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http://mathoverflow.net/questions/59245?sort=votes | ## What relations exist among (quasi-) modular forms of different levels?
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Given a (quasi-) modular form $f(\tau)$ for some congruence subgroup (say) $\Gamma(k)$, we know that $f(N\tau)$ is a (quasi-) modular form... | {"extraction_info": {"found_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://math.stackexchange.com/questions/135917/calculating-a-real-integral-using-complex-integration | # Calculating a real integral using complex integration
$$\int^\infty_0 \frac{dx}{x^6 + 1}$$
Does someone know how to calculate this integral using complex integrals? I don't know how to deal with the $x^6$ in the denominator.
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## 2 Answers
Thankfully the integrand is even, so we have
$$\int^\infty_0 \frac{dx}{x... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 27, "mathjax_display_tex": 13, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathematica.stackexchange.com/questions/17342/how-do-i-get-the-equivalent-of-the-latex-tag-in-mathematica?answertab=votes | How do I get the equivalent of the $\LaTeX$ \tag{} in Mathematica?
How do I get the equivalent of the $\LaTeX$ \tag{} in Mathematica?
$a+b=x \tag{1}$
I'm not necessarily asking how to use the $\LaTeX$ `\tag{}` itself in Mathematica, I'm just looking for some feature that will allow me to mark an equation like that.
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/94838/what-are-the-properties-of-a-prime-number/94899 | # What are the properties of a prime number?
For instance, we know that odd numbers behave like:
$$x = 2y + 1 \quad\text{where}\quad x,y\in\mathbb Z$$
For even numbers:
$$a = 2b \quad\text{where}\quad a,b\in\mathbb Z$$
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2
Clearly all primes other than $2$ must be of the form $2k + 1$ for some integer $k$ (else i... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 33, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/73193/dirichlet-series-of-the-reciprocal-radical-function | ## Dirichlet series of the reciprocal radical function
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Define $rad(n):=\prod_{p|n}p$ and $a_n:=\frac{n}{rad(n)}.$ For example $a_n=1$ whenever n is a squarefree integer. The assosiated Dirichlet series $$F(s):=\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": 11, "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/40830/how-to-define-a-partial-derivative-invariantly?answertab=votes | # How to define a partial derivative invariantly?
Let $M$ be a smooth manifold and $f$, $g$ be smooth functions in some neibourhood of a point $x_0\in M$, $\nabla g\ne0$.
1) How to define $\displaystyle \frac{\partial f}{\partial g}$ invariantly? If $M$ is a domaqin in $\mathbb R^n$ then the derivative in the directi... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/34435?sort=oldest | ## Automatic proving some expression is positive
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Is there any automated (i.e., some algorithm) to prove that a certain algebraic expression is always non-negative in some range ? If so, is there any implementatio... | {"extraction_info": {"found_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": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/38289/comparing-lower-central-series-and-augmentation-ideal-completions/38318 | ## Comparing lower central series and augmentation ideal completions
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Let G be a group. Let $G^p$ be the completion of G with respect to the mod p lower central series of G.i.e. $G^p=\varprojlim_{q} G/\gamma_qG$, ... | {"extraction_info": {"found_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://mathoverflow.net/questions/50243/questions-on-central-simple-algebras/112763 | ## questions on central simple algebras
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Suppose $A$ is a finite dimensional central simple algebra over a field $F$, $B$ is a simple subalgebra of $A$. $C$ is the centralizer of $B$ in $A$.
From Wedderburd-Artin... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/5963/note | ### Rotating Triangle
What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?
### Doodles
A 'doodle' is a closed intersecting curve drawn without taking pencil from paper. Only two lines cross at each intersection or vertex (never 3), that is the... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/98196/multiple-linear-regression-estimation-without-full-recalc | ## Multiple Linear Regression Estimation without full recalc
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Ok, so I am running a classic linear regression where betahat = (X'X)^-1X'y
Due to performance issues, I would like to estimate betahat with an additi... | {"extraction_info": {"found_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/number-theory/206021-can-there-ever-more-primes-n-2n-than-0-n.html | # Thread:
1. ## Can there EVER be more primes from n to 2n than from 0 to n?
Thank you for considering my question. It is a very simple question. But it is one I need to find the answer to for something I am working on.
The question is this:
Is it conceivably, morally, imaginably POSSIBLE for there ever to be more ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/19269?sort=oldest | ## What are some examples of narrowly missed discoveries in the history of mathematics?
