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http://physics.stackexchange.com/questions/20432/gauss-law-changes-in-the-magnitude-of-e-field-inside-the-closed-surface | # Gauss' law - changes in the magnitude of E field inside the closed surface
Gauss's law says that the flux through a closed surface which contains neither a sink nor a source will be zero.
It's quite clear that all field lines will have to exit somehow, but the strength of the E-field is also proportional to the inv... | {"extraction_info": {"found_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/differential-equations/202799-frobenius-equation-w-second-order-root.html | # Thread:
1. ## Frobenius equation w/ second-order root
I am given this: $y'' + \frac{2}{x}y' + y = 0$
Using Frobenius' Theorem, I was able to get the equation into this: $r(r+1)a_{0} + (r+1)(r+2)a_{1} + \sum\limits_{k = 1}^\infty[(k+r+3)(k+r+2)a_{k+2} + a_{k} = 0$
Obviously, for the $a_{0}$ term, I have to find th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://gambasdoc.org/help/comp/gb.opengl/gl/copypixels?pt_BR&v3 | 2.0 3.0 > comp > gb.opengl > gl > copypixels
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Gl.CopyPixels (gb.opengl)
`Static Sub CopyPixels ( X As Integer, Y As Integer, Width As Integer, Height As Integer, Buffer... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 30, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/97992/lie-algebras-and-integral-curves?answertab=active | # Lie algebras and integral curves
I am trying to understand the proof of the following which comes from "Matrix Groups for Undergraduates" by Kristopher Tapp.
Let $G \subset GL_n(\mathbb K)$ be a matrix group with Lie algebra $\mathfrak g \subset gl_n(\mathbb K)$. Then for all $X \in \mathfrak g$, $e^X \in G$.
It 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": 63, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://divisbyzero.com/2011/10/28/applet-to-illustrate-the-epsilon-delta-definition-of-limit/ | # Division by Zero
A blog about math, puzzles, teaching, and academic technology
Posted by: Dave Richeson | October 28, 2011
## Applet to illustrate the epsilon-delta definition of limit
Here’s a GeoGebra applet that I made for my Real Analysis class. It can be used to explore the definition of limit:
Definition. T... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 9, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/tagged/optics?page=2&sort=newest&pagesize=50 | # Tagged Questions
Optics is the study of light, and its interaction with matter. It includes topics such as imaging systems, fiber optics, lasers, quantum optics, and more.
2answers
43 views
### How do you calculate heat flux (Kw/m2) at the focal point of a mirror? [duplicate]
can anyone help me to determine the h... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/business-math/196442-college-savings-plan.html | # Thread:
1. ## College Savings Plan
Hey Guys,
I am trying to figure out this problem dealing with a college savings plan for my kids.
Its currently September.....my kids are 14,13, and twins at 11. They are all planning on going to college in September of the year they turn 18. We estimate that tuition will cost 56... | {"extraction_info": {"found_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://crypto.stackexchange.com/questions/2434/question-about-hash-collisions?answertab=oldest | # Question about hash collisions
If we have a hash function $h(x)$ and then a hash function $H(X) = h(h(X_0) || h(X_1))$ where $X_0$ is the first half of $X$, $X_1$ is the second half of $X$ and $||$ is concatenation. Then assuming we can easily find a collision for $H$, then it would be easy to find a collision 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": 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/4582/upper-bound-on-the-area-of-a-midpoint-pentagon/5668 | ## Upper bound on the area of a midpoint pentagon?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Starting with a convex pentagon P, we define the "middle polygon" Q, whose vertices are the middle points of the sides of the initial pentagon. The ratio between... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 46, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://vec3.ca/gjk/ | From the artist, to your screen; this is everything between.
# GJK
By request, an accessible explanation of the GJK (that’s short for Gilbert-Johnson-Keerthi) intersection algorithm. I’ll note in advance for the uninitiated – this algorithm only works for convex objects. Arbitrary convex objects, yes, but they must 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": 53, "mathjax_display_tex": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/trigonometry/84212-trig-id.html | # Thread:
1. ## trig id
Hey all, I was wondering if someone can walk me through this one:
[cot^2(B) - cos^2(B)]/[csc^2(B) -1]
My solution is as follows:
[cot^2(B)/-sec^2(B)] - cos^2(B)/-sec^2(B)
-cos^4(B)/sin^2(B) +1
and now i am a bit stuck. the correct answer is cos^2(B). Can someone please finish this off or t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/200853/does-apparent-retrograde-motion-of-planets-begin-and-end-at-quadrature?answertab=votes | # Does apparent retrograde motion of planets begin and end at quadrature?
