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http://www.physicsforums.com/showthread.php?t=623516 | Physics Forums
## Logarithmic spiral
1. The problem statement, all variables and given/known data
a logarithmic spiral is given. The center lies on the x-axis. after a turn of 180 degrees counterclockwise I am 86.23m away from the starting point, after 360 degrees I'm 75.41m away from the start (radius, not along th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/287942/series-convergence-divergence-and-tests-and-sums | Series convergence divergence and tests and sums
1. For which values of $p$ is the series $$\sum_{n=1}^\infty\frac1{(n (1+\ln n)^p)}$$ convergent/divergent?
I've been trying to solve this earlier but the best I can come up with is the ratio test and I know that's not the proper way to solve for $p$.
2. Where are eac... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/1793/is-rsa-of-a-random-nonce-with-no-padding-safe | # Is RSA of a random nonce with no padding safe?
Consider the following protocol: Bob has a private RSA key $B_{priv}$, and Alice knows the public key $B_{pub}$. Alice wants to send confidential messages to Bob (no integrity intended). To send a message, Alice randomly generates a single-use symmetric key (say, an AES... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/80177/scheme-of-dual-numbers-over-a-field/80196 | # Scheme of dual numbers over a field
Let $k$ be a field and $D:=\operatorname{Spec}(k[t]/(t^2)$ the scheme of dual numbers over $k$.
Then what is the fibre product $D \times_k D$ with itself over $k$? In other words, what is $\operatorname{Spec}(k[t]/(t^2) \otimes_k k[t]/(t^2)$ And how do line bundles over this sche... | {"extraction_info": {"found_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://lalashan.mcmaster.ca/theobio/worden/index.php/Consensus_Dynamics_Notes | # Consensus Dynamics Notes
From Worden
## Historically
Historically, this research program starts with this research proposal, which I wrote for an opening at the Santa Fe Institute.
## Lit review
Currently this is more like "literature to review"...
### Collective, evolutionary and other search processes
• go b... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 20, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/162792/smallest-subfield-containing-transcendental-or-algebraic-element?answertab=votes | # smallest subfield containing transcendental or algebraic element
Consider the extension $\mathbb R/ \mathbb Q$. what is the smallest subfield $\mathbb Q(\pi)$ of $\mathbb R$ containing $\mathbb Q$ and $\pi$. I think it is $\mathbb R$. A more general question: for all transcendental elements $a$ in an extension $L/K$... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 131, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/319120/struggling-with-technique-based-mathematics-can-people-relate-to-this-and-wh | Struggling with “technique-based” mathematics, can people relate to this? And what, if anything, can be done about it?
I'm a 3rd year undergraduate, majoring in pure mathematics. I've done well in the "proof-based" subjects I've taken, and I think that's because I understand the "rules of the game." That is, predicate... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 99, "mathjax_display_tex": 13, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/104244/if-c-bx-separable-then-x-is-a-compact-metrizable-space | # If $C_b(X)$ separable then $X$ is a compact metrizable space
I am very familiar with the proof of the following statement: If $X$ is a compact Hausdorff space such that the Banach algebra $C(X)$ is separable, then $X$ is metrizable.
Can this be used to prove a more generalized version of this statement with the set... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/307015/non-linear-diophantine-equation-in-three-variables | # Non Linear Diophantine Equation in Three Variables
Find all positive integer solution to $abc-2=a+b+c$.
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## 2 Answers
None of the variables can be greater than $4$, and at least two of them have to be greater than $1$. Also, by looking at the equation modulo 2, you can not have exactly one of them being odd. 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": 17, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/1866/note?nomenu=1 | ## 'Take Three from Five' printed from http://nrich.maths.org/
### Why do this problem?
This problem looks like a number task, possibly revision about multiples, but it becomes a question about establishing why something can never happen, and creating a real proof of this. When it comes, the proof often feels powerfu... | {"extraction_info": {"found_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://mathoverflow.net/questions/71272/height-of-ordered-set | ## Height of ordered set
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In all "constructive" fixed-point theorems for functions on ordered sets that I am aware of, where the fixed point is obtained as the limit of a stationary increasing transfinite sequence... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 48, "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/4648?sort=newest | ## When to pick a basis?
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Picking a specific basis is often looked upon with disdain when making statements that are about basis independent quantities. For example, one might define the trace of a matrix to be 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": 28, "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/computational-complexity+functions | # Tagged Questions
2answers
34 views
### How can we denote the following function in terms of big-O notation?
I have got a function and want to denote it in terms of bigO notation. f(n) = log4n+n*(1/3). Is this function O(n)? (* here is the multiplication) Thanks for your help
2answers
32 views
### The growth 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": 15, "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/257857/divide-40-to-4-parts-such-that-every-number-from-1-40-can-be-realized?answertab=oldest | # Divide $40$ to $4$ parts such that every number from $1-40$ can be realized
How can you divide $40$ to $4$ parts such that every number from $1-40$ can be realized just by adding or subtracting those $4$ parts?
