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http://www.physicsforums.com/showthread.php?t=12999 | Physics Forums
## The distributive law
Is there any way to prove the distributive law for integers? I heard that there is yet I don't understand how being that the distributive law is an axiom and therefore what the understanding our number system is based on.
PhysOrg.com science news on PhysOrg.com >> Front-row 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": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?p=4254610 | Physics Forums
Reactive power with electromagnetic sources in free space
Good morning,
in circuit theory I know that reacting power arise from phasors and represents a power which can't be used, because not delivered to any load, but continuously flows back and forth between the load and the generator with a zero 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": 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/74545?sort=newest | ## Approximation to the ratio of a Gaussian CDF to PDF
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Johnstone and Silverman (2005) claimed that for large x
$\frac{1-\Phi(x)}{\phi(x)} \approx \frac{1}{x}$
where $\Phi(x)$ and $\phi(x)$ are the CDF and PDF 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": 14, "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/71188?sort=newest | Probabilistic (and other mathematical) methods of physics without the physics?
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Many of the methods of physics are vastly more general than their use in that discipline. For example, information theory overlaps with 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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/105012/if-one-sequence-is-convergent-so-is-the-other-one | # if one sequence is convergent, so is the other one [duplicate]
Possible Duplicate:
If $\sum a_n b_n <\infty$ for all $(b_n)\in \ell^2$ then $(a_n) \in \ell^2$
I have a question, can anyone help me?
Let $\{ a_i\} _{i=1} ^ { + \infty }$ be a sequence of positive real numbers such that for every sequence $\{ b_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": 24, "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/48779/computing-an-integral-where-the-poles-of-the-integrand-are-the-roots-of-unity | # Computing an integral where the poles of the integrand are the roots of unity
I am trying to compute the following integral: $$\int_0^{2\pi} \frac{y}{y^n-1} dy$$
I've tried to decompose $y^n-1$ into $(y-1)(y-e^{i\theta})(y-e^{i2\theta})...(y-e^{i(n-1)\theta})$ but I don't know what to do with this factorization. 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": 30, "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/65068?sort=votes | ## Why is the base manifold of a Lie groupoid required to be second-countable?
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I wonder why one requires that the base manifold of a Lie groupoid is second-countable?
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1
Isn't second-countability in the defini... | {"extraction_info": {"found_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://math.stackexchange.com/questions/182198/given-a-banach-algebra-a-and-elements-x-y-in-a-if-x-and-xy-are-inverti | # Given a Banach Algebra $A$ and elements $x,y \in A$. If $x$ and $xy$ are invertible, then so is $y$.
A silly question, but I don't see the answer. This question is from Rudin's Functional Analysis, Chapter 10, Exercise 1a).
It's obvious that $y$ has a left inverse as $((xy)^{-1}x)y=e$, where $e$ is the unit of the ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "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/118136/serge-langs-remarks-on-the-superiority-of-algebra-what-it-actually-means?answertab=oldest | Serge Lang´s remarks on the superiority of algebra. What it actually means? [closed]
I read two comments of Lang that basically places algebra over other math subjects. One of this comments is on his calculus book preface (see Remark 1 below); I am not finding his other comment, but it was an interaction he had with 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": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/3618/can-maxwells-equations-be-derived-from-coulombs-law-and-special-relativity/3674 | # Can Maxwell's equations be derived from Coulomb's Law and Special Relativity?
As an exercise I sat down and derived the magnetic field produced by moving charges for a few contrived situations. I started out with Coulomb's Law and Special Relativity. For example, I derived the magnetic field produced by a current 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": 30, "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/7329/fair-game-and-dice?answertab=active | # Fair Game and Dice
Two players put a dollar in a pot. They decide to throw a pair of dice alternatively. The first one who throws a total of $5$ on both dice wins the pot. How much should the player who starts add to the pot to make this a fair game?
So my interpretation of this problem is that I first throw a dice... | {"extraction_info": {"found_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/150420/a-mouse-leaping-along-the-square-tile | # A mouse leaping along the square tile
A $n \times n$ square is made of square tiles of dimensions $1\times1$. A mouse can leap along the diagonal or along the side of square tiles. In how many ways can the mouse reach the right lower corner vertex of the square from the lower left corner vertex of the square leaping... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/81040/do-etale-neighhbourhoods-of-a-subvariety-descend-along-base-field-extensions-doe/81089 | ## Do etale neighhbourhoods of a subvariety descend along base field extensions; does normalization commute with etale base change?
