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http://mathoverflow.net/questions/28703/rearrangement-of-dirichlet-series-and-continuity-at-the-abscissa-of-convergence | ## rearrangement of Dirichlet series and continuity at the abscissa of convergence
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Let $D(s):=\sum_{n\geq 1}a_n e^{-\lambda_n s}$ be a general Dirichlet series of type $(\lambda_n) _{n\geq 1}$ with finite absciss... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/125420/in-what-ways-is-an-inner-product-different-from-a-dot-product?answertab=votes | # In what ways is an inner product different from a dot product?
I assume I am correct when I say this but these two things aren't exactly the same thing, are they(dot product is a type of inner product right?) ? In what ways are they different? I looked it up but all I could find was some mentions of the Gram Schmidt... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 36, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/84148?sort=oldest | ## polynomial matrices and its spectrum
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Hello, all!
I have a polynomial non-singular square matrix over $\mathbf{F} _q[x]$, $$\underset{l \times l}{G(x)} = \left( \begin{matrix} g _{0,0}(x) & g _{0,1}(x) & \ldot... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/8062/about-the-complex-nature-of-the-wave-function | # About the complex nature of the wave function?
1.
Why is the wave function complex? I've collected some layman explanations but they are incomplete and unsatisfactory. However in the book by Merzbacher in the initial few pages he provides an explanation that I need some help with: that the de broglie wavelength 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": 44, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/brst+hilbert-space | # Tagged Questions
2answers
145 views
### Kugo and Ojima's Canonical Formulation of Yang-Mills using BRST
I am trying to study the canonical formulation of Yang-Mills theories so that I have direct access to the $n$-particle of the theory (i.e. the Hilbert Space). To that end, I am following Kugo 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": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/5243?sort=oldest | Why is it a good idea to study a ring by studying its modules?
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This is related to another question of mine. Suppose you met someone who was well-acquainted with the basic properties of rings, but who had never heard ... | {"extraction_info": {"found_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://mathoverflow.net/questions/49700/inverse-length-3-arithmetic-progression-problem-for-sets-with-positive-upper-dens | ## Inverse Length 3 Arithmetic Progression Problem for sets with positive upper density
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It is a famous theorem of Roth, which Szemerédi famously generalized, that if a set of natural numbers has positive upper de... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 57, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://amathew.wordpress.com/2010/11/14/the-koszul-complex-ii/ | # Climbing Mount Bourbaki
Thoughts on mathematics
November 14, 2010
## The Koszul complex II
Posted by Akhil Mathew under algebra, commutative algebra, MaBloWriMo | Tags: differential graded algebras, Koszul complex, regular sequences |
1 Comment
I’ve not been a very good MaBloWriMo participant this time around. 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": 0, "wp_latex": 82, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/100491/list | ## Return to Question
2 edit
We consider a Banach space $X$ and its dual $X^*$.
Let $Q\colon X^\ast \to X^\ast$ be an idempotent operator. Question: Can we find an idempotent operator $P\colon X^\ast \to X^\ast$ which is weak${}^\ast$ weak${}^\ast$-to-weak${}^\ast$ continuous and with range isomorphic to range of $Q... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://amathew.wordpress.com/tag/characteristic-classes/ | # Climbing Mount Bourbaki
Thoughts on mathematics
March 5, 2012
## The cohomology of projective hypersurfaces
Posted by Akhil Mathew under algebraic geometry, topology | Tags: characteristic classes, cohomology, hypersurfaces |
[6] Comments
Consider a smooth surface ${M \subset \mathop{\mathbb P}^3(\mathbb{C})}$ 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": 124, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/33768/change-in-appearance-of-liquid-drop-due-to-gravity/33777 | # Change in appearance of liquid drop due to gravity
A liquid drop is spherical in shape due to surface tension. But why does it appear as a vertical line under the free-fall due to gravity? (E.g. During a rain - falling raindrop) Is there a specified length for the line or does it vary with the size of drops?
-
5
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": 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/187618/finding-combined-time-to-repair-two-machines-where-time-is-exponentially-distrib?answertab=votes | # Finding combined time to repair two machines where time is exponentially distributed
I am trying to solve the following problem.