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2
– Marc van Leeuwen Dec 13 '12 at 12:41
## 2 Answers
All integers from 1 to 40 can be expressed by ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/advanced-algebra/111983-need-help-solving-equations-matrix.html | # Thread:
1. ## Need help solving equations from this matrix
I have a matrix
1 0 5 0 0
0 1 1 5 0
0 0 0 0 1
Which gives the three equations:
X1 + 5X3 = 0
X2 + X3 + 5X4 = 0
4X5 = 0
Now in my notes it says that you can solve it to get:
X1 = 2X3 + 0X4
X2 = 6X3 + 2X4
X3 = 1X3 + 0X4
X4 = 0X3 + 1X4
X5 = 0X3 + 0X4
Coul... | {"extraction_info": {"found_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/advanced-applied-math/4154-tennis-ball-example-coefficient-restitution.html | # Thread:
1. ## tennis ball example/coefficient of restitution
a tennis ball is hit from a height h above the ground with a speed V and at an angle alpha to the horizontal. it hits a wall at a horizontal distance d away . Air resistance is negligible
i was told to find expressions for the height and velocity of the ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/25386/power-of-chi-square-test-for-goodness-of-fit-as-function-of-sample-size | Power of chi-square test for goodness-of-fit as function of sample size
I would like to calculate the power of a Chi-Square test for goodness-of-fit as a function of sample size for a specified alpha-value (say 0.01). Specifically, I am referring to power as the probability that the test will correctly reject the null... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/72298/polynomial-vector-fields-on-the-3-sphere | ## Polynomial Vector Fields on the 3-Sphere
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
EDIT(3): I am looking for a basis for the Lie algebra of polynomial vector fields on $S^3$.
EDIT(2): I am fairly certain now that my question is more along the lines 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": 40, "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/292719/question-about-normal-distribution?answertab=votes | # question about normal distribution
I'm not being able to identify the mathematical pattern used answer this question:
Suppose that the length of a speficic kind of snake may be modelled by a normal distribution with mean 50.8 (cm) and standard deviation 0.8.
Calculate the length (cm) that is exceeded by only 7% of... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-statistics/192697-find-expected-number-print.html | # find the expected number
Printable View
• November 25th 2011, 08:16 PM
wopashui
find the expected number
Assume that Y denotes the number of bacteria per cubic centimetre in a particular liquid and that Y has a Poisson distribution with parameter $\lambda$ . Further assume that $\lambda$ varies from location to loc... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/76063?sort=votes | ## Does a bounded real function have an analytic continuation [closed]
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Consider the function $f:[0,1]\rightarrow\mathbb{R}$, where
• $f$ is real-analytic on the open interval $(0,1)$
• $f$ is bounded on the clos... | {"extraction_info": {"found_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/60451/classifications-of-finite-simple-objects/60460 | ## Classifications of finite simple objects
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I'm curious to know if other classifications are known of "finite simple structures" in the same spirit of the monumental classification of finite simple groups. Here 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": 27, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.msri.org/seminars/19946 | # Mathematical Sciences Research Institute
Home » Noncommutative Clusters (NAGRT)
# Seminar
Noncommutative Clusters (NAGRT) May 22, 2013 (03:30pm PDT - 04:30pm PDT)
Parent Program:
Noncommutative Algebraic Geometry and Representation Theory
MSRI: Simons Auditorium
Speaker(s) Arkady Berenstein (University of Oregon)
... | {"extraction_info": {"found_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/286473/proving-holders-inequality | # Proving Hölder's Inequality
Let $f,g,\alpha:[a,b]\rightarrow \mathbb{R}$ with $\alpha$ increasing and $f,g \in \mathscr{R}(\alpha)$, and $p,q>0$ with $\frac{1}{p}+\frac{1}{q}=1$. Prove that $$\left|\int_a^b f(x)g(x)d\alpha\right|\leq \left(\int_a^b \left|f(x)\right|^p d\alpha \right)^{1/p} \left(\int_a^b \left|g(x)\... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/tagged/time-series | # Tagged Questions
Time series are data observed over time (either in continuous time or at discrete time periods).
1answer
35 views
### First difference or log first difference?
I am evaluating the effect of covariances between series on returns. That is I run the following regression: $$r_t = \beta_0 + \beta_1\te... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "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/20810/geometric-argument-for-van-kampen | # geometric argument for van-kampen?