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I have some questions such that the corresponding statements are well-known 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": 80, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/63382/list | Return to Answer
2 I added material in response to the questioner's comments.
A Killing field is preserved by the Ricci flow. By a theorem of Daskalopoulos, Hamilton and Sesum (arXiv:0902.1158), on a compact surface an ancient (defined for all negative time) solution to the Ricci flow which is not a shrinking soliton... | {"extraction_info": {"found_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://cms.math.ca/10.4153/CMB-2004-021-1 | Canadian Mathematical Society
www.cms.math.ca
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| Site map | | | CMS store | |
location: Publications → journals → CMB
Abstract view
# Countable Amenable Identity Excluding Groups
Read article
[PDF: ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 20, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/184125-help-points-circle.html | Thread:
1. help with points on a circle
If I know a coordinate of a point (red dot on image) of a circle with radius x and i want to rotate it y degrees to the right, how do I get the coordinate of the new point (blue dot on image) ?
thanks
Attached Thumbnails
2. Re: help with points on a circle
As you are seeking... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/34749/is-causality-the-equivalent-of-a-claim-that-the-future-is-predictable-based-on/34767 | # Is “Causality” the equivalent of a claim that the future is predictable based on the present and the past?
In classical (Newtonian) mechanics, every observer had the same past and the same future and if you had perfect knowledge about the current state of all particles in the universe, you could (theoretically) comp... | {"extraction_info": {"found_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/74724/unique-limits-of-sequences-plus-what-implies-hausdorff | ## Unique limits of sequences plus what implies Hausdorff?
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It is known that there are non-Hausdorff spaces which admit unique limits for all convergent sequence (see here) and it is also known that unique limits ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 35, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/34586/limiting-distribution-of-alternating-renewal-process | # Limiting distribution of alternating renewal process
Consider an alternating renewal system that can be in one of two states: on or off. Initially it is on and it remains on for a time $Z_1$, it then goes off and remains off for a time $Y_1$, it then goes on for a time $Z_2$, then off for a time $Y_2$ ; then on, and... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=3849658 | Physics Forums
## Residue Theorem integral application
1. The problem statement, all variables and given/known data
Compute the integral: ∫ x2/(x4-4x2+5)
2. Relevant equations
Uses Residue theorem.
3. The attempt at a solution
So I found the zeroes of x4-4x2+5 to be 2+i and 2-i, and therefore the one that is 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": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/144337/lebesgue-integrable | # Lebesgue Integrable
Prove that $f(x)=x$ is not Lebesgue integrable on $[1, \infty)$. (hint: use def. of Lebesgue integrability for positive functions).
hint: Use integral $= \infty$ by defining simple function and $\chi_A$ characteristic function.
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4
What have you tried? – Alex Becker May 12 '12 at 20:36
## 1 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": 6, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/discrete-math/187039-show-nonempty-finite-subset-r-has-max-min.html | # Thread:
1. ## Show a nonempty finite subset of R has a max and min
Show that a nonempty finite subset of the Real Numbers has both a maximum and minimum.
I know I can use induction to solve this but I seem to be having some problems getting started:
Let P(n) be assertion: a nonempty finite subset of R has a max 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": 50, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/1518/light-emission-spectrum-units?answertab=oldest | # Light emission spectrum units
Do someone knows the units of the spectra provided here ? It seems obvious enough that it's said nowhere, but even Wikipedia and other sites are quite blurry on this point.
So, is it power ($W$), radiance($\:\rm{W/m^2sr}$), or something else ?
Thanks !
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The README file provided wit... | {"extraction_info": {"found_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/algebra/108675-complex-numbers.html | # Thread:
1. ## Complex numbers
Show that $%5Cmid%20z-2i%5Cmid%20=%204-z$ can be represented by the cartesian equation $%5Cfrac%7Bx%5E2%7D%7B3%7D+%5Cfrac%7B%28y-1%29%5E2%7D%7B4%7D=1$
2. Originally Posted by usagi_killer
Show that $%5Cmid%20z-2i%5Cmid%20=%204-z$ can be represented by the cartesian equation $%5Cfrac%7... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/22323/unknown-isotope?answertab=oldest | # Unknown isotope
Problem description:
The most common isotope of a single nucleus stripped of its electrons is accelerated through a potential difference of 1225V and fired horizontally into a B-field directed perpendicularly into the page (flat page lying on desk). The nucleus is observed to travel in a circular pa... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-statistics/119645-poisson-process-r-2-a-print.html | # Poisson process on R^2
Printable View
• December 9th 2009, 05:05 PM
kingwinner
Poisson process on R^2
Consider a Poisson process of rate λ on R^2. Let N(r) be the number of points in a circle of radius r centered at the origin and Y2 be the distance from the origin to the 2nd closest point.
