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http://mathoverflow.net/revisions/5638/list | ## Return to Answer
5 added 1553 characters in body
As other people in this thread have pointed out, it's unsatisfying to make an automorphism tower that only stabilizes transfinitely as a direct limit, when all of the finite terms of the tower are abstractly isomorphic to the base group $G$. I Googled around a bit 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": 30, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cms.math.ca/10.4153/CJM-2002-032-2 | Canadian Mathematical Society
www.cms.math.ca
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| Site map | | | CMS store | |
location: Publications → journals → CJM
Abstract view
# Spherical Functions for the Semisimple Symmetric Pair $\bigl( \Sp... | {"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://math.stackexchange.com/questions/204839/find-the-formula | # Find the formula
10 feet of common 2-inch-bore lead piping weighs 50 lb. What is the formula for the weight of x feet of such lead piping? --Sawyer, Mathematician's Delight
I am not sure about what I am asked to do here. It is known that $$10F*2=50$$ and I am asked to write it down as $$XF*2=W$$ or is it something ... | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://gilkalai.wordpress.com/2008/07/10/pushing-behrend-around/?like=1&source=post_flair&_wpnonce=5092e672ce | Gil Kalai’s blog
## Pushing Behrend Around
Posted on July 10, 2008 by
Erdos and Turan asked in 1936: What is the largest subset $S$ of {1,2,…,n} without a 3-term arithmetic progression?
In 1946 Behrend found an example with $|S|=\Omega (n/2^{2 \sqrt 2 \sqrt {\log_2n}} \log^{1/4}n.)$
Now, sixty years later, Michael... | {"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": 8, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/106953/number-of-possible-prufer-codes | # Number of possible Prüfer codes
I am trying to solve the following problem in my book: (Code stands for Prüfer code)
Consider labelled trivalent rooted trees $T$ with $2n$ vertices, counting the root labeled $2n$. The labels are chosen in such a way that the procedure leading to $P(T)$ has $1,2,\cdots 2n-1$ as firs... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://inperc.com/wiki/index.php?title=Homology_of_homotopic_maps | This site contains: mathematics courses and book; covers: image analysis, data analysis, and discrete modelling; provides: image analysis software. Created and run by Peter Saveliev.
# Homology of homotopic maps
### From Intelligent Perception
We know that if the realizations of two cell complexes are homeomorphic 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": 5, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/61814/ask-for-recommendations-for-textbook-on-mathematical-logic/61825 | Ask for recommendations for textbook on mathematical logic
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I studied mathematical logic using a book not written in English. I would now like to study it again using a textbook in English. But I hope I can read a tex... | {"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://www.birs.ca/events/2010/5-day-workshops/10w5025 | # Optimal transportation and applications (10w5025)
Arriving Sunday, April 18 and departing Friday April 23, 2010
## Organizers
Alessio Figalli (The University of Texas at Austin)
Yuxin Ge (Universite Paris Est Creteil)
Young-Heon Kim (University of British Columbia)
Robert McCann (University of Toronto)
Neil Trudin... | {"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://mathhelpforum.com/advanced-applied-math/180097-ugly-fourier-transform.html | # Thread:
1. ## Ugly Fourier Transform
Hi fellas,
Can you me help to solve this Fourier Transform?
$F[e^{(-\frac{(kt)^2}{2})}(kt)^2\ln{((kt)^2)}]$
I have an answer for it, but no explanation is available. I cannot understand the method or approximation which is made to find this answer.
Answer: $\propto \min \lef... | {"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": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/43171/why-can-beta-not-be-linearly-proportional-to-t-that-is-beta-constant | # Why can $\beta$ not be linearly proportional to $T$, that is $\beta = constant \times T$?
$\beta$ in statistical mechanics is equal to $\frac{1}{k_BT}$ in in thermodynamics, but I do not understand why $\beta\propto T^{-1}$ instead of, say, $\beta\propto T$?
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## 4 Answers
Because by convention, we want to write ... | {"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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://conservapedia.com/Expectation_(math) | # Expectation (math)
### From Conservapedia
The mathematical expectation of a continuously distributed random variable X with probability density function f(x) is
$\mbox{E}[X] =\int\limits_{-\infty}^\infty x f(x)dx.$
The expectation is also known as the mean of X.
The expectation with respect to some function g(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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/87480/explanation-on-a-scheme-which-is-not-affine-scheme | ## explanation on a scheme which is not affine scheme
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hartshorne at the end of page 76 of his Algebraic Geometry book gives an example of a scheme which is not an affine scheme. The scheme is constructed by gluin... | {"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": 40, "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/63747/differentiable-function?answertab=oldest | # Differentiable function?
I'm studying the function:
$$f(x,y) = \begin{cases} x+y & \text{if } x=0 \text{ or } y=0 \\ 1& \text{if } xy\neq 0 \end{cases}$$
The partial derivatives exist in $(0,0)$, and I can prove that directional derivative doesn't exist in $(0,0)$. Now, Is this function differentiable? Why?
