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http://en.wikibooks.org/wiki/Digital_Signal_Processing/Discrete_Data | # Digital Signal Processing/Discrete Data
This page may need to be reviewed for quality.
Continuous data is something that most people are familiar with. A quick analogy: when an analog data sensor (e.g., your eye) becomes active (you blink it open), it starts receiving input immediately (you see sun-shine), it conve... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/tagged/atoms?sort=unanswered&pagesize=15 | # Tagged Questions
A nucleus made of protons and neutrons surrounded by a cloud of electrons equal in number to the protons.
learn more… | top users | synonyms
1answer
280 views
### Why can free lithium atoms not take part in an Auger process?
Shouldn't it be possible for an incoming photon to excite one of the 1s... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/35181/ward-takahashi-identities-from-z-invariance | # Ward Takahashi identities from Z invariance
I'm trying to get Ward-Takahashi identities using the approach used in Ryder's book (pages 263-266). I like that he starts from demanding gauge invariance of Z in a explicit way and them explores the consequences of that to functional generators of vertex functions. But 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": 11, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/45150/an-issue-about-the-compactness-and-the-existence-of-ctcs | # An issue about the compactness and the existence of CTCs
There is a well known fact that a compact spacetime necessarily contains a closed timelike curve (CTC). Proof can be found in several books on GR (e.g. Hawking, Ellis, Proposition 6.4.2), and in essence goes like this:
The spacetime $M$ can be covered by open... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/2680/ecdsa-point-order-criterion?answertab=oldest | # ECDSA - point order criterion
i am creating some primitive demostration for ECDSA over small curve ( p < 229). But my implementation have some weird issues. Verify process return false even if the signature is correct. Because I am testing it for some time, trying to find problem I discovered that verify work only 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": 25, "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/172701-2-proofs-regarding-linear-transformations-operators-subspaces.html | # Thread:
1. ## 2 proofs regarding linear transformations and operators and subspaces
1.) Prove that $l^1(\mathbb{R}^w) = \{(\beta\subscript_1, \beta\subscript_2, \beta\subscript_3.......) \in \mathbb{R}^w : \sum\limits_{n = 0}^\infty |\beta\subscript_n| < \infty \}$ is a subspace of $\mathbb{R}^w$
2.) Prove that if... | {"extraction_info": {"found_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://math.stackexchange.com/questions/218735/using-newtons-method-for-three-dimensional-system-in-matlab | using Newton's method for three -dimensional system in matlab
Find the Jacobian matrix $J(x, y, z)$ for the functions
$f(x, y, z) = x^2 + y^2 + z^2 − 9 = 0,$
$g(x, y, z) = xyz − 1 = 0,$
$h(x, y, z) = x + y − z^2 = 0.$
Then using Newton’s method for nonlinear systems, starting with different initial guesses, find 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": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2009/08/28/subgroups-generated-by-shears/?like=1&source=post_flair&_wpnonce=a082172354 | # The Unapologetic Mathematician
## Subgroups Generated by Shears
Okay, when I introduced elementary matrices I was a bit vague on the subgroup that the shears generate. I mean to partially rectify that now that we’ve got elementary row operations to work with.
I assert that the upper shears — those elementary matri... | {"extraction_info": {"found_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": 15, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=142297 | Physics Forums
## Viscosity Woes :(
Hi,
I'm conducting a Physics Investigation where I'm changing the temperature of Motor Oil and seeing how the change in temperature affects viscosity of the oil. Im measuring the terminal velocity of the sphere in the oil (V). I'm Using Stokes' Law Equation: F=6piRNV. I've re-arra... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/88033/existing-proofs-of-rokhlins-theorem-for-pl-manifolds/88051 | ## Existing proofs of Rokhlin’s theorem for PL manifolds
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I'm looking for a comprehensive reference to existing proofs of Rokhlin's theorem that a 4-dimensional closed spin PL manifold has signature divisible by 1... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/15089/how-can-i-create-a-custom-control-which-evaluates-to-a-list-of-values-or-replace/15096 | # How can I create a custom control which evaluates to a list of values or replacements?
I have a set of variables which are used in various places in my calculations (solving a system, initial conditions, etc.). In order to make this easier to deal with, I want to make a control-like thing which makes them easier 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": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://terrytao.wordpress.com/tag/connectedness/ | What’s new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
# Tag Archive
You are currently browsing the tag archive for the ‘connectedness’ tag.
## Is there a countable certificate for connectedness?
13 April, 2010 in math.GN, math.LO, quest... | {"extraction_info": {"found_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": 143, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/45796/why-is-the-canonical-momentum-for-the-dirac-equation-not-defined-in-terms-of-t/45797 | Why is the “canonical momentum” for the Dirac equation not defined in terms of the “gauge covariant derivative”?