I've seen Van-Kampen's theorem presented algebraically many times; and although it provides a useful method of calculation; I don't have a very clear picture for "why" it should be true. Does anyone know of a more visual argument; or even an example that makes the it easier to see?... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 51, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=236524 | Physics Forums
## Explicit expressions for creation/annihilation operator of the free scalar field
I've been trying to work my way through some of my lecture notes, and have hit this snag. (n.b. I use $k_0 \equiv +\sqrt{\vec{k}^2 + m^2}$)
We have
$$a(q) = \int d^3 x e^{iqx} \{ q_0 \phi(x) + i \pi(x) \}$$
$$a^{\dagge... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/21998?sort=newest | ## Is there a nice way to characterise the derived equivalence induced by a flop?
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Hello, I'm interested in the case when all varieties are projective threefolds over the complex numbers.
Start with a flopping 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": 6, "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/2010/06/24/ | # The Unapologetic Mathematician
## Hahn Decompositions
Given a signed measure $\mu$ on a measurable space $(X,\mathcal{S})$, we can use it to break up the space into two pieces. One of them will contribute positive measure, while the other will contribute negative measure. First: some preliminary definitions.
We ca... | {"extraction_info": {"found_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": 74, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/27662/which-cfts-have-ads-cft-duals?answertab=active | # Which CFTs have AdS/CFT duals?
The AdS/CFT correspondence states that string theory in an asymptotically anti-De Sitter spacetime can be exactly described as a CFT on the boundary of this spacetime.
Is the converse true? Does any CFT in a suitable number of spacetime dimensions have an AdS/CFT dual? If no, can we 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": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.haskell.org/haskellwiki/index.php?title=Sinc_function&diff=2628&oldid=2541 | # Sinc function
### From HaskellWiki
(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": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/62997?sort=newest | ## Parallelizability of exotic structure
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I'd like to discuss a little bit about the problem I asked Diarmuid Crowley that whether all smooth structures on $S^7$ are parallelizable. He first came to using semi-cha... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Heath%e2%80%93Jarrow%e2%80%93Morton_framework | # Heath–Jarrow–Morton framework
The Heath–Jarrow–Morton (HJM) framework is a general framework to model the evolution of interest rate curve – instantaneous forward rate curve in particular (as opposed to simple forward rates). When the volatility and drift of the instantaneous forward rate are assumed to be determini... | {"extraction_info": {"found_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": 26, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/63177/for-any-natural-n-how-could-we-prove-that-sum-limits-i-1-n-i23i1-i | # For any natural $n$, how could we prove that $\sum\limits_{i=1} ^n (i^2+3i+1) i!= (n+3)(n+1)! - 3$
How could we prove this ?
$$\sum_{i=1} ^n (i^2+3i+1)\times i!= (n+3) \times (n+1)!-3$$
I did with induction, what I want to know is about other ways to prove this.
-
I am rolling back @Arturo Magidin's edit,seems d... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 15, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/16732/why-negative-energy-states-are-bad?answertab=oldest | # Why Negative Energy States are Bad
The argument is often given that the early attempts of constructing a relativistic theory of quantum mechanics must not have gotten everything right because they led to the necessity of negative energy states. What's so wrong with that? Why can't we have negative energy states?
As... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Two-point_tensor | Two-point tensor
"Double vector" redirects here. For dual vectors, see dual space. For bivectors, see bivector.
Two-point tensors, or double vectors, are tensor-like quantities which transform as vectors with respect to each of their indices and are used in continuum mechanics to transform between reference ("materia... | {"extraction_info": {"found_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": 20, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://rjlipton.wordpress.com/2012/11/08/the-power-of-guessing/ | a personal view of the theory of computation
by
Some results and ideas on guessing and nondeterminism
David Doty and Michael Wehar are theorists who work in different areas of computational complexity, and are at different stages of their careers. Doty is at the California Institute of Technology as a fellow in 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": 80, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/9756/list | ## Return to Question
3 additional info
I've gotten stuck in a project I have been working on, essentially on the following combinatorial question about the symmetric group.
I am interested in this because it may allow a way to directly interpolate the construction of these modules to complex rank, via Pavel Etingof... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 71, "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/132199/non-disjoint-partition-of-a-graph-into-cliques-of-bounded-size | # Non-disjoint partition of a graph into cliques of bounded size
I am looking for a method to list cliques in a graph such that:
• All vertices of the graph are included in at-least one clique
• The size of every clique is no greater than a bound K
The problem seems to be similar to the Clique Cover Problem. However... | {"extraction_info": {"found_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://mathoverflow.net/questions/72736?sort=newest | ## ZFC, set membership and FOL
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Hi,
Is set membership defined in the signature of ZFC, or is it *specified" in the signature of ZFC? The wikipedia article http://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 59, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/275556/find-the-marginal-density-f-yy-of-a-random-vector-x-y | # Find the marginal density $f_Y(y)$ of a random vector $(X,Y)$.
