url stringlengths 17 172 | text stringlengths 44 1.14M | metadata stringlengths 820 832 |
|---|---|---|
http://math.stackexchange.com/questions/40861/mathematical-notation-for-the-maximum-of-a-set-of-function-values | # Mathematical notation for the maximum of a set of function values
I have a question about the proper notation of the following (simplified) example:
I want to express that I have a value alpha, which is the maximum of a set of n values. Each value in the set is the result of a function $f(x)$, and the range of $x$ ... | {"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": 11, "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/98910/complex-analysis-correspodence-between-h-omega-1-and-h-omega-2?answertab=oldest | # Complex Analysis: Correspodence between $H(\Omega_1)$ and $H(\Omega_2)$.
If we let
$$\Omega_1=\left\{z \in \mathbb{C} : 0<\operatorname{Im}(z)< \pi\}, \quad \Omega_2=\{z \in \mathbb{C}: 0<\operatorname{Im}(z) \right\},$$
can we establish a one-to-one correspondence between $H(\Omega_1)$ and $H(\Omega_2)$ where $H(... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/9651/list | ## Return to Answer
3 Texified, since problem was on front-page anyway
space X.
• X $X$.
• $X$ is compact.
• Xκ
• $X^\kappa$ is Lindelöf for any cardinal
• Xω1$\kappa$.
• $X^{\omega_1}$ is Lindelöf.
• for 1 implies 2, since if X $X$ is compact, thenXκ$X^\kappa$ is compact and hence Lindelöf.
So suppose that we... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 71, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/21386?sort=newest | ## What is the nonrecursive formula for the following implicit function?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Given $f(0) = 1-c$, what is the non-recursive $f(n)$ that satify the following equation $f(n)-\frac{1}{2}f(n-1)f(n)+f(n-1) = 1$
for n = 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": 4, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://all-science-fair-projects.com/science_fair_projects_encyclopedia/Combinatorics | # All Science Fair Projects
## Science Fair Project Encyclopedia for Schools!
Search Browse Forum Coach Links Editor Help Tell-a-Friend Encyclopedia Dictionary
# Science Fair ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 4, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/127354/the-real-part-of-a-matrix-under-similarity-transformation | # The real part of a matrix under similarity transformation
I have a question regarding the real part of some matrix A, defined as $$Re\{A\} = \frac{1}{2}\left(A + A^\dagger \right).$$ Where $A^\dagger$ denotes the Hermitian conjugate. One can also assume that the real part is positive semi-definite, i.e. $Re\{A\} \ge... | {"extraction_info": {"found_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://nrich.maths.org/570/index?nomenu=1 | The areas of the faces are $3$, $12$ and $25$ square centimetres. | {"extraction_info": {"found_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/statistics/98906-proving-question.html | # Thread:
1. ## Proving question
Hi,
given that: $S^2=\frac{1}{n-1}\sum_{i=1}^{n}(X_i-\overline X)^2$.
I want to show that $E[S^2]=\sigma^2$
However, when i reached: $\frac{n}{n-1}(\frac{1}{n}\sum_{i=1}^{n}E[X_i^2]-E[\overline X^2])$, i was puzzled on finding $E[\overline X^2]$?
Since $E[\overline X^2]=Var(\overl... | {"extraction_info": {"found_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": 17, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/11117/h-space-structure-on-infinite-projective-spaces | H-space structure on infinite projective spaces
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Any Eilenberg-MacLane space $K(A,n)$ for abelian $A$ can be given the structure of an $H$-space by lifting the addition on $A$ to a continuous map $K(A\times A,n)=K(A,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": 41, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://logiciansdoitwithmodels.com/category/tarskis-theorem/ | # Logicians do it with Models
A self-guided jaunt in philosophical logic
## Archive for the ‘Tarski’s Theorem’ Category
### Hellman’s First Definability Example
September 15, 2010
What Tarski’s Theorem shows is that interpreted formal languages that are interesting (i.e., with enough expressive machinery to repres... | {"extraction_info": {"found_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": 67, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/134044-solved-equation-point-line-polar-coords.html | # Thread:
1. ## [SOLVED] Equation for a point on a line in polar coords
[FONT="]Suppose we are given the Polar points P1=(r1, θ1) and P2=(r2, θ2) and we are given a distance D1. How would I find the coordinates of the point P3=(r3, θ3) that lies along the line segment between P1 and P2, and is a distance D1 from ... | {"extraction_info": {"found_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://mathematica.stackexchange.com/questions/tagged/matrix?sort=faq&pagesize=30 | # Tagged Questions
Questions on the manipulation of matrices in Mathematica.
