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http://math.stackexchange.com/questions/138465/algebrically-independent-elements/138940 | # Algebrically independent elements [duplicate]
Possible Duplicate:
Why does K->K(X) preserve the degree of field extensions?
Suppose $t_1,t_2,\ldots,t_n$ are algebrically independent over $K$ containing $F$. How to show that $[K(t_1,\ldots,t_n):F(t_1,\ldots,t_n)]=[K:F]$?
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[K:F] is a finite extension – Jishnu Ray ... | {"extraction_info": {"found_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://mathhelpforum.com/advanced-algebra/116977-complex-numbers-theory-question.html | # Thread:
1. ## Complex numbers theory question
If $z = a+bi, w = c+di$ and $arg(z+w) = 90^{\circ}$ then which of the following is true?
a) z + w = 0
b) |z + w| = 0
c) a = -c
d) b = -d
I hate theory questions, I can't get them for some reason. Are there any properties that would help me with this question?
Here'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": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/49865/quantum-superposition-of-states-experimental-verification | # Quantum superposition of states: experimental verification
How can somebody demonstrate the quantum superposition of states directly by other means than the double slit experiment?
And why can't macroscopic objects like a pen be in superpostion of states? Will it ever be possible to have an object like a pen to 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": 11, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=223264&highlight=newtons+bucket | Physics Forums
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## Newton's Bucket
Hi. First post here. I have no formal math or physics training, but read popular books on physics and am pretty well read as far as that goes. Now for the question.
I'm fascinated by the Newton's Buc... | {"extraction_info": {"found_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/99570/a-question-from-titchmarshs-riemann-zeta-function-textbook | # A question from Titchmarsh's Riemann Zeta Function textbook.
I have one query, concerning the newest edition of this monograph.
1. At page 7, section 1.2, at the bottom of the page, it's written that: " It is easily seen that $\zeta(s)=2$ for $s=\alpha$, where $\alpha$ is a real number greater than 1..."
I am quit... | {"extraction_info": {"found_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://mathhelpforum.com/pre-calculus/102340-average-rate-change.html | # Thread:
1. ## Average rate of change
I am unsure as to which forum to put this in. I took a shot and put it here, apologies if wrong.
Okay, to the question I am having trouble with.
"Find the average rate of change of $f(x) = \sqrt{x + 11}$ with respect to x from $x = 5$ to $x = 5 +h$. [4 marks]"
My attempt to a... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 49, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/9402/pedagogical-question-about-linear-algebra | ## Pedagogical question about linear algebra
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Last semester I taught a linear algebra class that is intended to introduce young students (at a sophmore-junior level) to "abstract mathematics". It seems that a majo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 60, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showpost.php?p=3264559&postcount=5 | View Single Post
Hi Tom, You're after a unified description of scalar, fermion and gauge fields… very ambitious. But don't forget the gravitational spin connection and frame. Let $$A$$ be a 1-form gauge field valued in a Lie algebra, say spin(10) if you like GUTs, and $$\omega$$ be the gravitational spin connection ... | {"extraction_info": {"found_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": 16, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/plane-curves+bezier-curve | # Tagged Questions
1answer
29 views
### Understanding the Spiro Spline
My name's Wray. This is my first time here. Firstly, I like curves. I've been keeping a pet project for a long time that would implement a delightful new curve-interpolation algorithm named the Spiro ...
1answer
104 views
### An almost straight ... | {"extraction_info": {"found_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://unapologetic.wordpress.com/2011/02/25/classes-of-manifolds/?like=1&source=post_flair&_wpnonce=c8d80d4293 | # The Unapologetic Mathematician
## Classes of Manifolds
As we discussed the dimension of a manifold yesterday, we passed by an interesting construction that we want to look at in more detail.
Let $(U_1,\phi_1)$ and $(U_2,\phi_2)$ be two coordinate patches on an $n$-manifold $M$. We can restrict each coordinate map ... | {"extraction_info": {"found_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": 32, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2011/03/07/open-submanifolds/?like=1&source=post_flair&_wpnonce=c1c9c39881 | # The Unapologetic Mathematician
## Open Submanifolds
Eek! None of these drafts went up on time!
In principle, we know what a submanifold should be: a subobject in the category of smooth manifolds. That is, a submanifold $S$ of a manifold $M$ should be another manifold, along with an “inclusion” map which is smooth ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 15, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/31672-equation.html | # Thread:
1. ## The equation
The equation
$[x^{10}+(13x-1)^{10}=0$
has 10 complex roots
$r_1, \overline{r_1}, r_2, \overline{r_2}, r_3, \overline{r_3}, r_4, \overline{r_4}, r_5, \overline{r_5},,$
where the bar denotes complex conjugation. Find the value of
$\frac 1{r_1\overline{r_1}}+\frac 1{r_2\overline{r_2}}+\... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/116399/if-ell-a-mathfrakpn-infty-then-is-it-true-that-operatornamehom-a | # If $\ell_{A_\mathfrak{p}}(N)<\infty$, then is it true that $\operatorname{Hom}_A(N,E(A/\mathfrak{q}))=0$?
