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http://physics.stackexchange.com/questions/7871/angular-momentum-in-string-theory | Angular momentum in string theory
Since strings are extended objects, is all angular momentum in string theory essentially "orbital" angular momentum? Or is there still a kind of intrinsic angular momentum assigned to a string?
Either way, is there anything that prevents the "intrinsic spin" of a particle represented... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/42564/algorithm-for-weierstrass-preparation-theorem-for-formal-power-series | ## Algorithm for Weierstrass Preparation Theorem for Formal Power Series
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The Weierstrass preparation theorem for formal power series rings guarantees that if a given formal series $f(z) = \sum a_k z^k \in R[[z]]$... | {"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": 29, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/2074/index | ### Be Reasonable
Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.
### Janusz Asked
In y = ax +b when are a, -b/a, b in arithmetic progression. The polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2 and c be in arithmetic progression?
### Summats Clear
Find the 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": 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/revisions/104438/list | ## Return to Answer
5 added 222 characters in body
It is a consequence of the generalized Sato-Tate conjecture, that given a non-CM elliptic curve over $\mathbb Q$, any element of $Gal(\bar{\mathbb Q}/\mathbb Q)$, and a real number $\in[−1,1]$, one can construct an ultrafilter on the primes such that Frobenius conver... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 72, "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/99777/does-x-embed-in-y-and-y-embed-in-x-always-imply-that-x-isomorphic-on | ## Does $X$ embed in $Y$, and $Y$ embed in $X$, always imply that $X$ isomorphic onto $Y$?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $X$ and $Y$ be Banach spaces. The notion of the embedded spaces was introduced by D.S. Djordjevic. Say that $X$ embe... | {"extraction_info": {"found_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://math.stackexchange.com/questions/82654/derive-mean-and-variance-from-equation | # Derive mean and variance from equation
i have given a simplyfied one-dimensional Fokker-Planck equation : $\psi(p,t)=\frac{1}{\sqrt{2\pi vt}}\exp(-\frac{p^2}{2vt})$
My thoughts :
ok, this looks pretty similar to the gaussian distribution : $f(x)=\frac{1}{\sqrt{2\pi \sigma^2}}\exp(-\frac{(x-\mu)^2}{2\sigma^2})$
obv... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/87279/higher-homotopy-groups-of-slice-disk-complement | Higher homotopy groups of slice disk complement
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Let $K \subseteq{\mathbb{S}}^3=∂\mathbb{D}^4$ be a non-trivial slice knot, i.e. $K$ bounds a slice disk $\Delta$ in $\mathbb{D}^4$. Let $N(\Delta)$ be a regular neighbo... | {"extraction_info": {"found_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://mathhelpforum.com/trigonometry/102799-easy-trig-question-print.html | # easy trig question
Printable View
• September 17th 2009, 06:57 AM
Raj
easy trig question
How would i solve questions such as sin(x)= $\frac{1}{2}$ or cos(3x)= $\frac{-\sqrt{3}}{2}$ without using a calculator.
Thanks in advance
• September 17th 2009, 07:16 AM
mathaddict
Quote:
Originally Posted by Raj
How would 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": 25, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/176148-geoemtric-interpretation-norm-bounded-linear-functional-print.html | # Geoemtric interpretation of the norm of a bounded linear functional
Printable View
• March 28th 2011, 11:38 PM
raed
Geoemtric interpretation of the norm of a bounded linear functional
Dear Colleagues,
Show that the norm $||f||$ of a bounded linear functional $f\neq 0$ on a normed space $X$ can be interpreted geome... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/27080/direct-sum-of-anyons?answertab=votes | # direct sum of anyons?
In the topological phase of a fractional quantum Hall fluid, the excitations of the ground state (quasiparticles) are anyons, at least conjecturally. There is then supposed to be a braided fusion category whose irreducible objects are in 1-1 correspondence with the various types of elementary q... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 80, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/95826-solving-logarithms-difference-base.html | # Thread:
1. ## Solving logarithms of a difference base.
How do I solve for x of a logarithm that has two different base numbers?
For example:
log5 (x - 4) = log7x
Can you show me the steps?
Thanks.