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What are the examples of some mathematicians coming very close to a very promising theory or a correct proof of a big conjec... | {"extraction_info": {"found_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/algebra/21678-help-please-few-problems.html | # Thread:
1. ## Help please, few problems
1.) 4k+2
....____ > 2 Had to put periods in to keep it in place, but it is 4k+2 diveded by 5 is greater then 2, how do I solve that?
.......5
2.) A person'as body mass index is given by the expression Weight/h2 where W is the weight in kilogrammes and h is the height in mete... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cms.math.ca/Events/summer12/abs/nt.html | 2012 CMS Summer Meeting
Regina Inn and Ramada Hotels (Regina~Saskatchewan), June 2 - 4, 2012 www.cms.math.ca//Events/summer12
Number Theory
Org: Mark Bauer (Calgary), Richard McIntosh (Regina) and Eric Roettger (Mount Royal)
[PDF]
MICHAEL BENNETT, University of British Columbia
A problem of Erdos and Graham revisite... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 44, "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=454639 | Physics Forums
Recognitions:
Gold Member
## Prove using the definition of a limit, Please help! :)
1. The problem statement, all variables and given/known data
Prove using only the definition of a limit, that the sequence:
$$\frac{n}{(n+1)^1/2}$$ - $$\frac{n}{(n+2)^1/2}$$ converges.
2. Relevant equations
Let E>0 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": 32, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/55279/list | ## Return to Answer
4 added 292 characters in body
I'm a bit confused by the quoted wikipedia entry, because the category of reduced rings also has coproducts (take the tensor product, and then pass to the quotient by the nilradical), and hence the category of reduced schemes, the category of varieties over a field, ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 32, "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/185435-question-monotone-sequences.html | # Thread:
1. ## Question on monotone sequences
Let A be an infinite subset of the real numbers that is bounded above and let u=supA. Show that there exists an increasing sequence $(x_n)$ with $x_n \in A \forall n \in \mathbb{N}$ such that $u=lim(x_n)$.
The only way I can think of starting this question is to form so... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 29, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/navier-stokes | # Tagged Questions
The Navier-Stokes equations describe fluid flows in continuum mechanics.
1answer
37 views
### boundary conditions for liquid with surface tension
so one uses equations of motion to describe liquids (e.g. Navier–Stokes equations). These are equations for $\vec{v}(\vec{r},t)$ with boundary conditio... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://scicomp.stackexchange.com/questions/2391/derive-pca-with-svd | # Derive PCA with SVD
The context is I have a big matrix, 20K * 50K, and I want reduce the dimensionality. In R, it's impossible to apply PCA with more variables(columns) than observations(rows). Therefore, I am trying a partial SVD with this matrix, for instance, I calculate the top 100 left and right singular vector... | {"extraction_info": {"found_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://mathforum.org/mathimages/index.php?title=Lissajous_Curve&diff=34006&oldid=33398 | # Lissajous Curve
### 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": 76, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-statistics/35755-distribution-density-expected.html | # Thread:
1. ## Distribution to density to expected
A random variable X has the cumulative distribution function
$F(x) = 0$ for $x<1$
$F(x) = \frac{x^2 - 2x + 2}{2}$ for $1 \leq x < 2$
$F(x) = 1$ for $x \geq 2$
Calculate the variance of X.
The answer specifies that the density function is
$f(x) = 0.5$ if x=1
$f(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": 60, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/39124/what-is-a-killing-vector-field/39130 | # What is a Killing vector field?
I recently read a post in physics.stackexchange that used the term "Killing vector". What is a Killing vector/Killing vector field?
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2
+1, I also saw it when I was looking up the surface gravity of a black hole. Good question. – ja72 Oct 5 '12 at 12:50
2
please could you summarise... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/26950/extensions-of-dhr-superselection-theory-to-long-range-forces | # Extensions of DHR superselection theory to long range forces
For Haag-Kastler nets $M(O)$ of von-Neumann algebras $M$ indexed by open bounded subsets $O$ of the Minkowski space in AQFT (algebraic quantum field theory) the DHR (Doplicher-Haag-Roberts) superselection theory treats representations that are "localizable... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/44838?sort=oldest | A simple problem in markov chains
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I'm trying to understand a 1954 paper of Kubo intitled "Note on the stochastic theory of resonance absorption". The specific problem can be stated mathematically as follows: let $X(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": 86, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/tagged/diffie-hellman+dsa | # Tagged Questions
1answer
118 views
### Request for 1024-bit primes $p$ , subgroup $q$ and subgroup generator $g$
I need to find a prime $p$ of $1024$ bits with a $160$ bit sub group size $q$, such that $q|p-1$ , and $g$ is the generator of the sub group size $q$. I'm looking for the numeric values of $p$ , $q$ ...... | {"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": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/147493-partial-fractions.html | # Thread:
1. ## partial fractions
how do I get the answer shown in the attached problem? when I tried it out, I couldn't get the numerator to 1.