6answers
4k views
### Elegant operations on matrix rows and columns
Question The Mathematica tutorial has a section 'Basic Matrix Operations', describing operations like transpose, inverse and determinant. These operations all work on enti... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/110274/how-can-we-show-that-i-a-is-invertible | How can we show that $(I-A)$ is invertible?
$A$ is an $n\times n$ matrix with $\|A\|≤a<1$ . I need to prove that the matrix $(I-A)$ is invertible with $\|(I-A)^{-1}\|\le\frac1{(1-a)}$.
It doesn't say anything more. The norm makes me confuse. How can we start to solve this. Could you please help?
-
1
Do you know 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": 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/197278/confusion-related-to-context-sensitive-grammar-creation/197282 | # Confusion related to context sensitive grammar creation
I was reading this wikipedia article for generating grammar. They have mentioned that for generating null string in the grammar we can have a rule
$$S \rightarrow \lambda$$
only if $S$ doesn't appear on the right of any production rule.
However in some examp... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/11647/how-does-human-brain-compare-to-a-modern-cpu-in-energy-per-bit/11654 | how does human brain compare to a modern CPU in energy per bit?
Can someone compare the energy efficiency of human brain as a computer ? What is the energy in joules / flop ? may be some reasonable assumptions on the computational load of common tasks such as pattern recognition or speech synthesis can be used.
-
3
... | {"extraction_info": {"found_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://crypto.stackexchange.com/questions/5675/polynomials-and-efficient-computability?answertab=active | # Polynomials and efficient computability
In public key crypto, the popular definitions of security (CPA, CCA1,2) depend on PPT adversaries. I'm trying to understand why adversaries should be PPT.
It's clear that adversaries should be at most probabilistic sub-exponential, because otherwise they could exhaust the mes... | {"extraction_info": {"found_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/geometry/43983-resolution-triangles.html | # Thread:
1. ## Resolution of triangles?
If in a triangle ABC, length of the sides a,b & c are in Arithmetic Progression, then it is necessary that:
A)2/3 < b/c < 2
B)1/3 < b/c < 2/3
C)2/3 < b/a < 2
D)1/3 < b/a < 2/3
More than one options are correct. How to solve this problem?
2. Hello,
What about something usin... | {"extraction_info": {"found_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://mathoverflow.net/questions/105971?sort=oldest | ## How should an analytic number theorist look at Bessel functions?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
(And a related question: Where should an analytic number theorist learn about Bessel functions?)
Bessel functions occur quite frequently in ana... | {"extraction_info": {"found_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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=16742 | Physics Forums
## batteries
What does it mean when it's said that the positive terminal of a battery is at a higher potential than the negative end? How does electric potential (voltage) relate to electric current/electric fields?[o)]
PhysOrg.com science news on PhysOrg.com >> Front-row seats to climate change>> A... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/L1-norm | # Taxicab geometry
From Wikipedia, the free encyclopedia
(Redirected from L1-norm)
Jump to: navigation, search
Taxicab geometry versus Euclidean distance: In taxicab geometry all three pictured lines (red, yellow, and blue) have the same length (12) for the same route. In Euclidean geometry, the green line has length ... | {"extraction_info": {"found_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": 11, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/28803?sort=votes | ## What is the proper initiation to the theory of motives for a new student of algebraic geometry?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
A preliminary apology is in order: I realize that most of my contributions to this site are in the form of refere... | {"extraction_info": {"found_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/36249/speed-of-sound-and-the-potential-energy-of-an-ideal-gas-goldstein-derivation | speed of sound and the potential energy of an ideal gas; Goldstein derivation
I am looking the derivation of the speed of sound in Goldstein's Classical Mechanics (sec. 11-3, pp. 356-358, 1st ed). In order to write down the Lagrangian, he needs the kinetic and potential energies.
He gets the kinetic energy very easil... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/209818-forecast-cubic-spline-print.html | # Forecast with cubic spline
Printable View
• December 14th 2012, 06:25 AM
igorbaldacci
Forecast with cubic spline
Hi all,
I have a simple question: is it possible to make forecast with cubic spline? And, if yes, how?
Frecast, for me, meens that I can understend the value of my interpolation function OUTSIDE the dat... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/30113/geometric-model-for-classifying-spaces-of-alternating-groups/30115 | ## Geometric model for classifying spaces of alternating groups
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The classifying space of the nth symmetric group $S_n$ is well-known to be modeled by the space of subsets of $R^\infty$ of cardinality $n$. Various... | {"extraction_info": {"found_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-math-topics/137523-big-o-proof.html | Thread:
1. BIG O proof
How do I prove the following:
O(n^2 logn) is also O(n^3)?
2. Originally Posted by taurus
How do I prove the following:
O(n^2 logn) is also O(n^3)?