2. You can use the identity $log_bx = \frac{log_ax}{log_ab}$
In your case you can change $log_7x$ to base 5 as fo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/tagged/rationalhomotopy | ## Tagged Questions
0answers
1 views
### von Staudt-Clausen for other special values
The von Staudt-Clausen theorem expresses that the Bernoulli numbers' denominators have a very special form (see the wikipedia page on the theorem for more details). What interests …
1answer
125 views
### Doubt in the proof of Stick... | {"extraction_info": {"found_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://terrytao.wordpress.com/advice-on-writing-papers/dont-overoptimise/ | What’s new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
# Don’t overoptimise
We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil. (Donald Knuth, “Literate programming”, paraph... | {"extraction_info": {"found_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://mathhelpforum.com/advanced-algebra/80277-galois-check-solution.html | Thread:
1. galois -check solution
can someone check my solutions please
f is poly t^5 -3 in Q[t], where alpha= 3^1/5 in R, epsilon = e^(2pi/5)
(a) need to find zeros of f in terms of a and epsilon
my solution to (a)
alpha, alpha*epsilon, alpha*epsilon^2, alpha*epsilon^3, alpha*epsilon^4
(b) L = (alpha, epsilon).... | {"extraction_info": {"found_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": 62, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2010/10/14/the-character-of-a-representation/?like=1&source=post_flair&_wpnonce=9916d21231 | # The Unapologetic Mathematician
## The Character of a Representation
Now we introduce a very useful tool in the study of group representations: the “character” of a representation. And it’s almost effortless to define: the character $\chi$ of a matrix representation $X$ of a group $G$ is a complex-valued function 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": 0, "wp_latex": 37, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Wavelets | # Wavelet
(Redirected from Wavelets)
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like one might see recorded by a seismograph or heart monitor. Generally, wavelets are purposefully craft... | {"extraction_info": {"found_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": 26, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/16180/complexity-of-verifying-proofs?answertab=oldest | # Complexity of verifying proofs
My question can be read on many levels and so I welcome answers to any reading. The general question is:
What is the computational complexity of verifying a proof?
One way of looking at a computational complexity class (for decision problems) is that is is a set of theories (a theory... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/100635-radical-extension.html | # Thread:
1. ## Radical extension
Prove the splitting field of $x^3+x^2+1\in Z_{2}[x]$ is a radical extension...
when it comes to $Z_{2}$,I am a little bit confused. Since many theorem is based on $charF=0$..
2. Originally Posted by ynj
Prove the splitting field of $x^3+x^2+1\in Z_{2}[x]$ is a radical extension...
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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 60, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://reference.iucr.org/mediawiki/index.php?title=Refinement&oldid=2761 | # Refinement
### From Online Dictionary of Crystallography
Revision as of 20:35, 9 April 2008 by MassimoNespolo (Talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Affinement (Fr); Affinamento (It); 構造精密化 (Ja).
## Definition
In structure determination, the process of improv... | {"extraction_info": {"found_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://mathoverflow.net/questions/68721/parametrizing-the-realization-space-of-a-polyhedron-by-its-edges/68914 | ## Parametrizing the realization space of a polyhedron by its edges
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I alluded to this here, but at that point I hadn't really done enough work to know what I wanted to ask.
Call a polyhedron "trihedral" if three... | {"extraction_info": {"found_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://www.adaptiveagents.org/bayesian_causal_induction | Pedro A. Ortega
⚙
⚒
# Bayesian Causal Induction
This talk was first presented at the 2011 NIPS Workshop on Philosophy and Machine Learning. The talk slides are here, and the workshop paper here. Please cite this as: Pedro A. Ortega. Bayesian Causal Induction. 2011 NIPS Workshop in Philosophy and Machine Learning.
Ab... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 55, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://alanrendall.wordpress.com/2011/04/08/conference-on-modelling-the-immune-system-in-dresden-part-3/ | # Hydrobates
A mathematician thinks aloud
## Conference on modelling the immune system in Dresden, part 3
In my second ever post on this blog I quoted a celebrated paper of Ho et. al. on HIV therapy. One of the other authors of that paper was Avidan Neumann and on Wednesday I had the opportunity to hear him giving 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": 0, "wp_latex": 1, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/68213/families-of-curves-for-which-the-belyi-degree-can-be-easily-bounded | ## Families of curves for which the Belyi degree can be easily bounded
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I know (edit: three) families of smooth projective connected curves over $\bar{\mathbf{Q}}$ for which the Belyi degree is not hard to bound 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": 57, "mathjax_display_tex": 0, "mathjax_asciimath": 2, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/163345-find-antiderivative-here.html | # Thread:
1. ## Find antiderivative here
Is antiderivative of $(6x^2+1)$ is it $2x^3+x+C$?
Is antiderivative of $\frac{1}{4z}$ is it $\frac{1}{4}\ln4z+C$?
2. Originally Posted by Critter314
Is antiderivative of $(6x^2+1)$ is it $2x^3+x+C$?
Yes (Clap)
Is antiderivative of $\frac{1}{4z}$ is it $\frac{1}{4}\ln4z+C$?
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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/2588/what-does-it-mean-to-be-long-gamma?answertab=oldest | # What does it mean to be long gamma?
