content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
congruence and gcd
March 25th 2008, 04:43 PM #1
Member
Joined
Mar 2008
Posts
84
Can anyone please help me with this proof?
“ if ab≡0(mod n), then shows that gcd(a,n)∙gcd(b,n)=n. “
Any suggestions will be very appreciate.
denise,
This is a standard problem in elementary number theory.... | 4 | [
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I need help with solving inequalities via derivatives
January 15th 2010, 01:34 AM #1
Newbie
Joined
Jan 2010
Posts
2
I need help with solving inequalities via derivatives
Hello guys, I have a problem with solving these inequalities. If anyone could help me I would really appreciate it.
1. e^x>1+ln(1+... | 5 | [
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0.0208740234375,
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-0.03295898437... | 36,401 | 36401 | |
Centralizer of a subgroup is a subgroup of the main group
March 1st 2010, 07:10 AM #1
Newbie
Joined
Mar 2010
Posts
5
Centralizer of a subgroup is a subgroup of the main group
Hello! This is my first post here, and I believe I checked all previous posts and could not find one like this.
The question ... | 4 | [
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0.04541015625,
-0.0255126953125,
-0.023071... | 36,402 | 36402 | |
Vector bundles on $\mathbb{P}^1\times\mathbb{P}^1$
up vote 10 down vote favorite
6
I have a question about vector bundles on the algebraic surface $\mathbb{P}^1\times\mathbb{P}^1$. My motivation is the splitting theorem of Grothendieck, which says that every algebraic vector bundle
$F$ on the projective line $\mathbb{... | 5 | [
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0.0063781... | 36,403 | 36403 | |
What is the double derivative(y") of x^2+y^2=25
Last edited by mr fantastic; January 24th 2010 at 04:36 PM. Reason: Copied title of post into main body.
dy/dx of x^2 + y^2 = 25 is gonna be 2x + 2y(dy/dx)=0 Simply take the second derivitive of that to find your answer. This is assuming that y is your dependent variable... | 5 | [
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... | 36,404 | 36404 | |
Quotient Ring
November 7th 2008, 03:31 PM #1
Quotient Ring
Just to make sure I get it right.
$\mathbb F_5[x]/(x^2+2)$ is a field.
We want to express $(x^2 + x) \cdot (x^3 + 1) - (x + 1)$ as a polynomial of degree less than 2.
$(x^2+2-2+x)\cdot(x^3+2 -2x+1)-(x + 1)$
$(x-2) \cdot (1-2x) - (x + 1)$
... | 5 | [
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-0... | 36,405 | 36405 | |
Homework Help
Posted by Anonymous on Saturday, October 31, 2009 at 12:06pm.
Given that sin pie/6 = 1/3,
use an equivalent trigonometric expression to show that
cos pie/3 = 1/2.
• math - Reiny, Saturday, October 31, 2009 at 12:36pm
First of all
sin pi/6 = 1/2 not 1/3,
recall that cos 2A = 1 - 2sin^2... | 4 | [
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0.002593994140625,... | 36,406 | 36406 | |
Algebra.. with 8 variables.
June 7th 2008, 11:55 PM #1
Newbie
Joined
Jun 2008
Posts
3
Algebra.. with 8 variables.
Ok i have these 4 equations:
a^2 + bc + w^2 + xy = (a+w)^2 + (b+x)(c+y)
ca + cd + yw + yz = (c+y)(a+w) + (c+y)(d+z)
ba + bd + xw + xz = (b+x)(a+w) + (b+x)(d+z)
cb + d^2... | 4 | [
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0.052978... | 36,407 | 36407 | |
Questions about ordering of reals and irrationals
up vote 8 down vote favorite
4
Three problems from G.Rosenstein "Linear orderings" (from the end of Chapter 2 and beginning of Chapter 4):
1) Is there a nondecreasing function from irrationals onto reals?
2) Is there a nondecreasing function from reals onto irrationa... | 5 | [
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-... | 36,408 | 36408 | |
Radstrom cancellation only for two convex sets?
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
I've seen this statement of Radstrom cancellation: if $A +C \subset B+C$ where $A,B$ are convex, $B$ is closed, and $C$ is b... | 5 | [
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Cyclic Distribution on the reals?
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
Do there exist binary operators *, **, and *** on the real numbers, such that * distributes over **, ** distributes over ***, *** distribu... | 5 | [
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0.029... | 36,410 | 36410 | |
Intermediate Value Theorem, location of roots
The assertion of the Intermediate Value Theorem is something which is probably ‘intuitively obvious’, and is also provably true: if a function $f$ is continuous on an interval $[a,b]$ and if $f(a) <
0$ and $f(b) > 0$ (or vice-versa), then there is some third point $c$ with ... | 5 | [
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-0.059814453125,
-0.049316... | 36,411 | 36411 | |
Solve 2x + 3 = 10
Date: 09/17/2001 at 20:43:24
From: Billy
Subject: Something like 2x+3=10
My problem: 2x + 3 = 10
You are supposed to subtract 3 from the 10, which is 7, then divide by
two, which is 3.5x + 10. I don't get what to do next to simplify the
problem.
Date: 09/18/2001 at 10:21:40
From: Doctor Rick
Sub... | 4 | [
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0.11572265625,... | 36,412 | 36412 | |
Rate of decay of variance for a tensor product Markov process (100 pt bounty for good answer by 1800 EST Fri)
up vote 1 down vote favorite
Let $Q$ be the generator of a well-behaved (not necessarily reversible) Markov process $X$ on $[n] = \{1,\dots,n\}$ and let $Q^\otimes = \sum_{m=1}^N I^{\otimes(m-1)} \otimes Q \ot... | 4 | [
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0.039306640625,
-0.01519775... | 36,413 | 36413 | |
Torsion in triangle groups
up vote 7 down vote favorite
5
A triangle group has a presentation of the form,
$G=\langle a, b; a^{\alpha}, b^{\beta}, c^{\gamma}, abc\rangle, \alpha, \beta, \gamma \geq 2$
(I believe that these are also called von Dyke groups, or "ordinary" triangle groups, with triangle groups being som... | 4 | [
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Normal Subgroup
October 22nd 2009, 03:53 PM #1
Junior Member
Joined
Oct 2009
Posts
58
Normal Subgroup
Define W= <(1 2)(3 4)>, the cyclic subgroup of $S_4$ generated by (1 2)(3 4). Show that W is a normal subgroup of V, where V ={(1), (1 2)(3 4), (1 3)(2 4), (1 4)(2 3)}, but that W is not a normal
sub... | 5 | [
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Geometric proof of the Vandermonde determinant?
