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http://stats.stackexchange.com/questions/6731/using-singular-value-decomposition-to-compute-variance-covariance-matrix-from-li | # Using Singular Value Decomposition to Compute Variance Covariance Matrix from linear regression model
I have a design matrix of p regressors, n observations, and I am trying to compute the sample variance-covariance matrix of the parameters. I am trying to directly calculate it using svd.
I am using R, when I take ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=79376 | Physics Forums
## Group theory problems
Question 1 a
Find the order of
$$(\mathbb{Z}_4 \times \mathbb{Z}_2) \backslash \langle (2,1) \rangle$$.
Question 1 b
Find the order of
$$(\mathbb{Z}_2 \times \mathbb{Z}_4) \backslash \langle (1,1) \rangle$$.
PhysOrg.com science news on PhysOrg.com >> Front-row seats to ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 55, "mathjax_display_tex": 19, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/45422?sort=votes | ## maximal coordinate on a sphere
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What is the easiest (preferably without calculations) way to see that the mean value of $\max(x_1,x_2,\dots,x_n)$ on the sphere $\mathbb{S}^{d-1}= \{ (x_1,\dots,x_n):\ x_1^2+\dot... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/121488?sort=votes | ## A sum involving mod(n) arithmetic
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Hi there, I have been studying the following set (in order to investigate the average of products of Ramanujan sums with some weights):
$$A=\lbrace (n,m) \in \mathbb{Z}/q\mat... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 33, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/49074/cauchy-schwarz-inequality-and-holders-inequality | # Cauchy-Schwarz inequality and Hölder's inequality
It might sound silly, but I am always curious whether Hölder's inequality $$\sum_{k=1}^n |x_k\,y_k| \le \biggl( \sum_{k=1}^n |x_k|^p \biggr)^{\!1/p\;} \biggl( \sum_{k=1}^n |y_k|^q \biggr)^{\!1/q} \text{ for all }(x_1,\ldots,x_n),(y_1,\ldots,y_n)\in\mathbb{R}^n\text{ ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 42, "mathjax_display_tex": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/number-theory/198882-calculation-300-digit-sophie-germain-prime-number.html | # Thread:
1. ## Calculation 300 digit Sophie Germain prime number
I have been set a challenge to produce a 300 digit Sophie Germain prime number using computer code.
Maths at this level is not something that I use a great deal and certain not with these size of numbers. So I apologise if this is all a bit "basic".
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/tagged/history+forces | # Tagged Questions
1answer
490 views
### Combining Proportions to get Newton's Law of Universal Gravitation
I've read a little on the history of Newton's Law of Gravitation and noticed that the formula can be separated into 3 distinct parts that lead to the end result of $F_g = G \frac{m_1 m_2}{r^2}$; the ...
1answe... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/4544/why-is-e-pi-sqrt163-almost-an-integer | # Why is $e^{\pi \sqrt{163}}$ almost an integer?
The fact that Ramanujan's Constant $e^{\pi \sqrt{163}}$ is almost an integer ($262 537 412 640 768 743.99999999999925...$) doesn't seem to be a coincidence, but has to do with the $163$ appearing in it. Can you explain why it's almost-but-not-quite an integer in layman'... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 41, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/30396?sort=newest | ## Derived Algebraic Geometry and Chow Rings/Chow Motives
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I recently heard a talk about Chow motives and also read Milne's exposition on motives. If I understand it correctly, the naive definition of the Chow rin... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 16, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/41784/roots-of-permutations/41866 | ## roots of permutations
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Consider equation $x^2=x_0$ in symmetric group $S_n$, where $x_0\in S_n$ is fixed. Is it true that for each integer $n\geq 1$, the maximal number of solutions (square roots) has identity ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 53, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/1646/is-it-possible-to-distinguish-a-securely-encrypted-ciphertext-from-random-noise/1648 | # Is it possible to distinguish a securely-encrypted ciphertext from random noise?
Say I have a bunch of data encrypted with a secure block cipher (such as AES). An attacker has unlimited access to this encrypted data. The attacker doesn't know whether the data is encrypted or if it's just purely random bits. Is it po... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?t=110545 | Physics Forums
rayleigh jeans formula
I am to derive the incorrect Rayleigh-Jeans formula from the correct Planck formula to show why plank's constant does not appear in the Rayleigh-Jeans formula. I should also recall the Stefen-Boltmann Law
here's what I have but I'm stuck...