When you are "long gamma", your position will become "longer" as the price of the underlying asset increases and "shorter" as the underlying price decreases.
source: http://www.optiontradingtips.com/greeks/gamma.html
My intuition tells me that if you're long gamma, all that mean... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/167553/division-and-number-scaling | # Division and number scaling
I'm trying to implement an interactive (secure) protocol which operates only on integers. Here's what I have:
$$f(x) = \sum_i{a_i K_i} + b$$
$$K_i = \dfrac{1}{1 + \gamma \|x - s_i\|^2}$$
where $0 < i \le M$ and $$\|x - s_i \|^2 = \sum_{j=1}^{N}{(x_j - s_{ij})^2}.$$
Because the server ... | {"extraction_info": {"found_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": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://en.m.wikipedia.org/wiki/Packing_in_a_hypergraph | # Packing in a hypergraph
In mathematics, a packing in a hypergraph is a partition of the set of the hypergraph's edges into a number of disjoint subsets such that no pair of edges in each subset share any vertex. There are two famous algorithms to achieve asymptotically optimal packing in k-uniform hypergraphs. One 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": 145, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/advanced-algebra/129285-conjugacy-classes-two-problems.html | Thread:
1. Conjugacy classes - two problems.
Hi, I was wondering if I could get some help with these questions?
1.Let G be a non-abelian group of order 21. Show that if m is the number of conjugacy classes of size 3 and n is the number of conjugacy classes of size 7 then 3m+7n = 20. Deduce that m = n = 2.
2. Let 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/pre-calculus/206183-how-show-following-equality-holds.html | # Thread:
1. ## any hints to solve the following !!
Show that $f(x)$ is the derivative of $f(.)$ at $x$ if and only if $lim_{h \to 0} \sup_{|t|\leqslant h} \frac{|f(x+t)-f(x)-tf^{'} (x)|}{h} = 0$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/math-topics/36764-physics-question.html | # Thread:
1. ## Physics Question
I just had my last physics lesson before my exam, but I have one question where I disagree with my teacher.
A dynamics Trolley A of mass 5kg is placed on a horizontal board. It is connected to block B (a hanging mass) of mass 2kg by a light, inextensible string over a frictionless pu... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/22648/maximum-distance-in-cycle-interval?answertab=oldest | # Maximum distance in cycle interval
Perhaps this is a very basic question, but I can't find a fast solution.
I have a cyclic interval [0,n] (distance from n to 0 is 1). I need a function that for a given value x returns the point in the interval where it maximizes the distance to all previous points (x-1, x-2...)
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": 15, "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/6603 | nrich enriching mathematicsSkip over navigation
### Lying and Cheating
Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!
### Muggles Magic
You can move the 4 pieces 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": 1, "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/39828/how-do-you-decide-whether-a-question-in-abstract-algebra-is-worth-studying/40551 | ## How do you decide whether a question in abstract algebra is worth studying?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Dear MO-community, I am not sure how mature my view on this is and I might say some things that are controversial. I welcome contradi... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/30691/hierarchy-is-no-problem-and-susy-is-a-mathematical-tool-for-data-fitting | # Hierarchy is no problem and susy is a mathematical tool for data fitting
I saw this paper in the arXiv: http://arxiv.org/abs/1206.4711. The author seems well-known and has many very well cited papers. But what he says sounds very strange.
What I get from this paper are the claims that: There's no naturalness or fin... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/47656/reference-request-is-mathematics-discovered-or-created?answertab=oldest | # Reference request: is mathematics discovered or created?
I have to write a short monograph as an assignment for a course on the philosophy of science. Being a math student, of course I want to opt for something math-related. After some initial ideas which would have needed way too much research, I imagined I could 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": 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/2011/08/24/an-example-part-2/?like=1&source=post_flair&_wpnonce=39170bc4ce | # The Unapologetic Mathematician
## An Example (part 2)
We follow yesterday’s example of an interesting differential form with a (much simpler) example of some $1$-chains. Specifically, we’ll talk about circles!
More specifically, we consider the circle of radius $a$ around the origin in the “punctured” plane. I use... | {"extraction_info": {"found_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": 20, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/19649/physical-construction-of-nonconstant-meromorphic-functions-on-compact-riemann-s | ## “Physical” construction of nonconstant meromorphic functions on compact Riemann surfaces?
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Miranda's book on Riemann surfaces ignores the analytical details of proving that compact Riemann surfaces admit noncon... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikibooks.org/wiki/Econometric_Theory/Asymptotic_Convergence | # Econometric Theory/Asymptotic Convergence
Wikipedia has related information at Convergence of random variables
## Asymptotic Convergence
### Modes of Convergence
#### Convergence in Probability
Convergence in probability is going to be a very useful tool for deriving asymptotic distributions later on in this boo... | {"extraction_info": {"found_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": 56, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2010/12/24/ | The Unapologetic Mathematician
Permutations and Polytabloids
We’ve defined a bunch of objects related to polytabloids. Let’s see how they relate to permutations.