$f(n)\in O(n^2 \log(n))$
means there exists a constant $k>0$ and an $N>0$ such that for all $n>N$:
$|f(n)|<k n^2 \log(n)$
Now for $n>0$ we have ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 23, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/19970/does-the-scientific-community-consider-the-loschmidt-paradox-resolved-if-so-wha/19976 | # Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution?
Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution?
I have never seen dissipation explained, although what I have seen a lot is descriptions of dissipation (i.e. 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": 23, "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/157445/the-limit-of-integral | # The limit of integral
Let $1 \le p < \infty$ and assume $f \in L^p(\mathbb{R})$. I'm trying to prove the limit of integral $$\lim_{x \to \infty} \int^{x+1}_x f(t)dt =0.$$
Can I use Riesz Theorem for Banach spaces?
-
Are you using the Lebesgue integral? What is your definition of it? – Alex Becker Jun 12 '12 at 16... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?p=1490589 | Physics Forums
Thread Closed
Page 1 of 3 1 2 3 >
Blog Entries: 6
## Shapiro time delay?
Can someone clear up what is observed in Shapiro time delay experiments.
As I understand it a delay is seen in the round trip signal time of a radar signal sent to a distant planet on the opposite side of the sun due 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": 30, "mathjax_display_tex": 11, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/34442/sum-of-sets-modulo-a-square/34471 | Sum of sets modulo a square
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I would be glad to see a reference to the following easy lemma in additive combinatorics: if $A_1$ and $A_2$ are two sets of remainders modulo $n^2$, each has cardinality $n > 1$ and all e... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 40, "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/72986/alternate-definition-of-ordinals | ## Alternate definition of ordinals ?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hello, recently I came upon some personal notes I'd made several years ago while reviewing some basic set theory (ordinals, transfinite recursion, inaccessible cardinals etc.... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.m.wikibooks.org/wiki/Strength_of_Materials/Loading_of_Beams | Strength of Materials/Loading of Beams
Strength of Materials
Strength of Materials in Engineering Mechanics
Introduction | Introductory Concepts | Loading of Beams | Torsion | General State of Stress | Weakest link determination by use of three parameter Weibull statistics
One of the areas where solid mechanics as ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 10, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/28286/general-introduction-to-functional-and-other-mathematic-notations/29030 | # General Introduction to Functional and other Mathematic Notations
I've been a programmer for a good while now. Fairly experienced at a bit of math as far as coming up with algorithms and such but I am far far behind on understanding quite a deal of notation.
Here and there I run into an issue where someone will not... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/9240/what-are-fields/9245 | # What are fields?
I'm following my first course in field theory and the professor began, like many books do, by introducing the scalar field. However, I am a bit hesitant about the physical idea of fields. My question is: what is the physical meaning of the fields? Why they are introduced? I read the introduction 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://mathoverflow.net/questions/101253/surjectivity-of-operators-on-linfty/101612 | ## surjectivity of operators on l^infty
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Can anyone give me an example of an bounded and linear operator `$T:\ell^\infty\to \ell^\infty$` (the space of bounded sequences with the usual sup-norm), such that T has d... | {"extraction_info": {"found_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://mathhelpforum.com/advanced-algebra/170970-more-algebraic-geometry-posted.html | # Thread:
1. ## More Algebraic Geometry
Again, I know this one looks like it should be easy (easier, in fact, even than what I posted before). My brain is just completely fried on this subject right now for some reason...
A hyperplane in $\mathbb{P}^N$ is a hypersurface [which means its dimension (as a topological s... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 22, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/67728/correspondence-between-normal-subgroups-of-a-group-and-normal-subgroups-of-a-quo | # Correspondence between normal subgroups of a group and normal subgroups of a quotient groups
Suppose $G$ be a group and $N$ be a proper normal subgroup such that it is not contained in any other proper normal subgroup. Does that mean $G/N$ is simple?
Is there one-one correspondence between the normal subgroups 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": 35, "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/103809/list | ## Return to Answer
2 added strengthening
Let $\vec{a} \in A^{<\omega}$. There are uncountably many automorphisms $f$ and only countably many possible values for $f(\vec{a})$, so there must be two different automorphisms $f_1$ and $f_2$ with $f_1(\vec{a}) = f_2(\vec{a})$. Then $f_2^{-1} \circ f_1$ is a nontrivial aut... | {"extraction_info": {"found_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://mathoverflow.net/revisions/79898/list | 2 switched tags
1
# zeros of a holomorphic function in several variable
Let $f$ be a holomorphic function in $n$ complex variables on a domain $D\subset \mathbb C^n$. Let $S$ be a subset of $D$ such that for a polynomial $P$ in $n$ variable, $P(S)=(a,b)$ for an interval $(a,b)$. Can $f$ be zero on $S$?