The canonical momentum is always used to add an EM field to the Schrödinger/Pauli/Dirac equations. Why does one not use the gauge covariant derivative? As far as I can see, the difference is a factor `i` in... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 40, "mathjax_display_tex": 11, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/284144/rank-of-a-subgroup-of-a-free-abelian-group | # Rank of a Subgroup of a Free Abelian Group.
Question:
Let $F$ be a free abelian group with countable rank. Let $G \leq F$. Is the rank of $G$ countable?
I know that this is true when $F$ has a finite rank.
Thanks
-
This has come up before, at least in greater generality (infinite rank as opposed to specifically ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 55, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Kinematics | Kinematics
Classical mechanics
Branches
Formulations
Fundamental concepts
Core topics
Scientists
Kinematics is the branch of classical mechanics that describes the motion of points, bodies (objects) and systems of bodies (groups of objects) without consideration of the causes of motion.[1][2][3] The term is the Engli... | {"extraction_info": {"found_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": 74, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/125877/generating-random-array-in-maple | # Generating random array in Maple
I'm trying to do simulation in Maple, but I can't figure out how to do the following:
How does one generate a set of random whole numbers in an array of 24 element (in 1 column) where the sum of the numbers has to be 10 and each numbers must be between 0 and 10?
-
What distribution... | {"extraction_info": {"found_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://amathew.wordpress.com/2012/10/20/a-spectrum-acyclic-with-respect-to-itself/ | # Climbing Mount Bourbaki
Thoughts on mathematics
October 20, 2012
## A spectrum acyclic with respect to itself
Posted by Akhil Mathew under topology | Tags: Brown representability, Brown-Comenentz duality |
[2] Comments
Let ${X}$ be a connective spectrum with finitely generated homotopy groups. Then the lowest ho... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 78, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/162992/laplace-transform | # Laplace transform
I want to find the Laplace transform of the following signal but I don't know what to do with the absolute value.
$$x(t)=e^{-|t|}\; u(t+1)$$
The first thing it came to my mind is to split in negative and positive sides and then find each one and add them. The problem is that I checked back to 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": 10, "mathjax_display_tex": 11, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/116739?sort=oldest | ## Generating spatially-aware degree-preserving random graphs?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
In the study of biological neural networks, researchers sometimes compare hypotheses vs. a degree-preserving random null model. One major criticism 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": 27, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://psychology.wikia.com/wiki/Random_permutation | # Random permutation
Talk0
31,725pages on
this wiki
Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language | Individual differences | Personality | Philosophy | Social |
Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology |
Statistics: Scientifi... | {"extraction_info": {"found_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://stats.stackexchange.com/questions/36050/how-to-determine-which-variables-are-dependent-or-independent | # How to determine which variables are dependent or independent?
I'm new to this, and am struggling with the concept of how to determine what is the independent variable and what is the dependent variable.
Here's an example that I think would go a long way for me: I'm studying baseball, specifically the home run rate... | {"extraction_info": {"found_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/209721/how-can-i-reconstruct-a-polynomial-with-access-to-its-roots-and-not-to-some-poin | # How can i reconstruct a polynomial with access to its roots and not to some points evaluation of it?
Is there any other element that can let me interpolate a polynomial other than the well known lagrange interpolation by which a polynomial of degree $d$ can be reconstructed from $d+1$ pairs: $x_i,f(x_i)$. If i have ... | {"extraction_info": {"found_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/139594/calculus-optimisation/140037 | # Calculus optimisation
This meant to be a relatively easy problem but I cannot get my head around it. It is from Burkill's "First course in Analysis", book $4$(f), $10$.
An open bowl is in the form of a segment of a sphere of metal of negligible thickness. Find the shape of the bowl if its volume is the greatest 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": 26, "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/96404/references-surveys-concerning-characteristic-classes-of-flat-vector-bundles | ## References/surveys concerning characteristic classes of flat vector bundles
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I'm looking for good surveys about characteristic classes of flat real vector bundles. Letting $G$ be $\text{SL}_n(\mathbb{R})$ with ... | {"extraction_info": {"found_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/59252?sort=oldest | geometric realization on $\mathbf{sTop}$
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Is geometric realization $|\cdot|:\mathbf{Top}^{\mathbf{\Delta}^{\textrm{op}}}\rightarrow \mathbf{Top}$ a left Quillen functor? If so, under what model structure on $\mathbf{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": 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/243125/proving-that-the-matrix-is-not-invertible | # Proving that the matrix is not invertible.
