic idea of
integration by sunstitution.
See the second bullet point: Trigonometric substitution - Wikipedia, th... | 5 | [
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Measure Noise Without A Calibrated Source
This new technique is based on a variation of the Y-factor method to achieve accurate noise-figure measurements without the need for a calibrated noise source.
What is in this article?:
• Making a noise-figure measurement
It is possible to measure the noise figure of a com... | 4 | [
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0.0654296875,... | 43,044 | 43044 | |
Weighted Averages
Weighted Averages
Definition: This is a term that is used, mis-used and often over used. Typically, many
individuals refer to average when they really mean the arithmetic average (mean). Average
can mean the mean, the median and the m... | 4 | [
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0.045898... | 43,045 | 43045 | |
matlab - defining boundaries
December 14th 2009, 09:21 PM #1
Newbie
Joined
Oct 2009
Posts
24
matlab - defining boundaries
Hi
I'm writing a script in matlab to simulate waves in a string such that "For this example, we assume a string of length 100 cm and a step size in x (along the string) of 1 cm. W... | 4 | [
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I'm so lost.... normal distribution & standard deviation
January 30th 2009, 02:54 PM #1
Newbie
Joined
Jan 2009
Posts
2
I'm so lost.... normal distribution & standard deviation
Ok, so I give in. I have no clue how to do this. Can anybody help?? I would love a step-by-step explanation of how to find the an... | 5 | [
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-0.0952... | 43,047 | 43047 | |
solve the exponential equation
December 7th 2009, 03:26 PM
cmmason
solve the exponential equation
Solve for x.
pi^7x-1 = e^8x
I think I need to take the natural log of both sides. but I don't know what to do after this step-
The answer should be exact, which means it should be written with ln and... | 5 | [
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-0.02197265625,
-0.11865234375,
-0.0194... | 43,048 | 43048 | |
A rate of change problem
Hi Frank,
I sketched the curve and marked a point P on the curve with first coordinate x. Since the curve is
y = x^2 + 1
the point P has coordinates (x, x^2 + 1).
Let s(x) be the distance between the origin O and the point P then
s(x) = [(x^2 + (x^2 + 1)^2 ]^1/2 = [x^4 + 3 x^2 + 1]... | 4 | [
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0.01544189453125,
... | 43,049 | 43049 | |
Math Help
July 17th 2006, 09:31 PM #1
Junior Member
Joined
Jun 2006
Posts
59
addition
NR
+ RN
_______
ABC
The addition problem above is correct. If N, R, A, B, and C are different digits, what is the greatest possible value of B+C?
Judi
NR
+ RN
_______
ABC
Th... | 4 | [
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-0.004547119140625,
-0.0184326171875,
-0.04150390625,
-0.015319... | 43,050 | 43050 | |
splitting field of a finite set of polynomials
splitting field of a finite set of polynomials
Lemma 1.
(Cauchy,Kronecker) Let $K$ be a field. For any irreducible polynomial $f$ in $K[X]$ there is an extension field of $K$ in which $f$ has a root.
Proof.
If $I$ is the ideal generated by $f$ in $K[X]$, since $f$ is ... | 5 | [
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0.0257568359375,
-0.050537109375,
0.09375,
-0.06787109375... | 43,051 | 43051 | |
acquired by Altair Engineering and
Isentropic and Ideal Gas Density Relationships
Consider the subsonic flow of a real gas through a smooth duct with a contraction and expansion forming a gradually converging and diverging nozzle. An idealization of this type of flow is to assume
that the flow is isentropic. i.e. en... | 4 | [
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-0.02... | 43,052 | 43052 | |
Area and Perimeter: Isoperimetric Quotient
Date: 12/05/2001 at 06:41:20
From: Ace
Subject: Isoperimetric Quotients
I am stuck on what the isoperimetric quotient of a two-dimensional
shape actually is. Is it a measure of compression? Please explain in
detail.
Ace
Date: 12/05/2001 at 16:08:18
From: Doctor Peterson
... | 4 | [
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0.0390625,
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0.10791015625,
-0.01324462890625,
-0.01531982421875,
0.046630859375,
0.086425781... | 43,053 | 43053 | |
Characteristic surface for systems of PDE
up vote 5 down vote favorite
2
Despite the title, this is probably actually a question in linear algebra or algebraic geometry. Let me write the question(s) first, before I explain the background.