What happens ... | {"extraction_info": {"found_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/133025-solved-just-need-help-setting-up-equation.html | # Thread:
1. ## [SOLVED] Just need help setting up the equation
In the section of integration by parts
Find the area of the region enclosed by y=lnx, the line x=e and the x-axis
2. Originally Posted by vinson24
In the section of integration by parts
Find the area of the region enclosed by y=lnx, the line x=e and 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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/number-theory/197765-generator-z-p.html | 3Thanks
• 1 Post By Sylvia104
• 2 Post By Deveno
# Thread:
1. ## generator of Z*p
if p,q are primes with p=2q+1, and we pick a random number g in Z*p, what is the probability that g is a generator of Z*p?
2. ## Re: Generator of Z*p
$\mathbb Z_p^\times$ is cyclic of order $p-1=2q$ and so has $\varphi(2q)$ generator... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/34839/how-do-nasas-curiosity-determine-the-elemental-composition-of-mars-using-spectr?answertab=votes | # How do NASA's Curiosity determine the elemental composition of Mars using spectrometer?
The resultant flash of glowing plasma is viewed by the system’s 4.3-inch aperture telescope, which sends the light down an optical fiber to a spectrometer located in the body of the rover. There, the colours of light from the fla... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Speed_of_sound | # Speed of sound
For other uses, see Speed of sound (disambiguation).
Sound measurements
Sound pressure p, SPL
Particle velocity v, SVL
Particle displacement ξ
Sound intensity I, SIL
Sound power Pac
Sound power level SWL
Sound energy
Sound energy density E
Sound energy flux q
Acoustic impedance Z
Speed of sound c
Audi... | {"extraction_info": {"found_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": 64, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=194650 | Physics Forums
## difference between a function being continuos at at point and havinga limit there...
I'm confused about a point that my book on real analysis is making about the difference between the definition of a function being continuos at at point and the definition of a function having a limit L at a point.
... | {"extraction_info": {"found_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": 35, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/33786-complex-variables.html | # Thread:
1. ## Complex Variables
Can anyone help me with this pls?
How can you prove that the integral of f(z) around the contour z= 1 is 0
where f(z) is Log(z+5)
Thx
2. I know Log(z) is ln r + i (theta). But i dont know how that applies to this situation.
Also, do I solve it as a normal integral or use the Cau... | {"extraction_info": {"found_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/81887/proving-sequence-equality-using-the-binomial-theorem | # Proving sequence equality using the binomial theorem
The problem: Prove that for $n \in \mathbb N$:
$$\left(1 + \frac{1}{n} \right)^n = 1 + \sum_{m=1}^{n} \frac{1}{m!} \left(1 - \frac{1}{n} \right) \left(1 - \frac{2}{n} \right) \cdots \left(1 - \frac{m-1}{n} \right).$$
The hint is to use the binomial theorem. So 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": 4, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/16817/penetration-of-armor-plate/16821 | # Penetration of armor plate
Is there a simple mathematical expression for the stopping power of a given thickness of armor, given the thickness of armor plate, the radius of a cannon ball, the density of the cannonball and the armor, the tensile strength and/or toughness of the armor, and the speed of the cannonball?... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/110320/list | ## Return to Answer
3 added 2 characters in body
Not sure if this question really qualifies for MO.
Anyway, the answer very much depends on the group $G$. In most cases $n_p(G)\ne n_q(G)$ for distinct prime divisors of the group order. However, there are infinitely many examples very where equality occurs: If $r$ 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": 30, "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/19592/how-to-read-the-temperature-of-an-abstract-system/19662 | # How to “read” the temperature of an abstract system?
How can I interpret the parameter temperature $T$, if I'm not given the description of the system in terms of the equation of state, $E(S,V\ )$ or $S(E,V\ )$ and so on.
In many systems it makes sense to think of it as an "energy" itself, e.g. when the entropy 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": 50, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/201315-help-homework-quadratics.html | Thread:
1. Help on homework!(Quadratics)
Hello...
I have this problem on my homework, I have to solve the quadratics by factorising;
x(x-7)=0
If you could explain how to do it (simple terms!) I would be grateful
2. Re: Help on homework!(Quadratics)
Originally Posted by RonnieSaha
Hello...