Calculate E(Y2) and E[Y2... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 22, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/13240?sort=votes | Do finite places of a number field also correspond to embeddings?
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Something that seems to be pretty standard in every introductory treatment is that the infinite places correspond to embeddings into $\mathbb{C}$. Do ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 102, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/calculus/151785-stationary-points-question.html | # Thread:
1. ## stationary points question
"find the stationary points of the following curves and determine whether the points are maxima, minima, or points of inflexion"
y= (x + 1)/ (x - 1)
I know how to these sorts of questions but for this example i find it tricky, I set it as:
y= (x + 1) (x - 1)^-1 but then d... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/240582/bernoulli-trials-with-two-random-variables-run-of-successes-and-faliures?answertab=votes | # Bernoulli Trials with two random variables - Run of successes and faliures
Consider a sequence of Bernoulli trials with probability of success $p$. Suppose you started the game with a run of succsses followed by the run of faliures (note that you can learn an unlucky run is over if and only if it is followed by a su... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/8132/phase-shifts-in-scattering-theory?answertab=active | # Phase shifts in scattering theory
I have been studying scattering theory in Sakurai's quantum mechanics. The phase shift in scattering theory has been a major conceptual and computational stumbling block for me.
How (if at all) does the phase shift relate to the scattering amplitude?
Also, any literature or book 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": 39, "mathjax_display_tex": 13, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/302132/thoughts-about-sectional-curvature | # Thoughts about sectional curvature
I'm currently trying to understand the sectional curvature of riemannian manifolds and I don't know if I'm thinking correctly.
So, say we have a riemannian manifold $(M,g)$ with constant sectional curvature $k$. As far as i know the curvature at any given point is completely deter... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/65185/are-textbfset-and-textbfab-distributive-categories/65186 | # Are $\textbf{Set}$ and $\textbf{Ab}$ distributive categories?
A quick one-line comment on wikipedia says that the category $\textbf{Set}$ is distributive, but does not offer proof. I think I intuitively see this, as the product of sets is just the cartesian product, and the coproduct is the disjoint union, and I bel... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/3700/explanation-for-e-8s-torsion/5306 | ## Explanation for E_8’s torsion
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To study the topology of Lie groups, you can decompose them into the simple compact ones, plus some additional steps, such as taking the cover if necessary. After that, the struct... | {"extraction_info": {"found_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://mathforum.org/mathimages/index.php/Russell's_Antinomy | Russell's Antinomy
From Math Images
The Set of All Sets Which Do Not Contain Themselves
Fields: Algebra, Number Theory, and Algebra
Created By: Peter Weck
Website: [ ]
The Set of All Sets Which Do Not Contain Themselves
The blob on the right represents the set of all sets which are not elements of themselves. At fi... | {"extraction_info": {"found_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": 14, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/248693/for-a-finite-group-g-and-field-k-of-char-p-if-p-p-are-projective-kg | # For a finite group $G$ and field $k$ of char$=p$, if $P,P'$ are projective $k[G]$-modules with $[P]=[P']$, is it true that $P=P'$?
That is -- is it true that if projective $k[G]$-modules have same composition factors then they are isomorphic?
This is easy to see for $\text{char}(k)=0$, or if $G$ is a composition 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": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/7780-z60.html | # Thread:
1. ## Z60
The ring Z60 is a field right?
So a list of all its ideals would be 0 and all the elements in Z60.
Is this correct?
And could someone just explain quickly what a homomorphic image is?
Thank you.
2. Originally Posted by Smitey42
The ring Z60 is a field right?
No, is it to a power of a prime? N... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/7713/predicting-decay-rates-via-the-standard-model | # Predicting Decay Rates via the Standard Model
Question 7584 illustrated a procedure to forecast the decay rates of isotopes with known long average lifetimes. Lifetimes of the many U isotopes vary from micoseconds to gigayears. F has only one stable isotope while Sn has 10. Can Standard Model principles be used to 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": 18, "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/tagged/descriptive-set-theory | ## Tagged Questions
0answers
109 views
### From universal measurability to measurability
Let $(\Omega,\Sigma)$ be a measurable space and $K$ be a compact metrizable space endowed with its Borel $\sigma$-algebra $\mathcal{B}(K)$. Let $A\subseteq\Omega\times K$ be …
1answer
325 views
### How long can it take to gener... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/27489/do-any-entanglement-measures-for-mixed-states-exist-that-use-only-single-site-co/27491 | Do any entanglement measures for mixed states exist that use only single site correlation functions?