A is a 2x3 matrix and B is a 3x2. How can i prove that the matrix D = AB is not invertible. I could not go further in this problem. The only thing that i have found is the multiply of these two matrix will be 2x2 matrix but how can i find it is not invetible?
-
1
Actually... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 41, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.nag.com/numeric/cl/nagdoc_cl23/html/G13/g13bjc.html | # NAG Library Function Documentnag_tsa_multi_inp_model_forecast (g13bjc)
## 1 Purpose
nag_tsa_multi_inp_model_forecast (g13bjc) produces forecasts of a time series (the output series) which may depend on one or more other (input) series via a previously estimated multi-input model. The future values of any input ser... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 235, "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/m... |
http://mathhelpforum.com/trigonometry/42436-help-hyperbolic-cotangent.html | # Thread:
1. ## Help with hyperbolic cotangent
I need some serious help solving for x in terms of known mathematical constants on this one:
$xln(2pi)=arctan(coth(((x(pi))/2))$
Good luck
2. Originally Posted by rman144
I need some serious help solving for x in terms of known mathematical constants on this one:
$xl... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/19827/patching-parametric-integrals-to-degenerate-properly | ## Patching parametric integrals to degenerate properly
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
While reading the question about fitting all answers to the question of getting a single formula which, in the limit, captures all the answers to $\int x^{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://mathforum.org/mathimages/index.php?title=Straight_Line_and_its_construction&diff=14427&oldid=14421 | # Straight Line and its construction
### From Math Images
(Difference between revisions)
| | ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 215, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/advanced-statistics/142359-normal-distribution-please-help-asap-2-a.html | # Thread:
1. ## Normal distribution - please help ASAP! 2
3) Suppose that a 100-point test (scores are whole numbers) is administered to every high school student in the
USA at the start of their senior year and that the scores on this test are normally distributed with a mean of 70
and standard deviation of 10. If... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/differential-geometry/158711-derivative-0-constant-function.html | # Thread:
1. ## Derivative 0 => constant function
Suppose that M, N are smooth manifolds and that M is connected. Let $f: M \rightarrow N$ be differentiable so that $d_x f = 0$ for all $x \in M$.
Show that f must be constant.
Anyone got any hint? Why do we need M to be connected?
2. If we don't require M to be con... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/301244/diophantine-equations-perfect-square-and-perfect-cube-related | # Diophantine equations - Perfect square and Perfect cube related
Solve following Diophantine equations:
$1) \ a^3-a^2+8=b^2$
2) \$a, \ b,\ c \in \mathbb{Z^+}$$$\frac{a^3}{(b+3)(c+3)} + \frac{b^3}{(c+3)(a+3)} + \frac{c^3}{(a+3)(b+3)} = 7$$
3) $a^3-8=b^2$
In Problem 2 I tried to use inequality, then I can 'limit' 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": 17, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/17176/how-to-create-help-for-a-function-as-documentation?answertab=active | # How to create 'help' ? for a function (as documentation)
I have defined a function `PassVeltB` in some complicated way. But now I would like to add a little documentation that gives the user information on how it is to be used.
I know that the `?` symbol could be placed before a built-in function to generate useful... | {"extraction_info": {"found_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": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/228801/solutions-of-legendre-equation-for-vert-x-vert-leq-1 | # Solutions of legendre equation for $\vert x\vert \leq 1$
Why books say that is necessary in Legendre equation to have $l$ integer if you want regular solutions in $\vert x\vert \leq 1$. It seems not necessary.
Thanks in advance.
-
"It seems not necessary." - what gave you the idea? Both kinds of Legendre function... | {"extraction_info": {"found_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://mathhelpforum.com/discrete-math/10473-how-many-vertices-does-graph-have.html | # Thread:
1. ## how many vertices does this graph have.....
Hello,
plz try to solve this question.
QUESTION:
Suppose that a connected planer simple graph has 25 edges. If a plane drawing of this graph has 10 faces, how many vertices does this graph have?
2. Originally Posted by m777
Hello,
plz try to solve this que... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Exponential_map | # Exponential map
The exponential map of the Earth as viewed from the north pole is the polar azimuthal equidistant projection in cartography.
In differential geometry, the exponential map is a generalization of the ordinary exponential function of mathematical analysis to all differentiable manifolds with an affine ... | {"extraction_info": {"found_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": 65, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/97288?sort=oldest | ## Primes with more ones than zeroes in their Binary expansion
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
This question is also motivated by the developement around my old MO question about Mobius randomness. It is also motivated by Joe O'Rourke's questio... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 66, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.citizendia.org/Geometric_progression | Diagram showing the geometric series 1 + 1/2 + 1/4 + 1/8 + . . . which converges to 2.