I have this problem on... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?t=310084 | Physics Forums
Thread Closed
Page 1 of 2 1 2 >
## Double slit experiment (one slit closed)
Hi,
In young experiment, say one slit is completely closed, what observed is looks like a single band light. But why is not a diffraction pattern? I wonder whether the reason is, the slit width(don't mean distance betwe... | {"extraction_info": {"found_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://mathoverflow.net/questions/80284/what-are-good-examples-of-string-manifolds | ## What are “good” examples of string manifolds?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Based on this mathoverlow question, I would like to have a similar list for the case of string manifolds. An $n$-dim. Riemannian manifold $M$ is said to be string,... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/191665-question-about-periodicity.html | # Thread:
1. ## Question about periodicity?
Ok as we know, if $f(x+P) = f(x)$ then the function is periodic.
So if the function is not periodic, $f(x+p) = f(x)$, what it the value of p?
2. ## Re: Question about periodicity?
It's just a positive real number, for example the $f(x)=\sin(x)$ is periodic with periodici... | {"extraction_info": {"found_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://math.stackexchange.com/questions/45904/if-f-is-differentiable-in-1-infty-and-lim-x-to-infty-fx-l-infty/45908 | # If $f$ is differentiable in $(1,\infty )$ and $\lim_{x\to\infty }f'(x)=L<\infty$ then $\lim_{x\to\infty }f(x)=l\le\infty$?
I need to prove or disprove this:
If $f$ is differentiable on $(1,\infty)$ and $\lim\limits_{x\to\infty}f'(x)=L\lt \infty$, then $\lim\limits_{x\to\infty}f(x)=\ell\leq\infty$.
After I didn't f... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "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/55333/is-the-quantization-of-gravity-necessary-for-a-quantum-theory-of-gravity-part-i | # Is the quantization of gravity necessary for a quantum theory of gravity? Part II
(At the suggestion of the user markovchain, I have decided to take a very large edit/addition to the original question, and ask it as a separate question altogether.)
Here it is:
I have since thought about this more, and I have come ... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?t=262942 | Physics Forums
## Log in a river
1. The problem statement, all variables and given/known data
Two rivers of unequal width (64m and 125m) meet at a right angle, forming an L-shaped channel. What is the longest possible log you can float on it?
2. Relevant equations
3. The attempt at a solution
I tried for equal wid... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?p=3786878 | Physics Forums
## questions on inductive definitions in a proof
Hi
I was trying to solve the following problem from Kenneth Ross's Elementary Analysis book.
here is the problem.
Let S be a bounded nonempty subset of $\mathbb{R}$ and suppose that
$\mbox{sup }S\notin S$. Prove that there is a non decreasing sequence
... | {"extraction_info": {"found_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?t=257124 | Physics Forums
## necessary and sufficient conditions: Fourier Transform
I don’t know if the question belongs to engineering or math but here it goes.
I was taught that a sufficient (not necessary) condition for existence of Fourier transform of f(t) is f(t) is absolutely integratble. I was wondering what are the “ne... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/21168?sort=newest | ## How to classify the algebras C^∞(M)?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
This continues my question about smooth Gelfand-duality. In the book
Juan A. Navarro González & Juan B. Sancho de Salas, C∞-Differentiable Spaces, LNM 1824
it is shown th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 83, "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/CMB-1997-013-7 | Canadian Mathematical Society
www.cms.math.ca
| |
Site map | CMS store
location: Publications → journals → CMB
Abstract view
# Continuous Self-maps of the Circle
Read article
[PDF: 76KB]
http://dx.doi.org/10.4153/CMB-1997-013-7
Canad. Math. Bull. 40(1997), 108-116
Published:1997-03-01
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": 17, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://alanrendall.wordpress.com/2009/03/30/the-fitzhugh-nagumo-model/ | # Hydrobates
A mathematician thinks aloud
## The FitzHugh-Nagumo model
As mentioned in a previous post the FitzHugh-Nagumo model is a simplified version of the Hodgkin-Huxley model describing the propagation of signals in nerve cells. In this post only the spatially homogeneous case is discussed. It is possible to c... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 14, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/81560-poisson-summation-formula-proof.html | # Thread:
1. ## Poisson Summation Formula Proof
I'm having trouble understanding a couple of parts of the proof presented here in Knapp's Basic Real Analysis : Book link from Google (pgs 389-390).