Problems
Let $h^{\mu\nu}_{ij}$ represent a map from $\mathbb{R}^4\otimes\mathb... | 4 | [
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0.000522613525390625,
0.0888671875,
-0.1015625,
0.040283203125,... | 43,054 | 43054 | |
Combinations of Prisoners
Date: 09/02/97 at 16:10:04
From: Sara
Subject: Combinations
Nine prisoners are taken for their daily exercise handcuffed together
in threes. How would the warden arrange the men each day so that no
two men are handcuffed together more than once over a six-day period?
I have tried out differ... | 4 | [
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-0... | 43,055 | 43055 | |
Integration by Parts
Associated Topics || Dr. Math Home || Search Dr. Math
Integration by Parts
Date: 04/10/2008 at ... | 5 | [
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-0.0001277923583984375,
0.02734375,
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0.046142578125,
-0.02685546875,
-0.08154296875,
0.0006256103515625,
0.04370117187... | 43,056 | 43056 | |
Gauge connections and Lie algebras?
up vote 4 down vote favorite
5
I'm probably missing something obvious, but I've been wondering what the motivation is for requiring the components $A_\mu$ in a local trivialization of a gauge connection on a smooth principal
$G$-bundle to lie in $\mathfrak{g}$, the Lie algebra of $G... | 4 | [
-0.134765625,
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-0.072265625,
0.00311279296875,
0.03076171875,
-0.0034637451171875,
0.007659912109375,
0.02819... | 43,057 | 43057 | |
M
2. LOCAL MOMENTS: VARIANCES AND LINEAR REGRESSION
Let x) be the field of mass-density fluctuations and g (x) the corresponding field of galaxy-density fluctuations, at a given time and for a given type of object. The fields are both smoothed with a
fixed window which defines the term ``local''. The local biasing re... | 4 | [
-0.03857421875,
-0.01361083984375,
0.09619140625,
0.052734375,
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0.0054931640625,
-0.055419921875,
-0.02978515625,
-0.0111083984375,
0.040771484375,
-0... | 43,058 | 43058 | |
convergence help
November 7th 2009, 02:24 PM #1
Junior Member
Joined
Sep 2009
Posts
53
convergence help
For each positive integer n, let
{y_n}= 1 + 1/2 +...+1/n- the integral of (1/x) from 1 to n.
Prove that the sequence {y_n} converges.
Proof of monotone decreasing: $y_{n-1}-y_n=\sum_{k=1... | 5 | [
-0.03271484375,
0.006134033203125,
0.11328125,
-0.031494140625,
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0.09765625,
-0.0703125,
-0.010498046875,
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0.005828857421875,
-0.007049560546875,
-0.0213623046875,
-0.04248046875,
0.007598876953125,
0.10498046875,
-0.0... | 43,059 | 43059 | |
Example 7.30: Simulate censored survival data
To simulate survival data with censoring, we need to model the hazard functions for both time to event and time to censoring.
We simulate both event times from a Weibull distribution with a scale parameter of 1 (this is equivalent to an exponential random variable). The ev... | 5 | [
-0.0019989013671875,
-0.0303955078125,
-0.042236328125,
0.0537109375,
0.07275390625,
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0.046142578125,
0.08056640625,
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0.08056640625,
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0.0576171875,
-0.00762939453125,
0.0250244140625,
-0.0927734375,
0.048095703125,
-0.062... | 43,060 | 43060 | |
equivariant cohomology
Context
Cohomology
Special and general types
Special notions
Variants
Operations
Theorems
Representation theory
Contents
Idea
Equivariant cohomology is cohomology in the presence of and taking into account group-actions (and generally ∞-group ∞-actions) both on the domain space and on t... | 4 | [
-0.08544921875,
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-0.0291748046875,
0.01422119140625,
-0.0228271484375,
-0.034912109375,
0.05078... | 43,061 | 43061 | |
The Theory of Monads and the Monad Laws
As promised, I’m finally going to get to the theory behind monads. As a quick
review, the basic idea of the monad in Haskell is a hidden transition function – a
monad is, basically, a state transition function.