Let $A$ be a Noetherian ring, $\mathfrak{p},\mathfrak{q}\subset A$ distinct prime ideals of the same height, $N$ an $A_\mathfrak{p}$-module of finite length. Then is it true that $$\operatorname{Hom}_A(N,E(A/\ma... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 21, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/periodic-functions+continued-fractions | # Tagged Questions
2answers
275 views
### Is the continued fraction of the square root of a base $\phi$ (golden ratio) number periodic when the continued fraction is expressed in base $\phi$?
I have been looking at concise ways to represent irrational numbers using only integers. I was thinking about base $\phi$ (go... | {"extraction_info": {"found_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://mathforum.org/mathimages/index.php?title=The_Golden_Ratio&diff=33504&oldid=33500 | # The Golden Ratio
### From Math Images
(Difference between revisions)
| | ... | {"extraction_info": {"found_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": 117, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/38492/will-cosmological-gravitational-waves-be-weaker-or-stronger-than-astrophysical-o | # Will cosmological gravitational waves be weaker or stronger than astrophysical ones?
Will gravitational waves of cosmological origin be weaker or stronger (higher amplitude $h \simeq\Delta L/L$) than those created from astrophysical sources?
I'm having a real hard time finding the amplitude of cosmological gravitat... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://embuchestissues.wordpress.com/2009/04/06/cardboard-dodecahedron/ | # Embûches tissues
## Cardboard dodecahedron
6 April 2009 at 12:01 am Leave a comment
I made a cardboard dodecahedron for the needs of a talk.
If you draw 5-coloured stars on all facets, by choosing smartly the colours, you can get five coloured cubes whose vertices are vertices of the dodecahedron. This trick can ... | {"extraction_info": {"found_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": 1, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/208851/need-a-tip-hint-evaluating-a-limit?answertab=votes | # Need a tip/hint evaluating a limit
I have the following limit:
$$\lim_{x\rightarrow\infty}\left(1+\frac{a}{x^{1/2+\epsilon}}\left(1-\exp\left(-\frac{b}{x^{1/2+\epsilon}}\right)\right)\ln\left(\frac{a}{x^{1/2+\epsilon}}\right)\right)^x$$
where $0<b<a$.
I care for the case where $\epsilon>-1/2$. I suspect that for ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/59313/evaluating-lim-limits-x-to-01x1-x/59322 | # Evaluating $\lim\limits_{x\to 0}(1+x)^{1/x}$?
How would I work out a limit of the form:
$$\lim_{x\to 0}\;(1+x)^{1/x}$$
I know these types of limits have a solution based on $e$ but how do I find this solution?
-
3
The limit is $1$. $1^0$ is not an indeterminate form. If you asked for $\lim_{x\to 0} (1+x)^{1/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": 26, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://simple.wikipedia.org/wiki/Pi_(mathematical_constant) | # Pi (math)
(Redirected from Pi (mathematical constant))
$\pi = \frac {C}{d}$ (pi is equal to the circumference divided by the diameter).
Pi is an endless string of numbers.
Pi or $\pi$ is a mathematical constant, one of the first ever discovered. It is the ratio of the distance around a circle to the circle's diamet... | {"extraction_info": {"found_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/78379/how-to-prove-sum-dn-tau3d-left-sum-dn-taud-right2 | # How to prove $\sum_{d|n} {\tau}^3(d)=\left(\sum_{d|n}{\tau}(d)\right)^2$
$\sum_{d|n} {\tau}^3(d)=\left(\sum_{d|n}{\tau}(d)\right)^2$, where $\tau(d)$ designates the number of positive divisors of d.
Now I only know that both sides are multiplicative functions, could you tell me what I need to do next?
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2
If you ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "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/71270/highest-weight-representation-and-electromagnetic-fields/71350 | ## highest weight representation and electromagnetic fields
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
An electromagnetic field is given by 6 components (Ex,Ey,Ez,Bx,By,Bz). Now this is a 6-dimensional irreducible representation of so(1,3) which is a high... | {"extraction_info": {"found_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://crypto.stackexchange.com/questions/5761/construct-an-election-protocol-for-the-following-election-problem | # construct an election protocol for the following election problem..? [closed]
I am something new to election protocols and I am trying to construct an election protocol for the following problem:
Let $A= \lbrace a_{1} , . . . , a_{n} \rbrace$ and $B = \lbrace b_{1} , . . . , b_{m} \rbrace$ be two groups of voters, ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/statistics/156369-question-normal-distribution-2-a-print.html | # Question on normal distribution #2
Printable View
• September 15th 2010, 09:51 PM
mngeow
Question on normal distribution #2
A manufacturer of electric light bulbs finds that his bulbs have an average life span of 1200 hours and a S.D of 200 hours.Assume that the distribution of lifetimes is normal.