He defines $c_n=\frac{1}{2L}\int_{-L}^{L}f(t)e^{-2\pi int/L}dt$. He then takes the Fourier series for L=1 on $F(x)=\sum_... | {"extraction_info": {"found_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": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/102829/is-the-mostowski-collapse-natural | ## Is the Mostowski collapse natural?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The Mostowski collapse lemma (see here for a quick ref) is one of the key basic tools in the set-theory arsenal. I wonder if the collapse is natural, in the functorial sense.... | {"extraction_info": {"found_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/questions/97969/convex-functions-from-surfaces-of-revolution | ## convex functions from surfaces of revolution
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Li-Tam (Ann of math 1987) proved some estimates on nonnegative harmonic functions on manifolds with sec $\geq 0$ outside a compact set. I just want to get some feel... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2009/01/27/ | # The Unapologetic Mathematician
## Determining Eigenvalues
Yesterday, we defined eigenvalues, eigenvectors, and eigenspaces. But we didn’t talk about how to actually find them (though one commenter decided to jump the gun a bit). It turns out that determining the eigenspace for any given eigenvalue is the same sort ... | {"extraction_info": {"found_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": 26, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/17181/numbered-symbols?answertab=active | # Numbered symbols
I work with an exterior algebra over $R^n$. I have the basis $\{1,\omega_i\}_{i=1}^n$ in this algebra, and my differential operator is defined as
$$d\omega_k=\sum_{i>j>0,i+j=k} (i-j)w_i\wedge w_j.$$
As you see, my sum depends directly on the indexes of the elements of the basis. I surely can defin... | {"extraction_info": {"found_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://mathhelpforum.com/pre-calculus/22656-coordinate-geometry-question.html | # Thread:
1. ## Coordinate geometry question
Just a really quick one, suppose I have a line of equation: y=1/2x+5/2
The next part of the question asks for this in the form of ax+by+c=0
How do I convert from y=mx+c to ax+by+c=0?
Thank youuu!
2. Originally Posted by hymnseeker
Just a really quick one, suppose I hav... | {"extraction_info": {"found_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/108430/free-resolution-of-this-determinantal-variety | ## Free Resolution of this determinantal variety.
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I am looking for a free resolution of the ideal generated by $2\times 2$-minors of a $3\times 3$ -matrix. More precisely let $M$ be a matrix (sorry but I cannot 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": 27, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/119416-standard-confusion-picturing-work-empty-tank.html | # Thread:
1. ## Standard confusion on picturing work to empty tank
Yes, I have searched the forums and google but nothing quite yet what I was looking for.
Problem:
A water tank in the shape of a cone is underground with the distance above ground being called D, the base of the cone is horizontal with the ground ie... | {"extraction_info": {"found_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://2brains.tumblr.com/tagged/mathematics | Belief
A true scientist must always be reminded that beliefs are a necessary evil. But in all situations he would do well to remember that his strongest and most fervent beliefs are always in those matters in which his ignorance is greatest.
Stupid Questions
It is often said that there are no stupid questions. Is th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/questions/5415/is-this-how-padding-can-work/5427 | # Is this how padding can work?
So for block ciphers you need a fixed size block.
If the plaintext length is not a multiple of the block length then you need to pad it.
One way you could do this is that for the last block you just pad the blocks with 0s or some random characters except for the last character 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": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://cms.math.ca/Reunions/hiver12/abs/de | Réunion d'hiver SMC 2012
Fairmont Le Reine Elizabeth (Montréal), 7 - 10 décembre 2012
Équations différentielles fonctionnelles non linéaires
Org: Hermann Brunner (Memorial)
[PDF]
URI ASCHER, UBC
Stochastic algorithms for inverse problems involving PDEs and many measurements [PDF]
Inverse problems involving systems... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/38624/determining-the-center-of-mass-of-a-cone/38630 | # Determining the center of mass of a cone
I'm having some trouble with a simple classical mechanics problem, where I need to calculate the center of mass of a cone whose base radius is $a$ and height $h$..!
I know the required equation. But, I think that I may be making a mistake either with my integral bounds or th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "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/53846/when-does-the-distributive-propertive-hold-for-inner-products | # When does the distributive propertive hold for inner products?
Going though some papers in clustering in machine learning, I often find the following claim:
$(a-b)(a-b) = \|a\|^2 + \|b\|^2 - 2a \cdot b$
My question is: When does this hold? (i.e. what type of norms or inner products satisfy this)? Is this only true... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/271141/number-of-roots-of-a-complex-equation-rouches-theorem | # Number of roots of a complex equation/ Rouche's theorem
For $n\geq2$ consider the equation $z^n+z+n=0$ for $z\in \mathbb C$. Show that if $k$ is an integer with $1\leq k \leq n$ then inside the sector
$$S_k=\{z\in \mathbb C: 0< Arg(z) < \dfrac{2\pi k}{n} \}$$
There are exactly $k$ roots of the above equation. $Arg... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/246761/find-a-basis-for-the-subspace-and-prove-it-is-a-basis-state-the-dimension | # find a basis for the subspace and prove it is a basis, state the dimension
Each of the following sets spans a subspace of the space of all functions from $\bf R$ to $\bf R$.