up vote 53 down vote favorite
25
The Vandermonde matrix is the $n\times n$ matrix whose $(i,j)$-th component is $x_j^{i-1}$, where the $x_j$ are indeterminates. It is well known that the determinant of this matrix is $$\prod_{1\leq
i < j \leq n} (x_j-x_i).$$
There are m... | 5 | [
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0.069... | 36,416 | 36416 | |
Balls In Bins With Limited Capacity
Given n indistinguishable balls and m bins, where each bin has a
capacity of c(i) (i = 1 to m) balls, in how many ways can the n balls
be distributed in the m bins? Note that n <= sum of c(i)'s; one
or more bins may have room for all n balls; we don't care which balls
are in whi... | 5 | [
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0.099609375,
-0.0224609375... | 36,417 | 36417 | |
Scientific
Worksheet on Powers of Ten and Scientific Notation
Scientific Notation is used a lot in astronomy. It helps us to write succinctly the very large and small numbers we often encounter (sizes, distances, times, etc). The appendix of Ben... | 4 | [
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Noooo, I got wasted o.O
November 23rd 2008, 02:24 AM #1
Noooo, I got wasted o.O
Prove teh Identitiy
$<br /> cosh (x+ y) = cosh x cosh y + sinh x sinh y<br />$
from the basic definitions of the hyperbolic functions. Hence, or otherwise show that if x and y satisfy the equations
cosh x cosh y = 2,
... | 5 | [
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Sine-Cosine-Tangent
To better understand certain problems involving rockets and propulsion it is necessary to use some mathematical ideas from trigonometry, the study of triangles. Let us begin with some definitions and
terminology which we will use on this slide. A right triangle is a three sided figure with one angle... | 4 | [
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0.0639648437... | 36,420 | 36420 | |
pairwise disjoint subset question
October 10th 2011, 06:11 PM #1
Senior Member
Joined
Jan 2010
Posts
273
pairwise disjoint subset question
A) Show that $N$ contains infinitely many pairwise disjoint infinite subsets. [Hint: It was shown that $N$~ $N$x $N$
what is a pairwise disjoint infinite subset... | 5 | [
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0.03173828125... | 36,421 | 36421 | |
Can anyone prove this determinant?
If A is a square matrix of order n and m ϵ R then the det(mA) = (mn) (detA)
Well, observe that for any scalar $m \in R$ and nxn matrix A. $mA = A*mI$ where I is the standard nxn identity matrix. So you got $mI = \begin{bmatrix} m && 0 && ... && 0 \\ 0 && m && ... && 0 \\ ..
&& .. && ... | 5 | [
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0.00140380859375,
0.0673... | 36,422 | 36422 | |
Definition of Chow groups over Spec Z
up vote 9 down vote favorite
3
Usually (eg, intro. in M. Rost's 'Cycle modules with coefficients'), for a variety, $X$, over a field one can define the Chow group of p-cycles, $CH_p (X)$, as $$CH_p (X) = coker\; \left[\bigoplus_{x
\in X_{p+1}} k(x)^\times \rightarrow \bigoplus_{x\... | 4 | [
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-0.01104736328125,
-0.05712890625,
-0.0032043457... | 36,423 | 36423 | |
Algebra Help Needed
June 15th 2007, 05:12 PM #1
Newbie
Joined
Feb 2007
Posts
17
Algebra Help Needed
Can anyone please show me the simpliest way to work out these ?
25-7a=27-4a
11-7(2-a) = 18
4
- (x+3) = 6
5
Thanks heaps
we want to solve for $a$, so our objective is to... | 4 | [
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-0.0576171875,
0... | 36,424 | 36424 | |
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Topic: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A s... | 5 | [
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0.038330078125,
-0.052978515625,
-0.0693359375,
-0.1235... | 36,425 | 36425 | |
Growth rate of number of loops in a graph
up vote 15 down vote favorite
4
Let G be a directed graph with a countable number of vertices, and suppose G is strongly connected (given any two vertices v and w, there exists a path from v to w). Fix a base vertex v[0]∈G, and let
L[n] denote the number of loops of length n b... | 4 | [
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0.042236328125,
-0.017578125,
0.00086212158203125,
0.00010538101196289062,
0.06201171875,
-... | 36,426 | 36426 | |
Find the arccos value?
Find the value of 2.arccos 3/√13 + arccot 16/63 + arccos 7/25 Answer: arctan 3/4 How to solve this?
I was told that assuming an inverse trigonometric function as an angle simplifies the problem. This doesn't seem to help me in this problem.