The time $T$ required to repair a machine is an exponentially distributed random variable with mean 10 hours.
a) What is the probability that a repair takes at least 15 hours given that ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "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/108792/irreducibility-of-fundamental-weyl-modules | ## Irreducibility of fundamental Weyl modules
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It is known that for a simple algebraic group over an algebraically closed field of positive characteristic (which I assume to be {\it good} for the group), the Weyl ... | {"extraction_info": {"found_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/197981/assigning-a-finite-value-to-a-divergent-integral | # Assigning a finite value to a divergent integral
Can someone help me to regularize the following divergent integral?
$$\int_0^{1/2}\, \frac{d x}{x^{3/2} (1-x)^{3/2}}$$
Guys, thank you very much for your answers. Thus if I have understood your procedure, the regularized result of this divergent integral (let's do 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": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/89556/easy-and-hard-problems-in-mathematics/89576 | ## Easy and Hard problems in Mathematics [closed]
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Modified question:
I would like to know some examples of problems in Mathematics, for pedagogical purposes, which do not involve difficult techiques to solve 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": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/statistics/82073-sample-spaces-events-print.html | # Sample Spaces and Events
Printable View
• April 3rd 2009, 12:13 AM
youvy
Sample Spaces and Events
43. From a group of 20 men and 16 women, 2 people are chosen at random. Find the probability of:
a) 1 man and 1 woman being chosen
b) 2 men being chosen
c) 2 women being chosen
Thank you:)
• April 3rd 2009, 12:35 AM
... | {"extraction_info": {"found_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/100999/fx-0-for-x-notin-mathbbq-and-fx-1-q-for-x-p-q-prove-f-is-in | $f(x)= 0$ for $x \notin\mathbb{Q}$, and $f(x)=1/q$ for $x=p/q$. Prove: $f$ is integrable
$f(x)= 0$ , if $x \notin \mathbb{Q}$, otherwise $f(x)=1/q$ for $x=p/q$ such that $p$ and $q$ don't share common divisor. I 'd love your help proving that $f$ is integrable and that $\int_{0}^{1}f=0$.
I showed that the lower Darbo... | {"extraction_info": {"found_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://math.stackexchange.com/questions/189693/every-vector-space-has-a-basis-proof-using-zorns-lemma-in-linear-algebra | # Every vector space has a basis proof using zorn's lemma in linear algebra
Every vector space has a basis proof by using zorn's lemma How will i prove this statement by using zorn's lemma
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1
– Bill Cook Sep 1 '12 at 16:35
1
A basis is a maximal linearly independent set under the $\subseteq$-ordering. – Michael Gr... | {"extraction_info": {"found_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://mathlesstraveled.com/2010/01/30/irrationality-of-pi-curiouser-and-curiouser/ | Explorations in mathematical beauty
## Irrationality of pi: curiouser and curiouser
Posted on January 30, 2010 by
I’ve been remiss in posting here lately, which I will attribute to Christmas and New Year travelling and general craziness, and then starting a new semester craziness… but things have settled down a bit,... | {"extraction_info": {"found_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": 55, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/20343/when-to-use-heat-diffusivity-eqn-and-when-to-use-fouriers-law-to-find-temperatu/20357 | # When to use Heat Diffusivity eqn and when to use Fourier's law to find temperature distribution?
Let's say that there is a circular conical section that has diameter $D=.25x$ without any heat generation and I need to find the temperature distribution.
Originially I thought I could use the heat diffusivity equation ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/194272/how-to-sample-from-a-product-of-sums-distribution?answertab=votes | # How to sample from a product-of-sums distribution?
$A$ is a $M$x$N$ matrix whose entries are positive. $x$ is a $N$ dimensional binary (i.e. consisting of $0$s and $1$s) vector and the number of $1$s in $x$ is constant. Let $y = Ax$. The distribution of $x$ is given by
$$p(x) \propto \prod_{i=1}^M y_i$$
where $y_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": 21, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://divisbyzero.com/2012/06/20/platos-approximation-of-pi/?like=1&_wpnonce=1e4d043b68 | # Division by Zero
A blog about math, puzzles, teaching, and academic technology
Posted by: Dave Richeson | June 20, 2012
## Plato’s approximation of pi?
Today I came across an assertion that Plato used ${\sqrt{2}+\sqrt{3}}$ as an approximation of ${\pi}$. Indeed, it is not a bad approximation: ${3.14626\ldots}$ (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": 19, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Two's_complement | # Two's complement
Two's complement is a mathematical operation on binary numbers, as well as a binary signed number representation based on this operation.
The two's complement of an N-bit number is defined as the complement with respect to 2N, in other words the result of subtracting the number from 2N. This is als... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/111361/can-second-order-arithmetic-make-aleph-1l-countable | ## Can second order arithmetic make $\aleph_1^L$ countable?