$\exp x, \sin(x), \cos(x)$
$\exp x, \cosh(x), \sinh(x)$
this is just an extra credit problem, but I have no clue how to go about it. If some... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cstheory.blogoverflow.com/2011/07/an-original-proof-of-a-folk-theorem/ | # An original proof of a folk theorem
2011-07-25 by Aaron Sterling. 4 comments
A folk theorem is a mathematical fact that is generally known (at least by experts), even though its proof may never have appeared in print, or may be difficult to locate. Recently, cstheory user Eli asked for a citation to a proof 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": 0, "mathjax_display_tex": 25, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/98708-limit-problem.html | # Thread:
1. ## limit problem
lim [f(x) - 8] / [x - 1] = 10
x ~> 1
What is the limit as x approaches 1 of f(x)?
(Hint: let g(x) = [f(x) - 8] / [x - 1])
i'm not sure how the hint helps me in solving this problem. all i did was multiply both sides of the equation [f(x) - 8] / [x - 1] = 10 by (x - 1) and then added 8 ... | {"extraction_info": {"found_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://nrich.maths.org/5749/clue | ### Plane to See
P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.
### Four Points on a Cube
What is the surface area of the tetrahedron with one vertex at O the vertex of a unit 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": 6, "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/14064/can-a-black-hole-be-formed-by-radiation | Can a black hole be formed by radiation?
I'm trying to find out if black holes could be created by focusing enough light into a small enough volume.
So far I have found (any or all may be incorrect):
• Maxwell's equations are linear, dictating no interaction of radiation.
• The Kerr effect and self-focusing has been... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.reference.com/browse/Matched_filter | Related Searches
Definitions
# Matched filter
In telecommunications, a matched filter is obtained by correlating a known signal, or template, with an unknown signal to detect the presence of the template in the unknown signal. This is equivalent to convolving the unknown signal with a time-reversed version of the tem... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 73, "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/ma... |
http://math.stackexchange.com/questions/244743/singular-value-proofs | # Singular value proofs
1.) Let $A$ be a nonsingular square matrix.
• a.) Prove that the product of the singular values of $A$ equals the absolute value of its determinant: $\sigma_1\sigma_2...\sigma_n=|detA|$.
• b.) Does the sum equal the absolute value of the trace? And a matrix whose determinant is very small 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": 19, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/29948/applications-of-topological-and-diferentiable-stacks | ## Applications of topological and diferentiable stacks
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
What are some examples of theorems about topology or differential geometry that have been proven using topological/differentiable stacks, or, some examples ... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/31767/indexing-schemes-of-binary-sequences/31812 | ## Indexing schemes of binary sequences
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I am looking for "low-complexity" indexing methods to enumerate binary sequences of a given length and a given weight.
Formally, let $T_k^n = \{x_1^n \in \{0,1\}^n: \sum_{... | {"extraction_info": {"found_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://mathhelpforum.com/calculus/156708-question-involving-collection-closed-intervals.html | # Thread:
1. ## Question involving a collection of closed intervals
Let $F$ be the collection of closed intervals $A_n=[1/n, 1-1/n]$ for $n=3,4,5,...$. What do you notice about $\bigcup F$? Is it closed, open, both, or neither?
I'm afraid the wording and available material has got me stumped on this, and being sick ... | {"extraction_info": {"found_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://mathematica.stackexchange.com/questions/tagged/list-manipulation?page=2&sort=newest&pagesize=15 | # Tagged Questions
Questions on the manipulation of List objects in Mathematica, and the functions used for these manipulations.
1answer
70 views
### Plot several lines with different starting points on the x-axis
First of all, I would like to apologize in advance if I don't use the correct terms or if I express my... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/statistics/124584-variance-problem-i-think.html | # Thread:
1. ## variance problem (i think)
Sorry, I was having difficulty with the equation editor on here. I've attached my problem as a picture file.
I need to show that the two equations are equal, and I'm not sure where to begin.
Thanks!
Attached Thumbnails
2. Assuming that $\overline{z}$ is the conjugate of 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": 17, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/1659/locating-the-quadrant-containing-a-point-on-an-n-sphere | # Locating the quadrant containing a point on an n-sphere
Suppose I have a point $x \in \mathbb{R}^n$ on an n-sphere. Suppose I divide the n-sphere into 4 sections (I think this makes sense in $n$ dimensions), how do I know which section $x$ lies on?
-
6
No, it doesn't make sense in n dimensions unless n=2. What are... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 16, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/70611?sort=oldest | ## Reference for proof that $C_b^* = rba$
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The following theorem seems to have folk status:
The topological dual of the space $C_b(X)$ of bounded continuous functions on a topological space $X$ is isomorphic to 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": 12, "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/295728/whats-the-solution-of-the-functional-equation/295759 | # What's the solution of the functional equation?