Hello,I've seen some problems solved this way, but I j... | 5 | [
-0.052490234375,
0.042236328125,
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0.06103515625,
0.0281982421875,
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0.0693359375,
-0.0211181640625,
0.04248046875,
0.00262451171875,
-0.1123046875,
0.00634765625,
0.05712890625,
-0.00933837890625,
-0.0021209716796875,
0.002426147460937... | 36,427 | 36427 | |
Martingale part of the discontinuous put payoff
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
I need the martingale part of the put payoff (not $C^2$..). Where $S_t=exp(\sigma W_t -\frac{\sigma^2t}{2})$
... | 5 | [
0.003662109375,
-0.02001953125,
0.046630859375,
0.00038909912109375,
0.016845703125,
0.01348876953125,
0.046142578125,
0.0311279296875,
0.029541015625,
0.08984375,
0.038818359375,
0.01373291015625,
0.0081787109375,
-0.06591796875,
-0.0595703125,
0.0120849609375,
0.05224609375,
0.03... | 36,428 | 36428 | |
Solve: tan2x + tan x = 0
Hi You can use the trig identity $\tan(2x) = \frac{2\tan x}{1-tan^2x}$ and factor
Hi SarahGr, Solve: $\tan 2x + \tan x = 0$ Recall that $\tan 2x=\frac{2 \tan x}{1-\tan^2 x}$ $\frac{2 \tan x}{1-\tan^2 x}+ \tan x=0$ $2 \tan x+\tan x(1-\tan^2 x)=0$ $2 \tan x+ \tan x - \tan^3 x=0$ $3
\tan x - \tan... | 4 | [
-0.0255126953125,
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0.01104736328125,
0.09423828125,
-0.0625,
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0.01385498046875,
0.0019683837890625,
-0.045654296875,
0.04345703125,
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0.00872802734375,
-0.0037078857421875,
0.061767578125,
-0.0223388671875,
-0.00714111328125,
... | 36,429 | 36429 | |
Math Help
September 20th 2008, 07:47 PM #1
factor
Find the value of P and q if 4x²-4x-3 is a factor of the expression 8x^4+px³+qx²+x+3.
The factor of it thta that get frm 4x²-4x-3 is (x-3/2)(x+1/2)
so i sub in as 8(3/2)^4+p(3/2)^3....
and 8(-1/2)^4...
then i get 3(3/8)p+2(1/4)q=-45 and (-1/8)p+(... | 4 | [
-0.00518798828125,
0.0625,
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0.055908203125,
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0.052001953125,
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0.068359375,
0.08154296875,
0.0089111328125,
0.0166015625,
-0.0181884765625,
-0.01019287109375... | 36,430 | 36430 | |
Cyclic subgroup
October 21st 2007, 04:02 PM
tttcomrader
Cyclic subgroup
Suppose that the order of some finite Abelian group is divisible by 10. Prove that the group has a cyclic subgroup of order 10.
My proof so far:
Suppose G is a finite Abelian group with 10 | |G|. By a theorem, I know that G contain... | 5 | [
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0.04296875,
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0.048095703... | 36,431 | 36431 | |
A complex rational equation I'm having trouble with
October 18th 2007, 09:41 PM
saywhat
A complex rational equation I'm having trouble with
I've posted before about my fractal project, and this is something else that is related. The function:
$f(z)=\frac{1-z}{(2-z)^{\frac{3}{2}}}$ where $|z|=1$.
The de... | 4 | [
-0.07177734375,
0.01446533203125,
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0.050537109375,
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-0.063476562... | 36,432 | 36432 | |
projectively cofibrant diagram
Context
Model category theory
Definitions
Morphisms
Universal constructions
Refinements
Producing new model structures
Presentation of $(\infty,1)$-categories
Model structures
for $\infty$-groupoids
for $n$-groupoids
for $\infty$-groups
for $\infty$-algebras
general
specific... | 4 | [
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0.03564453125,
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0.04345703125,
0.057373046875,
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0.0634765625,
0.02319335937... | 36,433 | 36433 | |
connectedness of the complement of the zero set of a polynomial $P: SL(N,\mathbb{C})^n \rightarrow \mathbb{C}$
up vote 2 down vote favorite
I know that the complement of the zero set of a polynomial $P: \mathbb{C}^n \rightarrow \mathbb{C}$ is connected in $\mathbb{C}^n$ (by the way, can anybody suggest a reference?).
... | 4 | [
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-0.05126953125,
-0.025146484375,
0... | 36,434 | 36434 | |
Example of two structures
up vote 5 down vote favorite
This is probably a very trivial question, still I don't seem to find an answer.
I'd like to see an example (in some language) of two countable structures $\mathcal{M}_1 $ and $ \mathcal{M}_2 $ with $$ \mathcal{M}_1 \equiv\mathcal{M}_2 $$ and the property that the... | 5 | [
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-0.0047607421875,
0.0454... | 36,435 | 36435 | |
Flat cohomology and Picard groups
up vote 6 down vote favorite
2
Let $(R,m)$ be a local complete intersection of dimension $3$. Let $X=Spec(R)$ and $U=Spec(R) -\{m\}$ be the punctured spectrum of $R$. I am trying to understand the following comment by Gabber (see
it here , page 1975-1976):
$Pic(U)$ is torsion-free is... | 4 | [
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0.0527343... | 36,436 | 36436 | |
Posts from June 2012 on Matt Dickenson
Recently I needed to combine data from two of the most widely used (at least in my subfield) cross-national time-series data sets: Arthur Banks’ time series and the Correlates of War Project (COW).
Given how often these data sets are used, I was a bit surprised that I could not fi... | 5 | [
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0.052490234375,
-0.046630859375,
-0.00256... | 36,437 | 36437 | |
Evaluate the following double integrals
November 29th 2010, 11:50 AM #1
Member
Joined
Jan 2010
Posts
232
Evaluate the following double integrals
I swear, our Prof. must get shot at at least once a year for some of the crazy assignments he gives out. At least one student per year in his class must go insa... | 5 | [
0.0301513671875,
0.00946044921875,
0.0030670166015625,
-0.0947265625,
-0.0164794921875,
-0.076171875,
-0.041748046875,
0.00072479248046875,
-0.042724609375,
-0.003204345703125,
-0.015625,
0.04638671875,
-0.015380859375,
0.038330078125,
-0.01043701171875,
0.08642578125,
-0.02856445312... | 36,438 | 36438 | |
Question on Probability
Given that $P(eg A)=0.6$ $P(B\mid A)=0.7$ $P(B)=0.3$ What is $P(eg A \wedge B)$?
Here is another way. Recall that $P(B) = P(B \cap A) + P(B \cap eg A)$ Solve for $P(B \cap eg A)$.