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Simpson's book Subsystems of Second Order Arithmetic shows $Z_2$ can interpret some fragments of ZF strong enough to give good theories of constructible... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?s=e78b8211e767063120e87157c1043ed7&p=4270421 | Physics Forums
## How does movement of an electric charge create a magnetic field?
I've been researching this for hours and yet cant seem to get an understanding.
So, let's take an electron fixed in space. At any given time it has an electrostatic field around it which decreases with distance and uses photons as a 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": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/72364?sort=newest | Finite, Étale Morphism Of Varieties
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I have a, probably very simple, question: My intuition tells me that the following statement should be true, but I couldn't find it anywhere and I wanted to make sure I am not miss... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 32, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.territorioscuola.com/wikipedia/en.wikipedia.php?title=Half-life | More results on: Download PDF files on: Download Word files on: Images on: Video/Audio on: Download PowerPoint on: More results from.edu web: Map (if applicable) of:
Half-life - Wikipedia, the free encyclopedia
# Half-life
Number of
half-lives
elapsed
Fraction
remaining
Percentage
remaining
0 1/1 100
1 1/2 50... | {"extraction_info": {"found_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": 27, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/37498/sequences-of-evenly-distributed-points-in-a-product-of-intervals/37509 | ## Sequences of evenly-distributed points in a product of intervals
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Let φ be the golden ratio, (1+√5)/2. Taking the fractional parts of its integer multiples, we obtain a sequence of values in (0,1) which are 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": 50, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/26798/calculations-of-apparent-magnitude?answertab=votes | # Calculations of apparent magnitude
I was attempting to do some calculations of apparent magnitude to help solidify my understanding of the topic, but have been running into some confusion.
According to Wikipedia, the apparent magnitude can be given as:
$m_x = -2.5\log_{10}(F_x/F^0_x)$
where $F_x$ is the observed ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://matthewkahle.wordpress.com/2010/11/05/ | # Packing tetrahedra
Last spring I saw a great colloquium talk on packing regular tetrahedra in space by Jeffrey Lagarias. He pointed out that in some sense the problem goes back to Aristotle, who apparently claimed that they tile space. Since Aristotle was thought to be infallible, this was repeated throughout the ag... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?t=311164&page=3 | Physics Forums
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## why doesn't the electron fall into the nucleus!?
Quote by feynmann Feynman never say that his explanation is "semiclassical fairytales", I believe he intended to explain i... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://simple.wikipedia.org/wiki/Ramanujan_prime | # Ramanujan prime
In mathematics, a Ramanujan prime is a prime number that satisfies a result proven by Srinivasa Ramanujan. It relates to the prime counting function.
## Origins and definition
In 1919, Ramanujan published a new proof of Bertrand's postulate (which had already been proven by Pafnuty Chebyshev).
Ram... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/175577-implicit-differentiation-02-a.html | # Thread:
1. ## implicit differentiation...02
problem: $1+x = sin(xy^2)$
solution attempt: differentiating both sides, I have
$1 = -cosx \cdot\frac{d}{dx}[xy^2]$
$1 = -cosx(y^2+2xyy')$
dividing by $-cosx$ on both sides, I have
$-\frac{1}{cosx} =y^2+2xyy'$
dividing by $2xy$ on both sides, I have
$-\frac{2xy}{cosx}... | {"extraction_info": {"found_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/187774/real-numbers-expressing-in-terms-of-series/187790 | # Real Numbers expressing in terms of series
From the literature, I have found the following: Any real number A (say) can be expressed as
$A = a_1 + (1/a_1) + (1/a_2) + (1/a_3) +\ldots$ Where $a_1\ge2$ and the recurrence relation $a_{i+1}\ge a_i(a_i - 1) + 1$ for $i \ge 1$.
I could not understand this statement due ... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=754980 | Physics Forums
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## A proof of RH using quantum physics...:)
why is not my method acceptable?..from the integral equation above you could construct the potential V(x) by solving a non-linear equation for numerical values V(xj) j=1,2,3.....n or for example we could use an ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 24, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/6949 | ### Number Detective
Follow the clues to find the mystery number.
### A-maze-ing
Did you know that ancient traditional mazes often tell a story? Remembering the story helps you to draw the maze.
### The Naked Pair in Sudoku
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in 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": 9, "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/2730/rsa-dsa-wouldnt-it-make-sense-to-sign-using-decoding-the-data-hash/2731 | # RSA/DSA: Wouldn't it make sense to sign using decoding the data hash?