First of all, I say that
$\displaystyle R_{\pi t}=\pi R_t\pi^{-1}$
Indeed, what does it mean to say that $\sigma\in R_{\pi t}$? It means that $\sigma$ pr... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 16, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/98343/list | ## Return to Question
3 edited tags
2 edited body
A long time ago I've seen a paper considering, given $\ell$ fixed, estimates for
$$\sum_{n \leq x, (n, \ell) = 1} 1$$
Of course, this is easy to estimate with a trivial error term of $O(\varphi(q))$. O(\varphi(l))\$. However in the paper I am looking for the authors... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/103613/is-there-a-software-to-prove-or-deduce-symbolic-inequalities | ## Is there a software to prove or deduce symbolic inequalities?
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I have a bunch of inequalities, and I'm trying to see if another inequality can be deduced from the first bunch. For example, assuming that $a \leq... | {"extraction_info": {"found_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/algebra/1534-rational-algebraic-expressions.html | # Thread:
1. ## Rational algebraic expressions
In a book stands that rational algebraic expression is ${\sqrt 2}$ and that are not rational algebraic expression ${\sqrt 2gh}, x+{\sqrt x}$
How can ${\sqrt 2}$ be rational algebraic expression? Why isn't irrational?
Why ${\sqrt 2gh}, x+{\sqrt x}$ are irrational?
2. 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": 17, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/1852-constants-composition-functions.html | # Thread:
1. ## Constants for Composition of functions
Let f(x) = ax+b and g(x) =cx+d where a,b,c,d are constants. Determine for which constants a,b,c,d it is true that f o g = g o f.
I am not very sure how to approach this problem. I simplifed the f o g and g o f but after that I am not sure how to go from there.
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/37593/easy-special-cases-of-the-decomposition-theorem | ## Easy special cases of the decomposition theorem?
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The decomposition theorem states roughly, that the pushforward of an IC complex, along a proper map decomposes into a direct sum of shifted IC complexes.
Are 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": 13, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/71534-solved-second-fundamental-form.html | # Thread:
1. ## [SOLVED] Second Fundamental Form
Hi there. I'm trying to understand the Second Fundamental Form but I'm stuck on something. Let:
$\textbf{X}=(x(u^1,u^2),y(u^1,u^2),z(u^1,u^2))$ is a parameterised form of a surface.
$\textbf{X}_i=\dfrac{\partial \textbf{X}}{\partial u^i}$
$\textbf{X}_{i j}=\dfrac{\p... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 32, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cust-serv@ams.org/bookstore-getitem/item=coll-52-r | 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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/10612/explain-how-or-if-a-box-full-of-photons-would-weigh-more-due-to-massless-photo?answertab=oldest | # Explain how (or if) a box full of photons would weigh more due to massless photons
I understand that mass-energy equivalence is often misinterpreted as saying that mass can be converted into energy and vice versa. The reality is that energy is always manifested as mass in some form, but I struggle with some cases:
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/211892-rationalize-fraction-fractional-exponent.html | # Thread:
1. ## Rationalize a fraction with fractional exponent
My question is, how are they getting from step 2 to step 3. Where is the 3^4/5 coming from?!
Not sure i understand the rationalize the denominator of (1/3)^1/5
Thanks for the help.
Attached Thumbnails
2. ## Re: Rationalize a fraction with fractional 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://pediaview.com/openpedia/RLC_circuit | RLC circuit
A series RLC circuit: a resistor, inductor, and a capacitor
An RLC circuit (or LCR circuit or CRL circuit or RCL circuit) is an electrical circuit consisting of a resistor, an inductor, and a capacitor, connected in series or in parallel. The RLC part of the name is due to those letters being the usual el... | {"extraction_info": {"found_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": 121, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/tagged/electroweak+renormalization | # Tagged Questions
0answers
60 views
### CP-violation in weak and strong sectors
There is a possible CP-violating term in the strong sector of the standard model proportional to $\theta_\text{QCD}$. In the absence of this term, the strong interactions are CP-invariant. In the ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "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/2483/minkowski-sum-of-small-connected-sets | ## Minkowski sum of small connected sets
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Suppose that the convex hull of the Minkowski sum of several compact connected sets in $\mathbb R^d$ contains the unit ball centered at the origin and the diameter of each... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 26, "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/203830-stuck-transforming-base-function-completing-table-values-graphing.html | # Thread:
1. ## Stuck on transforming a base function, completing a table of values, and graphing it
The question is as follows:
Complete the table of values and plot the transformed points to obtain the graph of y=-2(-1/3(x+2))2-4
| | | | |
|--------|------------|... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?t=91808 | Physics Forums
## Significance of isospin and hypercharge
This may sounds like a dumb question but I want to figure out the 'point' of them.