Hello, quiney! Yet another approach . . . Quote: Given that: . . $\begin{array}{ccc}P(\sim\!A)&=& 0.6 \\<br /> P(B... | 4 | [
0.006256103515625,
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-0.041259765625,
0.025390625,
0.08203125,
0.01019287109375,
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0.021484375,
0.07275390625,
0.07275390625,
-0.0269775390625,
-0.024780273437... | 36,439 | 36439 | |
solve: lx-3l - lx-1l << 2
solve: lx-3l - lx-1l << 2 I got x<<1 but i think its wrong. THank u
1. Use the definition of the absolute value: $|x-3| = \left\{\begin{array}{lcr}x-3&if&x \geq 3\\-(x-3)&if&x < 3\end{array}\right.$ $|x-1| = \left\{\begin{array}{lcr}x-1&if&x \geq 1\\-(x-1)&if&x < 1\
end{array}\right.$ 2. Thus... | 4 | [
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0.0126953125,
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0.01055908203125,
-0.02685546875,
-0.1... | 36,440 | 36440 | |
Combinatorial Inequality
up vote 2 down vote favorite
Consider a set of $2^n-1$ non negative integers $S= ${$ a_{i,j}|1\le i\le n; 1\le j\le 2^{i-1} $} such that:
{} 1.\ \ &a_{i,j}\le 2^{n+1-i} \\\\ 2.\ \ &a_{i,j}\le a_{i-1,j} \\\\ 3.\ \ &a_{1,1}+\sum_{i=2}^n\left(\sum_{j=2^{i-2}+1}^{2^{i-1}}{a_{i,j}}\right)\le 2^n P... | 5 | [
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0.022705078125,
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0.08935546875,
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0.06396484375,
0.08935546... | 36,441 | 36441 | |
Decreasing sequence Aleph's
December 24th 2009, 12:12 PM
Dinkydoe
Decreasing sequence Aleph's
I need to show: there does not exist a sequence:
$\left\langle X_n:n\in \omega \right\rangle$ such that $(\forall n)(\mathcal{P}(X_{n+1})\preceq X_n)$.
Supposing there exists such a sequence:
We can observ... | 5 | [
-0.08935546875,
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0.0277099609375,
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0.062255859375,
0.00506591796875,
0... | 36,442 | 36442 | |
Nefness of $h-e$ in the blowup of $\mathbb{P}^n$
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
Let $S$ be the blow up of $\mathbb{P}^n$ in a point $P$. Let $h$ be the class of the pullback of an hyperplane of $\mathbb{P}^n$ ... | 5 | [
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0.0361328125,
-0.005767822265625,
-0.046142578125,... | 36,443 | 36443 | |
v-Na generated by
up vote 4 down vote favorite
2
Given two free semicirculars X_1 and X_2 and a projection h in the von-Neumann algebra generated by X_1, how does one show that the von-Neumann algebra generated by {X_1, hX_2(1-h)} is a factor? It
is easy to show that the two elements in the generating set are free. B... | 5 | [
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0.01171875,
0.044189453125,
-0.053955078125,
-0.0830078125,
-0.... | 36,444 | 36444 | |
Finding the Complete Sufficient Statistic
January 21st 2010, 03:56 PM
statmajor
Finding the Complete Sufficient Statistic
Let $f(x; \theta) = \theta e^{-\theta x}$. Find the complete sufficient statistic for theta.
From what I understand, I have write the PDF in the "form" of the Regulat Exponential Class/F... | 4 | [
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0.0211181640625,
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0.08642578125,
0.01007080078125,
-0.03955078125,
-0.0194091796875,
-0.018798828125,
-0.0... | 36,445 | 36445 | |
Where do the real analytic Eisenstein series live?
up vote 11 down vote favorite
5
In obtaining the spectral decomposition of $L^2(\Gamma \backslash G)$ where $G=SL_2(\mathbb{R})$, and $\Gamma$ is an arithmetic subgroup (I am satisfied with $\Gamma = SL (2,\mathbb{Z})$) we have a
basis of eigenfunctions of the hyperbo... | 4 | [
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-0.001373291015625,
-... | 36,446 | 36446 | |
Continuity and Differentiability
June 29th 2008, 01:53 AM #1
Newbie
Joined
Jun 2008
Posts
7
I am confused about the definition of continuity and differentiability of n-variable functions. Also, what is the meaning of continuously differentiable?
Here are some examples that I don't understand fully. P... | 4 | [
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0.001678466796875,
0.0166015625,
-0.01031494140625,
-0.046142578125,
-0.... | 36,447 | 36447 | |
Integrals
July 21st 2008, 08:49 AM #46
I am actually going to use induction on this one, so if I mess it up please forgive me.
$\int_0^{1}\ln^n(x)~dx=(-1)^nn!\quad{n\in\mathbb{N}}$
Base Case
Let us start with the base case $n=0$
$\int_0^1\ln^0(x)~dx$
$=\int_0^1~dx$
$=1$
$=(-1)^00... | 5 | [
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0.010... | 36,448 | 36448 | |
Indeterminate "x" in Abstract Algebra/Ring Theory
up vote 4 down vote favorite
1
How do you interpret the indeterminate "x" in ring theory from the set theory viewpoint? How do you write down R[x] as a set? Is it appropriate/correct to just say that
$R[x] = \{ f: R \to R | \exists n \in \mathbb{N}, \mbox{ and } c_0, ... | 4 | [
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0.019775390625,
0.0079345703125,
-0.03... | 36,449 | 36449 | |
optimality of energy estimates for non smooth metric
up vote 2 down vote favorite
2
Consider the linear (geometric) wave equation in dimension (3+1) with non smooth background metric $g$ say $g \in L^\infty_t H^3_x$ and $\partial_t g \in L^\infty H^2_x$, then energy estimates enable
to propagate sobolev regularity of ... | 4 | [
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0.0147705078125,
0.034423828125,
-0.0... | 36,450 | 36450 | |
Two trig equations
I ran into problems with these two trig equations, can someone help me ? $arccosx-arcsinx=arccos\frac{\sqrt{3}}{2}$ $arccosx+arccos(1-x)=arccos(-x)$
For the first problem: $\arccos x - \arcsin x = \arccos \frac{\sqrt{3}}{2}$ $\cos (\arccos x - \arcsin x) = \frac{\sqrt{3}}{2}$ $\cos (\arccos x) \cos ... | 5 | [
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0.0223388671875,
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0.0048828125,
0.0157470703125,
-0.004302978515625,
-0.0022125244140625,
-0... | 36,451 | 36451 | |
To what extent does Poincare duality hold on moduli stacks?