I've read it several places that the apparent retrograde motion of planets (during which they seem, as viewed from Earth, to move in the opposite sense of their normal "direct" orbital motion against background stars at infinite distance) occurs... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 20, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://polymathprojects.org/2012/06/09/polymath7-discussion-thread/?like=1&_wpnonce=e3a0b2f395 | # The polymath blog
## June 9, 2012
### Polymath7 discussion thread
Filed under: discussion,hot spots — Terence Tao @ 5:50 am
The “Hot spots conjecture” proposal has taken off, with 42 comments as of this time of writing. As such, it is time to take the proposal to the next level, by starting a discussion thread (... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 133, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/differential-geometry/81631-prove-set-real-numbers-not-countable-set-print.html | # prove that the set of real numbers is not a countable set
Printable View
• March 31st 2009, 08:05 AM
rosebud
prove that the set of real numbers is not a countable set
1. Prove that R is equivalent to (0,1) and (0,1) is equivalent to [0,1]. Conclude that R is equivalent to R. Now prove that [0,1] is uncountable. Con... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-statistics/3160-auditory-signal.html | # Thread:
1. ## auditory signal
The ability to recognize an auditory "signal" presented against a background of auditory "noise" is important to a particular job. A company tests for this ability by presenting 100 trials of auditory noise. During each trial the subject must state whether or not a signal has also been... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.cfd-online.com/W/index.php?title=Turbulence_length_scale&diff=9084&oldid=9083 | [Sponsors]
Home > Wiki > Turbulence length scale
# Turbulence length scale
### From CFD-Wiki
(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": 6, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-statistics/143776-normal-equations.html | # Thread:
1. ## normal equations
Hi, for this model,
$y_{ijkl} = \mu + T_i + B_j + S_k + TB_{ij} + e_{ijkl},$ $i = 1,2,3; j = 1..3; k = 1..2; l=1..5$
am i supposed to have 1 + 3 + 3 + 2 + 5 = 14 normal equations?
or am i just meant to have 1 + 3 + 3 + 2 = 9 normal equations?
2. I use matrices
$\hat\beta=\left(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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/65378-inequality-prime-counting-function-print.html | # Inequality with the prime-counting function
Printable View
• December 17th 2008, 09:13 AM
HTale
Inequality with the prime-counting function
Hi there guys, I hope I've posted this in the right section;
I'm going through a paper, and there is one statement which is:
$n^{\pi(n)} < 3^n$
for sufficiently large $n$, 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": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/43958/cyclic-groups-whose-every-non-identity-member-is-a-generator | # Cyclic groups whose every non-identity member is a generator
Let G be a cyclic group. There's a theorem which states that if |G| is a prime, then every non-identity member of G is a generator.
What about a cyclic group whose order is not prime: Is there such a group whose every non-identity member is a generator?
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/1577/is-it-possible-to-create-an-easy-to-use-encryption-decryption-method-that-will-n?answertab=votes | # Is it possible to create an easy to use encryption/decryption method that will never be comprimised?
In the comments of the question "Why programming languages don't provide simple encryption methods?" the following statement was made:
A well thought out, tested and understood standard that has undergone extensive ... | {"extraction_info": {"found_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-statistics/80586-funtion-3-uniform-continuous-random-variables.html | # Thread:
1. ## A Funtion of 3 uniform, continuous random variables
The question is:
Given X,Y,Z are uniformly distributed on (0,1), and are independant, prove that (XY)^Z is also uniform on (0,1)
I know the PDF of XY. My main question is, how do I work out the PDF of W^Z, where W has pdf -ln(t) and Z has pdf of 1?... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/236046/is-every-above-the-second-level-of-the-arithmetical-hierarchy-independent-of-p/236065 | # Is every φ above the second level of the arithmetical hierarchy independent of PA?
If I am not wrong, every $\Sigma_n$ (or $\Pi_n$ ) statement $\phi$ is equivalent to a statement that says that a given Turing machine halts (or doesn't halt) on input $C$ using a $\Sigma_{n-1}$-oracle. Then, because we do not have ora... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://medlibrary.org/medwiki/Boiling_point | Boiling point
Welcome to MedLibrary.org. For best results, we recommend beginning with the navigation links at the top of the page, which can guide you through our collection of over 14,000 medication labels and package inserts. For additional information on other topics which are not covered by our database of medica... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 7, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/133891/kernel-of-a-homomorphism-from-a-free-group-into-mathbbz | # Kernel of a homomorphism from a free group into $\mathbb{Z}$.