I know that isospin was an attempt to describe the proton and nucleon as an isospin doublet and that hypercharge seems to me to be a nifty little relation between the electric ... | {"extraction_info": {"found_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": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/266684/evaluate-int-2x-over-x2-1dx/266689 | # Evaluate $\int {2x\over x^2-1}dx$
My friend evaluated this before he went to bed: $$\int {2x\over x^2-1}dx$$
The answer was $\log(x^2-1)$.
I just can't figure out how that works. I know that $\int \frac1x dx = \log|x|$, so what just happened to $2x$?
-
## 7 Answers
Let $\quad\quad u = \;x^2 - 1.\quad$ (Use "$\;... | {"extraction_info": {"found_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": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/47855/radicals-of-binomial-ideals | ## Radicals of binomial ideals
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $R=k[x_1,x_2,...,x_n]$ be the polynomial ring in $n$ indeterminates over a field $k$. An ideal (that can be) generated by monomials is called a monomial ideal. For the monomial ... | {"extraction_info": {"found_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://torus.math.uiuc.edu/cal/math/cal?year=2012&month=04&day=03&interval=day | Seminar Calendar
for events the day of Tuesday, April 3, 2012.
.
events for the
events containing
Questions regarding events or the calendar should be directed to Tori Corkery.
``` March 2012 April 2012 May 2012
Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa
... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/26778/how-do-we-know-dark-matter-is-non-baryonic | # How do we know Dark Matter is non baryonic?
It seems widely stated, but not thoroughly explained, that Dark Matter is not normal matter as we understand it. Wikipedia states "Consistency with other observations indicates that the vast majority of dark matter in the universe cannot be baryons, and is thus not formed ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/123773-triangular-matrices.html | # Thread:
1. ## Triangular Matrices
Hi!
Could you help me with the following problem:
Find an invertible matrix P such that $P^-1 AP$
is upper triangular, where A is the matrix:
$\begin{pmatrix}3&2&1\\\!\!\!-1&2&1\\1&0&1\end{pmatrix}$
Thanks a lot for suggestions/help! (general algorithms welcome)
Best Wishes,
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 20, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/8801/is-it-possible-to-know-the-exact-values-of-momentum-and-velocity-of-a-particle-s | # Is it possible to know the exact values of momentum and velocity of a particle simultaneously?
I know that by Heisenberg's Uncertainty Principle that it is not possible to know the exact values of position and momentum of a particle simultaneously, but can we know the exact values of momentum and velocity of a parti... | {"extraction_info": {"found_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": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/124225/factorial-divisors | # Factorial Divisors
Q. For what maximum value of $n$ will the expression $\frac{10200!}{504^n}$ be an integer? I have the solution to this question and I would like you to please go through the solution below. My doubt follows the solution :)
The solution can be found by writing $504 = 2^3 \cdot 3^2 \cdot 7$ 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": 52, "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/165405-give-equation-plane-parallel-plane-print.html | # give an equation for the plane that is parallel to the plane....
Printable View
• December 5th 2010, 04:08 PM
break
give an equation for the plane that is parallel to the plane....
give an equation for the plane that is parallel to the plane 5x-4y+z=1 and that passes through the point (2,-1,-2).
i used the formula... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Coanalytic_set | # Coanalytic set
In the mathematical discipline of descriptive set theory, a coanalytic set is a set (typically a set of real numbers or more generally a subset of a Polish space) that is the complement of an analytic set (Kechris 1994:87). Coanalytic sets are also referred to as $\scriptstyle\boldsymbol{\Pi}^1_1$ set... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/math-topics/15941-august-2004-help.html | # Thread:
1. ## August 2004 Help
Hello everyone. My name is Norman and although I'm asking specifically for help on one question now, I may have others later, so please don't get too angry at me if I start asking millions of questions. For now though, I have absolutely no idea in the name of heaven's sake how to do 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": 52, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2011/02/12/ | # The Unapologetic Mathematician
## Intertwinors from Semistandard Tableaux Span, part 2
We continue our proof that the intertwinors $\bar{\theta}_T:S^\lambda\to M^\mu$ that come from semistandard tableaux span the space of all such intertwinors. This time I assert that if $\theta\in\hom(S^\lambda,M^\mu)$ is not the ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 30, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2010/04/28/measurable-subspaces-i/?like=1&source=post_flair&_wpnonce=39170bc4ce | # The Unapologetic Mathematician
## Measurable Subspaces I
WordPress seems to have cleaned up its mess for now, so I’ll try to catch up.