The theory of monads comes from category theory. I’m going to assume... | 4 | [
0.01483154296875,
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0.036865234375,
0.01123046875,
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-0.0087890625,
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0.01043701171875,
0.0498046875,
0.00775146484375,
-0.003616333007... | 43,062 | 43062 | |
i
Math::PlanePath::CoprimeColumns -- coprime X,Y by columns
use Math::PlanePath::CoprimeColumns;
my $path = Math::PlanePath::CoprimeColumns->new;
my ($x, $y) = $path->n_to_xy (123);
This path visits points X,Y which are coprime, ie. no common factor so gcd(X,Y)=1, in columns from Y=0 to Y<=X.
13 | ... | 4 | [
0.054443359375,
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-0.032958984375,
-0.00... | 43,063 | 43063 | |
Thinking/InquiryProblem Solving: Logarithms
September 17th 2009, 11:46 PM #1
Member
Joined
Sep 2009
Posts
83
Thinking/InquiryProblem Solving: Logarithms
I am having some difficulty with this question. All I really know how to do is rewrite it.
If $\log{a}{b} = \frac{1}{x}$ and $\log{b}{\sqrt{a}} = 3... | 4 | [
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0.034912109375,
0.0810546875,
0.09619140625,
-0.1279296875,
0.096... | 43,064 | 43064 | |
Improper Integral Evaluation
September 14th 2009, 11:27 AM #1
Newbie
Joined
Aug 2009
Posts
6
Improper Integral Evaluation
Does anyone know how to find the integral of abs(x)e^((-x)^2)dx from negative infinity to infinity? I can't quite figure out how to do this...
See attachment
hmmm... strange... | 4 | [
0.009521484375,
0.0306396484375,
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-0.001953125,
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0.1279296875,
-0.08447265625,
... | 43,065 | 43065 | |
Perturbation Methods for Image Synthesis
Chen, Min (1999) Perturbation Methods for Image Synthesis. California Institute of Technology . (Unpublished) http://resolver.caltech.edu/CaltechCSTR:1999.cs-tr-99-05
Postscript
See Usage Policy.
15Mb
Other (Adobe PDF (1.30MB))
See Usage Policy.
1268Kb
Use this Per... | 4 | [
-0.0115966796875,
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0.0751953125,
-0.055908203125,
0.0299072265625... | 43,066 | 43066 | |
Arbitrary products of schemes don't exist, do they?
up vote 27 down vote favorite
11
Thinking of arbitrary tensor products of rings, $A=\otimes_i A_i$ ($i\in I$, an arbitrary index set), I have recently realized that $Spec(A)$ should be the product of the schemes $Spec(A_i)$, a
priori in the category of affine schemes... | 4 | [
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0.0135498046875,
-0.03662109375,
0.0439453125,
0.09716796875,
0.030517578125,
-0.... | 43,067 | 43067 | |
gaussian quadrature
up vote 1 down vote favorite
1
Gaussian quadrature allows us to integrate polynomials up to order $2 n-1$ using only $n$ function values.
$\int_{x_0}^{x_1} ( \sum_{i=0}^{2 n-1} a_i x^i ) dx = f(a_0, \dots , a_{2 n-1}) $
thus, the function $f(a_0, \dots , a_{2 n-1})$, which naively has $2 n$ param... | 4 | [
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-0.0703125,
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0.04248046875,
-0.01495361328125,
0.07324... | 43,068 | 43068 | |
Roundoff Error
Robert P. Munafo, 1996 Dec 3.
There are two ways to look at roundoff error, which are essentially "pure" and "applied".
The pure approach looks at the theoretical error term in each calculation in the iteration of a point, to see how far a point can be iterated while still guaranteeing that the answer... | 4 | [
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-0.09326171875,
-0.0235595703125,
-0.011... | 43,069 | 43069 | |
simplify log derivative/distribution
December 10th 2011, 09:08 PM #1
Member
Joined
Sep 2011
Posts
106
Thanks
1
simplify log derivative/distribution
I have been having trouble trying to follow along an example of, finding the derivative of $(11x)^{ln11x}$ .
Using the property $A^r = rlnA$
$l... | 5 | [
-0.00567626953125,
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0.099609375,
0.03466796875,
-0.0211181640625,
-0.08154296875,
0.0... | 43,070 | 43070 | |
On Benabou and Johnstone definition of "locally small" fibred (indexed) category
up vote 2 down vote favorite
Let $P: \mathcal{C}\to\mathcal{S}$ a fibration ($\mathcal{S}$ with finite limits).