Let $F$ be a non-abelian free group, that is, a free group of rank at least $2$, and let $\phi: F \rightarrow \mathbb{Z}$ be a nontrivial group homomorphism. How to prove that the kernel of $\phi$ is not finitely generated?
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## 3 Answers
This follows ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 54, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/116734/publishing-a-bad-paper/117769 | ## Publishing a bad paper?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
First, I apologize if mathoverflow is a bad fit for this question, but it is the only place where I can think to get advice from professionals given my circumstance. I'm also sorry abou... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/190237/does-the-identity-principle-hold-on-meromorphic-functions | # Does the identity principle hold on meromorphic functions?
Does the identity principle hold for meromorphic functions? (The identity principle states that if $Q$ is a connected set and $f(z)= g(z)$ for all $z$ in some subset $A$ of $Q$ which has limit points in $Q$, then $f(z) = g(z)$ for all $z$ in $Q$)
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Use 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": 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/13016/generic-fiber-of-morphism-between-non-singular-curves/13037 | ## Generic fiber of morphism between non-singular curves
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
This is prop 2.6b on p.28 of Silverman's the Arithmetic of Elliptic curves.
It says that let $\phi: C_1 \rightarrow C_2$ be a non-constant map of projecti... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 105, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/geometry/107302-problems-cubes.html | # Thread:
1. i have an additional problems which i also have difficulty solving with
3. Find the distance in inches between two vertices of a cube that are farthest from each other if an edge measures 10 inches
4. If an edge of a cube is increased by 33%, by how much is the total surfaced area increased?
2. Origina... | {"extraction_info": {"found_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/58567/spectral-gap-of-a-product-of-markov-processes | ## Spectral gap of a product of Markov processes
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
For `$m \in [N] \equiv \{1,\dots, N\}$`, let $Q^{(m)}$ be the generator of a (well-behaved) continuous-time Markov process on a finite state space $[n_m]$. Write $... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.citizendia.org/Harmonic_mean | In mathematics, the harmonic mean (formerly sometimes called the subcontrary mean) is one of several kinds of average. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and In Mathematics, an average, or central tendency of a Data set refers to a measu... | {"extraction_info": {"found_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": 8, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/5591/why-do-people-use-p-values/5592 | Why do people use p-values?
Roughly speaking a p-value gives a probability of the observed outcome of an experiment given the hypothesis (model). Having this probability (p-value) we want to judge our hypothesis (how likely it is). But wouldn't it be more natural to calculate the probability of the hypothesis given 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": 55, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/264544/how-to-find-number-of-prime-numbers-up-to-to-n | # How to find number of prime numbers up to to N?
Is there any way or function to find out the number of primes numbers up to any number? (Say $10^7$ or $10^{30}$ or $200$ or $300$?)
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I really do not understand your question. Please rephrase it and give an example of what you want? From what I understand, you are 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": 32, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/6932/learning-class-field-theory-local-or-global-first/6956 | ## Learning Class Field Theory: Local or Global First?
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I've noticed that there seem to be two approaches to learning class field theory. The first is to first learn about local fields and local class field 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": 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/32676/transcendental-galois-theory | # Transcendental Galois Theory
Is there a good reference on transcendental Galois Theory?
More precisely, if $K/k$ admits a separating transcendence basis (or maybe if it is a separably generated extension) it seems to me that many of the usual theorems of Galois theory go through. Moreover, the group $\text{Aut}(K/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": 33, "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/11343?sort=oldest | ## algorithm for calculating the Chow groups of a variety over a finite field
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Is there an algorithm for calculating the Chow groups of a variety over a finite field?
It is know that $H^{2i,i}_\mathrm{mot}(X,\mat... | {"extraction_info": {"found_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://math.stackexchange.com/questions/292806/the-measure-of-one-angle-of-an-octagon-is-twice-that-of-the-other-seven-angles | # The measure of one angle of an octagon is twice that of the other seven angles. What is the measure of each angle?
Help would be greatly appreciated.
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1
– Parth Feb 2 at 14:48
2
It is up to you what you accept, however, my post is not really an answer. It is a comment that can't be posted as a comment. Clayton 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": 7, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2010/11/08/the-character-table-of-s4/?like=1&source=post_flair&_wpnonce=a082172354 | The Unapologetic Mathematician
The Character Table of S4
Let’s use our inner tensor products to fill in the character table of $S_4$. We start by listing out the conjugacy classes along with their sizes:
$\displaystyle\begin{array}{cc}e&1\\(1\,2)&6\\(1\,2)(3\,4)&3\\(1\,2\,3)&8\\(1\,2\,3\,4)&6\end{array}$
Now we hav... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 25, "mimetex.cgi": 0, "/images/ma... |
http://www.purplemath.com/learning/viewtopic.php?f=15&t=2327&p=6763 | # The Purplemath Forums
Helping students gain understanding and self-confidence in algebra.