What should 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": 27, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/79583/when-does-every-point-in-the-volume-of-a-polytope-lie-along-a-chord-between-its-e | ## When does every point in the volume of a polytope lie along a chord between its edges?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Consider the 3-simplex, or tetrahedron, in 3-space. Regardless of the positions of the vertices, every point in the volume... | {"extraction_info": {"found_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/39594-arithmetic-geometric-sequences.html | # Thread:
1. ## Arithmetic and Geometric Sequences
Here is the question:
In an old story, a king asked a peasant to come and work for him. They both agreed that the job to be done could be completed in a month (30 days). The peasant asked the king if he could be paid in the following way: "On the first day that I wo... | {"extraction_info": {"found_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/90129/orthogonality-in-non-inner-product-spaces/90136 | ## Orthogonality in non-inner product spaces
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I have come across a notion of orthogonality of two vectors in a normed space not necessarily inner product space. Two vectors $x$ and $y$ in a normed space are said 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": 50, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.aps.org/synopsis-for/print/10.1103/PhysRevC.79.054304 | # Synopsis:
Getting closer to the Bohr model
#### Bohr model as an algebraic collective model
D. J. Rowe, T. A. Welsh, and M. A. Caprio
Published May 5, 2009
In the algebraic collective model, the five variables define the quadrupole moments of a nucleus. A group theoretical approach is used to separate the... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 3, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/115921/laplace-transform-how-to-derive/115938 | # Laplace transform. How to derive
I have this integral related to a Laplace transform and I was wondering if anyone knows of a clever way to derive it. I know we usually look these up in a table, but this form is not in a table I have. The transform is:
$$\mathcal{L}\left\{ \frac{\sin 1/t}{\sqrt{t}} \right\}(s)=\int... | {"extraction_info": {"found_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": 16, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathforum.org/mathimages/index.php?title=Harter-Heighway_Dragon&oldid=2797 | # Harter-Heighway Dragon
### From Math Images
Revision as of 14:58, 29 May 2009 by Ryang1 (Talk | contribs)
Jump to: navigation, search
Harter-Heighway Dragon Curve (3D- twist)
The image above is an example of a Harter-Heighway Curve (also called Dragon Curve). This fractal was first described in 1967 by American Ma... | {"extraction_info": {"found_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": 7, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/60235?sort=newest | ## Overview of the interplay of Harmonic Analysis and Number Theory
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I'm kind of disappointed that the question here was never sharpened.
The Laplacian $\Delta$ on the upper half-plane is $-y^{2}(\partial^{2}/\pa... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 30, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/tags/quantum-information/info | Tag info
About quantum-information
Quantum information is the study of the informational content of quantum states. The most common object of study is the "qubit", the information in a two-state quantum system such as spin-1/2 or photon polarization.
Quantum systems have infinitely more information than the correspo... | {"extraction_info": {"found_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.reference.com/browse/exothermicity | Definitions
# Spontaneous process
A spontaneous process is the time-evolution of a system in which it releases free energy (most often as heat) and moves to a lower, more thermodynamically stable, energy state. The sign convention of changes in free energy follows the general convention for thermodynamic measurements... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/9506/tunneling-rate-constant?answertab=active | # Tunneling Rate Constant
I am trying to "decode"/derive an expression for the macroscopic rate constant for the tunneling of protons through a potential energy barrier that I read in a journal article: $$k_{\rm tun}(T)=(2\pi\hbar)^{-1}\int_0^{V_{\rm max}} Q(V,T) P_{\rm tun}(V)\ dV.$$ So basically: the authors say wor... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://sbseminar.wordpress.com/2009/10/07/how-to-almost-prove-the-4-color-theorem/ | ## How to almost prove the 4-color theorem October 7, 2009
Posted by Noah Snyder in planar algebras, quantum topology.
trackback
Vaughan Jones often quips at the beginning of talks on Planar Algebras (see these lectures, for example) that the worst thing you can say about Planar Algebras is that they have not yet ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 8, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/173400/solving-for-x-the-following-linear-equation-is-the-solution-a-unique-rectangu/173413 | # solving for $X$ the following linear equation, is the solution a unique rectangular matrix?