For a pure state $\rho_{AB}$, the entropy of entanglement of subsystem $A$ is
\begin{equation} S( \rho_A) = -tr (\rho_A \log \rho_A) \end{equation}
where $\rho_A$ is the reduced density matrix of A.
For a single sit... | {"extraction_info": {"found_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://stats.stackexchange.com/questions/48024/likelihood-ratio-test-for-mle-markov-chain | # Likelihood ratio test for MLE (Markov Chain)
As suggested in Calculating log-likelihood for given MLE (Markov Chains) I want to perform a likelihood ratio test for two fitted models (i.e., first and second order markov chains). Simply comparing the resulting log-likelihood values is as suggested in the other 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": 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/102802/quasi-unipotent-monodromy-for-general-families | ## Quasi-unipotent monodromy for general families
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This must be a naive question, but I'm wondering about the definition of the quasi-unipotent monodromy for general (not only 1-parameter families). The problem is... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 26, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/187205-absolute-value-equations.html | # Thread:
1. ## Absolute Value Equations
How, when you are given an absolute value equation, solve it graphically on a real-number line?
2. ## Re: Absolute Value Equations
Originally Posted by Bashyboy
How, when you are given an absolute value equation, solve it graphically on a real-number line?
You should know 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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/33679/as-the-universe-expands-why-do-some-things-stretch-but-not-others/33684 | # As the universe expands, why do some things stretch but not others?
I got into watching a video on Olbers' Paradox a few days ago, and from there read about the origins of the universe, its expansion, and so on... it's always fascinated me, but now something about it bothers me. I've heard many analogies about it (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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/109957-polynomial-ring-print.html | # polynomial ring
Printable View
• October 23rd 2009, 10:19 AM
knguyen2005
polynomial ring
Let R be a ring, suppose that 2 non-zero functions f and g with:
f = a_0 + a_1x +...+ a_mx^m belongs to R[x] , a_m not equal 0 and deg(f) = m
g = b_0 + b_1x +....+ b_nx^n belongs to R[x], b_n not equal 0 and deg(g) = n
(a) Let... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 31, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/10955/what-is-quantum-discord?answertab=votes | # What is quantum discord?
What is quantum discord? I stumbled upon this term on Quantum Computing: The power of discord, but have never heard of it before. Can you give a bit more mathematical explanation of the term here?
-
There are some progress in calculating discord for X states in 2 qubit bipartite systems. 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": 23, "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/22811/charge-distribution-on-a-parallel-plate-capacitor/22828 | # Charge Distribution on a Parallel Plate Capacitor
If a parallel plate capacitor is formed by placing two infinite grounded conducting sheets, one at potential $V_1$ and another at $V_2$, a distance $d$ away from each other, then the charge on either plate will lie entirely on its inner surface. I'm having a little t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/204994/largest-number-obtained-from-products | # Largest number obtained from products?
What is the largest number that can be obtained as the product of two or more positive integers that add up to 20?
-
1
do they have to be distinct? – Jean-Sébastien Sep 30 '12 at 19:10
There are some IMO problems regarding things like this. – Beni Bogosel Sep 30 '12 at 19:24
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/111915/a-question-about-first-order-hyperbolic-equations | ## a question about first-order hyperbolic equations
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Performing certain manipulations on pseudo-differential equations I have come across the following first order equation: $$D_{t}u-\lambda(t,x,D_{t},D_{x})u=0, ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 27, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/tagged/differential-topology | ## Tagged Questions
1answer
171 views
### Differentiable manifolds by Serge Lang question
I have started reading "Introduction to differentiable manifolds" by Serge Lang. In this book, Lang takes a different approach, by immediately introducing manifolds on arbitrary Ba …
0answers
64 views
### Topological classific... | {"extraction_info": {"found_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://math.stackexchange.com/questions/103657/differentiability-in-mathbbrn-and-chain-rule | # Differentiability in $\mathbb{R}^n$ and chain rule
I have a question:
Consider a function $g:\mathbb{R}^{n}\rightarrow \mathbb{R}$ is differentiable. Find the derivative of the function: $G(x)=[ g\left ( x,x^{2},...,x^{n} \right )]^{2}$ where $x\in \mathbb{R}$.