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Ye... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/64888/product-of-two-algebraic-subgroups-of-a-solvable-group-another-algebraic-subg/64970 | ## Product of two algebraic subgroups of a (solvable) group = another algebraic subgroup?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $G$ be a linear algebraic group over a field $K$. (Say $K=\mathbb{F}_q$ or $K=\mathbb{C}$; do not assume $K$ is algebr... | {"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": 136, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://gottwurfelt.wordpress.com/2012/07/21/fibonacci-subset-fun/ | A mathematician blogs.
# Fibonacci subset fun
A week ago I wrote a post on bitwise set trickery in which I asked a question from James Tanton: how many subsets S of {1, 2, …, 10} have the property that S and S+2 cover all the numbers from 1 to 12? To solve this is a one-liner in R. Slightly generalizing, we can repla... | {"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": 15, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/statistics/30123-i-cant-get-help.html | # Thread:
1. ## I cant Get this... HELP>>>
How many distinct Permutations of the letters of the word OTTAWA begin and end with the letter T?
2. Originally Posted by wikji
How many distinct Permutations of the letters of the word OTTAWA begin and end with the letter T?
The number of permutations of a set with n elem... | {"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": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://cms.math.ca/Reunions/hiver11/abs/fm | Réunion d'hiver SMC 2011
Delta Chelsea Hotel, Toronto, 10 - 12 décembre 2011 www.smc.math.ca//Reunions/hiver11
Mathématiques financiers
Org: Matt Davison (Western), Marcus Escobar (Ryerson), Sebastian Ferrando (Ryerson), Pablo Olivares (Ryerson) et Luis Seco (Toronto)
[PDF]
ALEXANDER ALVAREZ, Ryerson University
Loca... | {"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/147935/calculate-the-mass-of-the-ball-x2y2z2-1-with-point-density-exeyez?answertab=oldest | # Calculate the mass of the ball $x^2+y^2+z^2=1$ with point density $e^x+e^y+e^z$
I'm asked in an exercise to calculate the mass of the ball $x^2+y^2+z^2=1$ with a density of $e^x+e^y+e^z$ at a given point. We've only learned triple integration with Cartesian coordinates so far so I'm trying to set up a triple integra... | {"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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2011/09/16/oriented-manifolds-with-boundary/?like=1&_wpnonce=d19428bcb3 | # The Unapologetic Mathematician
## Oriented Manifolds with Boundary
Let’s take a manifold with boundary $M$ and give it an orientation. In particular, for each $p\in M$ we can classify any ordered basis as either positive or negative with respect to our orientation. It turns out that this gives rise to an orientatio... | {"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": 64, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/110147/series-for-envelope-of-triangle-area-bisectors | ## Series for envelope of triangle area bisectors
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The lines which bisect the area of a triangle form an envelope as shown in this picture
It is not difficult to show that the ratio of the area of the red deltoid... | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://quant.stackexchange.com/questions/1250/how-do-i-estimate-convergence-in-monte-carlo-methods | # How do I estimate convergence in monte carlo methods?
I am experimenting with Monte Carlo methods. I'd like to measure/estimate convergence with a graph/chart. How do I do that? Can anyone please direct me to relevant documentation/links or even give me tips or general guidelines? Thanks in advance, Julien.
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Conv... | {"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://math.stackexchange.com/questions/219846/does-a-contour-of-local-extrema-of-a-function-f-mathbbr2-to-mathbbr?answertab=active | # Does a contour of local extrema of a function $f : \mathbb{R}^2 \to \mathbb{R}$ need always be smooth?
Consider a smooth function $f : \mathbb{R}^2 \to \mathbb{R}$, I wonder that any contour (curve) in $\mathbb{R}^2$ where every point of it is a local maxima of $f$, need be a smooth curve?
Edit : $f$ need to be smo... | {"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://crypto.stackexchange.com/questions/2846/what-is-the-difference-between-known-plaintext-attack-and-chosen-plaintext-attac/2850 | # What is the difference between known-plaintext attack and chosen-plaintext attack?
I am very confused between the concept of known-plaintext attack and chosen-plaintext attack. It seems to me that these two are the same thing, but it definitely is not.
Can anyone explain to me how these two differ?
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1
Welcome 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": 10, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2007/06/13/zero-objects-kernels-and-cokernels/?like=1&_wpnonce=cb13afa090 | # The Unapologetic Mathematician
## Zero objects, Kernels, and Cokernels
A zero object in a category $\mathcal{C}$ is, simply put, both initial and terminal. Usually we’ll write $\mathbf{0}$ for a zero object, but sometimes $Z$, or even $\mathbf{1}$ in certain circumstances. While initial objects and terminal objects... | {"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": 59, "mimetex.cgi": 0, "/images/ma... |
http://topologicalmusings.wordpress.com/2007/11/29/another-elementary-number-theory-problem/ | Todd and Vishal’s blog
Topological Musings
Another elementary number theory problem
November 29, 2007 in Problem Corner | Tags: andreescu, elementary, mathematical, number, reflections, theory, titu
This one, by Dr. Titu Andreescu (of USAMO fame), is elementary in the sense that the solution to the problem doesn’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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 3, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/45117/what-is-a-null-set/45126 | # What is a null set?