When we’re considering the category of measurable spaces it’s a natural question to ask whether a subset $X_0\subseteq X$ of a measurable space $(X,\mathcal{S})$ is itself a measur... | {"extraction_info": {"found_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": 44, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/6704/how-to-think-about-cm-rings/6724 | ## How to think about CM rings?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
There are a few questions about CM rings and depth.
1. Why would one consider the concept of depth? Is there any geometric meaning associated to that? The consideration of regular... | {"extraction_info": {"found_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/algebra/169742-factoring-cubic.html | # Thread:
1. ## Factoring a cubic
I tried factoring by grouping and everything else I could think of but I can't seem to end up with a solution.
$r^3 - 6r^2 + 11r - 6 = 0$
Would there be a systematic way of factoring this or is it just guesswork?
The final factored form is:
$(r-1)(r-2)(r-3)$
Any help is apprecia... | {"extraction_info": {"found_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://quant.stackexchange.com/questions/4139/unsystematic-and-systematic-risk-of-a-portfolio?answertab=active | # Unsystematic and systematic risk of a portfolio
I have 8 country stock indexes and 1 world stock index. I do not actually have time series data but I'm given the following data:
• $\mu$, the vector of expected future returns for all 8 country indexes and world index (9 indexes).
• $\Omega$, the variance covariance ... | {"extraction_info": {"found_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://quant.stackexchange.com/questions/2841/how-to-obtain-true-probabilities-from-black-scholes?answertab=votes | # How to obtain true probabilities from Black-Scholes?
How to obtain true probabilities from Black-Scholes option pricing equation? Suppose, that we know risk adjusted discount rate for the underlying asset (the drift term in the physical measure) and risk free rate. The task is to find a real (not risk neutral) expec... | {"extraction_info": {"found_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/advanced-statistics/155753-help-question.html | # Thread:
1. ## Help with question~~
Hi everyone,
I need help with answering a question:
Question:
A pseudo-random number generates uniformly distributed random variables Xi on the interval [0,1]. This random number generator is to be used to produce random variables Yi, which have a Pareto distribution, described... | {"extraction_info": {"found_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://openwetware.org/index.php?title=Biomod/2011/Caltech/DeoxyriboNucleicAwesome/Simulation&oldid=521965 | # Biomod/2011/Caltech/DeoxyriboNucleicAwesome/Simulation
### From OpenWetWare
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# Simulations
## Overview
Our proposed sorting mechanism depends very heavi... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?p=4200118 | Physics Forums
Page 1 of 2 1 2 >
## induction, magnetism and conductivity
Relative motion between a permanent magnet and a conductor wire produces electric current in the wire. Would induced electric current be greater in a wire made of "magnetic" material like iron, "non-magnetic" material like copper, or it ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/discrete-math/174751-find-simple-expression-f28.html | # Thread:
1. ## Find simple expression for f28
For the functions
f1(x)=(2x-1)/(x+1)
f(n+1)(x)=f1(fn(x)) for n>=1
it can be shown that f35=f5.Find the simple expression for f28.
2. Originally Posted by chris86
For the functions
f1(x)=(2x-1)/(x+1)
f(n+1)(x)=f1(fn(x)) for n>=1
it can be shown that f35=f5.Find the simpl... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/75785/prime-number-density-vs-connectedness-threshold-coincidence | ## Prime number density vs. connectedness threshold: coincidence?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
(1) $\pi(n)$, the number of primes at most $n$, is asymptotic to $n / \ln n$.
(2) In the Erdős-Rényi random graph model, $p = \ln n / n$ is a sha... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/11760/landaus-ambiguous-statement-about-the-existence-of-inertial-frames?answertab=votes | Landau's ambiguous statement about the existence of inertial frames
Landau writes "It is found, however, that a frame of reference can always be chosen in which space is homogeneous and isotropic and time is homogeneous."
Does he mean that we can prove the existence of an inertial frame or does he want to say that it... | {"extraction_info": {"found_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/algebra/207452-equation-line-help.html | 2Thanks
• 1 Post By darthjavier
• 1 Post By HallsofIvy
# Thread:
1. ## equation of a line - help
Hi,
I'm stuck on a problem and I need help... I'm supposed to find the general equation of a line (Ax+By+C=0) from two points. I did a couple of these problems and everything went well but not for this one... so here 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 20, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://freelance-quantum-gravity.blogspot.com/2010/06/heterotic-phenomenology.html | # DiY quantum gravity
An independent viewpoint about quantum gravity.