In "Sketches of an Elephant I", pag. 272 P. Johnstone define $P$ a locally small if:
given any two objects $X, Y\in \mathcal... | 4 | [
0.0167236328125,
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0.0419921875,
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0.0257568359375,
0.0771484375,
0.002044677734375,
-0... | 43,071 | 43071 | |
Approach to this integral
May 28th 2008, 07:58 AM #1
Junior Member
Joined
Feb 2008
Posts
45
Approach to this integral
This needs to be integrated:
1/(e^(2x) + e^(x)) w/respect to x
Can't do partial fractions because e^x never equals zero. Right? Any suggesions? Thanks,
JN
I would go a... | 5 | [
-0.05712890625,
0.0654296875,
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0.04541015625,
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0.021728515625,
0.035888671875,
0.0089111328125,
-0.0732421875,
0.050537109375,
... | 43,072 | 43072 | |
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Topic: fsolve trust-region radius question
Replies: 2 Las... | 5 | [
-0.00160980224609375,
-0.0255126953125,
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0.004425048828125,
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0.05712890625,
0.01202392578125,
0.041015625,
0.0546875,
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0.053955078125,
0.039794921875,
0.0303955078125,
-0.012451171875,
-0.048828125,
-0.11... | 43,073 | 43073 | |
A very very good approximation to Ramanujan constant. Why?
up vote -2 down vote favorite
(2 * 2 * 2 * 3 * 5 * 5 * 5 * 415752385339879101618702506672691517522274861954331757391122938598028498597433207031)^1/5 ~ (very very close to Ramanujan constant)
Would anyone have an idea of why this prime factorisation to the 1/5... | 4 | [
-0.038818359375,
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0.07568359375,
0.043212890625,
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0.02294921875,
0.07177734375,
-0.006561279296875,
-0.0169677734375,
-0.0296630859375,
-0.000469207763671875,
-0.036865234375,
0.0546875,
-0.01361083984375,
-0.053466796875,
0.0588378... | 43,074 | 43074 | |
Accelerated Motion Lab
Phy 211: General Physics I Lab Fall 2006
PCC-Cascade page 1 of 4
Experiment: Accelerated Motion
You... | 4 | [
-0.05615234375,
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0.03271484375,
-0.018798828125,
0.03955078125,
-0.0213623046875,
0.0089... | 43,075 | 43075 | |
Interpolating between piecewise linear functions, with a family of smooth functions
up vote 13 down vote favorite
2
Let $[a,b)\subset\mathbb R$, and $F,G:[a,b)\to\mathbb R$ two decreasing piecewise linear functions so that $F(x)\leq G(x)$ for any $x\in[a,b)$. We assume that:
1. there is a number $k\in\mathbb N-\{0\}... | 4 | [
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-0.0791015625,
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-0.08740234375,
0.031494140625,
0.03173828125,
0.033447265625,
-0.0039978027343... | 43,076 | 43076 | |
Classifying a Quadrilateral | Geometry How To Help
If you are reading this lesson, then you are pretty far through your geometry course. The focus of that course has probably concentrated on proving lines parallel and triangles congruent. In a
traditional textbook, this is usually the first lesson in a unit about quadr... | 4 | [
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0.006103515625,
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0.01708984375,
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0.04248046875,
-0.0164794921875,
-0.06201171875,
-0.0576171875,
0.0576171875... | 43,077 | 43077 | |
Hausdorff Dimension and Hölder Continuity
up vote 10 down vote favorite
1
Suppose we have a curve γ : [0,1] -> ℝ^n. It is well known that if this curve is Hölder continuous for some exponent α then the Hausdorff dimension of γ[0,1] is bounded above by 1/α.