I am very confused with null sets. I get that a set which has no elements will be called a null set but I am not getting the examples given below.
Please help me by explaining how $P$,Q,R\$ are null sets? Thank-you
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1
Can you please clarify further? The page you linked to at Google books isn'... | {"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": 34, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/37926-exponential-function.html | Thread:
1. Exponential function
How to complete the following table?
And also:
a) f(x) = 2x^3 + 3x^2 - 12x + 6 has critical points at x = -2 and x = 1. Use the second derivative test to determine whether these are local maximum or local minimum values.
b)
how to Calculate f(-2) and f(1) . Briefly explain the approp... | {"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://mathhelpforum.com/advanced-algebra/172991-linearly-independent-polynomials-answer-not-checking-out.html | # Thread:
1. ## Linearly independent polynomials; answer not checking out.
Are the following vectors in $P_2$ linearly dependent? If yes, express one vector as a linear combination of the rest.
${3t+1,3t^2+1,2t^2+t+1}$
This forms the matrix $<br /> \[<br /> <br /> \left[ {\begin{array}{ccc}<br /> 0 & 3 & 2 \\<br /> ... | {"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": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/23799/first-order-logic-vs-second-order-logic | # First-Order Logic vs. Second-Order Logic
Wikipedia describes the first-order vs. second-order logic as follows:
First-order logic uses only variables that range over individuals (elements of the domain of discourse); second-order logic has these variables as well as additional variables that range over sets of indi... | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/54912/representing-forces-as-one-forms?answertab=oldest | # Representing forces as one-forms
First of all, sorry if any of those things are silly or nonsense, I'm just trying to understand better how the concepts of forms, exterior derivative and so on can be used in physics.
This question arose because of my first question Interpreting Vector fields as Derivations on Physi... | {"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": 48, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://johncarlosbaez.wordpress.com/2012/08/21/network-theory-part-23/ | # Azimuth
## Network Theory (Part 23)
We’ve been looking at reaction networks, and we’re getting ready to find equilibrium solutions of the equations they give. To do this, we’ll need to connect them to another kind of network we’ve studied. A reaction network is something like this:
It’s a bunch of complexes, which... | {"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": 184, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/differential-geometry/194567-distance-between-sets.html | # Thread:
1. ## Distance between sets (metric spaces)
Hi there. I was working on this problem. And I wanted to know if my demonstration is right, I'm not sure if it's complete.
The problem says: The distance D(A,B) between two nonempty subsets A and B of a metric space (X,d) is defined to be:
$D(A,B)=inf d(a,b),a\in... | {"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": 46, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/35236?sort=newest | # Background
The complexity classes BPP, BQP, and QMA are defined semantically. Let me try to explain a little bit what is the difference between a semantic definition and a syntactic one. The complexity class P is usually defined as the class of languages accepted in polynomial time by a deterministic Turing machine.... | {"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://mathoverflow.net/revisions/92929/list | ## Return to Question
6 added 142 characters in body
Let $C$ be a symmetric monoidal category, and $f : x \to y$ be a morphism in $C$. I would like to construct the localization $C_f$ explicitly, which solves the universal property $$\mathrm{Hom}_{\otimes}(C_f,D) = \{F \in \mathrm{Hom}_{\otimes}(C,D) : F(f) \text{ 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": 211, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathematica.stackexchange.com/questions/3583/trying-to-prove-that-x-sin-frac-pix-ge-pi-cos-frac-pix-for-x-ge/3647 | Trying to prove that $x\sin(\frac{\pi}{x})\ge\pi \cos(\frac{\pi}{x})$ for $x\ge 1$
Consider the function
````f[x_] := x Sin[Pi/x]
````
I want to prove that this function is increasing for $x\ge 1$. This can be done with the first derivative. We have to prove that $f'[x]\ge 0$ for $x\ge 1$. First I tried
````FullSim... | {"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": 78, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/45300/e2-mc22-pc2-what-units-are-used-to-measure-e-m-c-and-p | # $E^2 = (mc^2)^2 + (pc)^2$: What units are used to measure $E$, $m$, $c$ and $p$?
\begin{equation} E^2 = (mc^2)^2 + (pc)^2 \end{equation}
If I am using this equation to figure out the energy of something, what units would I use? Would it be the metric system? I.e. kilograms for $m$, meters per second for $p$, kilome... | {"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": 30, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://0fps.wordpress.com/2012/07/12/smooth-voxel-terrain-part-2/ | Mostly geometry
## Smooth Voxel Terrain (Part 2)
Posted on July 12, 2012 by
Last time we formulated the problem of isosurface extraction and discussed some general approaches at a high level. Today, we’re going to get very specific and look at meshing in particular.
