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http://mathoverflow.net/questions/75127/automorphisms-of-a-matrix-in-smith-normal-form | ## Automorphisms of a matrix in Smith normal form?
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Added: Amritanshu Prasad's answer makes it clear that I am really asking for a description of the group of integer unimodular matrices $P$ such that $D^{-1}PD$ 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": 129, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/90731/commutator-baker-campbell-hausdorff-formula | ## Commutator Baker-Campbell-Hausdorff formula
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Consider the Baker-Campbell-Hausdorff formula $\Phi(X,Y)\in\mathbb{Q}\langle\langle X,Y\rangle\rangle$ in non-commutative variables. Define $X*Y:=\Phi(X,Y)$ and $[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": 32, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/159407-recurrence-fibonacci-sequence.html | # Thread:
1. ## Recurrence and Fibonacci sequence
Hi. I have this problem that im stuck on.
Define a sequence $(G_n)_{n \ge0}$ by the recurrence $G_n = G_{n-1}+G_{n-2}$ for $n \ge2$. Subject to the initial values $G_0=2$, $G_1=1$. Let $(F_n)_{n \ge0}$ denote the Fibonacci sequence.
a) Write out explicitly $(G_n)_{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": 29, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/2012/computing-eigenvectors-and-eigenvalues/2040 | # Computing eigenvectors and eigenvalues
I have a (non-sparse) $9 \times 9$ matrix and I wish to obtain its eigenvalues and eigenvectors. Of course, the eigenvalues can be quite a pain as we will probably not be able to find the zeros of its characteristic polynomial.
Actually, what I really want is find the eigenvec... | {"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://nrich.maths.org/1830 | ### At a Glance
The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
### Pent
The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.
### Pentakite
ABCDE is a regul... | {"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://math.stackexchange.com/questions/157701/direct-product-of-center-of-group | # direct product of center of group
Let $Z(G)$ denote the center of a group $G$, let $J_n=Z(G)\times\dots \times Z(G)$, is it true that as a subset of external direct product $G\times\dots\times G$, $J_n$ is a subgroup?normal sybgroup?is it isomorphic to $Z(G)\times\dots \times Z(G)$ ($(n-1))$ times ? I know $Z(G)$ ... | {"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": 74, "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/143583/is-there-a-natural-way-to-multiply-measures/143642 | Is there a natural way to multiply measures?
Given two measures $\mu$ and $\nu$ on some measurable space $X$, is there a way to multiply them to get $\mu \cdot \nu$, another measure on $X$ (and not $X \times X$, as for the usual notion of product measure)?
Here's a case where I know how to give a definition: if both ... | {"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": 104, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/revisions/24083/list | 2 edited tags
1
# reversible Turing machines
Hello, Let T be a Turing machine such that
1) it operates on the alphabet {0,1},
2) its set of states is A
3) the language it accepts is $L$ .
Does there exists a Turing machine S which also operates on the alphabet {0,1} and such that the language it accepts is L (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": 5, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/tagged/tiling+number-theory | # Tagged Questions
3answers
942 views
### Minimum number of integer-sided squares needed to tile an $m$ by $n$ rectangle.
Let $T(m,n)$ for integers $m,n$ be the least number of integer-sided squares needed to tile an $m\times n$ rectangle. Clearly $T(kx,ky)\leq T(x,y)$. Are there integers $x,y,k\gt 1$, such that ...... | {"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://mathoverflow.net/revisions/58967/list | ## Return to Answer
4 edited body
Can't we base-change $f : X \to Y$ with $Z$ and obtain: $g : f^{-1}(Z) \to Z$? This also is a universal homeomorphism by construction, right? So now we have a universal homeomorphism to a regular scheme, but a regular scheme is weakly normal, see A. Andreotti and E. Bombieri, Sugli 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": 37, "mathjax_display_tex": 0, "mathjax_asciimath": 4, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/13609/models-of-zfc-set-theory-getting-started/29693 | ## Models of ZFC Set Theory - Getting Started
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For just any first-order theory: What are the sets I am supposed/allowed to think of when thinking of models as sets (of something + additional structure)?
Provided:... | {"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://amathew.wordpress.com/tag/geodesics/ | # Climbing Mount Bourbaki
Thoughts on mathematics
November 26, 2009
## Towards Cartan’s fixed point theorem: Cosine inequalities and derivative of the distance
Posted by Akhil Mathew under differential geometry, MaBloWriMo | Tags: Cartan fixed point theorem, cosine inequality, geodesics, negative curvature |
[2] Co... | {"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": 133, "mimetex.cgi": 0, "/images/m... |
http://www.physicsforums.com/showthread.php?s=1e361ec2d93607a340b51c20d338d7f7&p=4263307 | Physics Forums
Page 2 of 2 < 1 2
Mentor
## Classical Fields and Newton's 2nd Postulate of Motion
Quote by dr_k where Newton's 2nd Postulate is ${\bf F}_{net} = f(q_I,m_I) {\bf a}$ , here $m_I$ is the inertial mass
This doesn't work. By DEFINITION inertial mass is the proportionality between for... | {"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": 43, "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/7112 | ### Telescoping Series
Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.