## Discrete Math Logic Problems
Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.
2 posts • Page 1 of 1
### Discrete Math Logic Problems
by toogood4007 on Wed 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": 0, "wp_latex": 0, "mimetex.cgi": 11, "/images/ma... |
http://mathoverflow.net/questions/7666?sort=votes | ## Lax Functors and Equivalence of Bicategories?
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Lax functors of bicategories were introduced at the very inception of bicategories, and I'm trying to get a better feel for them. They are the same as ordinary 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": 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/294156/is-a-finite-dimensional-vector-space-always-countable | # Is a finite dimensional vector space always countable?
Given a vector space of finite dimension, can we always find an injective map to the natural numbers?
z.
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5
$\Bbb R$ is a one-dimensional vector space over $\Bbb R$. – Brian M. Scott Feb 4 at 1:53
@BrianM.Scott, is this true in ZF+AD? – alancalvitti Feb 4 at... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/118315/infinitely-many-units-in-mathbbz-sqrtd-for-any-d1/118567 | # infinitely many units in $\mathbb{Z}[\sqrt{d}]$ for any $d>1$.
I am working through Neukirch's Algebraic Number Theory on my own. Exercise 6 in Section 1 (page 5) is to show that the ring $\mathbb{Z}[\sqrt{d}]$, for any squarefree rational integer $d>1$, has infinitely many units.
I know that in $\mathbb{Z}[\sqrt 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": 92, "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/65463/hausdorff-dimension-for-invariant-measure/65473 | Hausdorff dimension for invariant measure?
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A fractal set has a Hausdorff dimension. In some cases, we may generate a fractal by iterating $f,$ and let the fractal be the set of starting points $x$ such that $|f^{\cir... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 62, "mathjax_display_tex": 6, "mathjax_asciimath": 3, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://asmeurersympy.wordpress.com/2011/05/ | # Aaron Meurer's SymPy Blog
My blog on my work on SymPy and other fun stuff.
## Update for the Beginning of the Summer
May 26, 2011
So the Google Summer of Code coding period officially started on Monday, and in solidarity with the students, I will be blogging once a week about various things. Some of the posts wil... | {"extraction_info": {"found_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/122465/strongly-complete-profinite-groups | ## Strongly Complete Profinite Groups.
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I've been reading about profinite groups and have encountered the notion of strong completeness. I.e. that a profinite group $G$ is strongly complete if it is isomorphic to ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "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/System_of_linear_equations | # System of linear equations
A linear system in three variables determines a collection of planes. The intersection point is the solution.
In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables. For example,
$\begin{alignat}{7} 3x &&\; ... | {"extraction_info": {"found_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": 53, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/13282/good-algebraic-number-theory-books/13315 | ## Good Algebraic Number Theory Books
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I have just finished a master's degree in Mathematics and want to learn everything possible about algebraic number fields and especially applications to the generalized Pell ... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/53991/the-theory-of-strings-stretching-between-intersecting-d-branes?answertab=votes | The theory of strings stretching between intersecting D-branes
I am trying to understand various aspects of intersecting D-branes in terms of the gauge theories on the worldvolume of the D-branes. One thing I'd like to understand is the worldvolume action for strings stretching between the D-branes. One thing I have 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": 21, "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/19526?sort=newest | ## Reference request for a “well-known identity” in a paper of Shepp and Lloyd
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I ran into a "well-known identity" on page 345 of Shepp and Lloyd's On ordered cycle lengths in a random permutation: $$\int_x^{\inft... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/91188/intuition-for-graphing-sine-cosine/91234 | Intuition for graphing Sine/Cosine
So I'm working my way through some basic trig (Khan Academy) - I'm trying to get a better intuition for what graphs of sine and cosine represent.
I've seen the nice unit circle animations that do explain it fairly well.
But would it be fair to say that:
The period of the curve 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": 22, "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/98821?sort=oldest | ## How often do people read the work that they cite?
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I have the following question:
How likely it is that an author carefully read through a paper cited by him?
Not everyone reads through everything that they h... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "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/thermodynamics | # Tagged Questions
Covers the study of (mostly homogeneous) macroscopic systems from a heat/energy/entropy point of view. Maybe combine with [tag:statistical-mechanics].
learn more… | top users | synonyms
0answers
26 views
### Lattice model completely constrained by boundary data
I am dealing with a lattice model ... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/53957/frequency-of-light/53971 | # Frequency Of Light
I am confused on few topics...