For the sake of concreteness, let us suppose tha... | {"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": 9, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/55821/the-antipodal-action-on-a-connected-one-dimensional-manifold/55825 | ## The antipodal action on a connected one dimensional manifold
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
When I am reading one paper, I have met the following statement:
It is impossible to define a $Z_{2}\times Z_{2}$ action on a connected closed curv... | {"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": 38, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/30881-quick-check.html | # Thread:
1. ## Quick Check:
EDIT:
NVM, I verified it.
/EDIT
Suppose you make napkin rings by drilling holes with different diameters through two wooden balls( which also have different diameters). You discover that both napkin rings have the same height h, as shown in the figure.
(a) Guess which ring has more wood... | {"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://crypto.stackexchange.com/questions/2531/which-attacks-can-be-avoided-by-the-use-of-ofb-instead-of-ecb | # Which attacks can be avoided by the use of OFB instead of ECB?
For a file encryption program, I was told to use Output Feedback mode (OFB) instead of ECB (Electronic code book) mode.
Which attacks can I avoid by this choice?
-
– B-Con May 3 '12 at 18:02
When you are considering using a particular mode, it is 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": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://nrich.maths.org/4313/solution | ### The Lady or the Lions
The King showed the Princess a map of the maze and the Princess was allowed to decide which room she would wait in. She was not allowed to send a copy to her lover who would have to guess which path to follow. Which room should she wait in to give her lover the greatest chance of finding her?... | {"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://crypto.stackexchange.com/questions/5921/how-and-why-can-a-decryption-program-tell-me-that-a-key-is-incorrect | # How and why can a decryption program tell me that a key is incorrect?
I have noticed that some programs used for file encryption will tell you if an entered key is wrong when you try to decrypt. It seems (to me at least) that this would mean that the key somehow is written into the encrypted file. And the algorithms... | {"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://gauravtiwari.org/tag/mathematics/ | # MY DIGITAL NOTEBOOK
A Personal Blog On Mathematical Sciences and Technology
Home » Posts tagged 'mathematics'
# Tag Archives: mathematics
## Welcome 2012 – The National Mathematical Year in India
Wednesday, December 28th, 2011 08:23 / 18 Comments
Srinivasa Ramanujan (Photo credit: Wikipedia)
I was very pleased... | {"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": 76, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/131629-lagrange-multiplier-help.html | Thread:
1. Lagrange Multiplier help
I've got two Lagrange Multiplier questions I need help on.
They both say "Use Lagrange multipliers to find the maximum and minimum values of the frunction subject to the given constraint(s).
Here is the first:
$f(x,y)=e^{xy}; x^3+y^3=16$
I've gotten to $f_x=(\lambda)g_x$ which 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": 28, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/65082-tangents.html | # Thread:
1. ## tangents
find an equation of the line tangent to f(x)=x^2-4x at P(3,-3)
thank you
2. Originally Posted by mxhockey140
find an equation of the line tangent to f(x)=x^2-4x at P(3,-3)
thank you
Hi mxhockey,
The tangent line you are looking for has the form $y=mx+b$ where m is the same as the gradient o... | {"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": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/43268/computing-a-best-fit-of-discrete-points-from-a-multipole-expansion-i-e-inver | # Computing a “best-fit” of discrete points from a multipole expansion, i.e. invert the multipole moments
Take a field $\phi(\bf{x})$ created from a charge distribution contained within a radius $R$. The multipole expansion in spherical harmonics $Y_{\ell,m}$ outside of $R$ is approximated by:
$$\phi({\bf x}) \approx... | {"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/advanced-applied-math/204309-prove-sequence-converges-1-a.html | # Thread:
1. ## Prove a sequence converges to 1
I am new to the world of proofs and I'm working on an assignment for Analysis. While I understand the concept of convergence I'm finding that writing the proofs is difficult for me and I want to ask if my logic is sound here and what I can improve on.
Problem: For each... | {"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": 31, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cms.math.ca/10.4153/CMB-2011-135-9 | Canadian Mathematical Society
www.cms.math.ca
| | | | |
|----------|----|-----------|----|
| | | | | | |
| Site map | | | CMS store | |
location: Publications → journals → CMB
Abstract view
# On the Smallest and Largest Zeros of Müntz-Legendre Polynomials
... | {"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://crypto.stackexchange.com/questions/2068/complexity-of-arithmetic-in-a-finite-field/2070 | # Complexity of arithmetic in a finite field?
I am wondering what the complexities are of adding/subtracting and muliplying/dividing numbers in a finite field $\mathbb{F}_q$. I need it to understand an article I am reading.