Thanks!
Attached Thumbnails
remember that:
$a^2 - b^2 = (a+b)(a-b)$
Can you do it now?
3. Originally Posted by calculus0
how do I get the answer shown in the attached 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": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/263492/can-you-explain-this-card-trick?answertab=votes | # Can you explain this card trick?
Can you explain the card trick that is explained here?
Edit: Here's a summary of the trick as explained in the video:
Start by asking a spectator to pick any three cards they like out of a standard 52-card deck, without showing them to you, and write them down (to make sure they 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": 56, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showpost.php?p=3796410&postcount=5 | View Single Post
Recognitions:
Gold Member
Quote by faen Yes I thought about this too. But the result seems strange to me, because it now predicts that time goes slower in the rest frame and not in the moving frame, just because we changed the location of the experiment. For example if we had done 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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-statistics/142719-characteristic-functions.html | # Thread:
1. ## Characteristic functions
Given that E(e^(itx)) (the characteristic function of a Cauchy rv)=e^(-abs(t)), use this fact to find the pdf for X bar for all n.
I have no idea how to do this, and it was on the test. I got 4/25 points, and the professor doesn't give the correct answers.
I just started com... | {"extraction_info": {"found_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/22562/convex-hull-of-finite-set-is-compact | ## convex hull of finite set is compact [closed]
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In a Banach space, is the convex hull of finite set compact?
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The convex hull of a set of $n$ points is the image of the $n$-simplex in $\mathbb R^n$ under 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": 21, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/142210-measure-theory.html | Thread:
1. Measure Theory
Quick question: Does the sigma-algebra generated by a countable number of sets have a countable number of elements?
2. It can be shown that any infinite sigma algebra has cardinality greater than or equal to that of the continuum.
3. Thanks, but how? I tried proving that you can't have a 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": 29, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/99462/alternative-solutions-to-a-probability-problem/99514 | # Alternative solutions to a probability problem
Some fellow students ran a contest this past summer. I had stopped following it by the time this problem came out. I looked back through some of the older problems, saw this and thought I'd try to solve it.
Let $S$ be an infinite sequence of random variables, all $0$ 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": 47, "mathjax_display_tex": 11, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://nrich.maths.org/6962/solution | ### Shapes in the Alphabet
In this problem, we're going to find sets of letter shapes that go together.
### Logic Block Collections
What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?
### Our Numbers
These spinners will give you the tens and unit digits of ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://agtb.wordpress.com/2009/11/27/economists-and-complexity/ | Turing's Invisible Hand
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Economists and Complexity
November 27, 2009 by Noam Nisan
One of main culture clashes between computer scientists and economists on the CS-econ frontier is whether “complexity of equilibria” matters. The CS-y view of the matter is captured in Kamal Jain’s quote: “If 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": 0, "wp_latex": 2, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2007/07/28/the-simplicial-category/ | # The Unapologetic Mathematician
## The Simplicial Category
There’s another approach to the theory of monoids which finds more direct application in topology and homology theory (which, yes, I’ll get to eventually) — the “simplicial category” $\mathbf{\Delta}$. Really it’s an isomorphic category to $\mathrm{Th}(\math... | {"extraction_info": {"found_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": 98, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/tagged/weyl-law | ## Tagged Questions
1answer
235 views
### Weyl law for SL(2,C)
Are there any estimates for the eigenvalues of the Laplace operator for $\Gamma \backslash SL(2, \mathbb{C})/SU(2)$ known beyond the main term? Here, $\Gamma$ should be congruence … | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/132363-solved-determine-if-line-plane-parallel.html | # Thread:
1. ## [SOLVED] Determine if a line and plane are parallel
x = -5 - 4t
y = 1 - t
z = 3 +2t
and x + 2y + 3z - 9 = 0
Now how do I approach a problem like this? I am capable of calculating dot products, cross products, finding vectors from two points.
What is involved in this? Just a little boost will help 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": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/90016/the-most-general-context-of-mathers-cube-theorems | ## The most general context of Mather’s Cube Theorems
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Quite simply, I'd like to know what is the broadest or most natural context in which either (or both) of Mather's cube theorems hold. If you like, this may me... | {"extraction_info": {"found_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://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Calculating_Machines | # 1911 Encyclopædia Britannica/Calculating Machines
From Wikisource
Calculating Machines
See also Calculating machine and Planimeter on Wikipedia, Slide rule on Wikipedia, and our 1911 Encyclopædia Britannica disclaimer.