Here, G is a function of one variable, so I tried 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": 21, "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/7823/negative-gromov-witten-invariants/7873 | ## Negative Gromov-Witten invariants
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I understand the heuristic reason why Gromov-Witten invariants can be rational; roughly it's because we're doing curve counts in some stacky sense, so each curve $C$ contribut... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-statistics/89070-poisson-process-renewal-processes.html | # Thread:
1. ## Poisson process & renewal processes
Question: "Traffic on Snyder Hill Road is a Poisson process with rate 1 car per minute. That is, the times between cars are independent exponentials $t_1, t_2, . . .$ with mean 1. Let $T_k = t_i + ... + t_k$ be the time the k-th car passes. A turtle needs two minute... | {"extraction_info": {"found_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://cstheory.stackexchange.com/questions/tagged/tree | # Tagged Questions
A tree is a special type of graph which only allows for a hierarchical set of edges similar to a tree . Mathematically it is actually an arborescence. Trees have a root node and children nodes. In formal terms it is described as a acyclic connected graph.
0answers
51 views
### How many Trees are 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": 42, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Radar_and_Triangulation | # A-level Physics (Advancing Physics)/Radar and Triangulation
Radar and triangulation are two relatively easy methods of measuring the distance to some celestial objects. Radar can also be used to measure the velocity of a celestial object relative to us.
## Radar
Essentially, radar is a system which uses a radio pu... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 10, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/33911/why-linear-algebra-is-funor/80946 | ## Why linear algebra is fun!(or ?)
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Edit: the original poster is Menny, but the question is CW; the first-person pronoun refers to Menny, not to the most recent editor.
I'm doing an introductory talk on linear 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": 139, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://nrich.maths.org/2292/solution | ### Weekly Problem 14 - 2012
Weekly Problem 14 - 2012
### Lost
Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.
### Square Coordinates
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction 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": 33, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.reference.com/browse/caustic-surface | Definitions
# BKL singularity
A BKL (Belinsky-Khalatnikov-Lifshitz) singularity is a model of the dynamic evolution of the Universe near the initial singularity, described by a non-symmetric, chaotic, vacuum solution to Einstein's field equations of gravitation. According to this model, the Universe is oscillating (e... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 96, "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://mathhelpforum.com/advanced-algebra/64982-finding-best-fitted-hyperplane-print.html | # Finding the best fitted hyperplane
Printable View
• December 14th 2008, 03:21 PM
TriKri
Finding the best fitted hyperplane
Given a number of points in $\Bbb{R}^n$, how can you find (one of) the hyperplane(s) from which, according to the least square method, the points is closest located to? That is, minimizing the ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/98523/linear-algebra-problem-intersection-of-a-subspace-with-a-cone | # Linear Algebra problem: intersection of a subspace with a cone.
In $\mathbb{R}^n$, consider the closed cone $$C^+ = \{ (x_1, \ldots, x_n) : x_i \geq 0,~~i= 1, \ldots, n\}.$$ Let $S \subseteq \mathbb{R}^n$ be a subspace (of any dimension) such that $S \cap C^+ = \{0\}$. Prove that $S^{\perp}$ has non-empty intersecti... | {"extraction_info": {"found_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://math.stackexchange.com/questions/153607/what-is-the-chance-to-get-a-parking-ticket-in-half-an-hour-if-the-chance-to-get/153629 | # What is the chance to get a parking ticket in half an hour if the chance to get a ticket is 80% in 1 hour?
This sounds more like a brain teaser, but I had some kink to think it through :( Suppose you're parking at a non-parking zone, the probability to get a parking ticket is 80% in 1 hour, what is the probability 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": 47, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/212331-line-equation-vectors.html | # Thread:
1. ## line equation in vectors
"find the equation of the line passing through B, with positiion vector b, which is perpendicular to the line r=a + $\lambda$c, c=/=0, given that B is not a point on the line". hi, i dont even get this at all to be honest, how is r=a + $\lambda$c a line? in terms of normal lin... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 18, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/255067/using-fermats-little-theorem-prove-if-p-is-prime-prove-1p-2p-3p/255074 | # Using Fermat's Little Theorem Prove if $p$ is prime, prove $1^p + 2^p + 3^p +…+(p-1)^p \equiv 0 \bmod{p}$
Using Fermat's Theorem Prove if $p$ is prime, prove $1^p + 2^p + 3^p +...+(p-1)^p \equiv 0 \bmod{p}$
The two definitions of Fermat's Little Theorem is $a^p \equiv a \bmod{p}$ and $a^{p-1} \equiv 1 \bmod{p}$ but... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cstheory.stackexchange.com/questions/4928/alphabet-of-single-tape-turing-machine | Alphabet of single-tape Turing machine
Can every function $f : \{0,1\}^* \to \{0,1\}$ that is computable in time $t$ on a single-tape Turing machine using an alphabet of size $k = O(1)$ be computed in time $O(t)$ on a single-tape Turing machine using an alphabet of size $3$ (say, $0,1,$ and blank)?