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. Mathe... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 38, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/139217/area-under-a-curve-difference-between-dy-and-dx/139225 | # Area under a curve, difference between dy and dx
I am trying to find the area of $y = 1$ and $y = x^\frac{1}{4}$ from 0 to 1 and revolving around $x = 1$
In class we did the problem with respect to y, so from understanding that is taking the "rectangles" from f(y) or the y axis. I was wondering why not just do it 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": 37, "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/41675/how-generalized-eigenvalues-combine-into-producing-the-spectral-measure | ## How “generalized eigenvalues” combine into producing the spectral measure?
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Hi... I am wondering how 'eigenvalues' that don't lie in my Hilbert space combine into producing the spectral measure. I study probabi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 38, "mathjax_display_tex": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/tagged/curvature?sort=votes&pagesize=30 | # Tagged Questions
The curvature tag has no wiki summary.
5answers
2k views
### Laplace operator's interpretation
What is your interpretation of Laplace operator? When evaluating Laplacian of some scalar field at a given point one can get a value. What does this value tell us about the field or it's behaviour 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": 23, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/4199/does-bunching-reduce-synchrotron-radiation | # Does bunching reduce synchrotron radiation?
A continuous charge distribution flowing as a constant current in a closed loop doesn't radiate. Is it therefore true that as you increase the number of proton bunches in the LHC, while keeping the total charge constant, the synchrotron radiation decreases?
-
Please someb... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/188207/convergence-of-a-function-in-a-metric-space-to-its-metric?answertab=active | # Convergence of a function in a metric space to its metric
Given a metric space $(\mathbb{A},d)$ with a metric $d$ being the Euclidean metric, if $\lim_{t \rightarrow \infty}||A_{t+1}-A_t||\rightarrow 0$ is a convergent sequence where $A$ is a matrix with the rows being the points in the metric space and there exists... | {"extraction_info": {"found_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://runescape.wikia.com/wiki/Drop_rate | # Drop rate
Discuss12
22,492pages
on this wiki
Drop Rate is the probability that a monster is expected to yield a certain item when killed once by a player. When calculating a drop rate, divide the number of times you have received the certain item, by the total number of that NPC that you have killed. For example:
... | {"extraction_info": {"found_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": 41, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/118148/list | ## Return to Answer
2 Addressed issue of rational functions rather than polynomial functions.
This would contradict the Harris-Mumford(-Eisenbud) theorem that $M_g$ is non-uniruled for $g$ at least $23$. Let $C$ be a general curve of genus $g$. If $C$ is in "Zieve form", then it is the normalization of the (almost ce... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 85, "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/68132/fundamental-groups-of-surfaces/68133 | ## fundamental groups of surfaces
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What are the properties that hold for a fundamental group of a surface and does not hold necessary for the fundamental groups of manifolds of higer dimensions ??
-
9
"fundament... | {"extraction_info": {"found_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/288739/uniform-integrability-for-a-single-random-variable | # Uniform integrability for a single random variable
Let $X$ be a random variable. Are the following three equivalent?
• $X \in L^1$, i.e. $E |X| < \infty$.
• $X$ is uniformly integrable. That is, if given $\epsilon>0$, there exists $K\in[0,\infty)$ such that $E(|X|I_{|X|\geq K})\le\epsilon$, where $I_{|X|\geq K}$ 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": 25, "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/45567/conformal-mapping-of-c-d-onto-c-1-1 | Conformal mapping of C \ D* onto C \ (-1, 1) [closed]
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Which is the concrete formula for the conformal mapping (normalized at infinity), acting from $\mathbb C \backslash D^*$ onto
$\mathbb C\backslash[-1, 1]$?
Here... | {"extraction_info": {"found_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://quant.stackexchange.com/questions/3114/risk-parity-portfolio-construction?answertab=active | Risk Parity portfolio construction
If I would like to construct a fully invested long only portfolio with two asset classes (Bonds $B$ and Stocks $S$) based on the concept of 'risk parity' the weights $W$ of my portfolio would be the following:
Then the weight of the bonds $W_B = \textrm{Vol}(S)/[\textrm{Vol(S)}+\tex... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/14586?sort=votes | ## When can a function be recovered from a distribution?
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What properties does a distribution (in the generalized function sense) has to have in order to be a function. That is, when is $T(\varphi) = \int f \varph... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/induction+functions | Tagged Questions
4answers
287 views
$f: \mathbb{R} \to \mathbb{R}$ satisfies $(x-2)f(x)-(x+1)f(x-1) = 3$. Evaluate $f(2013)$, given that $f(2)=5$
The function $f : \mathbb{R} \to \mathbb{R}$ satisfies $(x-2)f(x)-(x+1)f(x-1) = 3$. Evaluate $f(2013)$, given that $f(2) = 5$.