Rayleigh-Jeans formula: $$u(\lambda)=... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 24, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/302465/half-sine-and-half-cosine-quaternions | # half sine and half cosine quaternions
Something is a little bit unclear to me. In the image below you see that you need to divide the angle by a half. Acccording to wikipedia they say that this is so that I could rotate clockwise or counter clockwise. The sine function returns a value between 1 and -1. So I don't un... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 51, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.nag.com/numeric/CL/nagdoc_cl23/html/F11/f11grc.html | NAG Library Function Documentnag_sparse_herm_basic_setup (f11grc)
1 Purpose
nag_sparse_herm_basic_setup (f11grc) is a setup function, the first in a suite of three functions for the iterative solution of a complex Hermitian system of simultaneous linear equations. nag_sparse_herm_basic_setup (f11grc) must be called ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 222, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://particlephd.wordpress.com/2009/02/07/the-spin-connection/ | # High Energy PhDs
A discussion of particle physics and strings
February 7, 2009
## The spin connection
Posted by Sparticles under Field Theory
[4] Comments
I’ve been spending some time thinking about spinors on curved spacetime. There exists a decent set of literature out there for this, but unfortunately it’s sc... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 27, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/10086/the-category-of-representations-of-a-group | ## The Category of Representations of a Group
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Do people study the category of representations of a compact finite group (not just irreducible ones)? I'm more interested in small cases like S_3 and SU(2) but I'd b... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/8186/when-do-the-multiples-of-two-primes-span-all-large-enough-natural-numbers | # When do the multiples of two primes span all large enough natural numbers?
It is well-known that given two primes $p$ and $q$, $pZ + qZ = Z$ where $Z$ stands for all integers. It seems to me that the set of natural number multiples, i.e. $pN + qN$ also span all natural numbers that are large enough. That is, there e... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/8095/measuring-acceleration-of-earth-due-to-its-fall-around-the-sun?answertab=votes | # Measuring acceleration of earth due to its fall around the sun
Every orbiting of a satellite around a mass is nothing else but a constant fall - and therefore acceleration - towards this mass. In a way it is a "falling around" that mass.
My question
Is it possible to measure this acceleration on earth due to its "f... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/trigonometry/140871-tricky-sin-equation.html | # Thread:
1. ## Tricky sin equation
Hello!
This is the equation Im stuck with:
$2sin (0.5x) = 3/3x+2$
Im not sure where to start, because I cant take out any of the x values,
should i let 0.5x be a completely new vale like 'y' and but then i will still be stuck
Thank you!
2. Originally Posted by appleseed
Hello!
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 21, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/7197/index | nrich enriching mathematicsSkip over navigation
### Folium of Descartes
Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.
### Witch of Agnesi
Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.
### Quick Route
What is th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/differential-geometry/99114-induction.html | # Thread:
1. ## induction
Suppose that $R > 0$, $x_{0}>0$, and
$x_{n+1}= \frac{1}{2}(\frac{R}{x_{n}}+x_{n})$, $n\geq0$
Prove: For $n\geq1$, $x_{n}>x_{n+1}>\sqrt{R}$ and
$x_{n}-\sqrt{R}\leq\frac{1}{2^n}\frac{(x_{o}-\sqrt{R})^2}{x_{o}}$
MY attempt at a solution:
I really don't know how to go about this... at first i... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 55, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/31663/distinct-numbers-in-multiplication-table | ## Distinct numbers in multiplication table
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Consider multiplication table for numbers $1,2,\cdots, n$. How many different numbers are there? That is how many different numbers of the form $ij$ with $1 \le i, j \l... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/124833-solved-show-r-b.html | # Thread:
1. ## [SOLVED] Show that r|b
if r belongs integer and r is a non zerosolution of x^2+ax+b=0 (where a,b belongs to integers), prove that r|b.
2. Originally Posted by Deepu
if r belongs integer and r is a non zerosolution of x^2+ax+b=0 (where a,b belongs to integers), prove that r|b.
We are told that $r^2 + ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/202870-separable-element-extension-field-also-field.html | 3Thanks
• 1 Post By Vlasev
• 1 Post By Deveno
• 1 Post By Deveno
# Thread:
1. ## A separable element in an extension field is also in the field
Last problem I had from my exam:
Let $F$ be an extension field of a field $K$ whose char is $p$. Let $c$ be an element of $F$ which is separable over $K$ and for which ther... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 82, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/85497/on-the-existence-of-the-laplace-transform | ## On the existence of the Laplace Transform [closed]
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Most of the lectures on the Laplace transform :
• define the Laplace transform Lf as a complex-valued function ;
• give the same example of function that doe... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/33130/cyclic-co-ordinates-implying-the-constant-velocity-motion-of-center-of-mass-of-a | # Cyclic co-ordinates implying the constant velocity motion of center of mass of a system of particles
I'm reading the section on Central Force in my textbook (Goldstein's Classical Mechanics has a similar argument in the chapter titled "The Central Force Problem", first section), where we have the following:
The Lag... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/177553-help-project.html | # Thread:
1. ## Help With Project
Very lost with a project in math class.