up vote 6 down vote favorite
2
Poincare duality gives us, for a smooth orientable $n$-manifold, an isomorphism $H^k(M) \to H_{n-k}(M)$ given by $\gamma \mapsto \gamma \frown [M]$ where $[M]$ is the fundamental class of the
manifold, and $\frown$ is the cap pr... | 4 | [
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0.07958984375,
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0.06982421875,
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-0.03369140625,
0.045166015625,
0.10302734375,
-0.0234375,
0.05590820312... | 36,452 | 36452 | |
Probability Question
up vote 2 down vote favorite
You have $N$ boxes and $M$ balls. The $M$ balls are randomly distributed into the $N$ boxes. What is the expected number of empty boxes?
I came up with this formula:
$\sum_{i=0}^{N}i\binom{N}{i}\left(\frac{N-i}{N}\right)^{M}$
This seems to yield the right answer. Ho... | 5 | [
0.1083984375,
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-0.0026397705078125,
0.052978515625,
0.1005859375,
0.1083984375,
-... | 36,453 | 36453 | |
Limits.
September 4th 2012, 06:01 PM
Zirrick
Limits.
"Find the limit or explain why it does not exist"
Attachment 24702
I'm having trouble with these problems, I can't factor/these into a different form.
Having trouble with the algebra.
I've just started calculus and we haven't gone very far so w... | 5 | [
-0.08740234375,
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0.0159912109375,
0.05126953125,
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-0.072265625,
0.0111083984375,
0.006622314453125,
0.061767578125,
-0.10791015625,
-0.032958984375,
0.06787109375,
0.0042724609375,
-0.0172119140625,
-0.0380859375,
0.0115356445312... | 36,454 | 36454 | |
Do sufficiently regular distances on manifolds come from riemannian metrics?
up vote 6 down vote favorite
1
Hi to all!
Let $M$ be a compact smooth manifold without boundary and let $$d:M\times M\rightarrow [0,+\infty)$$ a distance on $M$ compatible with its topology. Suppose there exist $\varepsilon\in (0,+\infty)$
s... | 5 | [
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0.0255126953125,
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0.046875,
-0.07421875,
0.05810546875,
0.0... | 36,455 | 36455 | |
Double Integral question
March 6th 2011, 09:00 AM #1
Newbie
Joined
Jan 2007
Posts
16
Double Integral question
Hey everyone, I'm having some trouble in my Multivariable Calculus class. I hope someone can help! I'm sorry that I don't know how to properly make the integral look pretty! Thanks in advance.
... | 4 | [
-0.00159454345703125,
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0.03955078125,
0.0205078125,
0.... | 36,456 | 36456 | |
More Thoughts on DiMaggio’s 56-Game Hitting Streak
This article was published in the Summer 2010 Baseball Research Journal.
Each time a player is at bat in a game, there is a certain probability that he will get a hit or not.
Probability theorists usually think about this in terms of a tossing a biased coin (that is... | 4 | [
0.02197265625,
0.08984375,
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0.076171875,
0.06884765625,
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0.0712890625,
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-0.04150390625,
0.00205993652... | 36,457 | 36457 | |
21^100 - Last Two Digits
Date: 09/04/97 at 21:19:52
From: K
Subject: 21^100
What are the last two digits of 21 to the 100th power?
Date: 09/05/97 at 07:32:48
From: Doctor Anthony
Subject: Re: 21^100
The last two digits follow a pattern:
Number Last two digits
21 21
21^2 ... | 4 | [
0.0133056640625,
0.08203125,
-0.0020751953125,
0.003387451171875,
-0.0225830078125,
0.00689697265625,
0.01031494140625,
0.0260009765625,
0.004486083984375,
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0.0289306640625,
0.019775390625,
0.06787109375,
-0.0184326171875,
0.0230712890625,
-0.1572265... | 36,458 | 36458 | |
Finding a potential function for conservative vector fields
The process of finding a potential function of a conservative vector field is a multi-step procedure that involves both integration and differentiation, while paying close attention to the variables
you are integrating or differentiating with respect to. For t... | 5 | [
-0.024658203125,
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0.031494140625,
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-0.047119140625,
-0.0305... | 36,459 | 36459 | |
LINEAR
make some arithmetic inequality rules
Major Section: RULE-CLASSES
See rule-classes for a general discussion of rule classes and how they are used to build rules from formulas. An example :corollary formula from which a :linear rule might be built is:
Example:
(implies (and (eqlablep e) if inequali... | 4 | [
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0.0791015625,
0.06494140625,
-0.000492095947265625,
0.07763671... | 36,460 | 36460 | |
Running Problem (Time and Distance)
Date: 8/31/96 at 18:53:20
From: Anonymous
Subject: Time and distance problems
If Lucy runs 3 mph and Jan runs 7 mph, when will Jan catch up with
Lucy if she gives Lucy a head start?
I think I solved it with a proportion, but I wonder if this is the
best approach. Here is my "sol... | 4 | [
-0.0284423828125,
0.05029296875,
0.038818359375,
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0.0152587890625,
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0.0106201171875,
-0.057861328125,
0.0166015625,
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0.01043701171875,
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-0.010009765625,
-0.01... | 36,461 | 36461 | |
Question on Riemann integration
May 30th 2011, 03:32 AM
worc3247
Question on Riemann integration
Suppose that f is Riemann integrable on $(-\pi,\pi )$. Prove that:
$\lim_{n \to \infty} \int_{-\pi}^{\pi} \! f(x)cos(nx)dx=0$.
I can't see how to start this question, could someone help?
Thanks.
May 30th... | 4 | [
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0.002777099609375,
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-0.097167... | 36,462 | 36462 | |
∫∫∫ xy dV Triple Integration. Help with bounds!
