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
[ -0.080078125, 0.06494140625, 0.01171875, -0.083984375, 0.031982421875, 0.00909423828125, 0.0830078125, 0.0177001953125, -0.00885009765625, -0.048583984375, 0.05859375, 0.0245361328125, 0.007171630859375, -0.0247802734375, 0.029541015625, -0.01031494140625, 0.040283203125, -0.070800...
36,400
36400
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
[ -0.047119140625, 0.0185546875, 0.02294921875, -0.0283203125, 0.01220703125, -0.0888671875, -0.004974365234375, 0.005859375, -0.06689453125, 0.0301513671875, 0.0322265625, -0.0263671875, 0.036376953125, -0.024169921875, 0.0263671875, 0.0208740234375, -0.0108642578125, -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
[ 0.01806640625, 0.06103515625, 0.0693359375, -0.0615234375, 0.00007963180541992188, 0.0267333984375, 0.06591796875, 0.005889892578125, -0.09619140625, -0.07421875, -0.01953125, -0.09521484375, 0.053955078125, -0.07958984375, 0.010986328125, 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
[ -0.08251953125, -0.0213623046875, -0.0283203125, 0.0179443359375, 0.087890625, 0.018310546875, 0.0830078125, 0.0181884765625, -0.044677734375, 0.0030059814453125, 0.01031494140625, 0.06201171875, -0.04052734375, 0.08203125, 0.0174560546875, 0.03564453125, -0.060302734375, 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
[ 0.0223388671875, -0.01275634765625, 0.05859375, -0.017578125, 0.0262451171875, -0.06689453125, -0.002349853515625, 0.02099609375, -0.004638671875, 0.037109375, 0.142578125, 0.028076171875, -0.02978515625, 0.061767578125, 0.00830078125, 0.049560546875, -0.057861328125, 0.00390625, ...
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
[ -0.05712890625, 0.0213623046875, 0.048095703125, 0.022216796875, 0.037109375, -0.03857421875, 0.005096435546875, 0.0263671875, -0.0146484375, -0.08251953125, 0.036376953125, 0.00109100341796875, 0.033935546875, -0.047607421875, -0.1005859375, -0.045654296875, -0.003021240234375, -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
[ -0.0751953125, 0.046142578125, -0.052001953125, 0.0072021484375, -0.109375, 0.0439453125, -0.0390625, 0.0296630859375, 0.057373046875, -0.0068359375, 0.005645751953125, -0.109375, 0.0216064453125, -0.00592041015625, 0.09814453125, -0.0654296875, -0.0277099609375, 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
[ -0.08642578125, 0.0283203125, -0.0135498046875, 0.058349609375, -0.0267333984375, 0.050048828125, 0.01446533203125, -0.08642578125, -0.0086669921875, -0.02587890625, 0.01806640625, -0.058837890625, 0.046142578125, 0.07470703125, -0.02490234375, 0.09326171875, -0.048828125, 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
[ -0.07275390625, -0.059814453125, -0.0257568359375, -0.034423828125, -0.01275634765625, 0.07421875, 0.03271484375, -0.0257568359375, -0.03369140625, 0.0693359375, 0.00787353515625, 0.03466796875, -0.006439208984375, 0.10009765625, 0.007080078125, -0.049560546875, -0.0189208984375, -...
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
[ -0.054931640625, -0.0341796875, -0.0693359375, -0.00994873046875, 0.0294189453125, 0.0201416015625, 0.06884765625, 0.0225830078125, 0.059326171875, 0.0703125, -0.125, 0.04541015625, 0.06201171875, -0.01068115234375, -0.0235595703125, 0.054443359375, 0.0234375, -0.032958984375, -0...