### Incircles
The incircles of 3, 4, 5 and of 5, 12, 13 right angled triangles have radii 1 and 2 units respectively. What about triangles with an inradius of 3, 4 or 5 or ...?
... | {"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://quant.stackexchange.com/questions/3562/when-do-finite-element-method-provide-considerable-advantage-over-finite-differe | # When do Finite Element method provide considerable advantage over Finite Differences for option pricing?
I'm looking for concrete examples where a Finite Element method (FEM) provides a considerable advantages (e.g. in convergence rate, accuracy, stability, etc.) over the Finite Difference method (FDM) in option pri... | {"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://physics.stackexchange.com/questions/51498/dynamics-of-a-vertical-mass-spring-simple-harmonic-oscillator-with-gravity?answertab=votes | # Dynamics of a Vertical Mass-Spring Simple Harmonic Oscillator with Gravity
I am having some trouble obtaining the elastic potential energy and gravitational potential energy of a simple mass spring system.
In this experiment, masses attached to a spring were dropped from a position in which the spring had not be ex... | {"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": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://gowers.wordpress.com/2013/02/28/whither-polymath/ | # Gowers's Weblog
Mathematics related discussions
## Whither Polymath?
Over at the Polymath blog, Gil Kalai recently proposed a discussion about possible future Polymath projects. This post is partly to direct you to that discussion in case you haven’t noticed it and might have ideas to contribute, and partly to sta... | {"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": 171, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/284600/trigonometric-substitution-arc-length/284610 | # Trigonometric Substitution - Arc Length
Good day to everyone,
I'm not so good in maths as I wish. But, I'm doing my job to improve it. So, be patience and thanks in advance for any detailed clue.
Description of the problem:
The arc is described by this parabola: $\ x=y^2$. Having the integral of the length of 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": 28, "mathjax_display_tex": 13, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/119448/self-complementary-cartesian-products | ## Self complementary cartesian products
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Given two graphs $G$ and $H$ is there a nice way to check whether the cartesian product $G\Box H$ is self complementary without directly computing its complement and searc... | {"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/revisions/12418/list | ## Return to Answer
2 added 10 characters in body
There is a simple argument by comparing to the unit ball of $\ell_1^n$.
Let $K$ be the unit ball of $\ell_1^n$, i.e. the set of points with sum of coordinates (in absolute value) bounded by $1$. Then $K$ is the disjoint union of $2^n$ simplices (one per octant), and ... | {"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": 28, "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/56386-isomorphisms.html | # Thread:
1. ## isomorphisms
How does one show that a G is isomorphic to the external direct product of H and K if G=HK and if H and K have unique elements.
Also how does one apply this to proving U(15) is isomorphic to the external direct product of U(3) and U(5) and how would you show if U(15) is cyclic or not?
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": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.wikiwaves.org/Category:Symmetry_in_Two_Dimensions | From WikiWaves
# Introduction
If we consider the problem of an incident wave from the left on a body, or group of bodies, which are symmetric about $x=0$ then we can decompose the problem into an symmetric and anti-symmetric problem. The first problem can be thought of as having Neuman boundary conditions at $x=0$ 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 30, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/37849/closedness-of-finite-dimensional-subspaces | ## Closedness of finite-dimensional subspaces
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Is the (algebraic) span a finite set of vectors in a Hausdorff topological vector space over a complete field always closed?
I suspect yes, but I can't come up 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": 54, "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-statistics/165776-poisson-processes.html | # Thread:
1. ## Poisson processes
A radioactive source emits particles according to a Poisson process with rate $\lambda=2$ particles per minute. What is the expected time of emission of the second particle given that three particles have been emitted in the first four minutes?
2. Originally Posted by adnaps1
A radi... | {"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://cms.math.ca/Events/winter12/abs/egs | 2012 CMS Winter Meeting
Fairmont Queen Elizabeth (Montreal), December 7 - 10, 2012
Enumerative Geometry and String Theory
Org: Keshav Dasgupta and Johannes Walcher (McGill)
[PDF]
PER BERGLUND, University of New Hampshire
Global Embeddings for Branes at Toric Singularities and Moduli Stabilization [PDF]
We discuss ... | {"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://math.stackexchange.com/questions/94822/question-about-notation | Question about Notation
What does $\mathbb{R}∗\mathbb{R}$ mean? I'm sure this has been asked before, but I do not know how to search for notations in past questions.