July 13th 2008, 06:38 PM
crabchef
∫∫∫ xy dV Triple Integration. Help with bounds!
∫∫∫ xy dV, where the solid is a tetrahedron with vertices (0,0,0), (1,0,0),(0,2,0), and (0,0,3)
I tried this with 0<x<1, 0<y<-2x+2, and 0<z<3 with no luck =\ Are my bounds wrong ... | 4 | [
-0.0005035400390625,
0.021728515625,
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0.0279541015625,
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0.0234375,
-0.0233154296875,
-0.... | 36,463 | 36463 | |
L^2-Flattening Lemma
up vote 4 down vote favorite
2
I am reading a significant paper of Bourgain and Gamburd on "Uniform expansion bounds for Cayley graphs of $\mathrm{SL}_2(\Bbb{F}_p)$". They have proven a proposition which in their new papers they
call it "$L^2$-Flattening Lemma" (Indeed this proposition says more)... | 4 | [
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0.004852294921875,
... | 36,464 | 36464 | |
Applied Math: Beam Deflection using Separation of Variables
May 11th 2011, 06:17 AM #1
Newbie
Joined
May 2011
Posts
14
Applied Math: Beam Deflection using Separation of Variables
Beam's dynamic deflection is governed by the following PDE
EI(∂^4w/∂x^4)+(rho)*A* (∂^2w/∂t^2)=f(x,t)
where E = the m... | 4 | [
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... | 36,465 | 36465 | |
Change of variable for Laplace equation
November 21st 2009, 05:22 PM #1
Newbie
Joined
Nov 2009
Posts
4
Change of variable for Laplace equation
How do I show that the change of variable:
x = rcosθ , y = rsinθ
converts the Laplace equation uxx + uyy = 0 to
urr + 1/r ur + 1/r2 uθθ = 0
H... | 4 | [
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0.01507568359375,
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-0.04541015625,
-0.057373046875,
-0.0209... | 36,466 | 36466 | |
[SOLVED] Operations with ideals in a ring.
May 18th 2010, 02:15 PM
ENRIQUESTEFANINI
[SOLVED] Operations with ideals in a ring.
Hi:
Let a, b be elements of a commutative ring R, P ideal in R. I am frustrated by the fact that I cannot prove the following: if (ab) $\subset$ P then (a)(b) $\subset$ P. I think th... | 5 | [
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... | 36,467 | 36467 | |
Using Cauchy Integral Formula
February 4th 2013, 08:52 PM
Mazerakham
Using Cauchy Integral Formula
I thought I was a good math student, but for some reason I am getting tripped up on complex analysis. Can someone please explain what I am doing wrong when I try to solve the following problem?
Problem: Given ... | 4 | [
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... | 36,468 | 36468 | |
Orthocentric Tetrahedron
Date: 11/30/2002 at 03:19:08
From: Mrs. D
Subject: Orthocentric tetrahedron
I am a high school math teacher and a student came to me with this
problem:
Recall that the opposite edges of an orthocentric tetrahedron are
perpendicular. Let ABCD be an orthocentric tetrahedron. Show that
AB^2 + C... | 4 | [
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-0.0546875,
0.009643554... | 36,469 | 36469 | |
Prove that an isomorphism produces a basis of W
September 30th 2010, 08:26 AM #1
Member
Joined
Jan 2010
Posts
232
Prove that an isomorphism produces a basis of W
I think I may have the answer for this one, but I could use a second opinion.
Suppose $V$ and $W$ are vector spaces over a field $F$.
... | 5 | [
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-0.03564453125,
0.1005859375,
-0.023681640625,
0.01940... | 36,470 | 36470 | |
Basis for space which contains the image of a matrix
October 7th 2010, 11:14 PM
acevipa
Basis for space which contains the image of a matrix
Find a basis for $\mathbb{R}^3$ which contains a basis of $im(A)$, where
$A=\begin{pmatrix}1&2&3&4\\ 2&-4&6&-2\\-1 & 2& -3 & 1 \end{pmatrix}$
After row reduction
... | 4 | [
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-0.072265625,
-0.0908203125,
-0.02099609375,
... | 36,471 | 36471 | |
Another problem I posted, but not getting it.
November 21st 2009, 09:03 AM #1
Member
Joined
Jan 2009
From
Ontario Canada
Posts
219
Another problem I posted, but not getting it.
Bill can do a jobin 3.8 j, and john can do the same job in 5.4h. How will it take them to do the job together? ROUND your an... | 4 | [
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0.055908203125,
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-0.031005859375,
-0.0216064453125,
-0... | 36,472 | 36472 | |
Classifying all Equivariant Bilinear Forms on a Finite-Dimensional Module
up vote 2 down vote favorite
Given a finite dimensional (real) vector space $V$, and two non-degenerate bilinear forms $(\cdot,\cdot)_1$ and $(\cdot,\cdot)_2$, one can use a basic linear algebra argument to show that there
exists a unique invert... | 5 | [
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0.0908203125,
-0.06103515625,
0.05... | 36,473 | 36473 | |
Variational characterization of curvature?
up vote 4 down vote favorite
5
Consider a surface $S$ smoothly embedded in $\mathbb{R}^3$. Classically, the (Riemannian) curvature of $S$ is described by the second fundamental form, which is constructed from partial derivatives
of a local parameterization.
Alternatively, is... | 4 | [
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... | 36,474 | 36474 | |
Transfer function by differential equation
September 4th 2009, 02:26 AM #1
Newbie
Joined
Sep 2009
Posts
9
Transfer function by differential equation
How can I obtain the transfer function of system Y(s)/ X(s), which has the differential equation below ?
d^3/dt^3 + 3(d^2*y/dt^2) +5(dy/dt) + y = d^3*... | 5 | [
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0.03271484375,
-0.04345703125,
0.088378906... | 36,475 | 36475 | |
proof question about positive semidefinite matrix(important 4 regression analysis)
May 30th 2009, 01:16 AM
phoenicks
proof question about positive semidefinite matrix(important 4 regression analysis)
this is a proof I encounter in William Greene econometric analysis appendix section.