36,409
36409
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
[ -0.0693359375, -0.07275390625, -0.09814453125, -0.01116943359375, -0.08154296875, -0.04296875, 0.04150390625, -0.1044921875, 0.035400390625, -0.05517578125, 0.0274658203125, 0.00506591796875, 0.1083984375, 0.050537109375, 0.048095703125, -0.00982666015625, 0.0032501220703125, 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
[ -0.029541015625, -0.00738525390625, -0.0361328125, 0.057373046875, -0.0322265625, -0.003936767578125, -0.09521484375, 0.0712890625, 0.095703125, 0.0247802734375, 0.0439453125, -0.0223388671875, 0.02001953125, 0.04541015625, 0.012451171875, -0.02685546875, -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
[ -0.1103515625, 0.1455078125, 0.08447265625, 0.0279541015625, 0.0302734375, 0.0272216796875, -0.03515625, -0.003936767578125, -0.0439453125, 0.060546875, 0.037841796875, -0.06298828125, 0.0029144287109375, 0.025146484375, 0.0458984375, -0.0189208984375, -0.0966796875, 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
[ -0.02880859375, -0.033935546875, 0.0224609375, -0.008056640625, -0.0517578125, 0.0419921875, 0.05126953125, -0.002777099609375, 0.06884765625, 0.002471923828125, 0.0067138671875, 0.037353515625, 0.03369140625, 0.013427734375, 0.0888671875, 0.10986328125, 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
[ -0.09375, 0.0244140625, -0.000949859619140625, 0.01361083984375, -0.0927734375, 0.0299072265625, 0.09033203125, -0.0595703125, 0.0242919921875, -0.0145263671875, 0.046142578125, 0.0050048828125, -0.00787353515625, -0.07177734375, -0.011962890625, 0.044677734375, -0.0556640625, -0.0...
36,414
36414
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
[ 0.06689453125, 0.006195068359375, 0.0419921875, 0.0174560546875, 0.0274658203125, 0.0208740234375, -0.040283203125, -0.0888671875, -0.06201171875, -0.004180908203125, 0.025390625, -0.035888671875, 0.05615234375, -0.035888671875, -0.11083984375, 0.00958251953125, 0.0052490234375, -0...
36,415
36415
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
[ -0.034912109375, 0.031982421875, 0.023193359375, -0.064453125, 0.04345703125, 0.01171875, 0.0478515625, -0.050048828125, -0.040283203125, 0.00933837890625, -0.04736328125, 0.0654296875, 0.06884765625, -0.0791015625, -0.047119140625, 0.07421875, 0.009765625, 0.0303955078125, 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 &lt= 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
[ 0.023193359375, 0.0005645751953125, -0.024169921875, 0.0086669921875, 0.021728515625, 0.0198974609375, 0.06494140625, 0.00830078125, -0.01019287109375, 0.07080078125, -0.068359375, -0.08642578125, 0.0693359375, 0.07568359375, 0.02490234375, 0.04931640625, 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
[ 0.0052490234375, 0.044677734375, -0.061279296875, 0.0026702880859375, -0.00201416015625, -0.03662109375, 0.01141357421875, 0.08251953125, 0.0703125, 0.01611328125, 0.0272216796875, -0.010498046875, 0.0126953125, 0.08154296875, -0.049560546875, 0.00909423828125, -0.03759765625, -0.0...
36,418
36418
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
[ 0.02001953125, 0.04443359375, 0.09716796875, -0.057373046875, 0.02783203125, -0.032958984375, -0.004150390625, -0.016845703125, -0.032470703125, -0.00128173828125, 0.1416015625, -0.1201171875, -0.019775390625, -0.00958251953125, -0.00921630859375, -0.0184326171875, 0.004669189453125,...
36,419
36419
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
[ -0.07568359375, 0.10595703125, 0.0179443359375, -0.02197265625, -0.06396484375, 0.0458984375, -0.01123046875, 0.0927734375, 0.007080078125, 0.055908203125, 0.058349609375, -0.06591796875, -0.0269775390625, 0.042724609375, 0.0079345703125, -0.06298828125, -0.0693359375, 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
[ -0.04931640625, 0.06982421875, -0.00543212890625, 0.006134033203125, 0.027099609375, 0.021484375, 0.115234375, 0.017333984375, 0.01361083984375, -0.034423828125, -0.058837890625, -0.00099945068359375, 0.09716796875, -0.00118255615234375, 0.015380859375, 0.0225830078125, 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
[ -0.0361328125, -0.009765625, 0.034423828125, 0.0166015625, 0.002044677734375, -0.00860595703125, 0.00689697265625, -0.1083984375, 0.005523681640625, -0.017578125, 0.0849609375, 0.0103759765625, 0.028076171875, 0.01373291015625, -0.03857421875, 0.0478515625, 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
[ -0.0966796875, 0.0196533203125, 0.00848388671875, 0.0181884765625, 0.02734375, -0.0322265625, 0.060546875, 0.005096435546875, 0.0045166015625, -0.07421875, 0.07275390625, -0.072265625, 0.039306640625, -0.0052490234375, 0.06103515625, -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
[ -0.060791015625, 0.00970458984375, 0.08154296875, -0.06689453125, -0.05712890625, 0.051513671875, -0.0198974609375, 0.014892578125, 0.007354736328125, 0.09033203125, 0.03564453125, -0.03369140625, 0.006256103515625, 0.06201171875, 0.0498046875, -0.0013275146484375, -0.0576171875, 0...