1911 Encyclopædia Britannica, Volume 4 — Calculating Machines
CALCULATING MACHINES. Instrument... | {"extraction_info": {"found_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": 38, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://scicomp.stackexchange.com/questions/4636/thermoplastic-equation-solving | # Thermoplastic Equation solving
I was given a problem by my professor as follows
Solve the
System
$pV=S$
$pcT=kT+BS\frac{dG}{dt}$
$\frac{dS}{dt}=\mu(V-\frac{dG}{dt})$
$\frac{dG}{dt}=f(S,T)$
Where $p$, $c$, $B$, $\mu$ are constant and $f(S,T)$ is a function to be reasonably assumed
Where do I even begin... I 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": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/18430/2d-simulation-shooting-projectiles-that-inherit-the-guns-veocity-at-a-moving-ta | # 2d simulation shooting projectiles that inherit the gun's veocity at a moving target while also moving
Overview: I'm working on programming a simulation that requires 'shooting' projectile-type objects at other moving objects. How can I calculate the angle at which to shoot the object to hit?
Details:
Imagine 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": 23, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/mass?sort=votes&pagesize=15 | # Tagged Questions
The property of an object that determines how much it responds to a force in Newtonian mechanics, and how much it interacts with gravity in the Newtonian framework. Mass also refers to the intrinsic energy of a particle in particle physics.
14answers
69k views
### How Does Mass Leave the Body When... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 16, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=87066 | Physics Forums
Thread Closed
Page 1 of 3 1 2 3 >
## confused about fourth spatial dimension
lets consider a sphere and let there be a two dimensional man and for him he is living on a two dimensional place.we r observing it from third dimension.
now this two dimensional man be fred.
one day fred decides to 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": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://nrich.maths.org/7289/index?nomenu=1 | What is the sum of: $$6 + 66 + 666 + 6666 + \cdots + 666666666\cdots6$$ where there are $n$ sixes in the last term?
Many functions, including the trigonometric and exponential functions that you meet in school, can be approximated by infinite power series and good approximations can be found using a finite number of te... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.aps.org/synopsis-for/print/10.1103/PhysRevB.81.100501 | # Synopsis:
Keep it local
#### Local measurement of the penetration depth in the pnictide superconductor Ba(Fe0.95Co0.05)2As2
Lan Luan, Ophir M. Auslaender, Thomas M. Lippman, Clifford W. Hicks, Beena Kalisky, Jiun-Haw Chu, James G. Analytis, Ian R. Fisher, John R. Kirtley, and Kathryn A. Moler
Published Mar... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 17, "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://nrich.maths.org/6481&part= | ### Degree Ceremony
What does Pythagoras' Theorem tell you about these angles: 90°, (45+x)° and (45-x)° in a triangle?
### Loch Ness
Draw graphs of the sine and modulus functions and explain the humps.
### Squareness
The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2008/03/21/integrability-over-subintervals/?like=1&source=post_flair&_wpnonce=bbf4ba6a50 | # The Unapologetic Mathematician
## Integrability over subintervals
As I noted when I first motivated bounded variation, we’re often trying to hold down Riemann-Stieltjes sums to help them converge. In a sense, we’re sampling both the integrand $f$ and the variation of the integrator $\alpha$, and together they’re no... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 40, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/astronomy | # Tagged Questions
The science dealing with objects and phenomena located beyond Earth. In particular, this applies to observations and data. At its core, astronomy is the physically informed cataloging and classifying of the contents of the universe in order to better understand what is out there.
1answer
49 views
... | {"extraction_info": {"found_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://mathoverflow.net/questions/48888/what-is-the-divisibility-theory-for-bezout-domains | ## What is the divisibility theory for Bezout Domains?
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There are many facts about integer gcds which can be proved by appealing to unique prime factorization (up to sign). for example $\gcd(a^2,b^2)=\gcd(a,b)^2$.... | {"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": 57, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Summation | # Summation
"Sum" and "Summation" redirect here. For other uses, see Sum (disambiguation) and Summation (disambiguation).
Calculation results
Addition (+)
addend + addend = sum
Subtraction (−)
minuend − subtrahend = difference
Multiplication (×)
multiplicand × multiplier = product
Division (÷)
dividend ÷ divisor = quo... | {"extraction_info": {"found_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": 63, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://inperc.com/wiki/index.php?title=Projection | This site contains: mathematics courses and book; covers: image analysis, data analysis, and discrete modelling; provides: image analysis software. Created and run by Peter Saveliev.