5answers
465 views
IMO 1987 - function
Sho... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/71071/easiest-shortest-proof-of-the-following-theorem | # Easiest/shortest proof of the following theorem
If $f$ is a rational function defined on the complex plane. Then the number of the zeros is equal to the number of the poles (counting multiplicity) and considering points at infinity.
I can imagine a proof using the argument principle. Is this the simplest route to 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": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/208700-conditional-second-order-derivative-degree-homogeneity.html | # Thread:
1. ## Conditional Second-order Derivative and Degree of Homogeneity
I have a function $f(a,b)$ with first-order derivatives $f_a>0, f_b>0$ and second-order derivatives $f_{aa}<0, f_{bb}<0, f_{ab}>0$.
Additionally I know that the degree of homogeneity of the function is larger than $0$ but smaller than $1$.... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/160431-calculus-3-optimization-without-constraints.html | # Thread:
1. ## Calculus 3 - Optimization without Constraints
The behavior of a function can be complicated near a critical point where D=0. Suppose that f(x,y)= x^3 - 3xy^2.
a.) Show that there is one critical point at (0,0) and that D=0 at that point.
b.) Show that the contour for f(x,y)=0 consists of three lines i... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/35516/why-is-the-heisenberg-uncertainty-principle-stated-the-way-it-is/35551 | # Why is the Heisenberg uncertainty principle stated the way it is?
I spent a long time being confused by the Heisenberg uncertainty principle in my quantum chemistry class.
It is frequently stated that the "position and momentum of a particle cannot be simultaneously known to arbitrary precision" (or any other obser... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/44457/what-is-force-how-does-a-constant-force-output-a-nonconstant-power?answertab=votes | What is force? How does a constant force output a nonconstant power?
For a constant force, P=Fv. I understand the mathematical derivation of this, but this seems to me, intuitively, to be nonsense. I feel that my discomfort with this comes from a fundamental misunderstanding of force and Newton's Second Law, so I'm no... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "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=3961002 | Physics Forums
Blog Entries: 6
## Visualisation of Brian Greene's concept.
I thought it would be interesting to do a visualisation of Brian Greene's concept that "everything moves at the speed of light". For a preamble see this old thread http://www.physicsforums.com/showthread.php?t=398590
First I should warn 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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://johncarlosbaez.wordpress.com/2013/03/11/game-theory-part-20/ | # Azimuth
## Game Theory (Part 20)
Last time we tackled von Neumann’s minimax theorem:
Theorem. For every zero-sum 2-player normal form game,
$\displaystyle{\min_{q'} \max_{p'} \; p' \cdot A q' = \max_{p'} \min_{q'} \; p' \cdot A q'}$
where $p'$ ranges over player A’s mixed strategies and $q'$ ranges over player B... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 105, "mimetex.cgi": 0, "/images/m... |
http://stats.stackexchange.com/questions/3286/distance-between-empirically-generated-distributions-in-r | # Distance between empirically generated distributions (in R)
I'm not a statistician, but I sometimes need I play around with data. I have two data sets, lists of values in the unit interval. I've plotted them as histograms, so I have an intuitive idea of how "far apart" they are. But I want to something a little more... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/44269/real-non-constant-scalar-field-with-special-properties-in-class-of-4-dimensiona/44689 | # Real, non-constant scalar field with special properties in class of 4-dimensional spacetimes
David Deutsch (Oxford University) asked the following question which I think is an interesting one:
In what class of 4-dimensional spacetimes does there exist a real, non-constant scalar field φ with the following propertie... | {"extraction_info": {"found_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://mathoverflow.net/questions/116133?sort=newest | Explicit Computations of Examples in Spin Geometry
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I have been trying to learn about spin geometry, Dirac operators, and index theory by reading Lawson/Michelson's "Spin Geometry" and Friedrich's "Dirac Operators 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": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/178523-method-least-squares.html | # Thread:
1. ## Method of Least Squares
Question:
A capacitor C is initially charged to 10V and then connected across a resistor R. The current through R is measured at 1 milisecond intervals is:
t : 0 1 2 3 4 ms +-0.5%
i : 4.5 2.8 1.5 1.0 0.6 mA +-2.5%
(Basically this is a table where i corresponds to the t value... | {"extraction_info": {"found_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://oop123.wordpress.com/ | # oop123
Java Beginner Rambling
September 3, 2011 / oop123
You can see the problem here: Problem #159.