I have an invertible matrix $A$ of size $n \times n$ and a matrix $U$ of size $n \times m$, for $m < n$. Matrix $U$ is orthonormal, meaning, the rows are orthonormal vectors. I also have an $m \times m$ diagonal matrix $\Sigm... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/177191-solving-rational-inequalties-application-problem-help.html | Thread:
1. Solving rational inequalties application problem help
Here's the problem:
An economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. These functions are $R(x)=-x^2+10x$ and $C(x)=4x+5$, respectively, where x is the number of snowboards produce... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/differential-geometry/28006-loci-complex-plane.html | Thread:
1. Loci In complex plane
Show that in an Argand diagram the equation
$\arg (z-2) - \arg (z-2i) = \frac{3 \pi}{4}$
represents an arc of a circle and that $\frac{|z-4|}{|z-1|}$ is constant on this circle.
Find values of z corresponding to the points in which the circle is cut by the curve given by
$|z-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": 141, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/calculus/208314-partial-fractions.html | 1Thanks
• 1 Post By Plato
# Thread:
1. ## Partial Fractions
Hi everyone!
The problem I need help with is:
Preform partial fraction decomposition: x / 4x2 + 4x + 1
In the solution to this exercise the author first factorizes the denominator, which factorizes into (2x + 1)2, but than he writes that
x / (2x + 1)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": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/25110/why-are-orbits-elliptical/25116 | # Why are orbits elliptical?
Almost all of the orbits of planets and other celestial bodies are elliptical, not circular.
Is this due to gravitational pull by other nearby massive bodies? If this was the case a two body system should always have a circular orbit.
Is that true?
-
## 9 Answers
No, any ellipse is 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": 1, "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/80721/vertex-cover-reduction?answertab=oldest | # Vertex Cover Reduction
I'm having a hard time figuring out how to reduce a problem to prove that it is NP-complete.
Basically, my problem is this:
Given an undirected graph, find a set $S$ such that for all nodes in $G \setminus S$ (i.e. all other nodes), there exists at least one edge from each node in $G \setmin... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 26, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/281175/complex-number-vector-prove/281182 | # Complex number vector prove
Prove that, where $z$ denotes complex numbers:
a.) $|z_1 - z_2| \le |z_1| +|z_2|$
b.) $||z_1| - |z_2|| \le |z_1 +z_2|$
For a. the book answer gives: $|z_1 -z_2| = |z_1 + (-z_2)| \le |z_1| +|-z_2| =|z_1| +|z_2|$, but that proof isn't helpful at all, to me, because it doesn't explain any... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/43274/list | Return to Answer
3 added 1087 characters in body
Hi Hailong,
I would add one more observation to the other comments. Let me not worry about (2) vs (3) as the difference is only about the zero module so this is more of a philosophical question than a mathematical one.
More specifically, a module could never satisfy ... | {"extraction_info": {"found_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://crypto.stackexchange.com/questions/2405/how-are-the-primes-used-to-generate-rsa-keys | # How are the primes used to generate RSA keys?
I am confused about how keys in RSA asymmetric encryption are generated and what the implications for open communications are. Textbooks say the one-way function is merely two primes (with some critical constraints) -- so how do the two primes generated get turned into 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": 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/number-theory/50631-elem-num-theo-help-w-proof.html | # Thread:
1. ## elem.num.theo - help w/proof
So - I know all the steps, I just need help with a gap.
Prove $n! > n^2 \exists n \geq4$
Ok, proof by Induction:
Since 4! = 24 which is $>(4)^2 = 16$, $n!>n^2$ for n=4.
Let k be a positive integer [math\geq4[/tex] and suppose $k!>k^2$.
Then, $k!(k+1) > k^2(k+1)$
$(k+1)! ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 31, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/75655/is-there-a-log-space-algorithm-for-divisibility?answertab=active | # Is there a log-space algorithm for divisibility?
Is there an algorithm to test divisibility in space $O(\log n)$, or even in space $O(\log(n)^k)$ for some $k$? Given a pair of integers $(a, b)$, the algorithm should return TRUE if $b$ is divisible by $a$, and FALSE otherwise. I understand that there is no proof 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": 20, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://rjlipton.wordpress.com/2009/11/04/on-mathematical-diseases/ | ## a personal view of the theory of computation
Mathematical diseases: symptoms and examples
Underwood Dudley is a number theorist, who is perhaps best known for his popular books on mathematics. The most famous one is A Budget of Trisections, which studies the many failed attempts at the ancient problem of trisectin... | {"extraction_info": {"found_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": 23, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2008/05/28/matrices-iv/?like=1&_wpnonce=68d26d17fa | # The Unapologetic Mathematician
## Matrices IV
Like we saw with the tensor product of vector spaces, the dual space construction turns out to be a functor. In fact, it’s a contravariant functor. That is, if we have a linear transformation $T:U\rightarrow V$ we get a linear transformation $T^*:V^*\rightarrow U^*$. As... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 33, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/108180/in-class-today-we-had-to-find-a-closed-generating-function-for-a-n-2n1-the | # In class today, we had to find a closed generating function for $A_n=2n+1$. The sequence of the odd natural numbers. Anyone with an idea?