-
I have never seen that before. Possibly the same as $\mathbb{R}\times\mathbb{R}$ as $*$ is sometimes used to denote multiplication in other settings, ... | {"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://www.physicsforums.com/showthread.php?p=4261202 | Physics Forums
## A possible Coasting Universe model vs ΛCDM
Two Coasting Universe model and comparison of the ΛCDM as well as Rh = ct models with Ia supernovae, GMB and CMB events. Both theory lead to the same result and fundamentals.
[Journal references below]
First model:
Rh = ct universe
"The backbone of stand... | {"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://www.physicsforums.com/showthread.php?t=204013 | Physics Forums
## Fresnel coeff
1. The problem statement, all variables and given/known data
The question involves the fresnel equations which I have derived. However, I seem to be missing something in the simplification. I arrive at these:
and I am trying to simplify to:
3. The attempt at a solution
No matter ho... | {"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": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathforum.org/mathimages/index.php?title=Divergence_Theorem&oldid=6668 | # Divergence Theorem
### From Math Images
Revision as of 10:38, 1 July 2009 by Bjohn1 (Talk | contribs)
Fountain Flux
The water flowing out of a fountain demonstrates an important theorem for vector fields, the Divergence Theorem.
Fountain Flux
Field: Calculus
Created By: Brendan John
# Basic Description
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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 19, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/17285/pca-to-decorrelate-variables | # PCA to decorrelate variables
I have 2 variables that I want to decorrelate. I was told I can use PCA to do so. I did PCA on the data and got all the parameters. Now how do I get the new set of transformed data that no longer correlates with the second variable? I want to use this set for further analysis. thanks,
-... | {"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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://skullsinthestars.com/2008/08/05/the-discovery-rediscovery-and-re-rediscovery-of-computed-tomography/ | The intersection of physics, optics, history and pulp fiction
## The discovery, rediscovery, and re-rediscovery of computed tomography
Posted on August 5, 2008 by
Note: This post is my contribution to The Giant’s Shoulders #2, to be held at The Lay Scientist. I thought I’d cover something a little more recent than 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 16, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/38299/what-is-the-variation-of-gauss-bonnet-term-a-total-derivative-of | # What is the variation of Gauss-Bonnet term a total derivative of?
What is the variation of Gauss-Bonnet term total derivative of?
i.e. Variation of Gauss-Bonnet combination $= \nabla_{\mu} C^{\mu}$.
What's $C^{\mu}$ in 4-dimensions?
-
## 2 Answers
If you just want to know why the Gauss-Bonnet Term is topologica... | {"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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://skepticalsports.com/?p=1854 | bucking the unconventional wisdom
# Bayes’ Theorem, Small Samples, and WTF is Up With NBA Finals Markets?
Seriously, I am dying to post about something non-NBA related, and I should have my Open-era tennis ELO ratings by surface out in the next day or so. But last night I finally got around to checking the betting 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 4, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/19417/path-integral-formulation-of-quantum-mechanics/19465 | # Path integral formulation of quantum mechanics
I'm a mathematics student with not much background in physics. I'm interested in learning about the path integral formulation of quantum mechanics. Can anyone suggest me some books on this topic with minimum prerequisite in physics?
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## locked by Manishearth♦Apr 14 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": 9, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/69800?sort=newest | ## Relation between Gerstenhaber bracket and Connes differential
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Let $C$ be an arbitrary algebra (more generally, a linear 1-category). The following structures are well-known:
A degree-0 product on the Hochschi... | {"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/calculus/39655-vectors-planes.html | # Thread:
1. ## Vectors and planes
Please help. A ray of light coming from the point (-1, 3, 2) is travelling in the directionof the vector 4i + j -2k and meets the plane x + 3y + 2z - 24= 0. Find the angle that the ray of light makes with the plane.
Tks!
2. Hello, pantera!
A ray of light coming from the point (-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": 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/97362/justification-of-algebraic-manipulation-of-infinitesimals/97524 | # Justification of algebraic manipulation of infinitesimals
As an engineering student, I regularly see people making arguments like this:
Consider a rectangle of dimensions $x\times 4x$. If we make $x$ bigger by a small quantity $dx$ then this will make $4x$ bigger by $4\cdot dx$ so the area of that $x \times 4x$ rec... | {"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": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://electronics.stackexchange.com/questions/37717/why-are-the-common-resistors-and-capacitors-rated-the-way-they-are | # Why are the “common” resistors and capacitors rated the way they are?
Very newbie question here...one to which I've been unable to find an answer in any of my books or online resources.