Need to find out and show work to see of this system is parallel, perpendicular or neither?
x-3y=-5
y=3x-9
Any Help on how to find this out?
2. You should know that an equation in the form $y = mx + c$ (or $y = ax + b$)
has the gradient as ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/Petersen_graph | Petersen graph
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Petersen graph
The Petersen graph is most commonly drawn as a pentagon with a pentagram inside, with five spokes.
Named after Julius Petersen
Vertices 10
Edges 15
Radius 2
Diameter 2
Girth 5
Automorphisms 120 (S5)
Chromatic number 3
Chro... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 15, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://boolesrings.org/mpawliuk/2012/09/14/stevos-forcing-class-fall-2012-class-1/ | # Stevo’s Forcing Class Fall 2012 – Class 1
By | Published: September 14, 2012
(In the fall of 2012 I will be taking Stevo Todorcevic’s class in Forcing at the University of Toronto. I will try to publish my notes here, although that won’t always be possible.)
Show Summary
• Discuss examples of ccc posets whose prod... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 80, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/189541-infinite-group-print.html | # Infinite group
Printable View
• October 4th 2011, 05:38 AM
dwsmith
Infinite group
Prove that if $\Omega=\{1,2,....\}$, then $S_{\Omega}$ is an infinite group.
Let $\sigma:\Omega\to\Omega$. I am guessing I need to define a map but I don't know as what.
• October 4th 2011, 03:44 PM
NonCommAlg
Re: Infinite group
Quot... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/314526/expressing-a-function-wrt-to-another-function | # expressing a function wrt to another function
I am having trouble wrapping my head around this problem
given a function $f=h(g_1,g_2,g_3)$ if $h=x^2-yz$ and $f=h(x+y, y^2, x+z)$ then is it correct to apply the pointwise vector coordinate function and get $f=(x+y)^2-y^2(x+z)$
-
Assuming $h(x,y,z)=x^2-yz$ then yes ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 21, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Autocorrelated | # Autocorrelation
(Redirected from Autocorrelated)
A plot showing 100 random numbers with a "hidden" sine function, and an autocorrelation (correlogram) of the series on the bottom.
Visual comparison of convolution, cross-correlation and autocorrelation.
Autocorrelation is the cross-correlation of a signal with itsel... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 60, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.onemathematicalcat.org/algebra_book/online_problems/practice_points.htm | PRACTICE WITH POINTS
• Jump right to the exercises!
• Want more basic practice with the coordinate plane and points first?
Locating Points in Quadrants and on Axes
As discussed in Locating Points in Quadrants and on Axes,
an ordered pair $\,(x,y)\,$ is a pair of numbers, separated by a comma, and enclosed in parenthes... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 89, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/762/roots-of-analytic-functions/2274 | ## roots of analytic functions
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Let $z$ be a complex variable and $f(z)$ be a formal power series with rational coefficients (an element in $\mathbb Q[[z]]$), with a finite radius of convergence, and assume $f(z)$... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 21, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/32672/list | ## Return to Answer
3 added 43 characters in body
Write $X_{B,b} = \{\alpha \in \mathbb{Z}^B : \sum_j \alpha_j = b\}$. Now using the convention $0^0 \equiv 1$, define the matrix $W_{\alpha, \alpha'} := \alpha^{\alpha'}$. For arbitrary $f:X_{B,b} \rightarrow \mathbb{K}$ we can write $f_\alpha \equiv \sum_{\alpha'} c_{... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 44, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/172275-question-about-norms-lp-spaces-chebyshev-norm-print.html | # Question About Norms in Lp spaces and Chebyshev Norm
Printable View
• February 22nd 2011, 05:22 PM
DmitroMoroz
Question About Norms in Lp spaces and Chebyshev Norm
Here is my question; I appreciate any and all help and hints.
We assume that $A$ is a finite dimensional linear subspace of the normed linear space $C[... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 16, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cogsci.stackexchange.com/questions/1826/should-always-selecting-the-same-response-on-the-iowa-gambling-test-result-in-a | # Should always selecting the same response on the IOWA Gambling Test result in a good value?