Given a (continuous) bivariate random vector $(X,Y)$ with a probability density:
$$f_{XY}(x,y)=\left\{ \begin{array}{l}\tfrac{1}{y}e^{-(y+\tfrac{x}{y})} & \text{if }x>0 \text{ and } y>0 \\ 0 & \text{otherwise}\end{array} \right.$$
Find the marginal 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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/57904/why-not-define-triangulated-categories-using-a-mapping-cone-functor | ## Why not define triangulated categories using a mapping cone functor?
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Recall that the usual definition of a triangulated category is an additive category equipped with a self equivalence called `$[1]$` in which... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 33, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/115145?sort=oldest | ## are immersions/submersions captured in generalised smooth spaces by some universal property?
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Immersions & sumersions are important in differential manifolds. They rely on their definition of the construction 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": 7, "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/70716/characterization-of-locally-free-modules-via-exterior-powers | ## Characterization of locally free modules via exterior powers
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Let $X$ be a scheme and $\mathcal{F}$ be quasi-coherent module on $X$. It is clear that if $\mathcal{F}$ is locally free of rank $n$, then $\det(\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": 88, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2008/01/18/the-heine-borel-theorem/?like=1&source=post_flair&_wpnonce=c327cf8c6a | # The Unapologetic Mathematician
## The Heine-Borel Theorem
We’ve talked about compact subspaces, particularly of compact spaces and Hausdorff spaces (and, of course, compact Hausdorff spaces). So how can we use this to understand the space $\mathbb{R}$ of real numbers, or higher-dimensional versions like $\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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 73, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/317874/calculate-the-angle-between-two-vectors | # Calculate the angle between two vectors
I comes from Stack Overflow and I though my question was more related to this forum. The problem is i'm not a matematician, so please excuse me if I ask a dumb question.
I'm trying to get the angle between two vectors. As numbers of posts says, here or here, I tried this solu... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 45, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-applied-math/131266-help-me-ques.html | # Thread:
1. ## Help me with this ques.
Hey i have a question i cant solve it but m very curious to know its solution
Help me!!
Here it is:
Two rays are drawn through a point at an angle of 30*.A point B is taken on one of them at a distance d from the point A.A perpendicular is drawn from the point B to other ray a... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/farey-sequences | # Tagged Questions
The Farey sequence of order $n$ is the sequence of all lowest-terms fractions between 0 and 1 whose denominators do not exceed $n$, in increasing order.
1answer
59 views
### How to prove that construction of Farey sequence by mediant is coverage?
Farey sequence of order $n+1$ ($F_{n+1}$) can be 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": 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/86259/mathbbq-sqrt1-sqrt2-is-galois-over-mathbbq?answertab=votes | # $\mathbb{Q}(\sqrt{1-\sqrt{2}})$ is Galois over $\mathbb{Q}$
I am trying to show that $E = \mathbb{Q}\left(\sqrt{1-\sqrt{2}}\right)$ is galois over $\mathbb{Q}$. The extension has the minimal polynomial
$$\left(x-\sqrt{1-\sqrt{2}}\right)\left(x+\sqrt{1-\sqrt{2}}\right)\left(x-\sqrt{1+\sqrt{2}}\right)\left(x+\sqrt{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": 34, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/89400-half-life-decay.html | # Thread:
1. ## Half Life and Decay
Hi guys,
New to this forum so let me know If I am doing anything wrong.
My question: Ive decided to take a calculus course after many years of not doing any math.. If you can give me hints in regards to this question it would be greatly appreciated.
A 96-milligram sample of a ra... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Ito_process | # Itō calculus
(Redirected from Ito process)
Itō integral of a Brownian motion with respect to itself.
Some or all of the formulas presented in this article have missing or incomplete descriptions of their variables, symbols or constants which may create ambiguity or prevent full interpretation. Please assist in recr... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 33, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.amamanualofstyle.com/view/10.1093/jama/9780195176339.001.0001/med-9780195176339-div1-215?rskey=qHBfrc&result=1&q= | • or Create
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## AMA Manual of Style Committee
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Oxford University Press
Print Publication Date:
Mar 2007
Print ISBN-13:
9780195176339
Published to AMA Manual of Style:
Apr 2009
DOI:
10.1093/jama/9780195176339.001.0001
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# Glossary of Sta... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/14043/plotting-a-wave-function-that-represents-a-particle/14046 | # Plotting a wave function that represents a particle
The problem is this:
A particle is represented by the wave function $\psi = e^{-(x-x_{0})^2/2\alpha}\sin kx$. Plot the wave function $\psi$ and the probability distribution $|\psi(x)|^2$.