What is meant by "Frequency of Light"? Does the Photon(s) vibrate, that is known as its frequency? If the Photons vibrate, then they have a specific frequency, then What is meant by "Higher frequency light" as used in Photo-electric Effect? In which directions/axis ... | {"extraction_info": {"found_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://gilkalai.wordpress.com/2009/03/13/extremal-combinatorics-on-permutations/?like=1&source=post_flair&_wpnonce=5092e672ce | Gil Kalai’s blog
## Extremal Combinatorics on Permutations
Posted on March 13, 2009 by
We talked about extremal problems for set systems: collections of subsets of an $n$ element sets, - Sperner’s theorem, the Erdos-Ko-Rado theorem, and quite a few more. (See here, here and here.) What happens when we consider colle... | {"extraction_info": {"found_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": 7, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/89118?sort=votes | ## Categorification and Schur functors
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Are Schur functors and categorification somehow related ?
If yes, probably looking on Schur functors (which I know) one can illustrate on this example why "categorification... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/169238/finding-height-of-a-triangle | # Finding Height of a Triangle
I am having problem with the following question:
From the triangle which is greater Area of the Triangle ABC or 27
Now how would I find the height of such a triangle.
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4
You do not need to. Note the height is less than 9. – David Mitra Jul 10 '12 at 22:39
## 2 Answers
From the inf... | {"extraction_info": {"found_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://crypto.stackexchange.com/questions/tagged/public-key?page=5&sort=newest&pagesize=15 | # Tagged Questions
Public key cryptography describes all cryptographic algorithms which have a pair of keys, one key that performs encryption and one key that performs decryption. One of these keys is made available publicly, allowing anyone to send messages that only the holder of the private key can read. You should... | {"extraction_info": {"found_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://math.stackexchange.com/questions/209547/how-do-i-differentiate-this-function-with-e-to-the-x-and-fraction | # How do i differentiate this function with e to the x and fraction?
I am lost on deriving this one function, because im kind of confused with the $9e^x$ and the fraction part. Maybe if someone can guide me through the steps that would be awesome.
$$y=9e^x+\frac{2}{\sqrt[3]{x}}$$
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Is this homework? – VF1 Oct 8 '12... | {"extraction_info": {"found_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": 11, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/217727/probability-of-a-map-being-surjective | # “Probability” of a map being surjective
What is the probability of randomly putting $n$ elements into $k$ boxes ($k\leq n$) such that there is no empty box?
I have two different ideas:
• I could use the principle of inclusions and exclusions with $A_i=\{\text{box$i$is empty}\}$: \begin{align}P(\text{no empty boxes... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 28, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://terrytao.wordpress.com/2009/01/19/an-inverse-theorem-for-the-uniformity-seminorms-associated-with-the-action-of-finfty_p/ | What’s new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
# An inverse theorem for the uniformity seminorms associated with the action of F^infty_p
19 January, 2009 in math.DS, paper | Tags: characteristic factor, cocycles, finite fields, Gow... | {"extraction_info": {"found_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": 148, "mimetex.cgi": 0, "/images/m... |
http://conservapedia.com/Triangle | # Triangle
### From Conservapedia
A triangle is a three-sided geometric shape. In Euclidean geometry, each side of a triangle is perfectly straight, and the sum of the internal angles of a triangle is always 180º. A triangle is defined by any three points that are not collinear.
## Naming conventions
Usually, the v... | {"extraction_info": {"found_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": 6, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/76629/domain-of-holomorphy/76632 | ## Domain of Holomorphy
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I found the following definition of domain of holomorphy in several places.
Def1: A connected open set $\Omega$ in the n-dimensional complex space ${\mathbb{C}}^n$ is called a domain of h... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 50, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/85845-radius-convergence-endpoints.html | # Thread:
1. ## Radius of convergence / endpoints
I am really having trouble with this problem. The n'th term is given in the problem,
(a) Determine the radius of convergence of the series.
(b) What are the endpoints of the interval of convergence?
left endpoint = x =
right endpoint = x =
Does the series converge at... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/115441-clarification-quotient-rule-print.html | # Clarification on the Quotient Rule
Printable View
• November 18th 2009, 02:17 PM
NBrunk
Clarification on the Quotient Rule
Hello, and thanks for your help in advance.
I recently learned the quotient rule in finding the derivative of more complicated expressions and had a question on it.
The way we've been taught ... | {"extraction_info": {"found_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://mathdl.maa.org/mathDL/23/?pa=content&sa=viewDocument&nodeId=3287&bodyId=3541 | Search
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# Visualizing Lie Subalgebras using Root and Weight Diagrams
by Aaron Wangberg (Winona State Univ.) and Tevian Dray (Oregon State Univ.)