I was taking the Iowa Gambling Task. I examined what happens when the same option is selected on every run. To my surprise I got a pretty good value when choosing options C and D (\$4500) in every run and a pretty bad one ($-... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/tagged/linear-systems?sort=unanswered&pagesize=15 | # Tagged Questions
The linear-systems tag has no wiki summary.
The fundamental question is Why is Hall conductance quantized? Let's start with the Hall bar, a 2D metal bar subject to a strong perpendicular magnetic field $B_0$. Let current $I$ flow in the ...
Really sorry for this simple question, but I think it will... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/206941/basis-for-the-solution-space | # basis for the solution space
Find the basis for the solution space of the system and describe all solutions:
$3x_1 - x_2 + x_4 = 0$
$x_1 + x_2 + x_3 + x_4 = 0$
I row reduce the matrix:
$\begin{pmatrix} 1&1&1&1\\ 0&-4&-3&-2 \end{pmatrix}$
And from here I do not know what to do.
-
## 1 Answer
The form of the r... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/tensor-calculus?sort=unanswered&pagesize=15 | Tagged Questions
The tensor-calculus tag has no wiki summary.
0answers
1k views
Superfields and the Inconsistency of regularization by dimensional reduction
Question: How can you show the inconsistency of regularization by dimensional reduction in the $\mathcal{N}=1$ superfield approach (without reducing to compone... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/70162?sort=newest | Why Lawvere theories have finite products? and more
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According to Wikipedia, a Lawvere theory consists of a small category $L$ with (strictly associative) finite products and a strict identity-on-objects functor $I:\a... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 146, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://www.territorioscuola.com/wikipedia/en.wikipedia.php?title=Linear_system | More results on: Download PDF files on: Download Word files on: Images on: Video/Audio on: Download PowerPoint on: More results from.edu web: Map (if applicable) of:
Linear system - Wikipedia, the free encyclopedia
# Linear system
A linear system is a mathematical model of a system based on the use of a linea... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 22, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/197909/any-interesting-number-theoretic-results-properties-concerning-particularly-valu?answertab=votes | # Any interesting number-theoretic results/properties concerning particularly values of $n$ in $2n+1$? [closed]
So this question has strange origins: I was looking at the Leibniz series for $\pi$, and I started to wonder about the relationship between the partial sum and the parity of the value $n$ in the denominator:... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 26, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/50275/a-puzzling-remark-of-manin-icm-1978 | ## A puzzling remark of Manin (ICM 1978)
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Manin ends his 1978 ICM talk with this remark:
I would also like to mention I. M. Gel'fand's suggestion that the $\zeta$-functions of certain special differential operato... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 21, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/2373/note | The graph of $y=\sin x$ lies above the line $y=2x/\pi$ joining the origin to the point $(\pi/2, 1)$. The graph of $\sin x$ lies below the line $y=x$. Why? What does this tell you about $\sin x$? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/28390/is-any-transposition-a-product-of-simple-transpositions/28396 | # Is any transposition a product of simple transpositions?
Is any transposition a product of simple transpositions? If yes, how can you prove this?
-
A simple transposition is a transposition in the form $(i,i+1)$ so (7,8) is a simple transposition but (7,10) is not. – Vafa Khalighi Mar 21 '11 at 23:47
## 3 Answers... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 32, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://electronics.stackexchange.com/questions/37431/help-finding-transfer-function-for-root-locus-using-matlab | # Help finding transfer function for root locus using Matlab
I'd like to pick $k_d$ using root locus method, but have problems deriving the necessary transfer function of the system presented below. Assume $k_p$ is fixed. The question originates from Randal Beard's paper: "Quadrotor dynamics and control", p.42. The an... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 21, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/33958/generalization-of-schurs-lemma-update | ## Generalization of Schur’s lemma (Update)
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I am not a mathematician nor physicist. I just know the basics of the representation theory. In my research, I realized that there is an orthogonality relation between ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 36, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/112980/pretty-simple-question-about-running-time/112982 | # Pretty simple question about running time
What is the smallest value of $n$ such that an algorithm whose running time is $100n^2$ runs faster than an algorithm whose running time is $2^n$ on the same machine?
-
1
– Arturo Magidin Feb 24 '12 at 19:41
Just doing some arithmetic, it's $n=15$. – David Mitra Feb 24 '12... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://wiki.math.toronto.edu/TorontoMathWiki/index.php/2009-2010_FAWG_Seminar | # 2009-2010 FAWG Seminar
### From TorontoMathWiki
The Fields Analysis Working Group Seminar takes place (usually) at the Fields Institute Room 210 on Thursdays at 12h10. The seminar is co-organized by J. Colliander, Colin Decker, R.J. McCann, and L. Guth.