My question is: Is there a partial converse of the following ... | 5 | [
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-0.00628662109375,
0.004119873046875,
-0.007476806640625,
-0.03466796875,
... | 43,078 | 43078 | |
Modeling antiviral resistance, VII: more on the rule book
[A series of posts explaining a paper on the mathematical modeling of the spread of antiviral resistance. Links to other posts in the series by clicking tags, "Math model series" or "Antiviral model
series" under Categories, left sidebar. Preliminary post here. ... | 4 | [
-0.057861328125,
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0.0296630859375,
0.06884765625,
-0.023681640625,
0.1298828125,
0.032958984375,
0.0849609375,
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0.0283203125,
0.10498046875,
0.0537109375,
-0.037353515625,
-0.00482177734375,
-0.0277099609375,
-0.040... | 43,079 | 43079 | |
Generators of symmetric group
up vote 2 down vote favorite
Hi
Let $n$ be an odd natural number (sufficiently large), and $ 1\leq t,k < n $. Let $A= \{ a_{1},a_{2},\ldots,a_{t} \} $, $B= \{ b_{1},b_ {2},\ldots,b_{n-t} \} $, $C= \{ c_{1},c_{2} \ldots,c_{k} \} $
and $D= \{ d_{1},d_{2},\ldots,d_{n-k} \} $ be subsets of $... | 5 | [
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-0.091796875,
-0.05712890625,
0.072265625,
0.038818359375,
-0.02... | 43,080 | 43080 | |
Math Forum Discussions
Re: Defining "f o g" with Functions
Posted: Oct 15, 2012 3:17 AM
f={(a,b)} implies f(a)=b
f o g (x)=f(g(x))
f o g =(1,6), (2,4),(3,7),(4,4),(5,3) since g maps 1 to 2, which f maps to 6, and g maps 2 to 3, which f maps to 4 etc.
g is not one-to-one since both 2 and 4 are mapped to 3. f is one-to-... | 4 | [
-0.03564453125,
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0.01239013671875,
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0.033203125,
0.005767822265625,
-0.091796875,
-0.052001953125,
0.07177734375,
-0.0541... | 43,081 | 43081 | |
The Union of Complexity Classes
We often see the intersection of two classes as an interesting class in and of itself. For example factoring is in NP∩co-NP. In some cases you get interesting equalities, like that ZPP is equal to
RP∩co-RP. But we rarely see the union of two classes. Every wonder why?
In fact, no comple... | 4 | [
-0.007659912109375,
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0.05810546875,
0.051513671875,
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0.0517578125,
0.0157470703125,
-0.037353515625,
-0.0179443359375,
-0.0502929... | 43,082 | 43082 | |
Fueling the AGN - F. Combes
2.4. Black hole growth by star accretion
Let us compute the time required to reach the critical mass M[c] where R[T] = R[g], above which stars are swallowed by the black hole without any gas radiation (M[c] = 3 10^8 M[]). When a tidal
breakup of a star (of mass m, radius R) occurs, the ener... | 4 | [
-0.039306640625,
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0.00299072265625,
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0.042236328125,
0.0189208984375,
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-0.030029296875,
-0.030029296875,
-0.0299072265625,
0.0174560546875,
0.057861328125... | 43,083 | 43083 | |
Sorting Strings with Three-Way Radix Quicksort
Jon is a member of technical staff at Bell Labs. Robert is the William O. Baker Professor of Computer Science at Princeton University. They can be reached at jlb@ research.bell-labs.com and
rs@cs.princeton .edu, respectively.
Quicksort is a champion all-around sorting alg... | 4 | [
-0.0211181640625,
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Poisson Lie algebroid
Context
$\infty$-Lie theory
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Examples
$\infty$-Lie groupoids
$\infty$-Lie groups
$\infty$-Lie algebroids
$\infty$-Lie algebras
Symplectic geometry
Backg... | 4 | [
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... | 43,085 | 43085 | |
How solve equation?
floor[(3x+1)/2] = x+1? - Homework Help - eNotes.com
How solve equation?
floor[(3x+1)/2] = x+1?
Using the definition of floor function yields that `floor[(3x+1)/2]` is the greatest integer `k <= x + 1` , hence, considering `x + 1 = k` , yields:
`x + 1 = k => x = k - 1`
Replacing `k - 1` for `x`... | 4 | [
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0.01306152343... | 43,086 | 43086 | |
Structural stability on the circle
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
How can i proove that on the space of circle diffeomorphisms with the C-r topology, Morse Smale diffeomorphisms and Structurally stable d... | 5 | [
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Stress, Strain
Tensors: Stress, Strain and Elasticity
by Pamela Burnley, University of Nevada Las Vegas
Outline
Introduction
Many physical properties of crystalline materials are direction dependent because the arrangement of the atoms in the crystal lattice are different in different directions. If one heats a ... | 4 | [
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Plotting the spirograph equations with 'gnuplot'
Universidad de Oviedo, Departamento de Química Física y Analítica, E-33006-Oviedo, Spain.