## Tuesday, June 01, 2010
### Heterotic phenomenology
I have talked quite often in this blog about F-theory. This is partially due to "historical" reasons, that is, the F-theory GUT revolution happened recently, while this blog growth. Also the 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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/math-software/153088-how-do-i-solve-equation-b1-b2-b3-using-maple-mathematica.html | # Thread:
1. ## How do I solve this equation for b1, b2, b3 using Maple or Mathematica?
(tH′′)^2 = [H′(2n + t + λ) - H]^2 − 4(tH′ − H + δ)[(H′)^2 + λH′]
where H(t) / (n^2)λ = (summation from k=1 to infinity) of [bk / (t^k)]
((where bk means b with subscript k))
I hope someone can help me..I desperately need to kno... | {"extraction_info": {"found_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://en.wikibooks.org/wiki/Microprocessor_Design/FPU | # Microprocessor Design/FPU
Similar to the ALU is the Floating-Point Unit, or FPU. The FPU performs arithmetic operations on floating point numbers.
An FPU is complicated to design, although the IEEE 754 standard helps to answer some of the specific questions about implementation. It isn't always necessary to follow ... | {"extraction_info": {"found_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/tagged/fresnel-integrals+calculus | # Tagged Questions
0answers
71 views
+100
### An integral involving Fresnel integrals $\int_0^\infty \left(\left(2\ S(x)-1\right)^2+\left(2\ C(x)-1\right)^2\right)^2 x\ \mathrm dx,$
I need to calculate the following integral: $$\int_0^\infty \left(\left(2\ S(x)-1\right)^2+\left(2\ C(x)-1\right)^2\right)^2 x\ \mathrm... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/138234/how-does-a-conformal-mapping-preserve-angles-in-hyperbolic-geometry/138292 | # How does a conformal mapping preserve angles in hyperbolic geometry?
Suppose I have a sector $D = \{0 < \arg z < \alpha\}$ where $\alpha \leq 2\pi$. If I apply the function $w = \frac{\zeta - i}{\zeta + i}$ from the upper half plane to the unit disc ($\zeta = z^{\frac{\pi}{\alpha}}$), I get that the vertex of the se... | {"extraction_info": {"found_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://math.stackexchange.com/questions/313152/the-edge-set-grown-in-kruskals-algorithm | # The Edge Set Grown in Kruskal's Algorithm
Let G = (V, E) be a weighted, connected and undirected graph. Let T be the edge set that is grown in Kruskal's algorithm and stopped after k iterations (so T might contain less than |E|-1 edges). Let W(T) be the weighted sum of this set. Let T’ be an acylic edge set such tha... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2009/04/28/the-gram-schmidt-process/?like=1&source=post_flair&_wpnonce=fe7f791e1e | # The Unapologetic Mathematician
## The Gram-Schmidt Process
Now that we have a real or complex inner product, we have notions of length and angle. This lets us define what it means for a collection of vectors to be “orthonormal”: each pair of distinct vectors is perpendicular, and each vector has unit length. In 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 39, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/121113/do-finitely-generated-groups-of-polynomial-growth-satisfy-a-uniform-covering-pro | ## Do finitely generated groups of polynomial growth satisfy a “uniform covering property?”
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $G$ be a finitely generated discrete group with a finite symmetric generating set $S=S^{-1}\subset G$. For every gro... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 43, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/59305?sort=votes | ## Parabolic induction for GL(2,Z/pn)
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Fix a finite extension $F$ of $\mathbb{Q}_p$. Consider its ring of integers $\mathfrak{o}$ with maximal ideal $\mathfrak{p}$. Set $R_n = \mathfrak{o}/\mathfrak{p}^n$. Let $\m... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 42, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/3744/are-picture-files-random-enough-to-be-usable-as-a-one-time-pad?answertab=votes | # Are picture files “random enough” to be usable as a one-time pad?
Say you have a picture with 1 megapixels taken at random and with $2^{24}$ possible colours per pixel (RGB-24). That image would be unique and the possible combinations $(2^{24})^{10^6}$ immense.
However when taking a picture in the real world, say 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": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/189130/prove-that-if-n-is-not-the-square-of-a-natural-number-then-sqrtn-is-irra?answertab=active | # Prove that if $n$ is not the square of a natural number, then $\sqrt{n}$ is irrational. [duplicate]
Possible Duplicate:
$\sqrt a$ is either an integer or an irrational number.
I have this homework problem that I can't seem to be able to figure out:
Prove: If $n\in\mathbb{N}$ is not the square of some other $m\in\m... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 48, "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/240687/recursive-integration-over-piecewise-polynomials-closed-form | # Recursive Integration over Piecewise Polynomials: Closed form?