This is my 100th question, woot! Now I just need to complete another 50 questions to become level 4. I doubt I can do another 20 questions, let alone 50, but I will try anyway. Now that little “celebration” is over... | {"extraction_info": {"found_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://math.stackexchange.com/questions/tagged/invariance+elementary-number-theory | # Tagged Questions
2answers
108 views
### Using the invariance principle: how to solve $n+d(n)+d(d(n))=m$?
Let $d(n)$ be the digital sum of $n$. How to solve $n+d(n)+d(d(n))=m$, where $n$ and $m$ are natural? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/101598/homotopy-of-random-simplicial-complexes/101626 | ## Homotopy of random simplicial complexes
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A random graph on $n$ vertices is defined by selectiung the edges according to some probability distribution, the simplest case being the one where the edge between any ... | {"extraction_info": {"found_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://rjlipton.wordpress.com/2009/08/07/fermats-little-theorem-for-matrices/ | ## a personal view of the theory of computation
by
Fermat’s little theorem for matrices with application to potential factoring algorithms
Pierre de Fermat is perhaps best known for the proof that he never wrote down, and perhaps never had.
I have discovered a truly remarkable proof which this margin is too small t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 98, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/205979/opposite-of-factorial?answertab=oldest | # Opposite of Factorial? [duplicate]
Possible Duplicate:
Is there a way to solve for an unknown in a factorial?
I was just wondering, what would be the opposite of factorial?
For example, If I had $n! = 120$. How can I then show algebraically that $n = 5$?
-
2
You could repeatedly divide your number by increasing ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/176853-resolving-vector-into-sum-two-other-vectors-using-dot-products.html | # Thread:
1. ## Resolving a vector into the sum of two other vectors (using dot products)
Hi, I'm having trouble with a linear algebra question and would really appreciate some help.
resolve the vector u = 5i + j + 6k into a sum of two vectors, one of which is parallel to and the other perpendicular to v = 3i - 6j +... | {"extraction_info": {"found_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-algebra/196430-find-minimal-polynomial-2-over-q-3-a-print.html | # Find the minimal polynomial for a = π^2 over Q(π^3)
Printable View
• March 26th 2012, 10:11 AM
lteece89
Find the minimal polynomial for a = π^2 over Q(π^3)
If it were in Q then the polynomial would be p(x) = x - π^2, but I don't know if being over Q(π^3) changes that. I think that when you compare the fields you ge... | {"extraction_info": {"found_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/156104/limit-of-a-function-tending-to-zero | # Limit of a function tending to zero.
If $F(t)$ is twice differentiable at $x$ and $$G(h)=\max_{t\in(0,h)}\left[\frac{F'(x+t)-F'(x-t)}{2t}-F''(x)\right],$$ where $x$ is fixed; then how can we show that $\displaystyle\lim_{h\to 0}G(h)=0$.
-
There are abstract duplicates of this question here and here. – Zev Chonoles... | {"extraction_info": {"found_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": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/chern-simons-theory | # Tagged Questions
Chern-Simons theory is an example of a topological quantum field theory. Its describes the field dynamics through the so-called Chern-Simons-form, hence its name.
0answers
42 views
### Supersymmetric Chern-Simons theories in $d=3$
I am reading up on Chern-Simons matter theories in $d=3$. Here 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": 19, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.nag.com/numeric/CL/nagdoc_cl23/html/G04/g04bcc.html | # NAG Library Function Documentnag_anova_row_col (g04bcc)
## 1 Purpose
nag_anova_row_col (g04bcc) computes the analysis of variance for a general row and column design together with the treatment means and standard errors.
## 2 Specification
#include <nag.h>
#include <nagg04.h>
void nag_anova_row_col (Integer n... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 166, "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/m... |
http://physics.stackexchange.com/questions/6946/what-does-it-mean-to-say-that-mass-approaches-infinity?answertab=oldest | # What does it mean to say that mass “approaches infinity”?
What does it mean to say that mass "approaches infinity"?
I have read that mass of a body increases with the speed and when the body reaches the speed of light, the mass becomes infinity.
What exactly does it mean to say that the mass "approaches infinity" ... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/31326/is-a-hard-drive-heavier-when-it-is-full/31700 | # Is a hard drive heavier when it is full?
Browsing Quora, I saw the following question with contradicting answers.
For the highest voted answer:
The bits are represented by certain orientations of magnetic fields which shouldn't have any effect on gravitational mass.