Why is encoding using the private key used for signing? Wouldn't it make sense to keep the premise, that private is for decoding and public is for encoding? i.e. create a hash and threat it as a result of the crypting and decrypt it. The decrypted... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/15498/could-hydrogen-liberated-from-water-provide-lifting-energy-which-exceeds-the-ene | # Could hydrogen liberated from water provide lifting energy which exceeds the energy it took to liberate it from water
I was thinking about Hydrogen balloons and that large ones which are used for weather balloons which sometimes go up to 100,000 ft (approx 30km). Then I was wondering, how much potential energy has 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": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/33787/questions-about-shimura-curves | ## Questions about Shimura curves
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
1: Suppose $A_3$ is the moduli space of abelian varieties of dimension 3 .Is the union of all one dimension shimura varieties in $A_3$ connected?
2: Given a Shimura curve (expli... | {"extraction_info": {"found_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/tagged/special-functions+riemann-zeta | # Tagged Questions
0answers
88 views
### Identity involving $\zeta(3)$
This is a follow-up of this question and my partial answer to it. I've found that the proof of the 2nd identity reduces to showing that ...
2answers
239 views
### Clausen and Riemann zeta function
This is an exercise from the American Monthly 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": 68, "mathjax_display_tex": 15, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/45782?sort=votes | What’s the name of this flavor of n-category?
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I'm looking for the name of a certain n-category definition. (Someone explained it to me a couple of years ago. I remember the definition, but not the name. Without the 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": 16, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/estimation+special-functions | # Tagged Questions
1answer
63 views
### Is the hypergeometric function $F(5/4,3/4; 2, z)$ bounded on $(0,1]$
Consider the classical hypergeometric function $F(5/4,3/4; 2, z)$ for $z\in (0,1]$. Is this bounded by some real number (independent of $z$)? I'm aware of Euler's formula: F(5/4,3/4; 2, z) = ...
2answers
141 ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/tags/minkowski-space/hot | # Tag Info
## Hot answers tagged minkowski-space
15
### Einstein's postulates <==> Minkowski space. (In layman's terms)
I will first describe the naive correspondence that is assumed in usual literature and then I will say why it's wrong (addressing your last question about hidden assumptions) :) The postulate of 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": 23, "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/51706/how-can-mass-affect-spacetime | # How can mass affect spacetime?
In General Relativity Theory, mass can warp spacetime. However, in my view interaction only occurs between pieces of matter. Spacetime is not matter; how can it be affected by matter?
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How do you understand the concept of spacetime? – elcojon Jan 20 at 16:23
@elcojon In my view, spac... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/204927/how-does-one-compute-the-minimal-bounding-sphere-of-a-k-simplex?answertab=active | # How does one compute the minimal bounding sphere of a k-simplex?
Suppose I have a list of $k+1$ points in $\mathbb{R}^n$, and I let $\sigma^k$ be their convex hull. I want to know two things:
1. How can I determine, for any $\varepsilon$, whether open balls of radius $\varepsilon$ centered at each point intersect?
... | {"extraction_info": {"found_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/80036/when-do-adjunctions-preserve-equivalence | ## When do adjunctions preserve equivalence?
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Let $\mathcal{C}'$ and $\mathcal{D}'$ be categories so that $\mathcal{C} \subseteq \mathcal{C}'$ and $\mathcal{D} \subseteq \mathcal{D}'$ are full subcategories. Suppo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikisource.org/wiki/The_Measurements_of_Kaufmann | # The Measurements of Kaufmann
From Wikisource
Jump to: navigation, search
The Measurements of Kaufmann on the Deflectability of β-Rays in their Importance for the Dynamics of the Electrons (1906) by Max Planck, translated by Wikisource
In German: Die Kaufmannschen Messungen der Ablenkbarkeit der β-Strahlen in ihr... | {"extraction_info": {"found_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": 119, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/5786?sort=newest | ## How do I check if a functor has a (left/right) adjoint?
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Because adjoint functors are just cool, and knowing that a pair of functors is an adjoint pair gives you a bunch of information from generalized abstract... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 116, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/3452/can-gravitational-potential-energy-be-released-in-a-fire | # Can gravitational potential energy be released in a fire?
If one takes a bundle of wood up high to the mountains so its potential energy increases, would there be obtained more heat by burning it?
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I just can't make any sense of this question... – David Zaslavsky♦ Jan 20 '11 at 23:27
4
I guess its just a bundle 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": 24, "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/53608/confused-over-complex-representation-of-the-wave | # Confused over complex representation of the wave
My quantum mechanics textbook says that the following is a representation of a wave traveling in the +$x$ direction:$$\Psi(x,t)=Ae^{i\left(kx-\omega t\right)}\tag1$$
I'm having trouble visualizing this because of the imaginary part. I can see that (1) can be written ... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.reference.com/browse/blood%20flow | Definitions
Nearby Words
# Blood flow
Blood flow is the flow of blood in the cardiovascular system. Mathematically, blood flow is described by Darcy's law (which can be viewed as the fluid equivalent of Ohm's law) and approximately by Hagen-Poiseuille equation.