In class today, we had to find a closed generating function for $A_n=2n+1$, where $n\in \mathbb{N}$ and $A_n$ is the sequence of odd natural numbers. Anyone with an idea? I tried ... | {"extraction_info": {"found_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": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/47951/calculate-partial-autocorrelation | # calculate partial autocorrelation [duplicate]
Possible Duplicate:
PACF manual calculation
I am trying to find a formula for how to calculate partial autocorrelation between variables. We know that aucorrealtion between variables at different lags are given by: $$\hat\rho_h=\frac{\sum^T_{t=h+1}(y_t-\bar y)(y_{t-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://mathhelpforum.com/advanced-algebra/152104-iisomorphic.html | # Thread:
1. ## iisomorphic
I have an example of 2sylow subgroup of S6.
I want to prove that this subgroup isomorphous to Z2XD4
2. Originally Posted by rtrt1
I have an example of 2sylow subgroup of S6.
I want to prove that this subgroup isomorphous to Z2XD4
The Sylow 2-sbgps. of $S_4$ are easily seen to be isomorph... | {"extraction_info": {"found_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.nag.com/numeric/CL/nagdoc_cl23/html/S/s21bhc.html | NAG Library Function Documentnag_elliptic_integral_complete_K (s21bhc)
1 Purpose
nag_elliptic_integral_complete_K (s21bhc) returns a value of the classical (Legendre) form of the complete elliptic integral of the first kind.
2 Specification
#include <nag.h>
#include <nags.h>
double nag_elliptic_integral_complet... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 10, "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://mathoverflow.net/questions/72684/quick-algorithm-for-finding-real-solutions-for-a-system-polynomial-equations | ## Quick algorithm for finding real solutions for a system polynomial equations
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Would you please recommend a computer program that could give quick answer Yes/No for the question: does there exist a real solution... | {"extraction_info": {"found_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/calculus/102090-first-calculus-assignment-year-print.html | # first calculus assignment of the year
Printable View
• September 13th 2009, 12:47 PM
OCD
first calculus assignment of the year
Hi, first post here. Also first calculus assignment; it's called preparation for calculus so I feel like it's supposed to be easy, and I feel a bit of shame that I'm asking for help, but he... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/advanced-statistics/122767-correlation-coefficient-help.html | # Thread:
1. ## correlation coefficient help
Hey, im a first year in leeds uni doing maths and there are some things im starting to get quiet stressed over and they arnt even hard so you'll probably see quite a few of my posts pop up with my exams coming in a few days.
The question im stuck on is:
Let X1 , X2 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": 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/revisions/17797/list | ## Return to Answer
2 Slightly expanded.
I agree that the correspondence between representations of the fundamental group(oid) and locally constant sheaves is not very well documented in the basic literature. Whenever it comes up with my students, I end up having to sketch it out on the blackboard. However, my recoll... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/206356-help-mathematical-induction-problem-print.html | # Help with mathematical induction problem
Printable View
• October 29th 2012, 06:18 PM
Walshy
Help with mathematical induction problem
Suppose we want to prove that: 1/2 * 3/4 ... 2n-1/2n < 1/sqrt(3n)
for all positive integers.
(a) Show that if we try to prove this inequality using mathematical induction, the basis... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/12611/why-can-we-treat-quantum-scattering-problems-as-time-independent/12628 | # Why can we treat quantum scattering problems as time-independent?
From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this:
1. Solve the time-independent Schrodinger equation to find the energy eigenstates. There will 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": 85, "mathjax_display_tex": 30, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/calculus/113327-improved-euler-s-method-help.html | # Thread:
1. ## Improved Euler's Method Help
I am trying to use the Improved Euler's Method to solve a homework problem, but I am having trouble with the notation and my book is extremely unhelpful.
Where the lower formula is the Improved Euler's method.
I am given:
y = 5e^(x(x+2))
y' = 2y(x+1)
y(0) = 5
dx = .3 (I... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/154022-odd-even-functions.html | # Thread:
1. ## Odd and Even functions
Prove that:
a) if f(x) is an even function, $\int^a_{-a}f(x)dx=2\int^a_0 f(x)dx$
b)if f(x) is an odd function, $\int^a_{-a} f(x)dx=0$
I tried using proof by contradiction:
f(x) is even, then $\int^a_{-a}f(x)dx\neq 2\int^a_0 f(x)dx$
My problem is I don't know how to continue.
I ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/54926?sort=votes | ## Longest element of Weyl groups.