### 2.3 Weights and Weight Diagrams
An algebra $$g$$ can also be re... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 81, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/227470/compute-sum-i-j-1-infty-frac-1iji2j2 | # Compute $\sum_{i,j=1}^{\infty} \frac{(-1)^{i+j}}{i^2+j^2}$
Compute
$$\sum_{i,j=1}^{\infty} \frac{(-1)^{i+j}}{i^2+j^2}$$
-
6
I don't think it converges absolutely, which means you have to say something about the order in which the terms are taken. – Gerry Myerson Nov 2 '12 at 11:30
## 1 Answer
Let us compute $$\... | {"extraction_info": {"found_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": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://crypto.stackexchange.com/questions/1116/threshold-secret-sharing-how-to-create-a-shared-secret-from-pre-existing-secre/1118 | # Threshold Secret sharing - How to create a shared secret from pre existing secret parts?
In usual $(t, n)$ secret sharing schemes, a secret $S$ is split into $n$ parts so that any $t$ out of $n$ parts reconstruct the original secret. So, suppose that there is a group of $n$ participants each one has a secret $x_i$ (... | {"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": 94, "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/34878/x-not-simply-connected-and-x-x-contractible/34932 | ## X not simply connected and X-x contractible
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Hello,
I was wondering if there is a nice counterexample to the following question.
Suppose $X$ is a CW-complex which is not simply connected and there is a point ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 45, "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/218116/definition-of-quotient-space/218164 | # Definition of quotient space
Let $W \subset V$ be vector spaces. I don't understand the quotient space $V/W$. I read the Wikipedia and searched this site.
I would have thought: say the vector space operation is $+$. let $Q = V/W$. Then $V = W+Q$ by "multiplying across". So $Q$ contains elements of the form $V + (-1... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Chinese_remainder_theorem | # Chinese remainder theorem
The Chinese Remainder Theorem is a result about congruences in number theory and its generalizations in abstract algebra. It was first published in the 3rd to 5th centuries by Chinese mathematician Sun Tzu.
In its basic form, the Chinese remainder theorem will determine a number n that whe... | {"extraction_info": {"found_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": 167, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/15178/what-is-the-highest-accuracy-of-measuring-time-differences-achievable-today | # What is the highest accuracy of measuring time differences achievable today?
I was wondering if it would be possible to shorten the distance between detectors when measuring the speed of neutrinos to, say, 7m rather than the current ~700km? In this way the distance traveled would be known directly. Something similar... | {"extraction_info": {"found_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/199988/existence-of-a-specific-refinement-of-an-open-cover-on-a-manifold | # Existence of a specific refinement of an open cover on a manifold
I've encountered a homework question I don't know how to solve, and most people I asked even tend to go so far as to say that the main statement in the question is false. I'm not really convinced of the latter (the question is from Warner's Foundation... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/42329/replacement-and-sets-of-natural-numbers/42372 | ## Replacement and Sets of Natural Numbers
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It's clear that the axiom of replacement can be used to construct very large sets, such as $$\bigcup_{i=0}^\infty P^i N,$$ where $N$ is the natural numbers. I assume 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": 49, "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/6276/obtaining-a-key-thats-using-ice-algorithm?answertab=votes | # Obtaining a key that's using ice algorithm
I have a text file that has been processed by the SNOW steganography tool that uses ICE encryption. However, I do not know the key that would enable me to decrypt and retrieve the message hidden.
What tools are available, that are proven to have worked that would help me 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": 4, "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/Stochastic_calculus | # Stochastic calculus
Calculus
Definitions
Concepts
Rules and identities
Integral calculus
Definitions
Integration by
Formalisms
Definitions
Specialized calculi
• Fractional
• Stochastic
• Calculus of variations
Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consiste... | {"extraction_info": {"found_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://en.wikibooks.org/wiki/Calculus/Finite_Limits | Calculus/Finite Limits
| | | |
|------------------------------------|----------|-------------------|
| ← Limits/An Introduction to Limits | Calculus | Infinite Limits → |
| Finite Limits | | |
Informal 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 58, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/240085/proving-a-is-invertible-if-a-a2-i/240112 | # Proving A is Invertible if $A + A^2 = I$
I'm trying to prove A is invertible by proving there is an $A'$, for $AA' = I$
So I got to this stage $A(I + A) = I$
Now I determine that $A' = I + A$,
and from that I get $AA' = I$, I wanted to know if this is valid, casue it doesn't seem to make sense,
and I can't find 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": 118, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/144885/counterexample-for-a-pullback-pushout-situation | # Counterexample for a pullback-pushout situation
Suppose you are in the category of sets or more generally in a topos (i.e. sheaf topos) and $f:A\rightarrow C$, $g:B\rightarrow C$ are two morphisms.