Whenever I see a capacitor/resistor assortment that features the most "common" ones (which, I understand can be quite subjective),... | {"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://math.stackexchange.com/questions/194792/what-is-the-meaning-of-the-range-and-the-precision/194797 | # What is the meaning of the range and the precision?
Using the scientific notation:
$$3.14 = 0.314 \times 10^1$$
From Tanenbaum's Structured Computer Organization, section B.1:
The range is effectively determined by the number of digits in the exponent and the precision is determined by the number of digits in 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": 17, "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/28124/trigonometric-identities/28130 | ## Trigonometric identities
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In the rant I wrote at
http://ncatlab.org/nlab/show/trigonometric+identities+and+the+irrationality+of+pi
I asked: Are these four identities the first four terms in a sequence that co... | {"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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/325/index | Slick Summing
Watch the video to see how Charlie works out the sum. Can you adapt his method?
Summing Geometric Progressions
Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
Double Trouble
Simple additions can lead to intriguing results...
Picture Story
Stage: 4 Ch... | {"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://unapologetic.wordpress.com/2008/03/14/riemanns-condition/?like=1&source=post_flair&_wpnonce=4ca8fc8c32 | # The Unapologetic Mathematician
## Riemann’s Condition
If we want our Riemann-Stieltjes sums to converge to some value, we’d better have our upper and lower sums converge to that value in particular. On the other hand, since the upper and lower sums sandwich in all the others, their convergence is enough for the res... | {"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": 48, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/46247/is-there-a-good-definition-of-the-universal-cover-for-non-connected-lie-groups/46260 | ## Is there a good definition of the universal cover for non-connected Lie groups?
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It is well-known that the universal cover $\tilde G$ of a connected Lie group $G$ has a Lie group structure such that the coverin... | {"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://unapologetic.wordpress.com/2010/03/17/products-of-algebras-of-sets/?like=1&source=post_flair&_wpnonce=671450efa2 | # The Unapologetic Mathematician
## Products of Algebras of Sets
As we deal with algebras of sets, we’ll be wanting to take products of these structures. But it’s not as simple as it might seem at first. We won’t focus, yet, on the categorical perspective, and will return to that somewhat later.
Okay, so what’s 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 72, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/100882?sort=newest | ## S-matrix for the HOMFLY/Hecke category
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This question concerns the HOMFLY-PT category, closely related to Hecke algebras. (See here for example.)
The minimal idempotents of this category are indexed by pairs $... | {"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://mathhelpforum.com/algebra/15688-prove-inequality.html | # Thread:
1. ## Prove an inequality
Can anyone prove the following inequality:
$<br /> \sum_{i=1}^N y_{i}^2/n_{i} - \frac{\left(\sum_{i=1}^N y_{i}\right)^2}{n} \ge 0,<br />$
where $n=\sum_{i=1}^N n_{i},\ \ n_{i} \ge 0$, and $y_{i}$ is a real quantity (can be both negative or positive)?
It appears that the inequali... | {"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": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://pediaview.com/openpedia/Boundary_conditions | # Boundary conditions
Shows a region where a differential equation is valid and the associated boundary values
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional restraints, called the boundary conditions. A solution to a bound... | {"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": 17, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/tagged/futures+time-series | # Tagged Questions
3answers
599 views
### How to normalize Futures data(different leverage) for cointegration test?
For example I want to construct 2 time series, one for ES and the other for NQ and test for cointegration. ES one point equal to 50$. NQ one point equal to 20$. If I have the following data: ...
2answe... | {"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-statistics/151700-can-random-variable-donimant.html | # Thread:
1. ## can a random variable donimant
Given two random variables x and y, and a constant c
What conditions are needed to make:
$Prob( w x + y < c ) \approx Prob( w x < c ), \text{ for } w \rightarrow \infty$
Can anyone help?
I think $E(x) < \infty$ and $E(y) < \infty$ might do. Is this right?
tks!!!!
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": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/36994-very-confused-matrices.html | # Thread:
1. ## very confused matrices
STUCK ON PART (III) hellp
(i) find the inverse of 4 1 k , k doesnt =5
3 2 5
8 5 13
DONE
(ii) solve the smultaneous equation
4x + y + 7z = 12
3x + 2y + 5z = m
8x + 5y +13z = 0
giving x,y,z in terms of m,,,DONE i got x= -6-11m
y= -6+2m
z=6+6m correct i think
(iii) find the value... | {"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": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/36211/proof-of-pauli-group-preservation-by-clifford-group-conjugation/36254 | # Proof of Pauli group preservation by Clifford group conjugation?
A well know result is that Clifford group preserve the Pauli group under conjugation or, in other words:
• $C(P_{1} \otimes P_{2})C^{\dagger} = P_{3} \otimes P_{4}$, with $C \in$ Clifford group and $P_{n} \in$ Pauli group.