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
What is a reduced expression of the longest element of each type of Weyl group. For type $A_n$ it is just $s_n(s_ns_{n-1})...(s_n...s_1)$. I know for type $B_n,C_n,E_7,E_8$,$G_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": 31, "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/tagged/probability-distributions?sort=faq&pagesize=50 | # Tagged Questions
Questions on using, finding, or otherwise relating to probability distributions, pdfs, cdfs, or the like.
2answers
1k views
### Given the pdf of independent RVs $I$ and $R$, how to find cdf of $W =I^2R$?
Given pdf of $I$ and $R$ (both $I$ and $R$ are independent RV's), how to find cdf of $W =I^2R... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 121, "mathjax_display_tex": 12, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://physics.stackexchange.com/questions/33916/what-is-the-escape-velocity-of-a-black-hole/33948 | # What is the escape velocity of a Black Hole?
The escape velocity of Earth is $v=\sqrt{\frac {GM}{R}}$, where $M$ is the mass of the Earth and $R$ it's radius (approximating it as a sphere), and is much less than light speed $c$.
What is the escape velocity of a Black hole? Is it much more than light speed?
-
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": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/16207/find-asymptotics-of-a-function?answertab=oldest | # Find asymptotics of a function
Can Mathematica find the asymptotics of a function in the following sense?
I have
````Log[1/n^2]/Log[4^(-Sqrt[Log[n]]) + (2^(-Sqrt[Log[n]]) - 1)^2]
````
and I would like to know an asymptotic approximation when $n$ is large. That is a simple function that is within a constant multip... | {"extraction_info": {"found_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://mathoverflow.net/revisions/68734/list | ## Return to Answer
3 added 4 characters in body
One way to see that there is a vector bundle $E$ over $J(C)$ with $C^{(n)}\cong \mathbb{P}(E)$ is using semi continuity. Consider the closed immersion $C^{(n-1)}\hookrightarrow C^{(n)}$. This is a divisor on a smooth variety and so corresponds to a line bundle $L$. 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": 49, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=578592 | Physics Forums
## Covariant derivative of connection coefficients?
The connection $$\nabla$$ is defined in terms of its action on tensor fields. For example, acting on a vector field Y with respect to another vector field X we get
[tex]\nabla_X Y = X^\mu ({Y^\alpha}_{,\mu} + Y^\nu {\Gamma^\alpha}_{\mu\nu})e_\alpha
=... | {"extraction_info": {"found_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": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.nag.co.uk/numeric/cl/nagdoc_cl23/html/E05/e05sbc.html | # NAG Library Function Documentnag_glopt_nlp_pso (e05sbc)
Note: this function uses optional arguments to define choices in the problem specification and in the details of the algorithm. If you wish to use default settings for all of the optional arguments, you need only read Sections 1 to 9 of this document. If, howev... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 625, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/advanced-algebra/127945-abstract-several-questions-print.html | # Abstract-several questions
Printable View
• February 9th 2010, 01:33 AM
WannaBe
Abstract-several questions
Well, I'm trying to solve some old exams in abstract algebra, and I need your help in the following:
Question 1:
Let $U(Z/15Z)$ be the multiplicative group of the invertible elemenets in $Z/15Z$ . Write $U(Z/... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 25, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/62312/is-every-p-point-ultrafilter-ramsey/62342 | ## Is every p-point ultrafilter Ramsey?
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A non-principal ultrafilter $\mathcal{U}$ on $\omega$ is a p-point (or weakly selective) iff for every partition $\omega = \bigsqcup _{n < \omega} Z_n$ into null sets, i.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": 22, "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/94634/how-many-smooth-functions-are-non-analytic | # How many smooth functions are non-analytic?
We know from example that not all smooth (infinitely differentiable) functions are analytic (equal to their Taylor expansion at all points). However, the examples on the linked page seem rather contrived, and most smooth functions that I've encountered in math and physics ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 56, "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/115533-solved-difference-harmonic-series-1-n-comparsion.html | # Thread:
1. ## [SOLVED] The difference of the harmonic series and 1/n comparsion
I recently had this classic example to determine if it converged or diverged
[MATH\frac{sin(n)}{n}][/tex]
I learned that you can use a comparison test using the squeeze theorem.
$\frac{-1}{n}\le\frac{sin(n)}{n}\le\frac{1}{n}$
Then yo... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/36017/complete-set-of-observables-in-classical-mechanics?answertab=oldest | # Complete set of observables in classical mechanics
I'm reading "Symplectic geometry and geometric quantization" by Matthias Blau and he introduces a complete set of observables for the classical case:
The functions $q^k$ and $p_l$ form a complete set of observables in the sense that any function which Poisson commu... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 51, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/40876/second-order-taylor-expansion-to-solve-system-of-equations/50168 | ## Second order Taylor expansion to solve system of equations
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Suppose you need to solve $f(\mathbf{x})=\mathbf{0}$ where $f:\mathbb{R}^n \to \mathbb{R}^m$, $m,n>1$. Newton's method relies on first order Taylor 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": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathforum.org/mathimages/index.php/Talk:Summation_Notation | # Response to checklist
Original response to checklist, in black, written by Kate 14:05, 14 July 2011 (UTC)
You'll find my comments in red AnnaP AnnaP 22:33, 14 July 2011 (UTC)
## References and footnotes
• Images are all cited.