There is a canonical map $u:D\to C$ from $D$ (defined as the pushout of the diagram $A\leftarrow A\times_C B\rightarro... | {"extraction_info": {"found_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://ilaba.wordpress.com/category/mathematics/mathematics-general/page/2/ | # The Accidental Mathematician
Because "exact science is not always exact science."
## Sucking at everything else
9 08 2010
The June/July issue of the Notices of the AMS features an interview with Gioia De Cari, a former graduate student in mathematics who quit somewhere along the way, went on to become an actress ... | {"extraction_info": {"found_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://mathoverflow.net/questions/88750?sort=votes | ## functions satisfying “one-one iff onto”
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Hello Everybody.
I need some more examples for the following really interesting phenomenon:
```` A function from the class ... is one-one iff it is onto.
````
Some... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 77, "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/96246/is-this-the-notation-you-use?answertab=oldest | # Is this the notation you use?
I've noticed that my terminology is a bit haggard. I do math on my own so I'm not entirely sure how everyone else refers to things and so I need a check.
so is this correct: $\lim\limits_{\delta x \to 0}\frac{\delta y}{\delta x} = \frac{dy}{dx}$
Where say, $\delta y$ is the change 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": 29, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/192252-finding-value-make-two-graphs-tangent.html | # Thread:
1. ## Finding value to make two graphs tangent
Find a negative value of k so that the graph of y = x2 - 2x + 7 and the graph of y = kx + 5 are tangent?
It says the answer is -2-2sqt2
I graphed this and it didn't look tangent to me. Thanks.
2. ## Re: Finding value to make two graphs tangent
It does look ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/51171/list | ## Return to Question
2 deleted 6 characters in body
There are two questions here, an explicit one, and another (more vague) one that motivates it:
I am pretty certain the following should have a negative answer, but at the moment I'm not seeing how to argue about this and cannot locate an appropriate reference.
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": 46, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-statistics/182308-random-variable-convergence-print.html | # random variable convergence
Printable View
• June 3rd 2011, 08:25 AM
waytogo
random variable convergence
Hello,
question is about about one point in proposition saying that convergence of random variable almost surely implies convergence in probability.
A sequence $(X_n),n\in \mathbb{N}$ of random variables is 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/20334/numerical-integration-of-a-numeric-data-available-as-a-nested-list/20343 | # Numerical integration of a numeric data available as a nested list
I have some numerical data in the form of a list with the following structure: {...{x,y,z},...} defining a surface z=z(x,y) in a 3D space (x,y,z). The data came from a simulation, and I am post-processing it within Mathematica. The precise numbers en... | {"extraction_info": {"found_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://nrich.maths.org/2047 | ### Golden Powers
You add 1 to the golden ratio to get its square. How do you find higher powers?
### 2^n -n Numbers
Yatir from Israel wrote this article on numbers that can be written as $2^n-n$ where n is a positive integer.
### And So on - and on -and On
Can you find the value of this function involving algebra... | {"extraction_info": {"found_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://mathoverflow.net/questions/10370/upper-bound-for-number-of-k-term-arithmetic-progressions-in-the-primes | ## Upper bound for number of k-term arithmetic progressions in the primes
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Normal heuristics give that number of k-term arithmetic progressions in [1,N] should be about
`\[c_k\frac{N^2}{\log^kN}\]`
for some cons... | {"extraction_info": {"found_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/calculus/30309-help-required.html | # Thread:
1. ## Help required...
Q. $(2x + y)dy - (4x +2y -1)dy = 0$
After using $Z = 2x +y$, I got the answer,
$c = 2y -ln(2x + y)$
However, its very different from the answer at the back of the book. I have checked and rechecked but ended up with the same wrong answer.
2. Originally Posted by Altair
Q. $(2x + 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": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/299071/question-about-relation-on-rational-numbers | # Question about relation on rational numbers
Define the relation on $\mathbb{Q}$ by $$[m,n]<[j,k]$$ if and only if $jn-mk$ belongs to $\mathbb{N}$, $j$ and $m$ belong to $\mathbb{Z}$, $n$ and $k$ belong to $\mathbb{N}$.