How we can prove this?
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": 4, "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?p=1580720 | Physics Forums
## Surface Integral
As you know surface integrals are integrated with respect to dS. We then tranform the integral into one in dxdy. Is this the end of the problem or must we calculate it for dxdz and dydz as well and if so do you add up all results at the end!?
PhysOrg.com science news on PhysOrg.co... | {"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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/discrete-math/142272-two-ordinal-problems-print.html | # Two ordinal problems
Printable View
• April 30th 2010, 04:47 AM
Ester
Two ordinal problems
I have this kind of problems:
1) Let $A$ be a set and let $\alpha = \{ \beta \mid \beta \mbox{ is ordinal and } \beta \preceq A \}$.
Show that a) $\alpha$ is a cardinal number, b) $card(A) < \alpha$
2) Let A and $\alpha$ be ... | {"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": 86, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/13124/ext-complexes/13130 | # Ext & Complexes
I have heard that given two sheaves $A$ and $B$ on a variety, one can identify elements of $Ext^d(A,B)$ with complexes of sheaves $$0\to B \to C_1 \to \cdots \to C_d \to A \to 0.$$
My questions are,
How do I see that this is true?
and
If I have obtained an element of $Ext^n$ by some other method,... | {"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://math.stackexchange.com/questions/297941/limits-in-c0-1 | # Limits in $C[0,1]$
Let $(x_i)$ be a sequence of numbers in $(0,1)$ such that $\lim_{n \to \infty} \left( \frac{1}{n} \right) \sum_{i = 1}^n x_i^k$ exists for all integers $k \geq 0$. Show that $\lim_{n \to \infty} \left( \frac{1}{n} \right) \sum_{i = 1}^n f(x_i)$ exists for all functions $f \in C[0,1]$.
I was wonde... | {"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/107877/list | ## Return to Question
2 Corrected notation
Suppose I have an infinite discrete topological space $X$ of cardinality $\kappa$. Then I know some things about the Stone-Cech compactification, $\beta X$: it is Hausdorff and compact but not sequentially compact, has a basis of clopen sets, etc. My question is the followin... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math-challenge-problems/73591-old-four-numbers-equal-24-problem.html | # Thread:
1. ## The old "Four numbers equal 24" problem
Any time I see a question like this: http://www.mathhelpforum.com/math-he...make-24-a.html I wonder:
Of the $9^4$ possibilities of digits, how many can be solved by the four simple operations, how many can be solved if we allow other symbols, and how many are u... | {"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://mathoverflow.net/questions/115980/projection-formula-for-immersions | ## Projection formula for immersions
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Let $i : Y \to X$ be a quasi-compact immersion of schemes and let $M$ be a quasi-coherent sheaf on $X$. There is a canonical homomorphism
`$M \otimes i_* \mathcal{O}_Y \to 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": 15, "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/16506/seeking-a-specific-quantum-spin-system-of-interacting-spin-1-2-particles?answertab=oldest | # Seeking a specific quantum spin system of interacting spin 1/2 particles
Is there a system of interacting quantum spin 1/2 particles (of any topology) whose the states where all spins are up or down are eigenstates of its Hamiltonian and yet does not conserve the total spin polarization (in the z-direction) ?
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##... | {"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://mathoverflow.net/questions/77425/failures-that-lead-eventually-to-new-mathematics/77486 | ## Failures that lead eventually to new mathematics [closed]
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Possible Duplicate:
Most interesting mathematics mistake?
In the 25-centuries old history of Mathematics, there have been landmark points when a famou... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/140167-finding-derivative-complex-fraction-radicals.html | # Thread:
1. ## Finding the Derivative - Complex Fraction with Radicals
So I've been doing good with these until this problem.
Find $f'(a)$
$f(x)=\frac{8}{\sqrt{x+2}}$
$\frac{\frac{8}{\sqrt{a+h+2}}-\frac{8}{\sqrt{a+2}}}{h}$
I began multiplying by a common denominator to get rid of the complex fraction, then multi... | {"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": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/202845-another-limit-problem.html | 4Thanks
• 2 Post By Plato
• 1 Post By Prove It
• 1 Post By SworD
# Thread:
1. ## Another limit problem
Hello everyone!
So, this is the question, and I am not sure I am able to find any reason why this statement is wrong, as the exercise requires.
Exercise 2.3.53
Show by example that the following statement is wro... | {"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": 26, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/247877/how-to-prove-that-for-every-finite-field-its-cardinality-is-pn?answertab=votes | # How to prove that for every finite field its cardinality is $p^n$?
How to prove that for every finite field its cardinality is $p^n$ where $p$ is prime and $n\in\mathbb{N}$?