If A is a n*k with full... | 4 | [
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0.12451171875,
0.00909423828125,
-0.04... | 36,476 | 36476 | |
Find cos x and csc x
June 21st 2005, 11:56 AM #1
Newbie
Joined
Jun 2005
Posts
10
Find cos x and csc x
If sin x = -3/5 and x is in the 3rd quedrant, find cos x ?
If cos x = 5/13 and x is in the fth quadrant, find csc x?
PLEASE HELP?
If sin x = -3/5 and x is in the 3rd quedrant, find cos x ... | 4 | [
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0.04833984375,
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0.00494384765625,
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0.00020503997802734375,
0.006744384765625,
... | 36,477 | 36477 | |
Eigenvalues of permutations of a real matrix: can they all be real?
up vote 20 down vote favorite
5
For a matrix $M\in GL(n,\mathbb R)$, consider the $n!$ matrices obtained by permutations of the rows (say) of $M$ and define the total spectrum $TS(M)$ as the union of all their spectra (counting
repeated values separat... | 4 | [
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-0.00049591064453125,
-0.0194091796875,
-0.0174560546875,
0.06005859375,
0... | 36,478 | 36478 | |
Homomorphisms from powers of Z to Z
up vote 8 down vote favorite
I believe it is known that if I is a set of non-measurable cardinality, then any homomorphism $Z^I\to Z$ factors through a finite power. Here $Z$ is the group of integers. Can anyone give a reference
for this?
ac.commutative-algebra gr.group-theory
1... | 4 | [
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0.0172119140625,
-0.053955078125,
0.011657714... | 36,479 | 36479 | |
How do minimal polynomials relate?
up vote 2 down vote favorite
1
How does the idea of a "minimal polynomial" for a matrix (i.e. for a matrix $A$, the polynomial, $\mu (x)$, of least degree, such that $\mu (A) =0$) relate the the "minimal polynomial" for some
element, $\alpha $ over a field (i.e. the minimal polynomia... | 5 | [
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-0.0035400390625,
0.0... | 36,480 | 36480 | |
Monday Math: The Uniqueness of Prime FactorizationsMonday Math: The Uniqueness of Prime Factorizations
Monday Math: The Uniqueness of Prime Factorizations
jrosenhouse on February 14, 2011
The big number theory class has moved on to prime factorizations and the fundamental theorem of arithmetic. As it happens, though,... | 4 | [
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0.07373046875,
0.000873565673828125,
-0.01092529296875,
0.022216796875,
-0.0361328125,
0.0... | 36,481 | 36481 | |
When is a submanifold of $\mathbf R^n$ given by global equations?
up vote 28 down vote favorite
13
Let $M \subset \mathbf R^n$ be a (smooth) submanifold of dimension $d$. Under which conditions does there exist global equations defining $M$? By global equations I mean : does there exist a smooth
function $f: \mathbf R... | 4 | [
-0.0159912109375,
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0.0211181640625,
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0.02587890625,
0.0257568359375,
0.059326171875,
0.0189208984375,
0.0089... | 36,482 | 36482 | |
integration by partial fractions
How do I integrate this integral using partial fractions? \int_ dx/( Asin[x] + Bcos[x])^2 where a =/ 0 Thanks
Say $A,Bot = 0$ $\int \frac{dx}{A\sin x+B\cos x}$ Write, $\frac{1}{A\sin x + B\cos x} = \frac{1}{A\cdot \frac{2\tan^2 \frac{x}{2}}{1+\tan^2 \frac{x}{2}} + B\cdot \frac{1-\tan^2... | 5 | [
-0.0361328125,
0.0302734375,
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-0.08251953125,
0.004852294921875,
0.013671875,
0.037841796875,
0.083984375,
0.0... | 36,483 | 36483 | |
Feeding Oxen
Date: 6/26/96 at 18:29:12
From: Anonymous
Subject: Pastures, Oxen Food
We have 3 pastures with grass of identical height, density and growth
rate. The first is 3 1/3 acres and can feed 12 oxen for 4 weeks. the
second is 10 acres and can feed 21 oxen for 9 weeks. The third is 24
acres. How many oxen can ... | 4 | [
0.0196533203125,
-0.0020294189453125,
-0.0108642578125,
0.058349609375,
0.0284423828125,
-0.0810546875,
-0.068359375,
-0.0341796875,
-0.0341796875,
-0.04833984375,
0.051513671875,
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-0.00579833984375,
0.035888671875,
-0.041015625,
0.052001953125,
-0.052490234375,
-0.04... | 36,484 | 36484 | |
Triangular distribution
I'd like to write up something that will generate random numbers that would plot into a triangle distribution. I know how to get a normal distribution, which is similar.
But there doesn't seem to be anything in the random module about triangle distribution. Does anyone know of a way to do it?
... | 4 | [
-0.0654296875,
0.04052734375,
-0.0986328125,
-0.07470703125,
-0.05810546875,
-0.0947265625,
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-0.0296630859375,
-0.045654296875,
0.043212890625,
0.034423828125,
-0.04052734375,
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0.060791015625,
0.09326171875,
-0.0272216796875,
0.0252685546875,
-0.0... | 36,485 | 36485 | |
coordinate geometry
Find the perpendicular distance between the pair of parallel lines 3x-4y+12 = 0 and 3x-4y+2=0 How do i start ??
With your question there are two different ways to find the answer: 1. Choose any arbitrary point on the 1rst line; determine the equation of a line perpendicular to the 1rst line passing... | 4 | [
-0.0159912109375,
0.037109375,
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0.07421875,
0.0172119140625,
0.05615234375,
0.09228515625,
0.0233154296875,
0.035400390625,
0.00811767578125,
-0.064453125,
0.034423828125,
-0.09326171875,
-0.02734375,
... | 36,486 | 36486 | |
Multiplying Polynomials
Date: 07/10/2003 at 00:19:46
From: Jalise
Subject: Foiling
(x+2)(x+2)(x+2)
How do you foil?
Date: 07/10/2003 at 12:21:22
From: Doctor Peterson
Subject: Re: Foiling
Hi, Jalise.