# Projection
### From Intelligent Perception
Given two sets $X$ and $Y$. Then $X×Y$ is the set of all pairs $(a,b)$ of elements in $X$... | {"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": 9, "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/2012/01/04/the-biot-savart-law/?like=1&source=post_flair&_wpnonce=3fdfac1636 | # The Unapologetic Mathematician
## The Biot-Savart Law
What I’m going to present is slightly different from what usually gets called the Biot-Savart law, but I think it’s the most natural parallel to the Coulomb law. As far as I can tell, it doesn’t get stressed all that much in modern coverage; in the first course ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 9, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/44839?sort=votes | ## Wikipedia’s definition of ‘locally free sheaf’
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Let $R$ be a, say, noetherian ring and $M$ an $R$-module. The Wikipedia article on 'locally free sheaf' tells me that the following two statements are equivalent:... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 93, "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/102648/amortized-analysis-for-2-5-tree | # Amortized Analysis for (2,5)-Tree
I need some help with the following problem
Definition: A (2,5)-tree is an external search tree, where all leaves have the same depth. Each inner node in a (2,5)-tree has at least 2, and at most 5 children.
An insert-operation consists of two parts. In the first part, we go down 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": 26, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/22941/is-an-infinite-compositions-of-arrows-meaningful | ## Is an “infinite compositions of arrows” meaningful?
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For example, deciding whether or not the following is a category seems to depend on the above question (from Awodey's Category Theory, pg. 6):
"What if we 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": 40, "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/2008/12/15/the-category-of-representations-is-abelian/?like=1&source=post_flair&_wpnonce=f636fc8316 | # The Unapologetic Mathematician
## The Category of Representations is Abelian
We’ve been considering the category of representations of an algebra $A$, and we’re just about done showing that $\mathbf{Rep}_\mathbb{F}(A)$ is abelian.
First of all, the intertwiners between any two representations form a vector space, ... | {"extraction_info": {"found_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": 19, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/144535/subgroup-structure-of-s-4 | # subgroup structure of $S_4$
In the list of Young subgroups of $S_4,$ we find $\langle(12)\rangle, \langle(13)\rangle, \langle(14)\rangle, \langle(23)\rangle, \langle(24)\rangle, \langle(34)\rangle,$ but we don't find $\langle(12)(34)\rangle, \langle(13)(24)\rangle,\langle(14)(23)\rangle,$ while they are all 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": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/48025/how-is-quantum-mechanics-compatible-with-the-speed-of-light-limit?answertab=oldest | # How is quantum mechanics compatible with the speed of light limit?
Consider a free electron in space. Let us suppose we measure its position to be at point A with a high degree of accuracy at time 0. If I recall my QM correctly, as time passes the wave function spreads out, and there is a small but finite chance of ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.aps.org/articles/large_image/f1/10.1103/Physics.2.22 | Illustration: Courtesy of V. V. Moshchalkov
Figure 1: Schematic of the spatial distribution of the superconducting order parameter $|ψ(x)|$ and the field profile $B(x)$ for two neighboring fluxons in (top) type-I, (middle) type-II, and (bottom) type-1.5 superconductors. The bottom sketch in each panel shows $|ψ(x)|$ i... | {"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://en.wikipedia.org/wiki/Larmor_frequency | # Larmor precession
(Redirected from Larmor frequency)
In physics, Larmor precession (named after Joseph Larmor) is the precession of the magnetic moments of electrons, atomic nuclei, and atoms about an external magnetic field. The magnetic field exerts a torque on the magnetic moment,
$\vec{\Gamma} = \vec{\mu}\time... | {"extraction_info": {"found_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": 33, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/99186/is-this-graph-known | ## Is this graph known?
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I came across the graph $G= (V, E)$, where
$V =$ { $(i, j)| 1 \leq i, j \leq n$ }
$E=${ $((i, j), (k,l))| i \ne l$ and $j \ne k$ }
Does this graph have a name? Is it well studied?
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": 32, "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/89665-p-adic-expansion.html | # Thread:
1. ## p-adic expansion
I just started learning about p-adic numbers so I am having trouble with a relatively easy question:
Compute the 2-adic expansion of 2/3 and then verify your answer.
Help would be appreciated. Thanks.