The one issue with this is that, based on a conversation we had last night, I went back... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/geometry/212437-intersection-known-line-two-lines-unknown-variable-each.html | # Thread:
1. ## Intersection of a known line and two lines with an unknown variable in each.
I'm trying to do number 7 on page 10 of this document: http://www.edexcel.com/migrationdocu...athematics.pdf
I have done parts a and b. The answers give x=-4 but I don't know how that is obtained.
The method used for part b... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/2317/including-air-resistance-what-is-the-escape-velocity-from-earth/2321 | # Including air resistance, what is the escape velocity from Earth?
Including air resistance, what is the escape velocity from the surface of the earth for a free-flying trajectile?
-
## 3 Answers
For the lower atmosphere, where most of the air is, the temp, pressure, and density of air is given by:
$T=T_0-Lh$
$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": 19, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/statistics/81406-cd-random-order-problem.html | # Thread:
1. ## CD random order problem
Hi,
I was listening to a CD a week ago in random playback. At one point three of the tracks played in the correct order (24 tracks on the CD).
For example:
8, 4, 17, 10, 11, 12, ...
(Can't remember the exact track numbers.)
How do I calculate the probability of this type o... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/203626/is-this-composition-of-polynomial-correct | # Is this composition of polynomial correct?
Suppose $p(x)=x^2+5x+3$ and $q(x)=3x^3-3x+7$. Write the expression $(q \circ p)(x)$ as a sum of terms, each which is a constant times the power of $x$.
Here is my work for the problem:
$(q\circ p)(x)=3(x^2+5x+3)^3-3(x^2+5x+3)+7$
$(q\circ p)(x)=3(x^6+125x^3+27)-3x^2-15x-9+7... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/B-spline | # B-spline
In the mathematical subfield of numerical analysis, a B-spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. B-splines were investigated as early as the nineteenth century by Nikolai Lobachevsky. A fundamental theorem states that every spline... | {"extraction_info": {"found_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": 39, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/4770-angles-degrees-arcs.html | # Thread:
1. ## Angles, Degrees, and Arcs
Hey there, I've got a few questions.
I have no idea how to figure out these kind of word problems. I'm taking an online class and I've got no source of help but here. So, is there some sort of formula I must follow with these? Draw a diagram? What does the "bearing" of 42.26... | {"extraction_info": {"found_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": 57, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/100266?sort=oldest | ## A covering problem for the Hamming cube
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Consider the set of all $k$-subsets of $\{1,\dots,n\}$, naturally identified with a subset $A$ of $\{0,1\}^n$ where each element has exactly $k$ ones. Is there a sharp b... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 39, "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/2008/02/25/integration-by-parts/?like=1&source=post_flair&_wpnonce=134bd2d71b | # The Unapologetic Mathematician
## Integration by Parts
Now we can use the FToC as a mirror to work out other methods of finding antiderivatives. The linear properties of differentiation were straightforward to reflect into the linear properties of integration. This time we’ll reflect the product rule through the FT... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 10, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/bounded-variation+complex-analysis | # Tagged Questions
4answers
189 views
### $\{z\in C:|z| = |\operatorname{re}(z)| +|\operatorname{im}(z)|\}$ open or closed [duplicate]
Possible Duplicate: Proving that a complex set in open/closed/neither and bounded/not bounded I think $\{z\in C:|z| = |\operatorname{re}(z)| +|\operatorname{im}(z)|\}$ is closed. But... | {"extraction_info": {"found_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://michaelnielsen.org/polymath1/index.php?title=Overlapping_Schwarz | # Overlapping Schwarz
### From Polymath1Wiki
Our goal is to either analytically solve, or numerically approximate, the 2nd Neumann eigenfunction of the Laplacian on a generic acute triangle $\Omega \equiv$ABC (see figure). Since we don't have an analytic solution on this domain, but can solve problems on sectors or 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": 28, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=129395 | Physics Forums
## Boson gas...
Let's suppose we have a Boson Non-interacting gas under an Harmonic potential so
$$V(x)= \omega (k) x^{2}$$
the question is if we know what the Partition function is $$Z= Z (\beta )$$ we could obtain the specific Heat, and other important Thermodinamical entities...but could we know w... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/93983/convergence-in-distribution-and-convergence-of-quantile | # convergence in distribution and convergence of quantile
Suppose real-valued random variables $\{X_{n}\}$ converges to $X$ in distribution. Then, will the quantile of the distribution of $\{X_n\}$ converge to the quantile of $X$? .