Thanks in advance!
-
3
– joriki Nov 30 '12 at 7:13
## 2 Answers
The prime field of $F$, which is the smallest subfield of $F$ or the field... | {"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/calculus/111290-integral-square-root.html | # Thread:
1. ## integral of a square root
how do you find the integral of a square root of a polynomial?
specifically,
the integral of the sqaure root of (t^2+t^4)
2. Originally Posted by cottekr
how do you find the integral of a square root of a polynomial?
specifically,
the integral of the sqaure root of (t^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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aoms/1177728491 | ### Distribution of Quadratic Forms and Some Applications
Arthur Grad and Herbert Solomon
Source: Ann. Math. Statist. Volume 26, Number 3 (1955), 464-477.
#### Abstract
The authors were prompted by a general problem concerning hit probabilities arising in military operations to seek the distribution of $Q_i = \sum^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": 7, "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/86773-group-element-order.html | # Thread:
1. ## group element order
Let G be an abelian group and let T={a in G|a^m=e for some m>1}. Prove that T is a subgroup of G and that G/T has no element - other than its identity element - of finite order.
Please show details of this proof. It is another practice problem for my final exam.
Thank you so much... | {"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://mathoverflow.net/revisions/77730/list | 2 better title
1
# A Problem on Graph Theory
Suppose that there are $n$ vertices, we want to construct a regular graph with degree $p$, which, of course, is less than $n$. My question is how many possible such graphs can we get? | {"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://mathhelpforum.com/differential-equations/181847-simple-first-order-diff-eq.html | # Thread:
1. ## Simple first order diff. eq
Hi! I have a simple question that i cant get thorugh at the moment. I have a differential equatoin of the form:
y' = C - y
where y' = dy/dt
How can I solve this. I cant do separation of variables here. Help plz
2. $y'=C-y\Leftrightarrow \dfrac{dy}{C-y}=dx$ (separated va... | {"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/2131/how-should-i-check-the-received-ephemeral-diffie-hellman-public-keys | How should I check the received ephemeral Diffie-Hellman public keys?
In my application I'm doing a DH key exchange, where both sides generate their own ephemeral key. No static keys are used. I am trying to make my application resistant against an active attack and therefore need to validate the public key that my co... | {"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": 45, "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/19605/is-it-possible-for-the-repeated-doubling-of-a-non-torsion-point-of-an-elliptic-cu/20412 | ## Is it possible for the repeated doubling of a non torsion point of an elliptic curve tstays bounded in the affine plane ?
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Let P=(x1,y1) be a non torsion point on an elliptic curve y^2=x^3+Ax+B. Let (xn,yn)=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": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/14752/checking-if-two-graphs-have-the-same-universal-cover/17518 | ## Checking if two graphs have the same universal cover
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It's possible I just haven't thought hard enough about this, but I've been working at it off and on for a day or two and getting nowhere.
You can define 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": 3, "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/50148/what-is-the-electrical-conductivity-s-m-of-a-carbon-nanotube | # What is the electrical conductivity (S/m) of a carbon nanotube?
I have been searching around for a while for this but I am having trouble finding any actual figures, all I can seem to find is that it is "very high".
So I am wondering, does anyone have any figures of what the electrical conductivity of a carbon nano... | {"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/52998/finding-the-nth-term-in-a-repeating-number-sequence | # Finding the nth term in a repeating number sequence
I'm trying to figure out how to solve these types of repeating number sequence problems. Here is one I made up:
Consider the following repeating number sequence: {4, 8, 15, 16, 23, 42, 4, 8, 15, 16, 23, 42, 4, 8, 15, 16, 23, 42,…} in which the first 6 numbers keep... | {"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-statistics/137953-distribution-function-function-random-variable.html | # Thread:
1. ## Distribution function for a function of random variable
Suppose that X is a random variable with distribution function $F_X(t)$ and let $Y=a+bX \ \ \ b<0$. Derive the distribution function for Y.
My solution:
I know that $F_Y(t)=P(T \leq t)=P(a+bX \leq t)$
$=P(X \geq \frac {t-a} {b} ) =1 - P( X \le... | {"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://mathoverflow.net/questions/21786/extending-methods-from-lubin-tate-theory | ## Extending methods from Lubin-Tate theory
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The first lemma in Lubin-Tate theory says the following:
Let $K$ be a local field, $A$ its ring of integers, and $f\in A[[T]]$ be such that $f(0) = 0$, $f'(0)$ is a 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": 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/advanced-algebra/175179-cyclic-groups-modulo.html | # Thread:
1. ## Cyclic groups modulo
Hi all,
Brief intro to what im talking about....