Is there a closed form to the following recursive integration? $$f_0(x) = \begin{cases} 1/2 & |x|<1 \\ 0 & |x|\geq1 \end{cases} \\ f_n(x) = 2\int_{-1}^x(f_{n-1}(2t+1)-f_{n-1}(2t-1))\mathrm{d}t$$ It's very clear that this converges against some function 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": 29, "mathjax_display_tex": 11, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://www.physicsforums.com/showthread.php?t=580832 | Physics Forums
Blog Entries: 1
## Writing Tensor Equations in Matrix Form
I'm trying to express the tensor equation $F'^{\mu\nu}=\Lambda^{\mu}_{\sigma}\Lambda^{\nu}_{ \rho }F^{\sigma\rho}$ in matrix form. Here the indices range from 0 to 3, so we need 4 by 4 matrices. Let F', F, and $\Lambda$ be the matrices associa... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/191400-how-long-does-take-3-people-do-job.html | # Thread:
1. ## How long does it take 3 people to do a job?
8. If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?
A. 0.8 days
B. 1.09 days
C. 1.23 days
D. 1.65 days
E. 1.97 days
So I know that the answe... | {"extraction_info": {"found_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/111008/use-of-axiom-of-choice-for-creating-an-infinitely-decreasing-sequence?answertab=oldest | # Use of Axiom of Choice for creating an infinitely decreasing sequence
Suppose I have a set with total order but no least element $S$.
I create an infinitely decreasing sequence $\{ a_i : i \in \mathbb N \}$ in the following way.
Now I pick one element $a_1 \in S$.
I pick $a_n$ such that $a_n < a_i$ for all $i \in... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/32266/dual-modules-and-first-cohomology | # Dual modules and first cohomology
Let $G$ be a finite group, $K$ a characteristic-$p$ algebraically closed field (say $p$ divides $|G|$), and let $M$ be a finite-dimensional $KG$-module.
What hypotheses are needed on $G$, $M$ to ensure that $H^{1}(G,M) \cong H^{1}(G,M^{*})$ where $M^{*}$ denotes the dual module Hom... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/113549-quick-question-homeomorphisms.html | # Thread:
1. ## Quick question... homeomorphisms...
Can a homeomorphism exist between an open and a half open set?
(ie: (0,1) and [0,1))
I know that to be a homeomorphism, a bijection must exist, they must be continuous, and they must have a continuous inverse... Where to go from here?
The fact that 0 is not includ... | {"extraction_info": {"found_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/51195/winning-strategy-at-chomp-a-chocolate-bar-game/51199 | ## Winning strategy at chomp (a chocolate bar game)?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The game of chomp is an example of a game with very simple rules, but no known winning strategy in general.
I copy the rules from Ivars Peterson's page http:/... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?p=4182399 | Physics Forums
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## Linear Independence/Dependence
Quote by Studiot Vectors of the form {a,b} with a, b contained in R. (I wish I could find the appropriate symbols more easily)
You just mean the co... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 16, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/3742/find-solutions-that-solve-the-equations?answertab=votes | # find solutions that solve the equations
I am implementing a timing attack on RSA for school and I need to generate two sets of messages $Y$ and $Z$ for which holds:
$(Y^d \mod N) \cdot Y < N$ and
$(Z^d \mod N) \cdot Z > N$
where $d$ and $N$ are known. How can I efficiently find solutions for $Y$ and $Z$?
I have 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": 53, "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/225875/calculating-the-absolute-value-of-a-complex-number-am-i-right | # Calculating the absolute value of a complex number - am I right?
To calculate the absolute value of a complex number u must use the following formular $(a^2+b^2)^½$=|a+bi|
So for instance with -4-5i would have the absolute value $((-4)^2+(-5)^2)^½$=$(16+25)^½$=$\sqrt(41)$
But how come it is so?
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## 2 Answers
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": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/79360/independence-of-rotated-spherical-harmonics/79368 | ## Independence of rotated spherical harmonics
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hi,
Consider a spherical harmonic of degree $l$, denoted by $y_l^m$. I rotate this harmonic using $2l+1$ different rotations. The set of functions I get is not an 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": 43, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.birs.ca/events/2008/5-day-workshops/08w5061 | # Recent Developments in Elliptic and Degenerate Elliptic Partial Differential Equations, Systems and Geometric Measure Theory (08w5061)
Arriving Sunday, March 30 and departing Friday April 4, 2008
## Organizers
David Cruz-Uribe (Trinity College)
Steven Hofmann (University of Missouri-Columbia)
Marius Mitrea (Univer... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/57965/list | ## Return to Question
2 added 148 characters in body
I can understand why $P^A = NP^A$ does not imply $P=NP$, $A$ can "contain" the powers of NP.
However, why does $P^B \neq NP^B$ not imply $P \neq NP$? It seems like if $P$ and $NP$ denote the same classes; then we should be able to arbitrarily substitute one for 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": 20, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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