-
## 1 Answer
Yes. If $X$ is a random variable with distribution function $F$, then... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 20, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/18392/signed-minimum | ## Signed minimum?
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I am looking for references to papers which might have defined a 'signed minimum' equivalent to $$smin(x,y) ::= \left(\frac{\textit{signum}(x)+\textit{signum}(y)}{2}\right)\cdot \min(|x|,|y|)$$... | {"extraction_info": {"found_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://math.stackexchange.com/questions/218051/math-contest-find-number-of-roots-of-fx-fracn2-involving-a-strange-int?answertab=active | # Math contest: Find number of roots of $F(x)=\frac{n}{2}$ involving a strange integral.
Edit summary: A good answer appeared. CW full answer added, based on given answers. Removing my ugly-looking attempts, as they still remain in the rev. history.
Here's a final-round calculus contest problem in our district in 200... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 76, "mathjax_display_tex": 25, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://www.physicsforums.com/showthread.php?t=38964&page=3 | Physics Forums
Thread Closed
Page 3 of 4 < 1 2 3 4 >
## mass gap in Yang-Mills theories
Quote by nrqed I am not sure I understand what you mean. If I follow your reasoning, you seem to be saying that short range of strong force -> massive carriers -> mass generated by SSB But that's 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": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/93218?sort=oldest | ## Convergence of stochastic process
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As we know, to prove the convergence of stochastic process, we could either show the convergence of finite dimensional distribution and tightness of the process, or use techni... | {"extraction_info": {"found_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://www.ams.org/bookstore?fn=20&arg1=stmlseries&ikey=STML-37 | New Titles | FAQ | Keep Informed | Review Cart | Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics 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": 0, "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/77816?sort=votes | ## Do these matrix rings have non-zero elements that are neither units nor zero divisors?
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First, a disclaimer: This is a repost of a question I asked on stackexchange (no answer there).
Let $R$ be a commutative ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 68, "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/144813-combinatorial-analysis.html | # Thread:
1. ## Combinatorial analysis
A set of playing cards consists of 36 cards. These 36 cars are subdivided into 9 types (A,B,C, (...)I) with four cards each. The cards within these subtypes do not differ (A1=A2=A3=A4). How many possibilites are there, to take up 9 cards? The order of taking up cards and the ord... | {"extraction_info": {"found_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": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/35220/cohomology-analogue-for-central-series-of-length-more-than-two/35693 | ## Cohomology analogue for central series of length more than two
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It is a basic result of group cohomology that the extensions with a given abelian normal subgroup A and a given quotient G acting on it via an act... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/35658/how-can-we-define-bf-theory-on-a-general-4-manifold/38356 | How can we define BF theory on a general 4-manifold?
(I have rewritten the question some, with new understanding)
4d BF theory is classically presented as the TFT arising from the Lagrangian
$B\wedge F$,
where $B$ is an abelian 2-connection (locally a real 2-form) and $F$ is the curvature of a connection $A$. Peopl... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 162, "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/118083/what-axioms-are-between-ac-and-countable-choice | ## what axioms are between AC and Countable choice !
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Hi All. Need some information. We all know axiom of choice (AC) and countable choice. Which axioms are between these two. I mean weaker that Axiom of choice bu... | {"extraction_info": {"found_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://mathoverflow.net/questions/2791?sort=oldest | ## “Understanding” Gal(\bar Q/Q)
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I have heard people say that a major goal of number theory is to understand the absolute Galois group of the rational numbers G = Gal(Q bar/Q). What do people mean when they say 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": 38, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math-topics/69107-math-help-plz-pure-30-a.html | # Thread:
1. ## math help plz for pure 30
In another city, the schools vary in size from 200 to 2 000 students. As a result, the
volleyball league is organized into three divisions. The first division is for schools with less than 500 students, the second division is for schools with 500 to 1 000 students, and the 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": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/99643/why-does-bosonic-string-theory-require-26-spacetime-dimensions/99650 | ## Why does bosonic string theory require 26 spacetime dimensions?
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I do not think it is possible really believe or experimentally check (now), but all modern physical doctrines suggest that out world is NOT 4-dim... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 82, "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/20128/where-does-the-energy-come-from-when-a-current-heats-a-wire-resistor?answertab=oldest | # Where does the energy come from when a current heats a wire (resistor)?
I'm trying to figure out an example from a textbook (Demtröder -- Experimentalphysik 2, pg. 198) where the energy transport caused by a current is depicted:
Assume you have a wire (with some resistance $R$) and a current $I$ flowing through 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": 16, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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