The seminar also has a page at the Fields Institute.
Of rela... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/differential-geometry/115591-continuity-1-x.html | # Thread:
1. ## Continuity of 1/x
Show that 1/x is continuous on at any c =/= 0
hint: chose delta to stay away from 0
i have a general idea of how it works but I'm not really sure how to
"use delta = min{[c]/2,c^2(e/2)} "(answer from book)
2. Originally Posted by mtlchris
Show that 1/x is continuous on at any c =/... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/questions/2970/can-i-pre-define-the-points-in-shamirs-secret-sharing-algorithm?answertab=active | # Can I pre-define the points in Shamir's Secret Sharing algorithm
With Shamir's secret sharing is it possible to pre-define the points returned by the algorithm?
For simplicity if I have (k, n) where k=2, and n=4, and I have the points X,Y,Z, and Q. Can I create the coefficients so that X,Y,Z, and Q are the points r... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 62, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/221841/poisson-or-binomial/221845 | # Poisson or Binomial?
In a fabric company, the fixed probability of a machine producing a bad fabric is $p$ independent on the fabric previously produced. At the output of the machine, $n$ fabrics are taken at random. $X$ is the random variable equal to the number of bad fabrics in a selection of $n$ fabrics at the m... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 36, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/formal-languages+computational-complexity | Tagged Questions
2answers
55 views
Sequences and Languages
Let $U$ be the following language. A string $s$ is in $U$ if it can be written as: $s = 1^{a_1}01^{a_2}0 ... 1^{a_n}01^b$, where $a_1,..., a_n$ are positive integers such that there is a 0-1 ...
1answer
108 views
Function problem vs. decision problem
Take ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/statistics/186700-desired-exam-question-paper-probability-question.html | # Thread:
1. ## The desired exam question paper (probability question)
There is an exam. There are 25 exam question papers for 25 students who are lined up outside of the classroom. Each time, a students gets into the classroom, pick one paper (RANDOMLY) and go, sits on its desk and start his exam.
You are the 5th p... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/107796/integrating-a-product | ## Integrating a product
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By trying to find a marginal distribution I came accross integration of the product series. For the sake of generality, lets assume the integral is of following form: $$\int \prod_{k=1}^{... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Gibbs'_phase_rule | # Gibbs' phase rule
Gibbs' phase rule[1] [2] was proposed by Josiah Willard Gibbs in the 1870s as the equality
$F\;=\;C\;-\;P\;+\;2$
where C is the number of components and P (alternatively π or Φ) is the number of phases in thermodynamic equilibrium with each other. Typical phases are solids, liquids and gases. A s... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/54861/in-klein-gordon-why-should-infinite-downwards-photon-cascades-be-possible | # In Klein-Gordon, why should infinite downwards photon cascades be possible?
Here is a simple point about the standard interpretation of the Klein-Gordon equation that for the life of me I've never been able to understand:
Why would the existence of true negative energy states result in an infinite downward cascade ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 21, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/8396?sort=newest | Does every ODE comes from something in physics?
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Not sure if this is appropriate to Math Overflow, but I think there's some way to make this precise, even if I'm not sure how to do it myself.
Say I have a nasty ODE, ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/4663/list | ## Return to Answer
2 admit defeat
Update: in response to comment below, I'm not sure anymore the probability in question was 0.
Let's try the measure that gives an equal weight for any true statement of fixed length $N$ (written in mathematical English).
Then we have statements of the form "S or 1+2=3" which form ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/99140-finding-formula-function.html | # Thread:
1. ## Finding formula for a function
I need to find the formula for this function, and i'm not sure what to do...
Code:
```x f(x)
-2 -25.22
0 3.50
2 32.22
4 60.94
6 89.66```
I've looked all over the internet and can't find anything to help me out
2. Originally Posted by JAMESvee... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/5643/how-is-it-possible-for-orbits-to-maintain-stability | # How is it possible for orbits to maintain stability?
According to $a = v^2/R$, the circular velocity and radial distance between two attracting objects (such as planets), must remain in perfect proportion in order for orbital motion to take place. How is it possible for objects in nature to achieve this proportion p... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.maths.manchester.ac.uk/~jm/wiki/Vortices/Ring?action=browse | # Ring
Other configurations
## A ring of n point vortices
### Region of Stability
for $$\theta\in[0,\pi]$$ the co-latitude, the ring is stable if $$\begin{array}{r:l}n=3 & \forall \theta\cr n=4 & \cos^2\theta > 1/3 \cr n=5 & \cos^2\theta > 1/2 \cr n=6 & \cos^2\theta > 4/5 \end{array}$$
For $$n\geq 7$$ the ring is ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 73, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/43036/list | Return to Answer
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1
Using $(a, b, ... )$ is handy to denote a column vector, which is the transpose of the row vector $[a, b, ... ]$, especially in linear text. Correspondingly, all displayed matrices should be written with brackets, not parentheses. This notation agrees with t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/79420?sort=votes | ## Generalising Gelfand’s spectral theory
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This is primarily a request for references and advices.