Thank you
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1
– mikeazo♦ Mar 10 '12 at 18:19
## 3 Answers
Well, if $q$ is a prime (and no... | {"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": 39, "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/38447/what-is-a-closed-orbit-that-is-not-separable-answered | ## What is a closed orbit that is not separable? (ANSWERED)
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
What is an example of an action of a linearly reductive group variety acting on an affine variety with the property that there exists a closed orbit tha... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/approximation+sequences-and-series | Tagged Questions
3answers
41 views
Series evaluated to $m$ terms, approximating the error
Given a series $\displaystyle\sum_{n=0}^\infty a_n$, how can we bound the error (which I shall denote with $R_n$) when we evaluate it to $m$ terms? $$\sum_{n=0}^\infty a_n \approx \sum_{n=0}^m a_n$$ ...
0answers
53 views
Expan... | {"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": 13, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/pre-calculus/72886-question-functions-domains.html | # Thread:
1. ## Question on functions & domains
Im having a hard time wrapping my mind around domains. I have no problem finding the domain of a function but what is stumping me is determining the function of a given domain. An example would be find the function with the given domain: [-5,-2)U(2,5].
Thanks for your ... | {"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://math.stackexchange.com/questions/61990/how-to-show-that-gcda-b-axby-implies-gcdx-y-1/62005 | # How to show that $\gcd(a,b) = ax+by \implies \gcd(x,y)=1$?
Assume that $$\gcd(a,b)=ax+by$$ for some $a, b, x, y \in \mathbb Z$. How do I show that $\gcd(x,y)=1$? (Hint: contradiction.)
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1
What do you mean with "syt"? – ulead86 Sep 5 '11 at 10:46
12
You have asked many questions and accepted few answers. Yet you ... | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2012/09/15/irreducible-modules/?like=1&source=post_flair&_wpnonce=5092e672ce | # The Unapologetic Mathematician
## Irreducible Modules
Sorry for the delay; it’s getting crowded around here again.
Anyway, an irreducible module for a Lie algebra $L$ is a pretty straightforward concept: it’s a module $M$ such that its only submodules are $0$ and $M$. As usual, Schur’s lemma tells us that any morp... | {"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": 13, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/179529/what-are-some-examples-of-vector-spaces-that-arent-graded | What are some examples of vector spaces that aren't graded?
From wikipedia: a vector space $V$ is graded if it decomposes into direct sum $\oplus_{n \geq 0} V_n$ of vector spaces $V_n$.
So as far as I understand things, any vector space with a countable basis is graded: Let $V$ be a vector space over a field $k$ with... | {"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/differential-geometry/192043-inequality-two-metrics.html | # Thread:
1. ## inequality with two metrics
I want to prove that $sup \ x \in C[0,1] |f_n(x)-f(x) | \geq ({\displaystyle\int^1_0 |f_n(x)-f(x)|^2 \ dx})^{1/2}$
$({\displaystyle\int^1_0 |f_n(x)-f(x)|^2 \ dx})^{1/2}$
$\leq$ (by c-s inequality)
$({\displaystyle\int^1_0 |f_n(x)|^2 \ dx})^{1/2} + ({\displaystyle\int^1_0 |... | {"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://math.stackexchange.com/questions/26258/the-laplace-transform-of-the-first-hitting-time-of-brownian-motion/26286 | # The Laplace transform of the first hitting time of Brownian motion
Let $B_t$ be the standard Brownian motion process, $a > 0$, and let $H_a = \inf \{ t : B_t > a \}$ be a stopping time. I want to show that the Laplace transform of $H_a$ is $$\mathbb{E}[\exp(-\lambda H_a)] = \exp (-\sqrt{2\lambda} H_a)$$ by consideri... | {"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": 25, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/5483/is-machs-principle-wrong | Is Mach's Principle Wrong?
This question was prompted by another question about a paper by Woodward(not mine). IMO Mach's principle is very problematic (?wrong) thinking. Mach was obviously influenced by Leibniz. Empty space solutions in GR would result in a Minkowski metric and would suggest no inertia. Mach's princi... | {"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://mathoverflow.net/questions/73741?sort=oldest | ## What does the “category” of $(\infty,1)$ category look like.
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
One knows that in higher category theory, the category of $(\infty,n-1)$ categories is naturally an $(\infty,n)$ category ,(I use the word category ... | {"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://stats.stackexchange.com/questions/14095/when-to-use-students-or-normal-distribution-in-linear-regression | # When to use Student's or Normal distribution in linear regression?
I am looking at some problems, and in some, to test the coefficients, sometimes I see people using Student's distribution, and sometimes I see Normal distribution. What is the rule?
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3
– cardinal Aug 10 '11 at 16:57
## 2 Answers
The normal distr... | {"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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/189947/when-proving-question-got-double-turnstile-symbol?answertab=votes | # when proving question got double turnstile symbol
For example: Prove that (something)⊨(another thing)
Is it the same as "Prove that (something)⊢(another thing)"?
The single turnstile symbol always appears during sample proofs in my lecture notes. Yet my homework question suddenly got the double turnstile symbol, 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": 18, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=3850309 | Physics Forums
## Why does a^x = e^(x(lna))
Hi every one, first post, so let me know if I'm not following any of the rules.