This the problem 2.1 in the book Fundamental University Physics Volume III ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2008/03/20/products-of-integrable-functions/?like=1&source=post_flair&_wpnonce=c327cf8c6a | The Unapologetic Mathematician
Products of integrable functions
From the linearity of the Riemann-Stieltjes integral in the integrand, we know that the collection of functions that are integrable with respect to a given integrator over a given interval form a real vector space. That is, we can add and subtract them a... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 23, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/187958/number-theory-least-common-multiple-question | # Number Theory Least Common Multiple Question
I don't know how I could find, WITH proof, the smallest possible least common multiple of three positive integers which sum to $2005$.
If someone can provide a proof I would be very happy.
-
I suppose you want strictly positive integers, otherwise the answer is $0$. – 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": 30, "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/2340/what-is-the-first-interesting-theorem-in-insert-subject-here/2351 | ## What is the first interesting theorem in (insert subject here)? [closed]
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In most students' introduction to rigorous proof-based mathematics, many of the initial exercises and theorems are just a test of a stud... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/44109/how-should-one-think-about-non-hausdorff-topologies/44113 | ## How should one think about non-Hausdorff topologies?
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In most basic courses on general topology, one studies mainly Hausdorff spaces and finds that they fit quite well with our geometric intuition and generally... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 114, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/revisions/9199/list | ## Return to Answer
1 [made Community Wiki]
I believe this is a problem given in J. Hirsch's Differential Topology. This may be much simpler than the ones posted here already. But for what it's worth, here it is.
Show that given a collection of spheres the product manifold embeds into an Euclidean space of one dimen... | {"extraction_info": {"found_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://ams.org/bookstore?fn=20&arg1=conmseries&ikey=CONM-525 | New Titles | FAQ | Keep Informed | Review Cart | Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Ana... | {"extraction_info": {"found_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://math.stackexchange.com/questions/205197/diagonalising-a-matrix/205209 | # Diagonalising a matrix
I've got a matrix $A = \begin{bmatrix}1&-1\\ 2&-1\end{bmatrix}$ and wish to diagonalise it. I find the eigenvalues as below.
$$\det(A - xI) = 0 = \det\begin{bmatrix}1-x&-1\\ 2&-1-x\end{bmatrix}$$
$$\det(A - xI) = (1-x)(-1-x) - (-2) = 1 + x^2$$
Then $x =i, -i$. So, now I need to find the eig... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/33102/on-the-tightness-of-chernoff-bounds-for-sum-of-poisson-trials?answertab=votes | # On the tightness of Chernoff bounds for sum of Poisson trials
For the sum $X$ of independent 0-1 random variables $X_i$ ($0 \le i \le n-1$) with $Pr(X_i)=p_i$, namely $X=\sum_{i=0}^{n-1}{X_i}$ the following Chernoff bound holds, $$Pr(X \ge (1+\delta)\mu) \le \left(\frac{e^\delta}{(1+\delta)^{1+\delta}}\right)^\mu$$ ... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://gauravtiwari.org/2011/07/13/famous-fox-rabbit-chase-problems-3/ | MY DIGITAL NOTEBOOK
A Personal Blog On Mathematical Sciences and Technology
Home » Featured » Fox – Rabbit Chase Problems
Fox – Rabbit Chase Problems
Start here
Part I:
A fox chases a rabbit. Both run at the same speed $v$. At all times, the fox runs directly toward the instantaneous position of the rabbit , 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 73, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/282042/define-infinite-path-with-a-finite-relation-in-a-graph-with-least-fixed-point-lo?answertab=votes | # Define infinite path with a finite relation in a graph with Least Fixed Point logic
Least Fixed Point(LFP) logic (p. 37ff) is an extension of first order logic which enables the usage of the least fixed point of FO-definable operators. For example consider a graph $G=(V,E)$ and binary operator $T(x,y)$ defined by
$... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "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/74338?sort=votes | ## Taylor Series Remainder
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Suppose I have a $C^\infty$ smooth function $f$ defined on the reals.
I can apply Taylor's formula and get the local expression
$$f(x) = \sum_{i=0}^l\frac{f^{(i)}(0)}{l!}x^i+ f^{(l+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": 37, "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/9851/can-the-phase-of-a-function-be-extracted-from-only-its-absolute-value-and-its-fo/128373 | # Can the phase of a function be extracted from only its absolute value and its Fourier transform's absolute value?