2. Originally Posted by curiousmuch
I just started learning about p-adic numbers ... | {"extraction_info": {"found_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://mathoverflow.net/questions/52995/complex-structure-on-l2-mathbb-r-generalizing-the-hilbert-transform | Complex structure on $L^2(\mathbb R)$ generalizing the Hilbert transform.
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The Hilbert transform on the real Hilbert space $L^2(\mathbb R)$ is the singular integral operator $$\mathcal H(f)(x) := \frac{1}{\pi} \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": 34, "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/75150/sheaf-with-free-stalks/75161 | Sheaf with free stalks
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Say we are given a complex manifold $X$ and an $\mathcal{O}_X$-module $\mathcal{F}$. Assume that for any point $P\in X$ the stalk $\mathcal{F}_P$ is a free $(\mathcal{O}_X)_P$-module of finite ... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/34805/confidence-intervals-when-using-bayes-theorem | # Confidence intervals when using Bayes' theorem
I'm computing some conditional probabilities, and associated 95% confidence intervals. For many of my cases, I have straightforward counts of `x` successes out of `n` trials (from a contingency table), so I can use a Binomial confidence interval, such as is provided by ... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/61779/problem-in-understanding-p-implies-q | # Problem in understanding p implies q
I am trying to understand what “$p$ implies $q$” means. I read that $p$ is a sufficient condition for $q$, and $q$ is a necessary condition for $p$. Further from Wikipedia,
A necessary condition of a statement must be satisfied for the statement to be true. Formally, a statement... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 36, "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/100085?sort=oldest | ## RS to RSK correspondence
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The RS correspondence is a correspondence which associates to each permutation a pair of standard Young tableaux of the same shape.
The RSK correspondence associates to each integer 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": 9, "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/139388/past-coin-tosses-affect-the-latest-one-if-you-know-about-them/139444 | # Past coin tosses affect the latest one if you know about them?
Suppose Mark and Paul are sitting on a table, and Mark starts tossing an unbiased and fair coin. He tosses it for 99 times, and he gets 99 consecutive tails. At this point Mark asks Paul: "let's bet \$100 on the next toss, do you want to pick tail or hea... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 27, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://psychology.wikia.com/wiki/Variance?interlang=all | Variance
Talk0
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this wiki
Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language | Individual differences | Personality | Philosophy | Social |
Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology |
Statistics: Scientific method · R... | {"extraction_info": {"found_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": 70, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/5355/which-risks-are-associated-with-deriving-multiple-keys-from-the-same-dh-secret-z?answertab=oldest | # Which risks are associated with deriving multiple keys from the same DH secret Z?
NIST recommends Krawczyk's HMAC-based key derivation function (HKDF) in SP-800-56C (PDF). HKDF shall e.g. be used to create keys from shared secrets after Diffie Hellman key establishment.
NIST states in the same doc:
Each call to 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": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/238753/evaluation-of-the-limit-lim-limits-n-to-infty-frac1-sqrt-n-left1-f/238761 | # Evaluation of the limit $\lim\limits_{n \to \infty } \frac1{\sqrt n}\left(1 + \frac1{\sqrt 2 }+\frac1{\sqrt 3 }+\cdots+\frac1{\sqrt n } \right)$
Evaluate the limit : $$\lim_{n \to \infty } {1 \over {\sqrt n }}\left( {1 + {1 \over {\sqrt 2 }} + {1 \over {\sqrt 3 }} + \cdots + {1 \over {\sqrt n }}} \right)$$
I can us... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 36, "mathjax_display_tex": 21, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://www.reference.com/browse/Geosynchronous+orbit+derivation | Definitions
Nearby Words
# Geosynchronous orbit
A geosynchronous orbit is an orbit around the Earth with an orbital period matching the Earth's sidereal rotation period. This synchronization means that for an observer at a fixed location on Earth, a satellite in a geosynchronous orbit returns to exactly the same plac... | {"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://mathoverflow.net/questions/112069/a-fibrant-objects-structure-on-top | ## A fibrant-objects structure on Top
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
(Sorry for the crossposting, but I'm really interested in this question).
One can define (Paragraph 1.5, page 10) a fibrant-object structure on a suitable cartesian closed c... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 67, "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/267140/why-is-f-v-lambda-true-for-a-standing-wave?answertab=votes | # Why is $f=v/\lambda$ true for a standing wave? [closed]
If a wave travels at speed $v$ and has wavelength $\lambda$ it's obvious that any given place in the medium through which the wave is travelling will undergo one full oscillation every $v/\lambda$ units of time, and so the frequency $f$ of the wave must be give... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/193673/find-the-line-equations-of-the-sides-of-a-triangle-finding-slopes | # Find the line equations of the sides of a triangle. (finding slopes)
```` A (10,15)
/\
/ \
/ \
/ \
/ \
C (x, y) /__________\ B (16, 10)
````
Given : $\angle BAC = 85^\circ$ ; $\... | {"extraction_info": {"found_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/116694/the-embedding-of-smooth-manifold | # The embedding of smooth manifold
I have run into a problem in my differential geometry book.