(From comments bel... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 59, "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/49084/transforming-a-sequence-using-polynomials/49195 | # Transforming a sequence using polynomials
Let $$f(x) = \sum_{n \geq 0} a_n x^n = \frac{x-2x^3}{4x^4 - 5x^2 + 1}$$
Now I need to identify a "concrete formula" for $a_n$. This should be done by using the following proposition:
For a sequence $a = (a_0,a_1,\cdots)$ with $a_i \in \mathbb{C}$ and a $d$-tuple $(\alpha_1... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 47, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/34231/what-is-the-particle-residence-time-for-given-flow-rates-of-gas-mixture-componen/34300 | # What is the particle residence time for given flow rates of gas mixture components?
For two different chemical substances there are two open valves with flow rates $$Q_1=a\frac{m^3}{h}\ \text{ and }\ \ Q_2=b\frac{m^3}{h},$$ leading into seperate cables.
Next, the cables join, the substances mix perfectly and they 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": 6, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Hill_sphere | All Science Fair Projects
Science Fair Project Encyclopedia for Schools!
Search Browse Forum Coach Links Editor Help Tell-a-Friend Encyclopedia Dictionary
Science Fair Project... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/algebra/67123-real-number.html | # Thread:
1. ## Real Number
Good evening all of our class is having a online debate with the following question, any feedback would be appreciated:
In the Real Number realm,
ab = 0 è a = 0 or b = 0
Is the same theorem true in the Complex Number realm? (Why or why not?)
2. Originally Posted by AlgebraicallyChallenge... | {"extraction_info": {"found_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": 35, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathforum.org/mathimages/index.php?title=Parabolic_Reflector&redirect=no | # Parabolic Reflector
### From Math Images
Parabolic Reflector Dish
Field: Geometry
Image Created By: Energy Information Administration
Website: [1]
Parabolic Reflector Dish
Solar Dishes such as the one shown use a parabolic shape to focus the incoming light into a single collector.
# Basic Description
The geomet... | {"extraction_info": {"found_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": 13, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/150284-simple-calculus-question.html | Thread:
1. Simple Calculus Question
Hi there,
There is no forum for basic calculus, so I will have to post in the university-level forum. I have been trying to refresh my maths for the last few months (I had forgotten everything, right down to how to do long division.) and I feel as if I have been making good progre... | {"extraction_info": {"found_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": 16, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/7566/list | ## Return to Answer
3 improved latex formatting
Work locally, assume that $f: R\to S$ is a local homomorphism. Let $cmd(R) \operatorname{cmd}(R) =dim R-depth \operatorname{dim} R-\operatorname{depth} R$ (this is the so-called Cohen-Macaulay defect of $R$). Claim: cmd $\operatorname{cmd}$ is preserved by l.c.i maps (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": 28, "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/9022/neutralino-dark-matter-detection?answertab=oldest | # Neutralino Dark Matter Detection
Assuming supersymmetry exists and a neutralino is stable, it's often seen as a leading dark matter candidate. What would be expected from the interaction of a neutralino and its anti-particle? Has there been any unambiguous detection of such an interaction?
-
## 2 Answers
Dear Mic... | {"extraction_info": {"found_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/7864/false-beliefs-in-mathematics-conceptual-errors-made-despite-or-because-of-mat?answertab=votes | # False beliefs in mathematics (conceptual errors made despite, or because of, mathematical education)
Over on mathoverflow, there is a popular CW question titled: Examples of common false beliefs in mathematics. I thought it would be nice to have a parallel question on this site to serve as a reference for false beli... | {"extraction_info": {"found_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://math.stackexchange.com/questions/268071/schroder-functional-equation | # Schröder functional equation
I have the following Schröder functional equation:
$f(h(s))=c.f(s)$
where $f,h: ℂ→ℂ$, here $f$ is not analytic and $h$ is analytic and $c∈ℝ$.
My question is: How we can solve this equation (the form of $f$ and its domain of definition). We can take $h$ as $h(s)=1-s$ or $h(s)=s-1$ and ... | {"extraction_info": {"found_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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/21373-use-methods-frobenius-solve.html | # Thread:
1. ## use the methods of frobenius to solve
use the methods of frobenius to solve:
2xy"+y'+2y =0
i want to know not just the answer but the steps how to answer it (explanation of the answer)
2. Originally Posted by compufatwa
use the methods of frobenius to solve:
2xy"+y'+2y =0
i want to know not just ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/49737/article-or-book-about-the-history-of-spherical-geometry?answertab=oldest | # Article or book about the history of spherical geometry?