36,424
36424
Math Forum Discussions Math Forum Ask Dr. Math Discussions Internet Newsletter MathTools Teacher2Teacher Teacher Exchange Workshops Search All of the Math Forum: Views expressed in these public forums are not endorsed by Drexel University or The Math Forum. Topic: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A s...
5
[ -0.060302734375, 0.01422119140625, 0.07275390625, 0.0068359375, 0.04638671875, 0.03564453125, 0.06201171875, -0.049560546875, 0.05810546875, 0.013916015625, 0.0751953125, -0.035400390625, 0.0703125, 0.0859375, 0.08056640625, 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
[ -0.0301513671875, -0.031005859375, -0.07177734375, 0.005828857421875, 0.0478515625, 0.006805419921875, 0.004974365234375, 0.0034942626953125, 0.00262451171875, -0.05029296875, 0.0281982421875, 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, -0.001678466796875, 0.06103515625, 0.0281982421875, -0.08544921875, -0.02490234375, 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, -0.04736328125, 0.01104736328125, 0.09423828125, -0.0625, 0.0208740234375, 0.041015625, 0.01385498046875, 0.0019683837890625, -0.045654296875, 0.04345703125, -0.12060546875, 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, 0.053955078125, 0.028564453125, 0.01153564453125, 0.0810546875, 0.05322265625, 0.04931640625, 0.055908203125, -0.016357421875, 0.052001953125, -0.0172119140625, 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
[ -0.1259765625, 0.0311279296875, 0.0654296875, 0.006927490234375, 0.072265625, -0.04052734375, 0.0303955078125, 0.0242919921875, -0.07080078125, -0.053955078125, 0.07421875, 0.0294189453125, 0.039306640625, 0.006561279296875, 0.020263671875, 0.04296875, -0.0279541015625, 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, -0.017578125, 0.07177734375, 0.027587890625, -0.07666015625, -0.043212890625, 0.010009765625, 0.032958984375, 0.056396484375, 0.0888671875, -0.10986328125, 0.0030517578125, 0.07080078125, 0.050537109375, -0.0751953125, -0.035400390625, -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
[ -0.0576171875, -0.0869140625, -0.034912109375, 0.015869140625, -0.0037841796875, 0.033447265625, -0.0546875, 0.03564453125, -0.0184326171875, -0.01007080078125, 0.0556640625, -0.05810546875, -0.06396484375, 0.04345703125, 0.057373046875, 0.0047607421875, 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
[ -0.06298828125, 0.004425048828125, -0.06591796875, 0.1279296875, -0.0703125, 0.08154296875, -0.0091552734375, -0.0123291015625, 0.03759765625, -0.1484375, 0.095703125, 0.046630859375, -0.10009765625, -0.021484375, -0.037353515625, -0.0185546875, -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
[ -0.03466796875, -0.1171875, -0.034423828125, 0.045654296875, 0.01373291015625, 0.0026092529296875, -0.055908203125, 0.01458740234375, 0.078125, -0.06689453125, 0.050048828125, -0.041259765625, 0.11962890625, 0.0888671875, 0.033935546875, 0.0023956298828125, -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
[ -0.025390625, 0.0625, 0.0108642578125, -0.021484375, 0.08837890625, 0.00762939453125, 0.0517578125, -0.02587890625, -0.060546875, -0.09375, 0.1591796875, -0.036865234375, -0.06103515625, -0.0245361328125, 0.0279541015625, 0.01123046875, -0.042236328125, -0.047119140625, 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
[ -0.123046875, -0.041015625, -0.06396484375, 0.0069580078125, -0.0262451171875, -0.006622314453125, -0.05078125, 0.0233154296875, -0.0654296875, 0.01495361328125, 0.07421875, -0.0021514892578125, 0.03955078125, -0.033203125, -0.026123046875, 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, -0.0164794921875, 0.01531982421875, 0.0247802734375, -0.0283203125, 0.0205078125, 0.087890625, -0.041259765625, 0.025390625, 0.08203125, 0.01019287109375, -0.158203125, -0.0262451171875, 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