I'm studying Calculus, looking at the rules for deriving the function a^x. The first step is to change a^x to e^(x(lna)). From there, it's easy to use the chain rule to find the derivative.
Wh... | {"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://physics.stackexchange.com/questions/8813/how-do-i-derive-the-critical-temperature-for-bose-condensation-in-two-dimensions | # How do I derive the critical temperature for bose condensation in two dimensions?
In class we derived the 3D case, but there's a step I don't understand:
$$N = g \cdot {V \over (2 \pi \hbar)^3} \cdot \int\limits_{0}^{\infty}{1 \over{e^{\left( E_p \over{K_B T}\right)}-1}} d^3 p = g \cdot {V \over (2 \pi \hbar)^3} \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": 21, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/24281?sort=votes | ## Current status of Bloch Constant and Landau Constant bounds
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The Bloch constant B (based on a theorem introduced by André Bloch in 1925 on the maximum radius of a one-to-one disk in the image of a normalized 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": 6, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/trigonometry/4557-law-cosine-help-print.html | # Law of cosine Help!!
Printable View
• July 29th 2006, 12:31 PM
^_^Engineer_Adam^_^
Law of cosine Help!!
Cud u give me the formula of Law of Cosine on how to solve a triangle w/ 3 sides
given?
Im kind of confused with this problem:
a = 5, b = 6, c = 9
find all 3 angles A,B & C
• July 29th 2006, 01:10 PM
topsquark
Q... | {"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": 32, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/number-theory/96246-chinese-remainder-theorem.html | # Thread:
1. ## Chinese Remainder Theorem
For the question,
Find the smallest x which solves the system of congruence equations:
x =+ 3 mod 15
x =+ 6 mod 224, where =+ stands for congruence modulo operation.
I gave an argument oriented solution as follows.
Any multiple of 224 is even.
So, 6+ any multiple of 224 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": 34, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://climateaudit.org/2007/01/06/paul-linsays-poisson-fit/ | by Steve McIntyre
Paul Linsay's Poisson Fit
Paul Linsay contributes the following:
Using Landsea’s data from here, plus counts of 15 and 5 hurricanes in 2005 and 2006 respectively, I plotted up the yearly North Atlantic hurricane counts from 1945 to 2004 and added error bars equal to $\pm \sqrt{count}$ as is appropr... | {"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": 10, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/number-theory/200434-perfect-square-s-odd-number-factors.html | 2Thanks
• 1 Post By emakarov
• 1 Post By awkward
# Thread:
1. ## Perfect square s, odd number of factors
If a number is a perfect square, it will have an odd number of factors (e.g., 4 has factors 1, 2, 4), whereas all other numbers have an even number of factors.
Is the converse true? Please explain why?
2. ## Re... | {"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/184111/how-to-show-that-e-g-cosz-is-analytic-using-cauchy-riemann-differential-e/184112 | # How to show that e.g. $\cos(z)$ is analytic using Cauchy- Riemann differential equations?
How to show that e.g. $\cos(z)$ is analytic using Cauchy-Riemann differential equations [$u_x(x,y)=v_y(x,y)$ and $u_y(x,y)=-v_x(x,y)$]? Do all analytic functions satisfy Cauchy-Riemann differential equations (CRDE)? What 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": 54, "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/3805/encryption-scheme-with-equivalent-keys/3809 | # Encryption scheme with equivalent keys?
I've long been looking for a symmetric encryption scheme (or algorithm) with equivalent keys. Let me define what I want:
1. Symmetric encryption algorithm with encryption function $E_k$ and inverse decryption function $D_k$.
2. Existence of equivalent keys. Keys $k_i \neq k_... | {"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": 30, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/80056/using-slides-in-math-classroom/80551 | ## Using slides in math classroom
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I am toying with the idea of using slides (Beamer package) in a third year math course I will teach next semester. As this would be my first attempt at this, I would like to gath... | {"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://mathhelpforum.com/advanced-algebra/59832-mappings-question-urgent.html | # Thread:
1. ## Mappings question - Urgent
Hi,
The question is:
Let S, T and U be sets and let a and b be mappings from S to T and from T to U respectively. Assume that the mapping a is not onto.
a) Give an example of sets S, T and U and mappings a and b, such that b o a is onto.
b)Can the mapping b o a be invertib... | {"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://nrich.maths.org/2383/note | ### F'arc'tion
At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.
### Plutarch's Boxes
According to Plutarch, the Greeks found all the rectangles with integer sides, ... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/18559/is-there-a-machinery-describing-all-the-irreducible-representations | ## Is there a machinery describing all the irreducible representations ?
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Suppose we have a finite dimensional Lie algebra $g$， Is there a machinery to describe all the irreducible representation of $g$.