I teach a course on non-Euclidean geometry to high schoolers. I'm looking for an article or book that gives a thorough and interesting history of spherical geometry and trigonometry. I'm looking for it for my own learning and possibly to distribute to my stude... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/61695?sort=newest | ## Are there any finitely generated artinian modules that are not notherian?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
It is well known that for rings, Artinian implies Noetherian (the famous Hopkins–Levitzki theorem) and it is also well known that there... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/105705/basic-application-of-strong-law-of-large-numbers | # basic application of Strong Law of Large Numbers
In
$$\sum_{j=0}^q {q\choose j}{1\over n}\sum_{i=1}^n X_i^j(-\bar X)^{q-j} \quad \overrightarrow{a.s.} \quad \sum_{j=0}^q {q\choose j} \mathbb{E}(X^j) (-\mathbb{E}(X))^{q-j}$$
using the Strong Law, why is it, that we can say that
$$\frac{1}{n}\sum_{i=1}^n(-\bar 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": 15, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/1270/how-do-i-estimate-the-joint-probability-of-stock-b-moving-if-stock-a-moves/1294 | How do I estimate the joint probability of stock B moving, if stock A moves?
I have two stocks, A and B, that are correlated in some way.
If I know (hypothetically) that stock A has a 60% chance of rising tomorrow, and I know the joint probability between stocks A and B, how do I calculate the probability of stock 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": 10, "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/2011/11/24/compact-oriented-manifolds-without-boundary-have-nontrivial-homology/?like=1&source=post_flair&_wpnonce=a34a077b61 | # The Unapologetic Mathematician
## Compact Oriented Manifolds without Boundary have Nontrivial Homology
If we take $M$ to be a manifold equipped with an orientation given by an orientation form $\omega$. Then $\omega$ is nowhere zero, and $\omega(v_1,\dots,v_n)>0$ for any positively oriented basis $\{v_i\}$ of $\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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 34, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/5448/clue | Pebbles
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Adding All Nine
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each 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": 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/236624/nabla-times-x-is-given-on-a-surface-can-i-show-that-x-0-on-the-same-surfa | $\nabla \times X$ is given on a surface, can I show that X = 0 on the same surface
If I have a volume V enclosed by a surface S, and $\nabla \times X$ is given on the surface, what information does that give me about X on S. Is there a method of showing that X = 0 on S? (in the context of the divergence theorem?)
-
... | {"extraction_info": {"found_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/2300/what-is-the-field-with-one-element/2306 | ## What is the field with one element?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I've heard of this many times, but I don't know anything about it.
What I do know is that it is supposed to solve the problem of the fact that the final object in the categ... | {"extraction_info": {"found_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/147/what-are-some-useful-ways-to-imagine-the-concept-of-spin-as-it-relates-to-subato?answertab=oldest | # What are some useful ways to imagine the concept of spin as it relates to subatomic particles?
The answers in this question: What is spin as it relates to subatomic particles? do not address some particular questions regarding the concept of spin:
How are some useful ways to imagine a particle without dimensions - ... | {"extraction_info": {"found_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://mathhelpforum.com/advanced-math-topics/213163-vectors.html | # Thread:
1. ## Vectors!
HI I want to check if my answers are right here, I can't do the last part so I believe my answers in the previous parts must be wrong..
Points A,B,C,D have the following coordinates
A1,3,1) B1,2,4) C2,3,6) D5,-2,1)
ai.) Evaluate the vector product, giving your answers in terms of the unit 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": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-math-topics/204781-topologie-question.html | # Thread:
1. ## Topologie question
Hello, I've two questions:
1) Given X a set then $\mathcal{P}(X)$ is a topology on X off ( $\mathcal{P}(X)$ being the power set of X).
Now if I take c and $c \notin X$ is $( \{c \} \bigcup X ) \bigcup \mathcal{P}(X)$ still a topology on X? ( I'd say yes because the 3 axioms work...... | {"extraction_info": {"found_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://nrich.maths.org/6453/index?nomenu=1 | ## 'Global Warming' printed from http://nrich.maths.org/
### Show menu
In this investigation you will need to use a variety of pieces of physical data to come up with a reasonable estimate. What data will you need? Where will you find it? What estimates are sensible? What modelling assumptions are you making at each ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://tcsmath.wordpress.com/tag/integrality-gaps/ | # tcs math – some mathematics of theoretical computer science
## February 23, 2011
### PSD lifting and Unique Games integrality gaps
Filed under: Math, Open question — Tags: Integrality gaps, semi-definite programming, unique games — James Lee @ 9:51 am
By now, it is known that integrality gaps for the standard Uni... | {"extraction_info": {"found_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": 31, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=97320 | Physics Forums
## Diffraction grating
I did a physics lab about diffraction grating where we had to determine the angular positions of all spectral lines of the helium discharge tube.