(a) Show that $<$ is well defined, that is if $(m,n)\sim (m',n')$ and $(j,k)\sim(j',k')$, then $j... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://wiki.chemprime.chemeddl.org/index.php/CoreChem:Effect_of_Adding_a_Reactant_or_Product | CoreChem:Effect of Adding a Reactant or Product - ChemPRIME
# CoreChem:Effect of Adding a Reactant or Product
### From ChemPRIME
If we have a system which is already in equilibrium, addition of an extra amount of one of the reactants or one of the products throws the system out of equilibrium. Either the forward or ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 7, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/1743/what-is-the-constant-of-the-coppersmith-winograd-matrix-multiplication-algorithm/1747 | ## What is the constant of the Coppersmith-Winograd matrix multiplication algorithm
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Or at least it's order of magnitude.
I've only ever heard it described as "huge", and a google search turned up nothing.
Also,... | {"extraction_info": {"found_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.stackexchange.com/users/20032/markovchain?tab=activity | # markovchain
reputation
8
bio
website
location
age
member for 3 months
seen Apr 11 at 2:43
profile views 28
| | | bio | visits | | |
|----------|----------------|---------|----------|----------------|----------|
| | 365 reputation | websit... | {"extraction_info": {"found_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://math.stackexchange.com/questions/202867/intersection-of-a-unit-sphere-of-a-given-norm-in-finite-dimension-with-an-hyperp/202902 | # Intersection of a unit sphere of a given norm in finite dimension with an hyperplane.
Let $\|\cdot\|$ be a norm on $\mathbb{R}^n$. Let $C:=\{x\in\mathbb{R}^n\,:\,\|x\| \leq 1\}$, that is to say let $C$ be a convex compact symmetric set of non empty interior. Let $H$ be a linear subspace of $\mathbb{R}^n$ of dimensio... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 111, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/calculus/87028-limits-abs-function.html | # Thread:
1. ## Limits Of An abs function
I was told to use algrebaic manpulation to find the limit for
lim --> 4
$\frac{2|{x-4}|}{x-4}$
2. you get 2 if you approach from the right and you get -2 if you appoach from the left.
Hence there is no limit.
${|u|\over u}=1$ if u>0 and ${|u|\over u}=-1$ if u<0.
Hence th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://cheaptalk.org/2011/04/18/maximizing-consumer-surplus-part-ii-compromising/ | Cheap Talk
A blog about economics, politics and the random interests of forty-something professors
# Maximizing Consumer Surplus Part II: Compromising
April 18, 2011 in Uncategorized | Tags: economics, food and wine, incentives, vapor mill
Restaurants, touring musicians, and sports franchises are not out to gouge 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": 0, "wp_latex": 24, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/18464/what-are-the-correct-axioms-for-a-weakly-associative-monoidal-functor/18546 | ## Definitions and the main question
Recall that a category $\mathcal C$ is monoidal if it is equipped with the following data (two functors, three natural transformations, and some properties):
• a functor $\otimes: \mathcal C \times \mathcal C \to \mathcal C$,
• a functor $1: \{\text{pt}\} \to \mathcal C$,
• a natu... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 151, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/3150/is-there-a-t-dual-of-wittens-twistor-topological-string-theory | # Is there a T-dual of Witten's twistor topological string theory?
In late 2003, Edward Witten released a paper that revived the interest in Roger Penrose's twistors among particle physicists. The scattering amplitudes of gluons in $N=4$ gauge theory in four dimensions were expressed in a simple way using the twistor ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 21, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physicspages.com/2011/04/10/time-dilation/ | Notes on topics in science
## Time dilation
Required math: algebra, geometry
Required physics: basics of relativity
We saw in an earlier post that the events with a particular interval ${\Delta s^{2}}$ between them lie on an invariant hyperbola, and that this hyperbola can be used to calibrate the time or space 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 127, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/63969/what-is-an-explicit-example-of-a-variety-x-which-is-finite-over-spec-f-p-but-whic/64026 | ## What is an explicit example of a variety X which is finite over Spec F_p but which does not lift to a scheme Y which is finite and flat over Spec Z_p?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
What is an explicit example of a variety X which is 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": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/27041/linearizing-quantum-operators | # Linearizing Quantum Operators [duplicate]
Possible Duplicate:
Linearizing Quantum Operators
I was reading an article on harmonic generation and came across the following way of decomposing the photon field operator. $$\hat{A}={\langle}\hat{A}{\rangle}I+ \Delta\hat{a}$$
The right hand side is a sum of the "mean" va... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "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/281759/does-multiplicative-version-of-azumas-inequality-hold | # Does Multiplicative Version of Azuma's Inequality Hold?
We know that there are multiplicative version concentration inequalities for sums of independent random variables. For example, the following multiplicative version Chernoff bound.
Chernoff bound:
Let $X_1,\ldots,X_n$ be independent random variables and $X_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": 22, "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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