But, another answer contradicts that one:
Most... | {"extraction_info": {"found_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://pgraycode.wordpress.com/2011/02/23/solving-xkcds-nerd-snipping-problem/?like=1&_wpnonce=268a98b8c4 | # Code and Bugs
Coding things
### Solving XKCD’s Nerd Sniping problem
#### by Mithrandir
A while ago, during a period of free time, I implemented a solution in Haskell for the XKCD’s raptor problem. Now, I’ll try to solve another problem presented there, the one found in the Nerd Sniping comic. Of course, the imple... | {"extraction_info": {"found_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": 4, "mimetex.cgi": 0, "/images/mat... |
http://nrich.maths.org/7559 | # Graphs of Changing Areas
##### Stage: 5 Challenge Level:
The graph below shows the curve $y=\frac{10}{x}$.
Imagine $x$ and $y$ are the length and width of a rectangle.
Each point on the curve represents a rectangle - what property do these rectangles share?
What symmetry does the graph have? How do you know?
What... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/109487-problem-killing-me.html | # Thread:
1. ## This problem is killing me
Hi I'm new and need help desperately. I have to admit I am probably not as good in math than most of the people on this site, but I tried my best and just can't figure this problem out.
1.532 x 0.659 = 0.623
1.542 x 0.631 = 0.623
1.589 x 0.669 = 0.554
1.474 x 0.705 = 0.669
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/19243/do-the-empty-set-and-the-entire-set-really-need-to-be-open/19250 | ## Do the empty set AND the entire set really need to be open? [closed]
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My question is motivated by the previous discussion 'Why is a topology made of open sets?'. While the axioms for arbitrary unions and finite... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 52, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/185879-cauchy-residue-theorem-integral.html | # Thread:
1. ## Cauchy Residue Theorem Integral
Hey Guys,
Could you please clarify this problem to me?
When I separate the denominator, I get two values that I can use in the Cauchy Residue theorem.
Thus, should I only take one value (depending on the contour I use obviously), if so do I take the negative one or 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": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/4656-area-between-curve-x-axis.html | Thread:
1. Area between curve and x axis
If y = √ 4 - x^2 then the area of the region limited by this curve y and the x axis is
a) ¶
b) 2¶
Calculate the correct result.
2. Originally Posted by bret80
If y = √ 4 - x^2 then the area of the region limited by this curve y and the x axis is
a) ¶
b) 2¶
Calculate the c... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://electronics.stackexchange.com/questions/13746/why-does-a-resistor-need-to-be-on-the-anode-of-an-led | # Why does a resistor need to be on the anode of an LED?
Please be kind, I am an electronics nub. This is in reference to getting an LED to emit photons.
From what I read (Getting Started in Electronics - Forrest Mims III and Make: Electronics) electrons flow from the more negative side to the more positive side.
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": 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/27830/the-number-of-independent-variables-in-the-lagrangian-and-hamiltonian-methods-in/27831 | # The number of independent variables in the Lagrangian and Hamiltonian methods in Classical Mechanics
It's told in Landau - Classical Mechanics, that in the Hamiltonian method, generalized coordinates $q_j$ and generalized momenta $p_j$ are independent variables of a mechanical system. Anyway, in the case of Lagrangi... | {"extraction_info": {"found_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": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/2042/simpler-way-of-performing-gaussian-elimination | # Simpler way of performing Gaussian Elimination?
Is there a simpler way of performing Gaussian Elimination other than using RowReduce? Such as a single built in function?
Edit:
Look at the example from our simulation class. Not too difficult, but using this method to solve problems of the sort is new to most of us. ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://gilkalai.wordpress.com/2010/10/21/polymath3-polynomial-hirsch-conjecture-4/?like=1&source=post_flair&_wpnonce=a832ba55c5 | Gil Kalai’s blog
## Polymath3: Polynomial Hirsch Conjecture 4
Posted on October 21, 2010 by
So where are we? I guess we are trying all sorts of things, and perhaps we should try even more things. I find it very difficult to choose the more promising ideas, directions and comments as Tim Gowers and Terry Tao did so e... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 272, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/algebra/107414-x-y-intercepts.html | # Thread:
1. ## x and y intercepts.
I need to find the x and y intercepts of this:
f(x) = x^3 - 4x
The y-intercept is just zero right? So how about the x's? I haven't done this in a while. Do you just factor this or do you do something else? I know it's easy.. but I'm having a major brain fade here. I'm guessing 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": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/110062?sort=oldest | ## Start with a topological group, take the meet of the two uniformities, and take the topology. Is the result again a topological group? [xpost from math.SE]
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And what else can be said, if so?