If for a function $f(x)$ only its absolute value $|f(x)|$ and the absolute value $|\tilde f(k)|$ of its Fourier transform $\tilde f(k)=N\int f(x)e^{-ikx} dx$ is known, can $f(x) = |f(x)|e^{i\phi(x)}$ 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": 54, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/2177-recurrence-problem-print.html | # Recurrence Problem
Printable View
• March 11th 2006, 10:11 PM
hotmail590
Recurrence Problem
Suppose that the function f satisfies the recurrence relation
2 * f ( sqrt(n) ) + log(n)
whenever n is a perfect square greater than 1 and f(2) = 1
For this problem I am asked to find f(16).
If I pluged in n = 16 into t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/torque | # Tagged Questions
The torque tag has no wiki summary.
1answer
65 views
### How is torque equal to moment of inertia times angular acceleration divided by g?
How is the following relation true $$\tau = \large\frac{I}{g} \times \alpha$$ where $\tau$ is torque, $I$ is moment of inertia, $g= 9.8ms^{-2}$, and $\alpha=$... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/33367/can-i-use-a-difference-score-as-my-outcome-variable-pre-post-change-in-a-moder | # Can I use a difference score as my outcome variable (pre-post change) in a moderated multiple regression equation?
I am wanting to examine whether religiosity moderates intervention effects on stigmatized attitudes. Here are my variables: X = group (1 = experimental; 0 = control) Z = religiosity (14-item scale - usi... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/trigonometry/46692-trigonometry-triangles-question.html | # Thread:
1. ## A trigonometry in triangles question?
In an isoceles triangle, if the altitudes intersect on the inscribed circle, then the cosine of the vertical angle A is?
2. The options are:
A) 1/9
B) 1/3
C) 2/3
D) None
How do I correlate the facts given in the question?
3. Originally Posted by fardeen_gen
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": 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/55391/heisenberg-uncertainty-principle-derivation-unexplained-factor-of-4-sigma-k?answertab=votes | Heisenberg uncertainty principle derivation - unexplained factor of $4 \sigma_k^2$ in Gaussian
I did a Fourier transform of a gaussian function $\scriptsize \mathcal{G}(k) = A \exp\left[-\frac{(k-k_0)^2}{2 {\sigma_k}^2}\right]$
$$\scriptsize \begin{split} \mathcal{F}(x) &= \int\limits_{-\infty}^{\infty} \mathcal{G}(k... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 30, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/88972/finding-an-orthogonal-basis-for-an-inner-product-space-mathbfp-2?answertab=oldest | # Finding an orthogonal basis for an inner product space $\mathbf{P}_2$
The problem reads as follows:
Look at the inner product in $\mathbf{P}_2$ given by $\langle p,q \rangle = p(0)q(0) + p(\frac{1}{2})q(\frac{1}{2}) + p(1)q(1)$.
Find an orthogonal basis $\mathbf{C}$ for $\mathbf{P}_2$.
Now, I know I can use the s... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/174674/if-n-balls-are-thrown-into-k-bins-what-is-the-probability-that-every-bin-gets-a | # If n balls are thrown into k bins, what is the probability that every bin gets at least one ball?
If $n$ balls are thrown into $k$ bins (uniformly at random and independently), what is the probability that every bin gets at least one ball? i.e. If we write $X$ for the number of empty bins, what is $P(X=0)$?
I was 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": 17, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/142189-relations-functions-ordered-pairs-print.html | # Relations, functions and ordered pairs.
Printable View
• April 29th 2010, 02:47 PM
jamieirl
Relations, functions and ordered pairs.
Hello all and thanks in advance for all of the help you'll be giving me for the next couple of weeks. I'm just finishing a college algebra class and admittingly I haven't been the best... | {"extraction_info": {"found_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": 45, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/101674-fraction-hard.html | # Thread:
1. ## fraction hard!
hi, i need to know what this is
i know i need to change tham to a top heavey fraction but i don't know how to do it, please could you show me what to do with workings out!!