I need help with this:
"Find functions $f$, $g : \mathbb{Z} \rightarrow \mathbb{Z}$, knowing that $g$ is injective and such that: $$f(g(x)+y) = g(f(x)+x), \mbox{ for all } x, y \in \mathbb{Z}.$$
-
Did you maybe mean $g(f(x)+y)$, or something to that effect? Otherwis... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/107192?sort=oldest | ## Dehn function for undistorted subgroups of a product of free groups
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $G$ be a finitely generated subgroup of a product of two finite rank free groups $F_m \times F_n$. If there is a Lipschitz retraction $F_... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 26, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?s=ea56b5c1a20722da15d3a5427a9a5a88&p=4085070 | Physics Forums
## Coexistence in phase diagram
In a nutshell, I am trying to see how to derive the conditions of coexistence between a solid and a liquid from a phase diagram.
The situation is as follows:
Consider a mixture of hard spheres of diameter σ. The potential energy
for a hard sphere system is given by
[ite... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Magnetic_domain | # Magnetic domain
Several grains of NdFeB with magnetic domains made visible with a Kerr microscope. The domains are the light and dark stripes visible within each grain.
A magnetic domain is a region within a magnetic material which has uniform magnetization. This means that the individual magnetic moments of the at... | {"extraction_info": {"found_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": 5, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/255624/borel-sets-including-infty | # Borel sets including $\infty$
Can someone give me a hint how to show the equality $\{ B \cup F \mid B\in \sigma(\{(-\infty,a) \mid a\in \mathbb{R}\}),\ F\subseteq\{-\infty,+\infty\} \}=\sigma(\{ [-\infty,a) \mid a \in \mathbb{R} \})$ ?
The set $\sigma(\{(-\infty,a) \mid a\in \mathbb{R}\})$ represents the usual Bore... | {"extraction_info": {"found_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://mathoverflow.net/questions/58856/advances-and-difficulties-in-effective-version-of-thue-roth-siegel-theorem/58877 | ## Advances and difficulties in effective version of Thue-Roth-Siegel Theorem
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
A fundamental result in Diophantine approximation, which was largely responsible for Klaus Roth being awarded the Fields Medal in 1958... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-applied-math/187921-permutation-tensor-explanation-needed.html | # Thread:
1. ## Permutation Tensor (Explanation Needed)
Can somebody help me understand the Permutation Tensor?
I know what it means when it says "if i=j or j=k or i=k, then the permutation tensor is 0".
However, I don't understand the concepts of even and odd permutation (ie, those cases when the permutation tenso... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/tagged/perturbation-theory+solar-system | # Tagged Questions
4answers
587 views
### Staying in orbit - but doesn't any perturbation start a positive feedback?
I am not a physicist; I am a software engineer. While trying to fall asleep recently, I started thinking about the following. There are many explanations online of how any object stays in orbit. 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": 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/2009/05/06/the-category-of-inner-product-spaces/?like=1&source=post_flair&_wpnonce=5b12459335 | # The Unapologetic Mathematician
## The Category of Inner Product Spaces
So far we’ve been considering the category $\mathbf{Vect}$ of vector spaces (over either $\mathbb{R}$ or $\mathbb{C}$) and adding the structure of an inner product to some selected spaces. But of course there should be a category $\mathbf{Inn}$ ... | {"extraction_info": {"found_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": 46, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/39616/what-is-the-physical-interpretation-of-force-times-area | # What is the physical interpretation of force times area?
I know that $\text{Force} \times \text{Distance = Work}$.
But, what would be the physical meaning of $\text Force \times \text Area?$
Is such a quantity used in physics?
-
An equation by itself is meaningless. You need context to be able to assign physical ... | {"extraction_info": {"found_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://unapologetic.wordpress.com/2011/08/10/functoriality-of-cubic-singular-homology/?like=1&source=post_flair&_wpnonce=b0679ce6ea | # The Unapologetic Mathematician
## Functoriality of Cubic Singular Homology
We want to show that the cubic singular homology we’ve constructed is actually a functor. That is, given a smooth map $f:M\to N$ we want a chain map $C_k(f):C_k(M)\to C_k(N)$, which then will induce a map on homology: $H_k(f):H_k(M)\to H_k(N... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 17, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=632953 | Physics Forums
## question on regular group actions
Hello,
we know that if $\bullet : G\times A \rightarrow A$ is a regular action of G on the set A, then the action $\bullet$ is isomorphic to the action of G on itself, where the action on G is given by the group operation, that is: $\circ : G\times G \rightarrow G$ ... | {"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": 6, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.