[ -0.051513671875, -0.03515625, 0.02392578125, -0.07763671875, -0.0186767578125, -0.028564453125, -0.0289306640625, 0.0126953125, -0.00057220458984375, -0.0673828125, 0.0252685546875, -0.1025390625, 0.12890625, -0.0257568359375, 0.0157470703125, 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
[ -0.00970458984375, 0.00555419921875, 0.0019989013671875, -0.00775146484375, 0.013916015625, -0.00909423828125, 0.0098876953125, 0.022705078125, -0.053466796875, 0.0274658203125, -0.1689453125, -0.0179443359375, 0.08935546875, -0.035888671875, -0.04052734375, 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, 0.0101318359375, 0.06494140625, -0.10205078125, 0.0157470703125, 0.08837890625, 0.038818359375, -0.0125732421875, 0.0654296875, 0.0177001953125, -0.025146484375, 0.019287109375, 0.005950927734375, 0.0277099609375, 0.0096435546875, 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
[ -0.029541015625, 0.0191650390625, 0.052734375, -0.0712890625, 0.11328125, 0.01263427734375, 0.08154296875, 0.0595703125, 0.0419921875, -0.040283203125, 0.0849609375, 0.01806640625, -0.06494140625, -0.044189453125, -0.0147705078125, 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
[ -0.08740234375, -0.046875, -0.0072021484375, 0.00140380859375, 0.1484375, 0.042236328125, 0.0291748046875, -0.06591796875, -0.04541015625, -0.08056640625, 0.057861328125, -0.10888671875, 0.08056640625, -0.1123046875, 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
[ -0.08984375, -0.00799560546875, 0.042236328125, -0.041748046875, 0.045166015625, 0.051025390625, 0.056640625, -0.01226806640625, 0.0211181640625, 0.033447265625, 0.08642578125, -0.031982421875, 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
[ -0.1162109375, -0.047607421875, -0.047607421875, 0.052490234375, 0.040283203125, 0.0927734375, 0.007568359375, 0.0218505859375, 0.0400390625, -0.0218505859375, 0.07763671875, 0.043212890625, -0.01190185546875, -0.053955078125, -0.051025390625, -0.022705078125, -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
[ 0.0390625, -0.06640625, -0.13671875, -0.0238037109375, -0.010498046875, -0.004180908203125, -0.00982666015625, -0.0264892578125, -0.00787353515625, -0.0791015625, 0.046142578125, 0.0693359375, -0.047607421875, 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
[ -0.0174560546875, -0.029052734375, 0.049072265625, -0.024658203125, 0.055419921875, -0.045654296875, 0.0233154296875, 0.04736328125, -0.0419921875, 0.03564453125, 0.001739501953125, 0.0057373046875, 0.04443359375, 0.022705078125, -0.07958984375, -0.0166015625, -0.03955078125, 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
[ -0.034912109375, 0.019287109375, -0.115234375, 0.07763671875, -0.041015625, 0.004302978515625, 0.053955078125, -0.00201416015625, 0.0196533203125, -0.0771484375, -0.05419921875, -0.023681640625, 0.03662109375, -0.0238037109375, -0.00732421875, 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
[ -0.0294189453125, -0.018310546875, 0.056396484375, -0.00830078125, 0.025390625, -0.018310546875, 0.004791259765625, -0.0185546875, -0.0947265625, -0.056884765625, 0.006011962890625, 0.0146484375, -0.0064697265625, -0.103515625, 0.0115966796875, 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
[ -0.064453125, -0.0654296875, -0.0234375, 0.07373046875, -0.0296630859375, -0.08251953125, -0.041015625, -0.04052734375, 0.0223388671875, -0.00067901611328125, 0.009765625, -0.0223388671875, 0.00909423828125, 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
[ -0.072265625, -0.04052734375, 0.02978515625, -0.031982421875, -0.0069580078125, 0.0203857421875, 0.0830078125, 0.07958984375, -0.018310546875, -0.042724609375, 0.06982421875, 0.050048828125, -0.00677490234375, -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, -0.026611328125, 0.00799560546875, 0.056884765625, -0.01519775390625, -0.06298828125, 0.06591796875, -0.0361328125, 0.01409912109375, 0.08349609375, -0.0634765625, -0.0032196044921875, 0.0260009765625, -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, -0.02880859375, 0.0159912109375, 0.05126953125, 0.0595703125, 0.0380859375, -0.015625, -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