2. The question isn't very clear in my opinion. Can you make it neater? :O
3. sorry i just saw that, it was ok ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 25, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://diracseashore.wordpress.com/2009/01/15/maldacenas-information-paradox/ | # Shores of the Dirac Sea
Feeds:
Posts
Comments
## Maldacena’s information paradox
January 15, 2009 by Moshe
Back in 2001, in a truly beautiful paper, Juan Maldacena formulated a version of Hawking’s information paradox, which has the added advantage that it could be discussed and analyzed in the context of a compl... | {"extraction_info": {"found_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://alanrendall.wordpress.com/2008/10/22/the-polarized-gowdy-equation/ | # Hydrobates
A mathematician thinks aloud
## The polarized Gowdy equation
The polarized Gowdy solutions are the simplest solutions of the vacuum Einstein equations which are dynamical and not spatially homogeneous. Physically they represent a one-dimensional configuration of polarized gravitational waves propagating... | {"extraction_info": {"found_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": 46, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=4182849 | Physics Forums
Deriving the algebraic definition the dot product
Is there a way of deriving the algebraic definition of the dot product from the geometric definition without using the law of cosines?
Recognitions: Gold Member Science Advisor Staff Emeritus What exactly do you mean by "the geometric... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/183045/can-one-solve-a-recurrence-that-contains-a-function | # Can one solve a recurrence that contains a function?
I'd like to solve a recurrence, so I've been reading about solving recurrences, and all the ones I've seen solved involve only previous terms of the recurrence, and constants. My recurrence is
$$t(n) = \frac{t(n-1)(1-\ln(n-1))}{\ln n}$$
and if I could get help s... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "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/60143/maximum-area-with-a-given-perimeter | # Maximum area with a given perimeter
An arbitrary pentagon (which is convex) is given to you, and it has a perimeter of $k$. Determine the i) maximum area, rigorously, in terms of $k$. ii) maximum INTEGRAL area, in terms of $k$.
-
1
Is it that u want to know when the area can be maximum? if so its in the case of 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": 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/140352/surjective-graded-homomorphism-of-rings-also-an-isomorphism | # Surjective graded homomorphism of rings also an isomorphism?
Suppose we are given two graded (commutative) rings $A$ and $B$ and a graded homomorphism $\psi:A\rightarrow{B}$ between them. Suppose moreover that $\psi$ is surjective in each degree i.e. that $\psi(A_n)=B_n$ for all $n$. If $\psi$ is injective in degree... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 31, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/48098/restriction-of-scalars-of-simple-algebraic-groups/112759 | ## Restriction of scalars of simple algebraic groups
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I'm trying to understand the following basic property of the restriction of scalars:
Given an absolutely simple algebraic groups $G$ defined over a number fie... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 87, "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/104731/instances-where-an-existence-result-precedes-the-constructive-version/104747 | ## Instances where an existence result precedes the constructive version
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The basic motivation here is to encourage and inspire - via examples - the pursuit of alternate proofs of existing results that might be mo... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-equations/190219-basic-laplace-transform-1st-order-differential-equation.html | # Thread:
1. ## Basic Laplace Transform of a 1st order Differential Equation
Just wondering if someone could have a quick look over what I've done so far:
Assuming zero initial conditions, solve the following DE:
$\dot{x} + x = 2$
The Laplace Transform gives:
$sX(s) - x_0 + \frac{1}{s^2} = \frac{2}{s}$
Rearrangi... | {"extraction_info": {"found_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": 41, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/44528/a-simple-decomposition-for-fractional-brownian-motion-with-parameter-h1-2/101173 | ## Background
Let `$X = \{X(t):t \geq 0\}$` be a (standard, real-valued) fractional Brownian motion (fBm) with parameter `$H \in (0,1)$`, i.e., a continuous centered Gaussian process with covariance function given, for `$0 \leq s \leq t$`, by $$C_X {(s,t)} := {\rm E}[X(s)X(t)] = \frac{1}{2}[t^{2H} + s^{2H} - (t - s)^{... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/50298-position-function.html | Thread:
1. Position Function?
Hey, I am in MAT270 and I can't find how to do this problem anywhere in my book, can someone help me out?
I am going to post a similar problem because I would like to figure out how to do this by the steps taken to find the answer to the similar problem.
"Use the position function f(t)... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.scholarpedia.org/article/Zinn-Justin_equation | # Zinn-Justin equation
From Scholarpedia
Jean Zinn-Justin (2009), Scholarpedia, 4(1):7120.
Curator and Contributors
1.00 - Jean Zinn-Justin
Quantum field theories in a naive formulation lead to physical results plagued with infinities due to short distance singularities and require a regularization, operation by wh... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 69, "mathjax_display_tex": 213, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://math.stackexchange.com/questions/231137/polynomial-orthogonal-complement/231170 | # Polynomial Orthogonal Complement
Let $V = \mathbb{P^4}$ denote the space of quartic polynomials, with the $L^2$ inner product $$\langle p,q \rangle = \int^1_{-1} p(x)q(x)dx.$$ Let $W = \mathbb{P^2}$ be the subspace of quadratic polynomials. Find a basis for and the dimension of $W^{\perp}$.