Blood is a heterogeneous medium consisting mainly of pl... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://quant.stackexchange.com/questions/4886/fastest-algorithm-for-calculating-retrospective-maximum-drawdown/4888 | Fastest algorithm for calculating retrospective maximum drawdown
Simple question - what would be the fastest algorithm for calculating retrospective maximum drawdown ?
I've found some interesting talks but I was wondering what people thought of this question here.
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1
Your question is not clear to me. Do you mean 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": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/210187/relation-between-positive-definite-matrix-and-strictly-convex-function | # Relation between Positive definite matrix and strictly convex function
I have a problem. From wikipedia http://en.wikipedia.org/wiki/Positive-definite_matrix any function can be written as $$z^TMz$$ where z is a column vector and M is a symmetric real matrix. However this quadratic function is strictly convex only w... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/55795/tough-probability-question-fair-and-unfair-die-rolling | # Tough probability question: Fair and Unfair die rolling
Have been trying for the last three hours, and going nuts. Please provide HINTS only, not the solution (or answer).
I'm doing this by a dumb approach, way too much of calculations and excel madness. I'm looking for an intelligent shortcut (or many of them). Lo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/8602/what-is-the-difference-between-0-rangle-and-0/8604 | # What is the difference between $|0\rangle$ and $0$
in the context of $$a_- |0\rangle =0$$
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Are you asking what the bra and ket formalism represent? – anna v Apr 13 '11 at 20:07
## 3 Answers
$|0\rangle$ is just a quantum state that happens to be labeled by the number 0. It's conventional to use that label to den... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/212285-prove-total-number-cosets-particular-subgroup-particular-group-m.html | 2Thanks
• 1 Post By Deveno
• 1 Post By Deveno
# Thread:
1. ## Prove the total number of cosets of a particular subgroup in a particular group is m?
I'm having difficulty in understanding a proof given on wikipedia under "Examples" section. The proof can be found at:
Coset - Wikipedia, the free encyclopedia
Math Pr... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 26, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.conservapedia.com/Fibonacci_sequence | # Fibonacci sequence
### From Conservapedia
The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding numbers, with the first two numbers being 0 and 1. The numbers are known as Fibonacci numbers.
Example: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 ...
Written mathematical... | {"extraction_info": {"found_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://unapologetic.wordpress.com/2007/09/23/ordered-linear-spaces-i/?like=1&source=post_flair&_wpnonce=eb8d9d939c | # The Unapologetic Mathematician
## Ordered Linear Spaces I
I saw a really great talk today by Howard Barnum of the Los Alamos National Laboratory. It dovetails wonderfully with what I’ve been talking about here, and I think I can help him by bringing my categorical inclination to bear on his subjects. I’ll omit the ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 26, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/4480/sangaku-a-geometrical-puzzle/4492 | # sangaku - a geometrical puzzle
Find the radius of the circles if the size of the larger square is 1x1.
Enjoy!
(read about the origin of sangaku)
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## 3 Answers
Here's a nicer approach ...
Given two segments emanating from a point and ending at points of tangency with a circle, we know that those segments are co... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 33, "mathjax_display_tex": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/27224/why-isnt-the-gear-predictor-corrector-algorithm-for-integration-of-the-equation?answertab=active | # Why isn't the Gear predictor-corrector algorithm for integration of the equations of motion symplectic?
Okumura et al., J. Chem. Phys. 2007 states that the Gear predictor-corrector integration scheme, used in particular in some molecular dynamics packages for the dynamics of rigid bodies using quaternions to represe... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/235578/finding-the-limit-of-x-1-0-x-n1-frac11x-n | # Finding the limit of $x_1=0 , x_{n+1}=\frac{1}{1+x_n}$
I have had big problems finding the limit of the sequence $x_1=0 , x_{n+1}=\frac{1}{1+x_n}$. So far I've only succeeded in proving that for $n\geq2$: $x_n>0\Rightarrow x_{n+1}>0$
(Hopefully that much is correct: It is true for $n=2$, and for $x_{n+1}>0$ exactly... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 73, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/653/basic-explanation-of-elliptic-curve-cryptography/656 | # Basic explanation of Elliptic Curve Cryptography?