[ 0.01275634765625, -0.00531005859375, -0.016357421875, -0.048828125, -0.03857421875, -0.0274658203125, 0.0255126953125, 0.052490234375, 0.0250244140625, -0.10205078125, 0.05517578125, -0.00141143798828125, -0.0198974609375, -0.0177001953125, 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, 0.006683349609375, -0.05029296875, -0.04736328125, 0.0306396484375, -0.060546875, -0.10400390625, -0.0198974609375, -0.06689453125, -0.012451171875, -0.04052734375, 0.08544921875, -0.0308837890625, -0.01458740234375, 0.07421875, 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, -0.0147705078125, -0.025390625, -0.0169677734375, 0.05322265625, 0.0021820068359375, 0.076171875, 0.06884765625, 0.0830078125, -0.068359375, 0.0037689208984375, -0.0177001953125, -0.034912109375, 0.0712890625, -0.01318359375, -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, 0.0654296875, 0.00189971923828125, 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, -0.010498046875, -0.030517578125, -0.049072265625, 0.078125, 0.04833984375, -0.059326171875, -0.03662109375, -0.0086669921875, 0.0025634765625, 0.0771484375, 0.0003662109375, -0.0157470703125, -0.0103759765625, 0.031494140625, -0.025390625, -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
[ -0.05712890625, 0.050048828125, 0.027099609375, -0.1259765625, -0.02392578125, 0.0478515625, -0.044677734375, 0.01513671875, -0.07763671875, 0.08056640625, -0.00665283203125, -0.036865234375, 0.07568359375, 0.037109375, 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, -0.0283203125, 0.0152587890625, 0.057373046875, -0.09326171875, 0.0106201171875, -0.057861328125, 0.0166015625, 0.04052734375, -0.06982421875, -0.021728515625, -0.02001953125, 0.01043701171875, -0.052490234375, -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
[ -0.043212890625, 0.027099609375, 0.016357421875, 0.032470703125, 0.07275390625, 0.09619140625, 0.04736328125, 0.14453125, -0.0220947265625, -0.0302734375, 0.0029144287109375, 0.0250244140625, 0.01007080078125, -0.03759765625, 0.002777099609375, -0.1796875, 0.057373046875, -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, -0.048095703125, -0.1337890625, -0.000782012939453125, -0.061767578125, -0.0186767578125, -0.0019073486328125, -0.07177734375, -0.00067138671875, -0.060302734375, -0.005706787109375, 0.0279541015625, 0.06298828125, 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
[ -0.038330078125, -0.003875732421875, 0.07275390625, -0.01043701171875, 0.07470703125, 0.051025390625, 0.035888671875, 0.07275390625, -0.0155029296875, -0.034423828125, 0.019287109375, 0.055419921875, -0.09130859375, -0.013671875, 0.044189453125, 0.0081787109375, 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
[ -0.0380859375, 0.0177001953125, 0.03955078125, 0.07177734375, -0.0026702880859375, -0.051513671875, 0.0140380859375, 0.000217437744140625, -0.083984375, -0.043701171875, 0.06298828125, 0.03955078125, 0.00933837890625, -0.04443359375, -0.01068115234375, 0.0458984375, -0.0771484375, ...
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
[ -0.0625, 0.01507568359375, 0.0146484375, -0.0125732421875, 0.080078125, 0.003082275390625, -0.0186767578125, -0.056396484375, 0.0084228515625, -0.0191650390625, 0.059814453125, -0.01507568359375, 0.03564453125, 0.08935546875, 0.040283203125, -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
[ -0.03759765625, 0.0673828125, -0.0045166015625, 0.0001468658447265625, 0.0216064453125, -0.07275390625, 0.10986328125, 0.048583984375, -0.006927490234375, -0.0106201171875, -0.11083984375, -0.022705078125, 0.083984375, -0.03271484375, 0.0830078125, 0.0267333984375, 0.044189453125, ...
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
[ -0.03173828125, 0.07275390625, -0.034423828125, 0.042236328125, -0.0211181640625, 0.014892578125, -0.04736328125, 0.0257568359375, 0.0260009765625, 0.0693359375, 0.0537109375, -0.01953125, -0.0400390625, 0.04638671875, -0.0556640625, -0.042236328125, -0.0703125, -0.042724609375, ...