The answer is $$t^3 - \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": 71, "mathjax_display_tex": 15, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/53999/industry-application-of-computational-quantum-mechanics/54000 | # Industry application of computational quantum mechanics?
I was wondering if anybody knew of an industry application of computational quantum mechanics. For example, the efficient placement of circuit elements on a PCB is in part motivated by classical FDTD simulations. I can make a long list of applications of class... | {"extraction_info": {"found_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/60227/chern-character-of-the-index-bundle-for-a-family-of-dirac-operators/60309 | ## Chern character of the index bundle for a family of Dirac operators
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Suppose we have a family of compact oriented even dimensional spin manifolds ${Y_x}$ parameterized by a compact even dimensional manifold $X$... | {"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": 83, "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/5888/how-can-super-massive-black-holes-have-a-lower-density-than-water?answertab=votes | # How can super massive black holes have a lower density than water?
I'm new here, so go easy!
I heard on a podcast recently that the supermassive black holes at the centre of some galaxies could have densities less than water, so in theory, they could float on the substance they were gobbling up... can someone expla... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/40921-i-need-help-trig.html | Thread:
1. I need help with trig!
Hi i really really need to answer these last two questions by the next 30minutes!! (i have online math) can anyone help me?
Use the formulas for functions of the difference and sum of two angles to find, without tables or calculator, the cosine, sine, and tangent of 15degrees(using ... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/43451/classical-mechanics-a-particle-move-in-one-dimension-under-the-influence-of-two | # Classical Mechanics: A particle move in one dimension under the influence of two springs [closed]
A particle of mass $m$ can move in one dimension under the influence of two springs connected to fixed points a distance $a$ apart (see figure). The springs obey Hooke’s law and have zero unstretched lengths and force 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": 7, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/differential-equations/189406-partial-differential-equation-method-characteristics-ode-solve.html | # Thread:
1. ## Partial Differential Equation -- method of characteristics (ode solve)
$u_t + cos(\pi x) u_x = 0$ using the method of characteristics. This amounts to solving the following odes:
$dt/ds = 1, t(0) = 0$ which implies $t = s$ and
$dx/ds = cos(\pi x), x(0) = x_0$.
This ode yields (if I'm right):
$|sec... | {"extraction_info": {"found_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://mathoverflow.net/questions/120150/can-fpa-really-prove-its-consistency/120216 | ## Can FPA really prove its consistency?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I will ask the question first and then explain.
QUESTION: FPA can prove its own consistency in the Godelian sense. But can it really prove its consistency?
FPA is a mult... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 108, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/revisions/76832/list | ## Return to Question
2 edited body
There are several definitions of 3D discrete lines, e.g. http://diwww.epfl.ch/w3lsp/publications/discretegeo/nratddl.html , http://dx.doi.org/10.1007/978-3-642-19867-0_4 . However, I know of none that has all the following properties:
• Minimal 6-connectedness: The discrete line 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": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://elidourado.com/blog/tag/copyright-term/ | • Research
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# Copyright Reform and the Incentive to Create
Mercatus has a new book out on copyright, edited by Jerry Brito, called Copyright Unbalanced: From Incentive to Excess. I am pleased to be one of an otherwise-illustrious group of contributors.
I expect that the book will create some 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": 0, "wp_latex": 22, "mimetex.cgi": 0, "/images/ma... |
http://mathforum.org/mathimages/index.php?title=First_Fundamental_Form&oldid=20631 | # First Fundamental Form
### From Math Images
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Let $M$ be a regular surface with $v_p,w_p$ points in the tangent space $M_p$ of $M$. Then the first fundamental form is the inner ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 10, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/2076/division-in-paillier-cryptosystem/2096 | Division in paillier cryptosystem
Is division possible in the Paillier Cryptosystem? i.e. given a the cipher-text $C$ of an integer $M$ the plain-text divisor $D$, and only the public key, can one compute the cipher-text of $M/D$ ?
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3 Answers
In general, no. There are, however, specific conditions that, when met, ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 56, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/320334/a-question-from-arhangelskii-buzyakova | # A question from Arhangel'skii-Buzyakova
Recently, I am reading the paper: On linearly Lindelöf and strongly discretely Lindelöf spaces by Arhangel'skii and Buzyakova. Here is the Lemma 2.2 in paper. (Sorry for the picture is not clear.)
The fifth line from last. How could I see that for any $a\in H$ and $z\in Z\set... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/104212?sort=newest | ## Adjoining a new isolated point without changing the space
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Suppose $X$ is a $T_1$ space with an infinite set of isolated points. Show that if $X^\sharp = X \cup \lbrace \infty \rbrace$ is obtained by adding a s... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "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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