I have been studying Elliptic Curve Cryptography as part of a course based on the book Cryptography and Network Security. The text for provides an excellent theoretical definition of the algorithm but I'm having a hard time understanding all of the theory involved 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": 26, "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/86864?sort=votes | ## When can a family of polynomials get a weight function to be made orthogonal?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $\lbrace P_n(z)\rbrace_{n\in\mathbb N_0}$ be a family of polynomials defined by a generating function $g(t,z)=\sum\limits_{n=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": 21, "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/24801/could-a-people-do-all-sort-of-gymnastics-movement-in-vacuum-space?answertab=oldest | # Could a people do all sort of gymnastics movement in vacuum space? [closed]
Could a people do all sort of gymnastics movement in vacuum space? I asked this because I am worry about that the astronaut leave the space shuttle during emergency could not go back to earth by himself if there are no fuel on the astronaut,... | {"extraction_info": {"found_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://gilkalai.wordpress.com/2010/08/10/faces-of-simple-4-polytopes/?like=1&source=post_flair&_wpnonce=420e8d64d7 | Gil Kalai’s blog
## Faces of Simple 4 Polytopes
Posted on August 10, 2010 by
In the conference celebrating Klee and Grünbaum’s mathematics at Seattle Günter Ziegler proposed the following bold conjecture about 4 polytopes.
Conjecture: A simple 4-polytope with $n$ facets has at most a linear number (in $n$) two dim... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 3, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?p=3733034 | Physics Forums
## Formula for the Electric Field Due to Continuous Charge Distribution
1. The problem statement, all variables and given/known data
I am having trouble understanding how
$\textit{Δ}\vec{E}\textit{ = k}_{e}\frac{Δq}{{r}^{2}}$
(where ΔE is the electric field of the small piece of charge Δq)
turns 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": 12, "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/tags/classical-cipher/hot?filter=all | # Tag Info
## Hot answers tagged classical-cipher
9
### Is a book cipher provably secure?
Using the book as a key is relatively similar to one-time pad, insofar as the book can be considered as a random stream of characters. But that's true only to some extent: a book consists of words, with meaning, which implies ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/191884-0-empty-sets.html | Thread:
1. 0 and empty sets
I'm having trouble understanding this question:
Does $0 \in \emptyset$? Does $\{ \emptyset \} \in \emptyset$. Explain Why.
My answer:
No for both.
Let me know if this is correct and also let me know how this works. Im having some trouble understanding it.
2. Re: 0 and empty sets
Orig... | {"extraction_info": {"found_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://mathoverflow.net/questions/97061?sort=newest | ## Adjoint of a Connection Using the Hodge Map?
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For a Riemannian manifold $(M,g)$ with exterior derivative d, the codifferential d$^\ast$ is defined to be the unique map for which $$g(\omega,d\omega') = g(d^* \om... | {"extraction_info": {"found_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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/32597/compact-surfaces-of-negative-curvature/82589 | ## Compact surfaces of negative curvature
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John Hubbard recently told me that he has been asking people if there are compact surfaces of negative curvature in $\mathbb{R}^4$ without getting any definite answers. I... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/181880/probability-of-drawing-a-blue-ball-if-i-draw-a-ball-10-times?answertab=oldest | # Probability of drawing a blue ball if I draw a ball 10 times?
Suppose there are $3$ red balls and $1$ blue ball. What's the probability that if I draw a ball $10$ times, I don't draw a blue ball?
Is it $1-\Pr(\text{no red ball}) = 1-\big(\frac{3}{4}\big)^3$?
Also, what is the chance that I draw at least $1$ blue 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": 7, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2010/06/28/the-banach-space-of-totally-finite-signed-measures/?like=1&source=post_flair&_wpnonce=c1c9c39881 | # The Unapologetic Mathematician
## The Banach Space of Totally Finite Signed Measures
Today we consider what happens when we’re working over a $\sigma$-algebra — so the whole space $X$ is measurable — and we restrict our attention to totally finite signed measures. These form a vector space, since the sum of two fin... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 24, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/geometry/30382-cone-height.html | Thread:
1. Cone Height
Ok, so here's the problem:
"The volume of a cone is found by using the formula V = 1/3*Pi(Squared)*h
Sarah is experimenting to find how high she needs to build a concial storage tower. She knows the volume of a material to be stored is 112 m(cubed). She decides to rewrite the formula so that ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/52604/calculating-electromagnetic-invariant-in-matrix-form | # Calculating electromagnetic invariant in matrix form
I'm kind of confused. I want to calculate the electromagnetic invariant $I := F^{\mu\nu}F_{\mu\nu}$, but I'm not sure what is the easiest way to do so. So, I was trying to do it in matrix form, i.e. defining $$\mathbf{F}:=\begin{pmatrix}0 & -E_{1} & -E_{2} & -E_{3... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/114711/baum-connes-like-conjecture-for-lp-spaces/115182 | ## Baum-Connes-like “conjecture” for $l^p$-spaces
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Let $G$ be a (discrete) group. For the Baum-Connes conjecture, one looks at the reduced group $C^{\star}$-algebra: Look at the Hilbert space $l^2(G)$ and the repr... | {"extraction_info": {"found_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/107726-chords-integral-length.html | # Thread:
1. ## # of Chords with Integral Length
If the Point Z is 6 units from the center of a circle who's radius is 10.