(Original math.SE ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 26, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=263335 | Physics Forums
## Earth/Moon Gravity
1. Locate the position of a spaceship on the Earth-Moon center line such that, at that point, the tug of each celestial body exerted on it would cancel and the craft would literally be weightless. Please answer in meters from the Moon
2. The only thing I can think of is that G=6.... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/158988/implicit-function-theorem-example-in-baby-rudin | # Implicit Function Theorem example in Baby Rudin
I am looking at example 2.29 of Baby Rudin (page 227) of my edition to illustrate the implicit function theorem. This is what the example is:
Take $n= 2$ and $m=3$ and consider $\mathbf{f} = (f_1,f_2)$ of $\Bbb{R}^5$ to $\Bbb{R}^2$ given by $$\begin{eqnarray*} f_1(x_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": 35, "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/37792/a-possible-generalization-of-the-homotopy-groups/37793 | ## A possible generalization of the homotopy groups.
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The homotopy groups $\pi_{n}(X)$ arise from considering equivalence classes of based maps from the $n$-sphere $S^{n}$ to the space $X$. As is well known, these... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 76, "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?s=9dab01a20e3d35f91d52f5b1b60a3489&p=3806830 | Physics Forums
Blog Entries: 1
Surface integral problem from H.M. Schey's book
I've been fooling around by myself with the book "div, grad, curl and all that" by H.M. Schey to learn some vector calculus. However, in the second chapter, when he performs the integrals, he skips the part where he finds the limits on 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": 10, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-statistics/27027-exponential-random-variables.html | # Thread:
1. ## Exponential Random Variables
Let's say we have $n$ exponential random variables $X_1,X_2, \ldots, X_n$. Now consider the following: $X_1 + X_2 + \ldots + X_n$.
What type of distribution would the sum of $n$ exponential random variables, each with mean $\lambda_i$ have?
2. Originally Posted by shilz2... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/28610/list | ## Return to Question
3 added 692 characters in body
Suppose we have a (n-1 dimensional) Unit Sphere centered at the origin: $$\sum_{i=1}^{n}{x_i}^2 = 1$$ What is the probability that a randomly selected point on the sphere, $(x_1,x_2,x_3,...,x_n)$, has coordinates such that $$\forall i, |x_i| \leq d$$ for some $d \i... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 42, "mathjax_display_tex": 15, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/122891/small-index-subgroups-of-sl3-z/123108 | ## Small index subgroups of SL(3,Z)
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I would like to know the smallest index subgroups of SL(3,Z).
The smallest I could find has even entries $a_{3,1}$ and $a_{3,2}$, along the bottom row. I could not figure out ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 85, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=2820867 | Physics Forums
## Equation of the circumference of an ellipse parametric equations
1. The problem statement, all variables and given/known data
Consider the ellipse given by the parametric equation x=3cos(t) y=sin(t) 0$$\leq$$t$$\leq$$2$$\Pi$$. Set up an integral that gives the circumference of the ellipse. Also find... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 33, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/104467/a-homotopy-equivalence-between-total-spaces-in-a-hurewicz-fibration-which-is-no/104469 | ## A homotopy equivalence between total spaces in a (Hurewicz) fibration which is not a fiber homotopy equivalence
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In Hatcher's Algebraic Topology book it is noted after 4.61 that:
fiber preserving map + homotop... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/number-theory/145584-number-theory.html | # Thread:
1. ## Number Theory
An unrestricted partition (order does not count, equality of sizes is ok) partition is called self-conjugate if it is identical with its conjugate. E. g 8 = 4 + 2 + 1 + 1.
Show that the number of self conjugate unrestricted partitions of n is equal to the number of partitions of n into ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/103715/list | ## Return to Answer
2 fixed upper endpoint of last integral
Let me set
$$k^2=\frac{4ar}{(r+a)^2} <1.$$
If we replace $\theta$ with $2\theta$ we reduce this to an integral;
$$2 \underbrace{\int_0^\pi \sqrt{1-k^2\cos^2\theta} d\theta}_{=I}.$$
Now set
$$x=\cos\theta$$
so that $$dx=-\sqrt{1-x^2} d\theta$$
and
$$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": 6, "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/76071/question-about-the-definition-of-hamiltonian-group-action/76092 | ## Question about the definition of hamiltonian group action.
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So I'm reading the part in Ana Cannas da Silva's book "Lectures on Symplectic Geometry" available (on her website) about hamiltonian group actions on ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 64, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/90866-simple-log-question-algorithm.html | # Thread:
1. ## Simple log question for algorithm
I'm terrible with logs (just can't get my head around them).
The question is about big-O notation but the part I don't understand is about logarithms.
I've been told the following:
$\log_3 N = O(\log_2 N)$ because $\log_3 N = \log_3 2 \times \log_2 N$.
I don't unde... | {"extraction_info": {"found_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... |
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