Consider... | {"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/math-challenge-problems/182995-improper-integral-4-a-print.html | improper integral #4
Printable View
• June 13th 2011, 08:57 PM
Random Variable
improper integral #4
Evaluate $\int_{0}^{\infty} \frac{\ln x}{(x+a)(x+b)} \ dx \ \ a,b>0 \ (a \ne b)$
Unlike the last integral, try not to use contour integration.
• June 14th 2011, 02:38 PM
Drexel28
Re: improper integral #4
Quote:
Origi... | {"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://physics.stackexchange.com/questions/2119/equivalent-spring-constant-for-infinite-square-grid-of-springs/2128 | # Equivalent spring-constant for infinite square grid of springs
Consider an infinite square grid, where each side of a square is a spring following Hooke's law, with spring constant $k$.
What is the relation between the force and displacement between two points? If they are proportional, what is the equivalent sprin... | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/120857/the-number-of-non-isomorphic-strongly-regular-graphs-on-n-vertices | ## The number of non-isomorphic strongly regular graphs on n vertices
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What is the number of strongly regular graphs on $n$ vertices? or at least how many non-isomorphic strongly regular graphs can exist?
-
Than... | {"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": 20, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=106277 | Physics Forums
Page 1 of 2 1 2 >
## Pressure of Fluid
I have noticed what appears to be a geometric theory of pressure vessels. Its probably already been proved, so has anyone heard of it? If not, I may play around to see if I can get any math out of it to work. I have noticed that if you have any closed body w... | {"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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/12411/is-it-valid-to-select-a-model-based-upon-auc | Is it valid to select a model based upon AUC?
I have plot ROC for several models. These models were used to classify my samples into 2 classes.
Using these commands, I can obtain sensitivity vs. specificity plots for each model:
````perf <- performance(pred, "sens", "spec")
plot(perf)
````
Should I rely on the area... | {"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://mathematica.stackexchange.com/questions/6633/check-homework-integration-in-mathematica/6634 | Check homework integration in Mathematica
Given in my homework I have to compute (by hand) $$\iint\limits_{x^2+y^2\leq 1}(x^2+y^2)\,\mathrm dx\,\,\mathrm dy.$$ My solution so far: Let $f(x,y)=x^2+y^2$ and $K=\{(x,y)\in\mathbb{R}^2:x^2+y^2\leq 1\}$. With the transformation of polar coordinates $\varphi:(r,\phi)\mapsto(... | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/187702-derivative-integral-print.html | # Derivative of an integral
Printable View
• September 10th 2011, 07:12 AM
flybynight
Derivative of an integral
Hey guys,
I am looking at this problem, and I don't have any idea how to do it: $\frac{d}{dx}\int_x^3e^{{-t}^2}dt$
Any help would be greatly appreciated.
Thanks,
Peter
• September 10th 2011, 07:25 AM
Plato... | {"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": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/93295?sort=newest | ## Separating vectors for C$^*$-algebras
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
(I asked this on math.stackexchange, without response).
Let $A$ be a C$^*$-algebra, concretely acting on a Hilbert space $H$. Suppose that $\xi_0\in H$ is cyclic and sepa... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/44876/lipschitz-properties-of-minima-minimizers-of-convex-functions-of-two-variables | ## Lipschitz properties of minima/minimizers of convex functions of two variables
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Suppose I have a function $f(x,y)$ from $\mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R}$ that is convex in both $x$ and $y$. Set
... | {"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://mathhelpforum.com/calculus/203823-taylor-series.html | # Thread:
1. ## Taylor Series
Use taylor series to verify $e^{-iz}= cos z - isinz$
i know cos z = $\sum_{n=0}^{\infty}\frac{(-1)^nz^{2n}}{2n!}$
and sin z = $\sum_{n=0}^{\infty}\frac{(-1)^nz^{2n+1}}{2n+1!}$
and $e^{-iz} =\sum_{n=0}^{\infty}\frac{(-iz)^n}{n!}$
but i cant get the steps to get there.
2. ## Re: Taylo... | {"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://crypto.stackexchange.com/questions/tagged/oblivious-transfer | # Tagged Questions
Oblivious transfer refers to a cryptographic protocol in which a sender possesses a set of data and a receiver queries the sender for a particular member of that set in such a way that the sender does not learn which member the receiver requests. In other words, the sender is oblivious of what she .... | {"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/289542/how-do-i-find-the-mle-of-theta-when-x-is-dependent-on-theta?answertab=active | # How do I find the MLE of $\theta$ when x is dependent on $\theta$?
Let $X_{1},X_{2},...,X_{n}$ represent a random sample from a distribution with pdf:
$f(x; \theta)=e^{-(x-\theta)}, \theta \le x<\infty, -\infty<\theta<\infty$ | zero elsewhere
I need to find the MLE $\hat {\theta}$ of $\theta$.
Since the support 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": 22, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/74621/invariants-and-base-change/74624 | ## Invariants and base change
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Suppose $R$ is a Noetherian commutative ring, and $M$ a finite free $R$-module, with an action of a finitely generated discrete group $G$ by $R$-linear maps.