Then, what is the number of chords with integral length, that run through Z.
2. Originally Posted by warriors837
Point P is 6 units from the center of a circle of radius 10.
Compute the number 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": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/52811/why-is-it-easier-to-work-with-function-fields-than-with-algebraic-number-field | # Why is it “easier” to work with function fields than with algebraic number fields?
I just bought a copy of Jürgen Neukirch's book Algebraic Number Theory. While browsing through it I found a section titled § 14. Function Fields in chapter I. In it the author describes some aspects of an analogy between function fiel... | {"extraction_info": {"found_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/differential-geometry/83604-two-lebesgue-integration-problems.html | # Thread:
1. ## Two Lebesgue Integration Problems
1. Let f be a nonnegative measurable function on $\Re$. Show that if $F : \Re \rightarrow \Re$ is defined by $\int_{(0,x]} f(t)dm(t)$ then F is continuous on $\Re$.
I know that to prove that a function is continuous, you have to show that for any open set $A \subsete... | {"extraction_info": {"found_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": 24, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/tags/models/hot?filter=year | # Tag Info
## Hot answers tagged models
20
### Why do people categorically dismiss some simple quantum models?
I can tell you why I don't believe in it. I think my reasons are different from most physicists' reasons, however. Regular quantum mechanics implies the existence of quantum computation. If you believe 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": 10, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/51329/does-a-scale-model-with-1-2-the-linear-length-have-1-8-the-mass?answertab=votes | # Does a scale model with 1/2 the linear length have 1/8 the mass?
If a scale model has 0.5x the original length in all directions, should its mass be 1/8th of the original mass?
-
probably yes, because the volume is proportional to the cube. – elcojon Jan 15 at 21:28
Does the model use material of the same density? ... | {"extraction_info": {"found_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/120647/surjective-functions/120662 | # Surjective Functions [duplicate]
Possible Duplicate:
Surjectivity of Function Compositions
I am trying to prove this statement:
If $f: A \rightarrow B$ and $g: B \rightarrow C$ are both surjective functions, show that $g \circ f : A \rightarrow C$ is also a surjective function.
I know that some elements B have co... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/23317/fourier-transforms | # Fourier Transforms
I'm having a terrible time trying to understand Fourier transforms. I'm very visual so leaving the $X,Y,Z,t$ domain is not working form me :)
I'm trying to figure out the basics at the moment. Like, taking a Sine wave (they're odd right?) and converting it into its real and imaginary numbers. I'm... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.sagemath.org/doc/reference/number_fields/sage/rings/number_field/order.html | # Orders in Number Fields¶
AUTHORS:
• William Stein and Robert Bradshaw (2007-09): initial version
EXAMPLES:
We define an absolute order:
```sage: K.<a> = NumberField(x^2 + 1); O = K.order(2*a)
sage: O.basis()
[1, 2*a]
```
We compute a basis for an order in a relative extension that is generated by 2 elements:
`... | {"extraction_info": {"found_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": 20, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/30495?sort=oldest | ## pure dimensional and embedded components
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Hi.
Let $X$ be a pure $n$-dimensional complex subspace of manifold $Z$. It is true that $X$ has no embedded components? (perhaps that is obvious with Weierstrass prep... | {"extraction_info": {"found_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://mathoverflow.net/questions/50684?sort=oldest | ## Why only three classical matrix ensembles in RMT? (Newbie question)
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I am just starting out on understanding random matrix theory from a background in applied mathematics. I have a very basic question about 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": 20, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/68942/weil-pairing-and-millers-algorithm/68955 | ## Weil pairing and Miller’s algorithm
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I'm studying Weil pairing and its applications in cryptography. I already know that it can be defined like this:
`$$w(P, Q) = (-1)^n\frac{f_P(Q)}{f_Q(P)}\frac{f_Q}{f_P}(\ma... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 37, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/77944-help-limits.html | # Thread:
1. ## help with limits
Hi
I need help with the following limit:
$\displaystyle\lim_{a\to0} \dfrac{\ln(r/a)}{\ln(b/a)}$
where a < r < b and that a,b are constants.
thanks in advance
2. Apply L'Hopital's rule.
Note the numerator can be written: $ln(r) - ln(a)$, and similarly the denominator can be writt... | {"extraction_info": {"found_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://stats.stackexchange.com/questions/22387/why-it-is-often-assumed-gaussian-distribution/27599 | # Why it is often assumed Gaussian distribution?