[ The author had specifically requested that we keep the large font used in his article in order to match the font size of the equation images; I agreed, since the two would look d... | 4 | [
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Infinite Dimensional Vector Space.
February 15th 2010, 09:13 AM #1
Junior Member
Joined
Oct 2009
Posts
30
Infinite Dimensional Vector Space.
There is a 3 part question that I have been working on.
The first 2 parts are show that for a finite dimensional vector space:
$S \circ T$ is invertible i... | 4 | [
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0.008911132... | 43,090 | 43090 | |
Inverse Kinematics (2 joints) for foot placement
Technology/ Code /
Introduction
Game sometimes need to solve Inverse Kinematics (IK) for more realistic look like foot placement on a terrain. There are different methods to solve an IK problems, some are numerical methods which
can be used for general cases, and analy... | 4 | [
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0.12792... | 43,091 | 43091 | |
integration of natural log
Last edited by Anonymous1; May 10th 2010 at 06:14 AM.
Substitute $t=3x-7$, to get : $\frac{1}{3}\int ln(t) \, dt$ Now, use integration by parts ..
the final answer i get is $(x - \frac{7}{3})ln(3x - 7) - \frac{ln(3x - 7)}{3} + C$ but the answer given is $(x - \frac{7}{3})ln(3x - 7) - x + C$... | 5 | [
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Algorithm to find all (up to isomorphism) perfect matchings of quartic plane graphs
up vote 2 down vote favorite
I need to find all (up to isomorphism) perfect matchings of some quartic plane graphs. I haven't found any specific algorithm to give me all the perfect matchings. Does anybody know about such an
algorithm ... | 5 | [
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0.000429153442... | 43,093 | 43093 | |
product of roots
October 4th 2012, 09:52 AM
ayushdadhwal
product of roots
let P(x)=0 be a polynomial equation of least possible degree with rational coefficients having $\sqrt[3]7+\sqrt[3]49$ as one of its roots
.then the product of all the roots of P(x)=0 is
October 4th 2012, 10:28 AM
HallsofIvy
Re: prod... | 4 | [
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-0.0... | 43,094 | 43094 | |
Differential equation solving related to 2nd Newton's law
February 17th 2011, 09:00 PM
bazingasmile
Differential equation solving related to 2nd Newton's law
Without taking into account friction and resistance to the air, but while taking into account the gravitation force and the altitude. The weight $W$ is dec... | 5 | [
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-... | 43,095 | 43095 | |
direct sum of Banach spaces
Direct sums of Banach spaces
Idea
The concept of direct sum extends easily from vector spaces to topological vector spaces; we wish to explore a similar but more general notion in the case of Banach spaces.
When taking the direct sum of two (or any finite number) of Banach spaces (i.e., i... | 4 | [
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0.0036163... | 43,096 | 43096 | |
Mommy’s Baby, Daddy’s Maybe: A Closer Look at Regression to the Mean
Regression analysis is one of the most useful techniques we have in statistics, and it is applied in a large number of disparate situations. It is used to explain the influence (independent)
variables have on the variability of (outcome) variables, a... | 4 | [
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-0.... | 43,097 | 43097 | |
How does one relate the monodromy of the KZ equations with the WRT representation of the braid group?
up vote 4 down vote favorite
2
The KZ equations on the configuration space of $n$ distinct points in $\mathbb C$ give rise to a representation of $B_n$ on $V^{\otimes n}$, where $V$ is any given representation of $SL(... | 4 | [
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Parametric Form for Equation of a Line
Date: 6/30/96 at 23:45:9
From: Anonymous
Subject: Parametric Form for Equation of a Line
Dr. Math, how can you convert an equation such as:
y = -3x/4 + 7/2
to parametric vector form?
In fact, how is it done generally?
Date: 7/1/96 at 7:37:40
From: Doctor Anthony
Su... | 4 | [
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0.04... | 43,099 | 43099 |