If n $\geq$ 2 is an integer, then Zn* denotes the set of invertible elements in the ring Zn. That is, it denotes the numbers in {1,2....n-1} which are coprime to n. The set Zn* is a group under multiplication modulo n.
Does anyon... | {"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/44130/what-are-the-properties-and-characteristics-of-a-single-quantum?answertab=votes | # What are the properties and characteristics of a single Quantum?
In Quantum mechanics , a quantum of energy called Quanta is origin of everything.
In physics, a quantum (plural: quanta) is the minimum amount of any physical entity involved in an interaction.
$E=n.h.\nu$
$\epsilon=h.\nu$.
But it's properties and ... | {"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://physics.stackexchange.com/questions/15169/if-the-earth-has-gravity-why-dont-we-all-collapse-to-the-center/16067 | # If the earth has gravity, why don't we all collapse to the center?
I'm sorry if the answer is obvious for you guys, but why don't we all (including buildings, road, people, the ground) collapse to the center of the earth because of gravity? Is it because we have velocity, just like the earth not falling to the sun (... | {"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://www.physicsforums.com/showthread.php?t=668424 | Physics Forums
Page 1 of 2 1 2 >
## Cross Product
What is the cross product of a constant and a vector? I know that the cross product between two vectors is the area of the parallelogram those two vectors form. My intuition tells me that since a constant is not a vector, it would only be multiplying with a vect... | {"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/250527/fun-question-anyone-know-why-e-eulers-number-was-chosen-for-wave-functio?answertab=oldest | # “Fun” question: anyone know why $e$ (Euler's Number) was chosen for wave functions?
First, let me say that this is merely something I have always wondered about, and can never seem to find a good reference for. I simply want to know... the geek in me.
Why was $e$ (Euler's Number) chosen for wave function descriptio... | {"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": 35, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/271837/functional-analysis-hilbert-spaces/272698 | # Functional analysis-Hilbert spaces
Let $X$ be an inner product space.
Show that $X$ is a Hilbert space if and only if for each continuous linear functional $L$ on $X$,there exists $z\in X$ such that $L(x)=\langle x,z\rangle$ .
Here,one part is exactly the Riesz Representation Theorem.
How can I prove the converse... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/speed+energy | # Tagged Questions
3answers
143 views
### If an electric car were to drive without having to stop, would the range be greatly affected by the speed at which the vehicle is moving?
Of course aerodynamics factors into this question, and the faster you are moving the more air you have to push out of your way, the more ... | {"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://mathhelpforum.com/advanced-algebra/165223-free-group.html | # Thread:
1. ## Free Group
Hi,
Prove that every free group is torsion-free and is non-abelian if its rank is $\geq 2$.
The second part is easy.
What about the first part? I think that we should suppose that this free group $F[X]$ is torsion (but I'm not sure).
Thanks for any help.
2. Originally Posted by Arczi1984... | {"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": 18, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Descriptive_set_theory | # Descriptive set theory
In mathematical logic, descriptive set theory is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces. As well as being one of the primary areas of research in set theory, it has applications to other areas of mathematics such as functional analysis, ... | {"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": 42, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/17457/the-meaning-of-unique-expression | # The meaning of “unique expression”
Let $G$ be abelian group, and let $A_k$ be a family of subgroups of $G$. Prove that $G=\sum A_k$ (internal) if and only if every non-zero element $g\in G$ has a unique expression of the form $g=a_{k_1}+...+a_{k_n}$, where $a_{k_i} \in A_{k_i}$, the $k_i$ are distinct and each $a_{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": 34, "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=4271094 | Physics Forums
## Understanding Vitali Sets...
I'm not sure if I understood Vitali Sets correctly, so I just want to write what I understood (because I don't know if it's right):
We have an equivalence relation where $x \sim y \iff x-y \in Q$. So if we look at the interval [0,1], each irrational number will have its... | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/279965/smoothening-viscosity-solution-to-classical-solution/280040 | # Smoothening viscosity solution to classical solution
Let $A$ be a linear second order differential operator with constant coefficients defined on real-valued functions of one-variable. Suppose that we have that for an upper-semicontinuous function $u:\mathbb{R}\to\mathbb{R}$ $$Au \leq 0\mbox{ holds in the viscosity ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 37, "mathjax_display_tex": 3, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/72699?sort=oldest | ## Maximum-bend TSP
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I've seen minimum-bend TSP studied, has anyone looked at max-bend TSP?
As a special case, I'm interested in the maximum number of turns a hamiltonian path can take in an $n \times n$ square g... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 30, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/152379-number-pattern.html | # Thread:
1. ## Number pattern
Hi, The question I have is:
Express a single generality that generalises all three related observations that
$1+3+5+3+1=3^2+2^2$
$1+3+5+7+9+7+5+3+1=5^2+4^2$
$1+3+1=2^2+1^2$
and show that your generalisation always holds true.