Is there any homologica... | {"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": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Fermi-Dirac_statistics | # Fermi–Dirac statistics
(Redirected from Fermi-Dirac statistics)
Statistical mechanics
• NVE Microcanonical
• NVT Canonical
• µVT Grand canonical
• NPH Isoenthalpic–isobaric
• NPT Isothermal–isobaric
• µVT Open statistical
Models
Scientists
In quantum statistics, a branch of physics, Fermi–Dirac statistics describes... | {"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": 114, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/247710/notation-for-repeated-application-of-function/247755 | Notation for repeated application of function
If I have the function $f(x)$ and I want to apply it $n$ times, what is the notation to use?
For example, would $f(f(x))$ be $f_2(x)$, $f^2(x)$, or anything less cumbersome than $f(f(x))$? This is important especially since I am trying to couple this with a limit toward 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": 37, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/115138/particles-chasing-one-another-around-a-circle | ## Particles chasing one another around a circle
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Two particles start out at random positions on a unit-circumference circle. Each has a random speed (distance per unit time) moving counterclockwise uniformly dist... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/92595/unbounded-sequences-in-banach-spaces | ## Unbounded sequences in Banach spaces
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Let $X$ be a Banach space and let $T$ be a bounded operator acting on $X$. Suppose for each linearly independent unbounded sequence $(x_n)$ in $E$, the sequence $(Tx_n)$ 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": 26, "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/235753/how-to-invert-this-function/263362 | # How to invert this function?
I need to invert this function:
$$y=\frac{\ln(x)}{\ln(x-1)}+1$$
-
Just out of curiosity: where did you come across this problem? – Thomas Nov 12 '12 at 16:42
## 3 Answers
In general, $\dfrac{\ln a}{\ln b}\ne \ln(a-b)$.
Remarks: $1.$ The false simplification was probably motivated 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": 18, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/81142/list | ## Return to Answer
2 edited body
Next, I suggest that you think about two special cases:
(1) When $\pi_1(X)$ is trivial. This will involve using the Serre spectral sequence for the contractible path fibration over $X4 X$ with fiber $\Omega X$, including the multiplicative structure.
(2) When $\pi_k(X)$ is trivial ... | {"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://crypto.stackexchange.com/questions/2739/safely-use-cryptsignandencryptmessage?answertab=active | # Safely use CryptSignAndEncryptMessage?
I am developing an application that sends messages which I want to encrypt and sign. The CryptoApi offers a function called CryptSignAndEncryptMessage. The description says, what this function actually does:
The CryptSignAndEncryptMessage function creates a hash of the specifi... | {"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/147771/rewriting-repeated-integer-division-with-multiplication/147832 | # Rewriting repeated integer division with multiplication
In many programming languages, such as C and C++, integer division of positive numbers is defined by simply ignoring the remainder. $5 / 2 == 2$.
In general, is it true of positive integers $a$, $b$, and $c$ that
$(a / b) / c$
will always give the same resul... | {"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/246142/maxium-value-of-discrete-convolution | # Maxium value of discrete convolution
I'm trying to calculate the maximum possible short-term energy $E[n]$ of a sampled signal $s$ in terms of $N$ and $\text{bitdepth}$.
$$E[n] =\sum_{m=-\infty}^{\infty} s^2[n]w[n-m]$$
where
$$w(n) = 0.54 - 0.46\; \cos \left ( \frac{2\pi n}{N-1} \right) \quad \text{(Hamming windo... | {"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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/tags/abelian-groups/info | Tag info
About abelian-groups
Should be used with the (group-theory) tag. A group $(G,*)$ is said to be abelian if $a*b=b*a$ for all $a,b\in G.$ | {"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://www.reference.com/browse/Artin-Schreier+covering | Definitions
Nearby Words
# Artin-Schreier theory
See Artin-Schreier theorem for theory about real-closed fields.
In mathematics, Artin-Schreier theory is a branch of Galois theory, and more specifically is a positive characteristic analogue of Kummer theory, for extensions of degree equal to the characteristic p.
I... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "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/mat... |
http://math.stackexchange.com/questions/65027/is-this-function-bounded | # Is this function bounded?
Suppose $f:\mathbb{R}\rightarrow\mathbb{R}$ is a $C^1$ function which satisfied the following differential inequality: $$\frac{df}{dt}\leq C(f+f^{\frac{3}{2}}).$$ If $f>0$ and $f(t)\rightarrow 0$ as $t\rightarrow\infty$, then is $f$ bounded?
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## 1 Answer
No, any monotonically decreasing... | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/acoustics+doppler-effect | # Tagged Questions
2answers
81 views
### In terms of the Doppler effect, what happens when the source is moving faster than the wave?
I'm just trying to understand this problem from a qualitative perspective. The Doppler effect is commonly explained in terms of how a siren sounds higher in pitch as it is approaching... | {"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... |
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