Question (edited on 10/29/2011). What's known about comprehensive generalisations of Gelfand's spectral theory fo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/72976/how-will-this-equation-imply-pnt | How will this equation imply PNT
So we have $$\sum_{n \leq x} \frac{\Lambda (n)}{n}=\log{x}+C+o(1)$$ where $C$ is a constant, its partial summation is $$\sum_{n \leq x} \frac{\Lambda (n)}{n}=\frac{\psi(x)}{x}+\int_1^x \frac{\psi (t)}{t^2} dt$$ How should I go from here to prove that $\psi(x) \sim x$, which is a equiva... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/9885/the-convergence-of-eisenstein-series-of-weight-zero | ## The convergence of Eisenstein series of weight zero
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Consider Eisenstein series of weight zero, i.e.
$E_{\mathfrak{a}}(z,\ s,\ \chi) = \sum_{ \gamma \in \Gamma_{\mathfrak{a}} \backslash \Gamma } \bar{\chi}(\ga... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.aimath.org/textbooks/beezer/MISLEsection.html | Matrix Inverses and Systems of Linear Equations
We begin with a familiar example, performed in a novel way.
Example SABMI: Solutions to Archetype B with a matrix inverse.
The matrix $B$ of the previous example is called the inverse of $A$. When $A$ and $B$ are combined via matrix multiplication, the result is the id... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 77, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/463/list-of-the-most-fundamental-assumptions-of-quantum-mechanics/471 | # List of the most fundamental assumptions of quantum mechanics?
Can anybody give a concise list of the most fundamental assumptions of quantum mechanics in plain english ?
-
what do you mean with assumptions ? – Stefano Borini Nov 10 '10 at 0:39
Just like we have a dimensionless point particle, the constant linear f... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/125873-does-mean-matrix-singular.html | # Thread:
1. ## does this mean a matrix is singular?
If a matrix A $\neq$ 0 and $A^k=0$ where k is a positive integer, does that mean A is singular?
2. A must be singular. Suppose not, then there exists $A^{-1}$ satisfying $AA^{-1}=A^{-1}A = I$. Then $A^k (A^{-1})^k = I = 0$, giving a contradiction.
3. so the =0 me... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/69199/how-can-i-verify-the-pythagorean-trig-identity-using-approximations-for-sin-x/69203 | # How can I verify the Pythagorean Trig Identity using approximations for $\sin x$ and $\cos x$ derived from their infinite series representations?
How can I verify the Pythagorean Trig Identity using approximations for $\sin x$ and $\cos x$ derived from their infinite series representations?
I can see that the infin... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 46, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.math.uah.edu/stat/applets/VarianceEstimateExperiment.html | ### The Variance Estimation Experiment
Confidence Interval
Sampling Distribution
| | | |
|-----------------------|--------------------|----------------------|
| Sampling Distribution | Pivot Distribution | Success Distribution |
| | ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 21, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/843/risk-neutral-probability-in-binomial-lattice-option-coming-greater-than-1-what?answertab=oldest | # Risk neutral probability in binomial lattice option coming greater than 1…what's wrong?
I am substituting reasonable values in the below fomula (like r=0.12, T=20, nColumn=16, sigma=0.004)...why is probability coming out to be greater than 1? Any help? Thanks!
````del_T=T./nColumn; % where n is the number of column... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/97777/non-characteristic-maps-ala-d-modules | ## Non-characteristic maps (ala D-modules)
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I am trying to understand a ``well known' fact (see Kashiwara's`Introduction to microlocal analysis page 63, remark 4.8) about non-characteristic morphisms. Here is the ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Difference_operator | # All Science Fair Projects
## Science Fair Project Encyclopedia for Schools!
Search Browse Forum Coach Links Editor Help Tell-a-Friend Encyclopedia Dictionary
# Science Fair ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/212843-evaluating-limit-area-under-graph-continuous-function.html | 3Thanks
• 1 Post By hollywood
• 1 Post By hollywood
• 1 Post By hollywood
Thread:
1. Evaluating limit of an area under the graph of a continuous function.
The area A of the region S that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles:
(a) Use this def... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-equations/68633-direction-field-diiferental-equation.html | Thread:
1. direction field-diiferental equation
Hi, i know how to Sketch the direction field but don't unbdestand the part
"Using the direction field decide whether a solution y(x) tends to a finite limit when x goes to infinity. How does this limit depend on the value of the initial condition y(0) ?" (Please look a... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/4147/covariant-description-of-light-scattering-at-a-fastly-rotating-cylinder?answertab=votes | # Covariant Description of Light Scattering at a fastly rotating Cylinder
Let us consider the following Gedankenexperiment:
A cylinder rotates symmetric around the $z$ axis with angular velocity $\Omega$ and a plane wave with $\mathbf{E}\text{, }\mathbf{B} \propto e^{\mathrm{i}\left(kx - \omega t \right)}$ gets scatt... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/70110/limit-of-sums-of-iid-random-variables-which-are-not-square-integrable | # Limit of sums of iid random variables which are not square-integrable
The Central Limit Theorem tells us that for an iid sequence of random variables $(X_n)_{n\geq 0}$ of finite variance $\sigma^2$ and zero mean
$$\lim_{n\to\infty}\frac{S_n}{\sqrt{n}}=^d N(0,\sigma^2)$$
where $S_n=X_1+\cdots+X_n$.
Suppose we have... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2009/04/23/the-polarization-identities/?like=1&source=post_flair&_wpnonce=c1c9c39881 | # The Unapologetic Mathematician
## The Polarization Identities
If we have an inner product on a real or complex vector space, we get a notion of length called a “norm”. It turns out that the norm completely determines the inner product.
Let’s take the sum of two vectors $v$ and $w$. We can calculate its norm-square... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 17, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/179950/what-are-the-points-of-discontinuity-of-tan-x/179985 | # What are the points of discontinuity of $\tan x$?
$f(x) = \tan x$ is defined from $\mathbb R - \{\frac{\pi}{2} (2n+1) \mid n \in \mathbb Z\}$ to $\mathbb R$. For every $x$ in its domain, $$f(x) = \frac{\sin x}{\cos x}$$ where $\cos x$ is never 0. Thus, (in short) $\tan x$ is defined for all points in its domain. Now... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 92, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/tagged/fourier-analysis | # Tagged Questions
Questions on the discrete and continuous Fourier analysis functions of Mathematica, as well as the FourierSeries` package.
1answer
76 views
### Tough Inverse Fourier Integral: why does the sign matter?
I'm computing the Inverse Fourier Integral of ((a^2 + omega ^2) c^2) /((b^2 + omega^2) ((r^2 + ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/17031-stumbled-upon-answer.html | # Thread:
1. ## Stumbled upon an answer....
Here's something I found interesting. "If $f(x) = 3x + 7$ and $g(x) = -2x + 5$, find the abscissa of a point which is on the graphs of both $f$ and $g$."
I really didn't know how to do it; the book certainly didn't spell it out anywhere. I started by graphing both equation... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 16, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-equations/182376-laplace-equation.html | # Thread:
1. ## laplace equation
$\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}=0, u=-K \quad\mbox{at} \quad x=\pm b, y=\pm h$
How to solve this?
2. If you let $u = v - K$ then $v$ satisfies
$\dfrac{\partial^2 v}{\partial x^2} + \dfrac{\partial^2 v}{\partial y^2} = 0$
where $v = 0$ on the bo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/differential-equations/64389-general-solution-differential-equations.html | # Thread:
1. ## general solution for differential equations
Hi I wasn't sure whether to post this in the linear algebra forum or the calculus forum, but it deals with differential equations. I'm having a hard time understanding this one question and how it differs from the normal case. The question is:
Find the gene... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/67863/a-criterion-for-a-group-to-be-abelian | # A criterion for a group to be abelian
I noted a discussion on groups being abelian under a certain restriction on powers of elements, e.g. http://tiny.cc/chs45. Maybe this result (probably not too well-known) concludes it all.
Let and $m$ and $n$ be coprime natural numbers. Assume that $G$ is a group such that $m$-... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 67, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/75522?sort=oldest | ## How can I write down a point in the Berezinian of a super vector space?
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A vector space $V$ of dimension $n$ has an associated determinant line $Det(V)$.
An element of $Det(V)$ is represented as a (formal limea... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 37, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/245158/isomorphic-abelian-groups-which-are-not-isomorphic-r-modules | # Isomorphic abelian groups which are not isomorphic R-modules
I'm looking for an example of of two isomorphic abelian groups, which are not isomorphic $R$ modules for some ring $R$.