I know that the answer (i.e. RHS of =) is always $\frac{(no... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 20, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.sagemath.org/doc/reference/graphs/sage/graphs/graph_coloring.html | Graph coloring¶
This module gathers all methods related to graph coloring. Here is what it can do :
Proper vertex coloring
all_graph_colorings() Computes all $$n$$-colorings a graph
first_coloring() Returns the first vertex coloring found
number_of_n_colorings() Computes the number of $$n$$-colorings of ... | {"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": 127, "mathjax_asciimath": 2, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/advanced-statistics/89977-continuous-random-variables-their-pdfs.html | # Thread:
1. ## Continuous random variables and their PDFs
The question goes:
Suppose the continuous random variable X has a probability density function (PDF)
$f_{X}(x)=\frac{c}{x^6}, x>1$
i) Show that for X to be a valid PDF, $c$ must be equal to $5$.
ii) Calculate $E(X^6e^{-2X})$.
For part i) I keep getting $-... | {"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": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/classical-mechanics?page=5&sort=votes&pagesize=15 | # Tagged Questions
[tag:classical-mechanics] entails the study of the trajectory of bodies under the influence of forces. More specific subtopics are: [tag:newtonian-mechanics], [tag:lagrangian-mechanics], [tag:hamiltonian-mechanics] for point particles and [tag:fluid-dynamics], [tag:statistical-mechanics] and ...
1a... | {"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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/20007?sort=oldest | ## Visualizing a complex plane cubic together with the real plane
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In Alain Roberts "Elliptic curves: notes from postgraduate lectures given in Lausanne 1971/72" page 11 (available on google books unless you alrea... | {"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://math.stackexchange.com/questions/88405/finding-the-decay-constant | # finding the decay constant
Given the following function, how does one rewrite the exponential part of the equation into $e^{-L/L_{0}}$, where $L_{0}$ is the decay constant
$$f(L)=16\frac{a}{b}\left(1-\frac{a}{b}\right)\exp\left(\frac{-2L}{c}\bigl(2d(b-a)\bigr)^{1/2}\right)$$
I know this problem (demi-vie) from sch... | {"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": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/44722/what-exactly-are-hamiltonian-mechanics-and-lagrangian-mechanics/44723 | # What exactly are Hamiltonian Mechanics (and Lagrangian mechanics)
• What exactly are Hamiltonian Mechanics (and Lagrangian mechanics)?
I want to self-study QM, and I've heard from most people that Hamiltonian mechanics is a prereq. So I wikipedia'd it and the entry only confused me more. I don't know any differenti... | {"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://mathoverflow.net/questions/35382?sort=votes | ## Untrustworthy people picking a random number
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Inspired by the party game Mafia, in particular those situations where nobody is clearly innocent or guilty and the group wants to decide on someone random to elimi... | {"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://mathoverflow.net/revisions/43581/list | ## Return to Question
2 deleted 118 characters in body
I'm not sure how long this iterative questions can go on, but let me try again. Let's say $X$ is a Cohen-Macaulay scheme with an action of $\mathbb{G}_m$ (i.e. if $X$ is affine, a grading on the coordinate ring). Are the schematic fixed points $X^{\mathbb{G}_m}$ ... | {"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": 12, "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/24746/proving-the-time-evolution-of-momentum-operator | # Proving the time-evolution of momentum operator
In QFT the evolution of momentum and field operators is given by $∂_0φ=i[H,φ]$ and $∂_0\pi=i[H,\pi]$.
Is it possible to derive these equations from the basic operator commutation relations or are they postulated?
Note: this is a follow-up to Canonical quantization of... | {"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://math.stackexchange.com/questions/326511/graphing-x2-3-a-question-of-domain | # Graphing $x^{2/3}$: a question of domain
I'm trying to graph $x^{2/3}$. If I enter $y=x^{2/3}$, my graphing program excludes negatives from the domain: However, if I enter it as either $y=\sqrt[3]{x^2}$ or $y=(x^{1/3})^2$, it includes the negative values of $x$:
I'd like to understand what's going on. My best guess... | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/16998/duality-and-fourier-transforms | # Duality and Fourier Transforms [closed]
I read that
$(FF(f))(x)=2\pi f(-x)$, where $F$ is the Fourier transform
and $F(f(x-a))(k)=\exp(-ika) X(k)$ where $X(k)=F(f(x))$
implies $F(\exp(iax)f(x))(k)=X(k-a)$.
But I don't see how that is done... I am quite happy with getting $F^{-1}X(k-a)=\exp(iax)f(x)$ by brute for... | {"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... |
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