Let $M$ be a smooth manifold and $F={C^\infty }(M,\mathbb R)$. Define a mapping $i:M \to {\mathbb R^F}$ by ${i_f}(x) = f(x)$ for $x \in M,f \in F$, then $i$ is an embedding. ($\mathbb R^F$ has product topology and $i_f$ mea... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/292515/bootstrap-argument-to-prove-regularity-of-a-special-solution | # Bootstrap argument to prove regularity of a special solution
Rabinowitz proves (using the Mountain Pass Theorem) that for a bounded smooth domain $\Omega \in \mathbb{R}^n$, and $f(x,\xi)\in C(\bar{\Omega}\times \mathbb{R},\mathbb{R})$ satisyfing the growth condition $$f(x,\xi) \leq A + B|\xi|^s,\ \ \text{where}\ \ 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": 98, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/52243-perpenicular-bisector.html | # Thread:
1. ## perpenicular bisector...?
find the equation of the perpendicular bisector of (2,-5) and (6,9), expressing your answer in the form: ax + by + c = 0
thanks for any help i can quite seem to get this one...
and its in for tomorrow!! gah!
2. Originally Posted by pop_91
find the equation of the perpendic... | {"extraction_info": {"found_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/advanced-statistics/90907-mean-lognormal-base-2-a.html | # Thread:
1. ## Mean of lognormal with base 2
Hi,
I am trying to figure out what the mean of a lognormal distribution that is in base-2 rather than in base-e. Could someone help with the derivation or at least with the formula itself?
The reason I ask is that I need to generate values with a known mean for a 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2007/05/29/special-kinds-of-morphisms-subobjects-and-quotient-objects/?like=1&source=post_flair&_wpnonce=c1ce40f6e1 | # The Unapologetic Mathematician
## Special kinds of morphisms, subobjects, and quotient objects
Last week I was using the word “invertible” as if it was perfectly clear. Well, it should be, more or less, since categories are pretty similar to monoids, but I should be a bit more explicit. First, though, there’s a few... | {"extraction_info": {"found_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": 103, "mimetex.cgi": 0, "/images/m... |
http://dwave.wordpress.com/2008/10/23/the-128-qubit-rainier-processor-ii-graph-embedding/ | The 128-qubit Rainier chip: II. graph embedding
Posted on October 23, 2008 by
In the previous post I introduced the concept of an allowed edge set in hardware, and presented the edge set we chose for our current processor designs. I mentioned that a reduction in edges reduces the capability of the processor. In this ... | {"extraction_info": {"found_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": 34, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/27471?sort=newest | ## on the computation of decomposition groups
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Let $L/K$ be a finite Galois extension of function fields, with Galois groups $G$. I want to look at the ramification of primes in the extension, i.e. to get $e_p$ an... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.m.wikibooks.org/wiki/C_Programming/Control | C Programming/Control
Very few programs follow exactly one control path and have each instruction stated explicitly. In order to program effectively, it is necessary to understand how one can alter the steps taken by a program due to user input or other conditions, how some steps can be executed many times with few li... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/tags/bose-einstein-condensate/hot?filter=year | Tag Info
Hot answers tagged bose-einstein-condensate
11
What prevents bosons from occupying the same location?