If you were told to use the FOIL method to do this, it won't work; it
applies only to the product of two binomial... | 4 | [
-0.037109375,
0.01092529296875,
0.01470947265625,
-0.01446533203125,
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0.01513671875,
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0.0615234375,
0.009765625,
-0.039794921875,
0.115234375... | 36,487 | 36487 | |
help me out to find the distance
May 23rd 2008, 08:30 PM
neha1
help me out to find the distance
(Doh)if a man walks at the rate of 5kmph,he misses a train by only 7 min.however if he walks at the rate of 6kmph he reaches the station 5 minutes before the arrival of train.find the distance
covered by him to re... | 4 | [
-0.00604248046875,
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0.037109375,
0.046875,
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0.06201171875,
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0.028564453125,
0.06689453125,
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-0.035400390625,
0.01141357421875,
-0.0150146484375,
-0.04150390625,
-0.035888671875,
-0.01019287... | 36,488 | 36488 | |
Factoring Very Large Numbers into Primes
Date: 12/05/2003 at 00:05:53
From: Chetan
Subject: finding the factors of any given number
Suppose I have a really big number to be factored into primes. What
is the best possible way of doing it? I know I can divide by
increasing primes, but that ges very hard for monstrous... | 5 | [
0.00124359130859375,
-0.004364013671875,
-0.031494140625,
-0.03564453125,
0.1005859375,
-0.02783203125,
-0.045166015625,
0.10302734375,
-0.06640625,
0.042724609375,
-0.019775390625,
0.134765625,
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0.044921875,
0.0269775390625,
-0.061767578125,
0.00555419921875,
0.061... | 36,489 | 36489 | |
Even-Numbered Magic Squares
Date: 04/30/2001 at 13:23:58
From: David
Subject: Magic square
Dear Dr. Math,
I believe your method of constructing magic squares (see
http://mathforum.org/dr.math/problems/magic_squares_needed.html ,
Magic Square Puzzle) is good for odd integers, but does not work for,
say, n = 4. Do ... | 5 | [
0.0203857421875,
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-0.0036773681640625,
-0.11865234375,
0.0206298828125,
-0.044189453125,
0.10058... | 36,490 | 36490 | |
12.3 Calculus
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12.3 Calculus
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• The slope-intercept form of a linear equation is a common way to represent the mathematics of change.
One of the key features of algebraic mathematics is the use of symbols instead of numbers. In algebra, we le... | 4 | [
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0.0625,
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0.078125,
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0.0... | 36,491 | 36491 | |
Cube problem
December 3rd 2009, 02:27 PM #1
Newbie
Joined
Oct 2009
Posts
7
Cube problem
While playing one day, Thomas decided to build larger cubes out of a box of individual sugar cubes. So, emptying out the box onto the floor and using the sugar cubes as if they were building
blocks, Thomas made th... | 4 | [
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-0.036865234375,... | 36,492 | 36492 | |
Is the 'massive' Calogero-Moser system still integrable?
up vote 6 down vote favorite
3
Background
The (rational) Calogero-Moser system is the dynamical system which describes the evolution of $n$ particles on the line $\mathbb{C}$ which repel each other with force proportional to the cube of
their distance. If the p... | 4 | [
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-0.03271484375,
-0.01458740234375,
-0.052978515625,
0.0449218... | 36,493 | 36493 | |
homotopy between solutions of Maurer-Cartan equation
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
If $S_0, S_1$ are two solutions of Maurer-Cartan equation $dS+\frac{1}{2}{S,S}=0$ for a dg-Lie algebra $g$, do we have a... | 4 | [
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0.0283203125,
-0.0218505859375,
0.05517578125,
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-0.039794921875,
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0.0286865234375,
-0.09619140625,
0.000003248453140258789,
0.03466796875,
-0.03173828125,
-0.0400390... | 36,494 | 36494 | |
How to construct matrices with periodicity
up vote 0 down vote favorite
Suppose I want to construct an $n\times n$ matrix ${\bf A}$ such that ${\bf A}^n={\bf I}$. Matrices that have period $n$ and admit such property are permutation matrices. However, I was wondering if
there is a general methodology to obtain such ma... | 5 | [
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0.00982666015625,
-0.010986328125,
0.02111... | 36,495 | 36495 | |
Gamma and factorial
March 1st 2010, 03:57 AM #1
Newbie
Joined
Oct 2009
Posts
22
Gamma and factorial
Is this expression true?
$(n+s)! \Gamma (s+1)= s! \Gamma (n+s+1)$
i was looking at the proof of $J_{-n} (x)= (-1)^n J_n (x)$ and i deduced that expression must be true for the proof provided to be ... | 4 | [
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-0.05859375,
0.07421875,
0.06225585937... | 36,496 | 36496 | |
Determine the current
August 28th 2008, 09:19 AM #1
Newbie
Joined
Aug 2008
Posts
17
A 30-volt electromotive force is applied to an-LR series circuit in which the inductance is 0.1 henry and the resistance is 50 ohms. Find the current i(t) if i(0)=0 Determine the current as t -->
infinity.
Can ... | 5 | [
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... | 36,497 | 36497 | |
construct a square when the sum of its diagonal and side is given
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Assuming we're familiar with ways ho... | 4 | [
0.040283203125,
0.07275390625,
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0.01953125,
-0.05078125,
0.0380859375,
0.0111083984375,
0.0529785... | 36,498 | 36498 | |
Prove Mersenne Number is Prime or Pseudoprime
Date: 10/11/2008 at 19:01:14
From: Jamie
Subject: Mersenne Number either prime or pseudoprime
Let p be a prime number. Prove that 2^p - 1 is either a prime number
or a pseudoprime number (2^n is congruent to 2 modulo n, where n is
composite).
I really don't know where t... | 5 | [
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0.0194091796875,
0.0294189453125,
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0.1376953125,
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0.1328125,
-0.035888671875,
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0.01708984375,
0.038330078125,
-0.00677490234375,
-0.02587890625,
-0.06591796875,
-0.00527... | 36,499 | 36499 |