I have 3 questions :
1. Why use a discharge tube instead of a light bulb?
- I think it might be because you would have to break up 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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/Phase_velocity | # Phase velocity
Frequency dispersion in groups of gravity waves on the surface of deep water. The red dot moves with the phase velocity, and the green dots propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity. The red dot overtakes two green dots when moving 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": 10, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/163532/unique-decomposition-of-primes-in-sums-of-higher-powers-than-2 | # Unique Decomposition of Primes in Sums Of Higher Powers than $2$
Primes of the form $p=4k+1\;$ have a unique decomposition as sum of squares $p=a^2+b^2$ with $0<a<b\;$, due to Thue's Lemma.
What is known about sums of $n$ higher powers resulting in primes?
I tried $a^3+b^3+c^3$, asked Wolfram and found $3,17,27,43... | {"extraction_info": {"found_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://mathhelpforum.com/pre-calculus/30419-cordinate-geometry.html | Thread:
1. Coordinate geometry
Dear forum members,
could you please check if my calculations are correct, I have tried several times, I alway keep getting the wrong answer though.
Problem
Find the values for k for which the lines $2x+ky-11=0$ and $(3-k)x+y+2=0$are perpendicular.
My solution
$-3x+kx= \frac{k}{2x}... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/87167-solved-prove-polynomials-generating-system-vector-spaces.html | # Thread:
1. ## [SOLVED] Prove polynomials are a generating system (vector spaces)
Let V be the vector space of the polynomials of degree $\leq$ 2 over $\mathbb{R}$.
Prove that the polynomials:
$p_1 = 2T^2 + T + 1$
$p_2 = 4T^2 + T$
$p_3 = -2T^2 + 2T + 1$
span, or are a generating system of, V.
If I solve the syst... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 21, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/111622?sort=votes | ## Background for Hejhal’s "The Selberg Trace Formula for $PSL(2, \mathbb{R})$
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Reposted from math.stackexchange where my question received only five views and no answers...
I'm trying to learn the Selberg trace ... | {"extraction_info": {"found_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/revisions/17366/list | ## Return to Answer
2 Added $v\wedge w$.
$V \wedge V$ is bad notation when $V$ is a representation, just as $V~ Sym ~V$ would be. $\wedge^2 V$ is less misleading.
You could try to define $V \wedge W = \wedge^2 (V \oplus W)$. This For $v\in V, w\in W$, we can naturally identify $v\wedge w$ and $w \wedge v$ with eleme... | {"extraction_info": {"found_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://unapologetic.wordpress.com/2010/12/06/inducing-the-trivial-representation/?like=1&_wpnonce=34114a6dfa | # The Unapologetic Mathematician
## Inducing the Trivial Representation
We really should see an example of inducing a representation. One example we’ll find extremely useful is when we start with the trivial representation.
So, let $G$ be a group and $H$ be a subgroup. Since this will be coming up a bunch, let’s jus... | {"extraction_info": {"found_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/86471?sort=votes | ## Can every finite poset be realized as divisors of an algebraic curve?
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Let $D_1$, ... , $D_n$ be a finite set of divisor classes on a nonsingular projective irreducible algebraic curve. We say that $D_1\geq D_n... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "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/2011/07/15/the-exterior-derivative/?like=1&source=post_flair&_wpnonce=55e0e6033e | # The Unapologetic Mathematician
## The Exterior Derivative
The Lie derivative looks sort of familiar as a derivative, but we have another sort of derivative on the algebra of differential forms: the “exterior derivative”. But this one doesn’t really look like a derivative at first, since we’ll define it with some al... | {"extraction_info": {"found_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": 27, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/1955 | ### Logosquares
Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.
### Shape and Territory
If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?
### So Big
One... | {"extraction_info": {"found_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://mathoverflow.net/questions/5143?sort=oldest | ## Pushouts in the Category of Schemes
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When does it make sense to glue schemes together along subschemes?
In particular: is there a way to glue two schemes together along a closed point (say we're working over 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": 37, "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/2008/12/31/ | # The Unapologetic Mathematician
## The Determinant
Let’s look at the dimensions of antisymmetric tensor spaces. We worked out that if $V$ has dimension $d$, then the space of antisymmetric tensors with $n$ tensorands has dimension
$\displaystyle\dim\left(A^n(V)\right)=\binom{d}{n}=\frac{d!}{n!(d-n)!}$
One thing sh... | {"extraction_info": {"found_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": 18, "mimetex.cgi": 0, "/images/ma... |
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