Er ... nothing prevents this. That's what a Bose-Einstein condensate is: lots of bosons in the same place and quantum state. You are observing that the sate is not perfectly localized, but that is a conseq... | {"extraction_info": {"found_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://mathhelpforum.com/calculus/69854-converting-parametric-equations-into-cartesian-form.html | # Thread:
1. ## converting parametric equations into cartesian form
show that x = sin t and y = sin (t + pi/6)
can be written in the form y = ax + b√1-x^2 stating the values of a and b
im really stuck
2. Originally Posted by sharp357
show that x = sin t and y = sin (t + pi/6)
can be written in the form y = ax + 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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.aps.org/authors/kimitoshi_kono | # Kimitoshi Kono
Kimitoshi Kono is the Chief Scientist of the Low Temperature Physics Laboratory, RIKEN. He received his Doctor of Science degree from the Department of Physics, University of Tokyo in 1982. He was an associate professor at the Hyogo University of Teacher Education, Tsukuba University, and the ISSP at ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "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/tagged/mathematics | # Tagged Questions
DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com The mathematics tag covers non-applied pure mathematical disciplines that are traditionally not part of the mathematical 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": 24, "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/87633?sort=newest | ## construct the elliptic fibration of elliptic k3 surface
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Hi all,
As we know, every elliptic k3 surface admits an elliptic fibration over $P^1$, but generally how do we construct this fibration? For example, ho... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 42, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/42981?sort=newest | ## Partial word orders on groups
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This is a followup question related to this question. Recall that a left-invariant partial order on a finitely generated group $G$ is called a partial word order if for every $a\l... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/7156/pricing-in-hjm-framework/7161 | # Pricing in HJM framework
As mentioned in earlier question, I am a math student, who attained a course in interest rate theory. However I have some question how these things actually work in reality.
So assume we are working with Heath-Jarrow-Morton (HJM) framework. We assume that the forward curve is given by $$f(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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/16622-help-finding-roots.html | # Thread:
1. ## Help finding roots
Hi, I need to solve for x in the following two equations:
(x-1/x)^2 - 77/12 (x-1/x) + 10 = 0
[I expanded out to get (x^2 + 1/x^2 - 77x/12 + 77/12x + 8). Then I used the factor theorem to plug in possible x's, and found that (x-4) is a factor. However, I don't know where to go from... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showpost.php?p=3785236&postcount=10 | View Single Post
Recognitions:
Gold Member
Quote by elfmotat When solving this equation, he found that EM waves travel at a speed given by: $v=\frac{1}{\sqrt{\mu_0 \epsilon _0}}$ , where μ0 and ε0 are the magnetic and electric constants.
Correct me if I'm wrong, but as I understand it, μ0 and ε0 are ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?p=4238089 | Physics Forums
## Question about SO(N) group generators
Hi all. I have a question about the properties of the generators of the SO(N) group.
What kind of commutation relation they satisfy? Is it true that the generators λ are such that:
$$\lambda^T=-\lambda$$ ??
Thank you very much
PhysOrg.com science news on Phy... | {"extraction_info": {"found_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/154197/proof-alpha-1-alpha-2-in-a-triangle/154200 | # Proof: $\alpha_1>\alpha_2$ in a triangle
I have to proof in a triangle, that $\alpha_1>\alpha_2$ holds. The inner point P (from where I draw the smaller triangle) is set randomly.
Does anyone have a suggestion where I have to start?
Greetings
-
1
You're probabaly missing one piece of vital information: The rando... | {"extraction_info": {"found_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/174693/decomposition-of-l-in-a-subfield-of-a-cyclotomic-number-field-of-an-odd-prime | # Decomposition of $l$ in a subfield of a cyclotomic number field of an odd prime order $l$
Let $l$ be an odd prime number and $\zeta$ be a primitive $l$-th root of unity in $\mathbb{C}$. Let $K = \mathbb{Q}(\zeta)$. Let $A$ be the ring of algebraic integers in $K$. Let $G$ be the Galois group of $\mathbb{Q}(\zeta)/\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": 43, "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/54452/is-momentum-still-conserved-in-non-phase-matched-nonlinear-optical-processes | # Is momentum still conserved in non-phase-matched nonlinear optical processes?
To be efficient, a phase-matching condition has to be fulfilled in many nonlinear optical processes. For instance, the phase-matching requirement for second-harmonic generation is
$k_{2\omega}=2k_{\omega}$ or $\Delta k = k_{2\omega}-2k_{\... | {"extraction_info": {"found_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://mathoverflow.net/questions/61999/iteration-of-a-nonlinear-map | ## Iteration of a nonlinear map
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Let $T\colon R^n\to R^n$ be a linear map. If we want to study the behavior of $T^kx$ for some $x\in R^n$ as integer $k$ grows, we usually look at the eigen structure of $T$.
Now l... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 37, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/32938/surfaces-in-mathbbp3-with-isolated-singularities/33238 | ## Surfaces in $\mathbb{P}^3$ with isolated singularities
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It is classically known that every smooth, complex, projective surface $S$ is birational to a surface $S' \subset \mathbb{P}^3$ having only ordinary singu... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 75, "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/83419?sort=oldest | ## What is a canonical set of representatives in $GL(n,F)$ for the vertices in the Bruhat Tits building?
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$F$ is a non archimedean field here. To be more precise, I would actually prefer a set of representative 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": 41, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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