Quoting from a Wikipedia article on parameter estimation for a naive Bayes classifier: "a typical assumption is that the continuous values associated with each class are distributed according to a Gaussian distribution."
I understand that a Gaussian distribution is 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": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/147076-solved-vector-spaces-over-division-rings.html | # Thread:
1. ## [SOLVED] Vector spaces over division rings.
Hi:
I have the following definition: let V be a vector space over
a division ring D. A mapping a of V into V is called a linear trans-
formation of V if it has the followiwng two properties:
(x+y)a = xa+ya for x,y $\in$ V,
(x $\alpha$)a = (xa) $\alpha$ for x... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/74252/things-that-should-be-positive-integers-really/74266 | ## Things that should be positive integers…really?
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Kronecker. Nuff said. Even the numbers themselves historically started as positive integers and were subsequently generalized to hell and back. Here are some oth... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 39, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/56718/list | ## Return to Question
6 added 10 characters in body
Let $X$ be a metrizable topological space and $G$ be a locally compact group. Given a continuous (left) action of $G$ on $X$, is there a metric on $X$, compatible with the topology, for which the action of $G$ becomes an isometric action? Conversely, given a metric ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 75, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/82485/dedekind-spectra | ## Dedekind Spectra
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Is there a class of ring spectra that corresponds to and/or extends the class of Dedekind rings from traditional algebra? Is there a notion of "ring of integers" of a ring spectrum? Additional... | {"extraction_info": {"found_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/57276/convolution-on-symmetric-group-sn/71717 | ## Convolution on symmetric group Sn
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I have question regarding convolution of functions (say g and h) defined on Sn. In Fourier space this is equivalent to IFT(G.H), where G = FT(g) and H = FT(h).
Fast Fourier 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": 11, "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/103399/how-can-i-prove-that-square-root-of-n-is-space-constructible?answertab=votes | # how can i prove that square root of n is space constructible
I know that square-root of n is space-constructible. I can't prove it by the space-constructible definition. How can I show that only $\sqrt{n}$ space is used?
-
1
I don't know what space-constructible means. I know $\sqrt n$ is "Euclid-constructible," 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": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/87486/reference-request-simple-facts-about-vector-valued-sobolev-space | ## Reference request: Simple facts about vector-valued Sobolev space
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Let $V,H$ be separable Hilbert spaces such that there are dense injections $V \hookrightarrow H \hookrightarrow V^*$. (For example, $H = L^2(\m... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 16, "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/1431/prove-that-this-function-is-bounded | # Prove that this function is bounded
This is an exercise from Problems from the Book by Andreescu and Dospinescu. When it was posted on AoPS a year ago I spent several hours trying to solve it, but to no avail, so I am hoping someone here can enlighten me.
Problem: Prove that the function $f : [0, 1) \to \mathbb{R}$... | {"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": 27, "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/31842/tensor-product-and-category-theory/31895 | ## Tensor product and category theory
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Hello. I'm trying to understand the definition of tensor product of two vector spaces. So far, I've read the one using free vector spaces and a quotient space (this one http:... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 53, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/33145/recovering-joint-distribution-from-marginals | ## Recovering joint distribution from marginals
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Suppose we have a Markov Random Field P(X1,...,Xn) on graph G. Suppose we know P(Xi,Xj) for every edge (i,j). Can we recover P(X1,...,Xn)?
If G is a tree, then 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": 6, "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/harmonic-oscillator?sort=unanswered&pagesize=30 | # Tagged Questions
The term "harmonic oscillator" is used to describe any system with a "linear" restoring force that tends to return the system to a equilibrium state. There is both a classical harmonic oscillator and a quantum harmonic oscillator. Both are used to as toy problems that describe many physical systems.... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/74552/a-formal-definition-of-scaling-limits/74590 | ## A formal definition of Scaling Limits?
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I'm looking for a formal definition of scaling limit in a rigorous math sense, also, if somebody knows a good translation to spanish. A good bibliography could be helpful... | {"extraction_info": {"found_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... |
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