I suppose we can just the same abelian group $M$ twice, and use a different operation $R\times M \rightarrow M$ so the $R$ modules aren... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 27, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/4834/threshold-calculation-for-buying-a-mean-reverting-asset/4849 | # Threshold calculation for buying a mean-reverting asset
I am trying to figure-out an optimal policy for buying a unit when its price follows a mean-reverting price process (Ornstein–Uhlenbeck), when I have a finite time deadline for buying the unit.
I tried to search the literature for it, but couldn't find anythin... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/72412/why-are-the-following-two-constructions-of-zeta-functions-equal | ## (why) Are the following two constructions of zeta functions equal?
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Let $X$ be a variety defined over $\mathbb{Q}$. One has the usual Hasse-Weil zeta function.
Now, let's do a different construction. Base chan... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 26, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/lienard-wiechert+electromagnetic-radiation | # Tagged Questions
0answers
40 views
### Mathematical equivalence between Liénard-Wiechert potential and 4-potential in Rindler coordinates
I'm studying the problem of the radiation of an uniformly accelerated point charge: $$x^{\mu}(\lambda)\to(g^{-1}\sinh g\lambda,0,0,g^{-1}\cosh g\lambda)$$ I found that when a po... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/88563/mathematical-research-inspired-in-fundamental-part-by-mathoverflow | ## Mathematical research inspired in fundamental part by mathoverflow
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Mathoverflow has led in several instances to new mathematical work that arose directly from mathematical ideas, questions or answers posted he... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/questions/2538/is-my-hmac-secure-if-i-have-a-complete-series-of-hmacd-prefix-strings/2607 | # Is my HMAC secure if I have a complete series of HMAC'd prefix strings
Let's say I have a long sentence, like "The quick brown fox jumped over the lazy dog." Let's further say that I need to keep this string encrypted, so I use an HMAC. Let's further further say I want to be able to do prefix searches for this strin... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/155694/when-does-this-sequence-start-repeating-itself/155720 | When does this sequence start repeating itself?
Given the sequence $a_j = b^j \mod q$, where $1 < b, q < 2^n$, how can I prove that the sequence starts repeating itself at some term $a_k$ where $k \leq n$?
I have been looking at this problem for hours and am completely stuck on how to do it :/ Any help would be appre... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 71, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2010/01/07/change-of-variables-in-multiple-integrals-iii/ | # The Unapologetic Mathematician
## Change of Variables in Multiple Integrals III
Today we finish up the proof of the change of variables formula for multiple integrals:
$\displaystyle\int\limits_Xf(x^1,\dots,x^n)\,d(x^1,\dots,x^n)=\int\limits_{g^{-1}(X)}f(g(u^1,\dots,u^n))\left\lvert\frac{\partial(x^1,\dots,x^n)}{\... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 58, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/61984?sort=votes | rational points on algebraic curves over $Q^{ab}$
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Motivation:
Let $Q_{\infty,p}$ be the field obtained by adjoining to $Q$ all $p$-power roots of unity for a prime $p$. The union of these fields for all primes is th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 96, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/152209/related-measures | # Related Measures
($\Omega, F,P)$ is a measure space, $\ Q \ll P$ ($Q$ is related to $P$) i.e. $\ Q(A)= \int 1_ADdP$ where $\ D=dQ/dP$. Then $X$ is integrable wrt $Q$ if and only if $XD$ is integrable wrt $P$ and $\int XdQ = \int XDdP$. How do I prove this? I can only do it for $X$ a simple Borel function, not a gene... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 31, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cms.math.ca/10.4153/CJM-1999-046-7 | Canadian Mathematical Society
www.cms.math.ca
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location: Publications → journals → CJM
Abstract view
# The Homology of Abelian Covers of Knotted Graphs
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[P... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://skullsinthestars.com/2012/07/16/optics-basics-refraction/ | The intersection of physics, optics, history and pulp fiction
## Optics basics: refraction
Posted on July 16, 2012 by
In all of my discussions of basic principles of optics, I’ve so far neglected to talk about one of the most fundamental and important: refraction! In short, refraction is the bending of a ray of lig... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 18, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/258228/probability-that-the-10th-class-this-semester-is-the-3rd-class-cancelled-when-ch/258231 | # Probability that the 10th class this semester is the 3rd class cancelled when chances are independent with 0.05 probability each day?
Every day, a lecture may be cancelled due to inclement weather with probability 0.05. Class cancellations on different days are independent. Compute the probability that the tenth cla... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
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