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
[ -0.04541015625, 0.1201171875, -0.0103759765625, -0.11669921875, -0.11572265625, 0.0255126953125, -0.041015625, -0.0002651214599609375, 0.0203857421875, 0.0869140625, 0.04541015625, -0.037109375, -0.031982421875, 0.03466796875, -0.06103515625, 0.034912109375, -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
[ -0.11376953125, -0.0189208984375, 0.04736328125, 0.028076171875, -0.0244140625, 0.06591796875, 0.0191650390625, -0.0634765625, -0.0400390625, -0.09423828125, -0.00775146484375, -0.0306396484375, -0.11962890625, 0.0042724609375, -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
[ -0.049560546875, -0.0208740234375, -0.052734375, -0.09375, 0.023681640625, -0.0546875, 0.0303955078125, -0.0203857421875, -0.0308837890625, 0.002777099609375, 0.043701171875, -0.039306640625, 0.0166015625, -0.0166015625, -0.06201171875, -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
[ -0.05322265625, 0.0771484375, 0.039794921875, -0.0294189453125, -0.07373046875, -0.035400390625, -0.03564453125, 0.010009765625, 0.0113525390625, -0.006591796875, -0.0179443359375, -0.05126953125, -0.01708984375, 0.055908203125, -0.03564453125, -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
[ -0.1015625, -0.0576171875, 0.054443359375, 0.0235595703125, -0.0191650390625, 0.006866455078125, -0.017578125, -0.0966796875, -0.0252685546875, -0.064453125, -0.01123046875, -0.01300048828125, -0.053955078125, -0.00823974609375, -0.00994873046875, 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
[ -0.0262451171875, -0.068359375, 0.033203125, -0.048828125, -0.056396484375, 0.0341796875, 0.026611328125, 0.028564453125, 0.033935546875, -0.0242919921875, -0.0361328125, 0.0206298828125, -0.0216064453125, 0.032958984375, 0.04833984375, -0.045654296875, 0.033203125, 0.11279296875, ...
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
[ -0.1279296875, -0.076171875, 0.0185546875, -0.022705078125, 0.0133056640625, 0.03564453125, -0.050048828125, 0.0118408203125, 0.0849609375, -0.033935546875, 0.08740234375, 0.011962890625, 0.045166015625, 0.01141357421875, 0.00396728515625, 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
[ -0.0084228515625, 0.01263427734375, -0.020263671875, -0.005645751953125, 0.051025390625, 0.056884765625, 0.0281982421875, -0.1015625, 0.053955078125, 0.1279296875, 0.07177734375, 0.07763671875, 0.013916015625, -0.016845703125, -0.033935546875, 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
[ -0.11376953125, 0.04833984375, -0.07080078125, -0.044189453125, 0.00494384765625, -0.01025390625, -0.0177001953125, 0.044677734375, 0.026123046875, -0.031982421875, 0.134765625, -0.014404296875, -0.035400390625, 0.02197265625, 0.048828125, 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
[ -0.06591796875, -0.10107421875, -0.08837890625, 0.031494140625, -0.08447265625, 0.08935546875, 0.0277099609375, -0.053466796875, -0.027099609375, -0.05419921875, 0.06689453125, 0.04052734375, 0.023193359375, -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
[ -0.04833984375, 0.068359375, -0.1044921875, 0.126953125, 0.05810546875, -0.02490234375, 0.1318359375, 0.0361328125, -0.017333984375, -0.0311279296875, -0.01324462890625, 0.0000782012939453125, 0.08740234375, -0.01214599609375, -0.09375, 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
[ 0.061279296875, -0.005462646484375, -0.054931640625, 0.01904296875, 0.00714111328125, 0.0034942626953125, -0.04248046875, -0.008056640625, 0.08544921875, -0.01519775390625, 0.03369140625, 0.0048828125, 0.0101318359375, 0.0306396484375, -0.0625, 0.060302734375, -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
[ -0.0908203125, -0.0517578125, -0.056396484375, -0.04443359375, 0.0927734375, 0.01458740234375, 0.050537109375, 0.01318359375, -0.06103515625, -0.042724609375, -0.0093994140625, 0.12353515625, 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, -0.0185546875, 0.015625, -0.042236328125, 0.051513671875, 0.01458740234375, -0.00927734375, 0.0211181640625, -0.050048828125, 0.0301513671875, 0.051513671875, -0.00994873046875, -0.0458984375, 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, 0.0172119140625, 0.0419921875, 0.0380859375, -0.00151824951171875, 0.0291748046875, -0.0098876953125, -0.0206298828125, 0.00860595703125, -0.00921630859375, -0.09228515625, -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, -0.0869140625, -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, -0.0032196044921875, -0.0296630859375, -0.045654296875, 0.043212890625, 0.034423828125, -0.04052734375, 0.056884765625, 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, -0.10205078125, -0.14453125, -0.0291748046875, 0.0439453125, -0.01055908203125, 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, -0.058837890625, 0.06201171875, -0.01806640625, 0.01513671875, -0.08203125, -0.042724609375, 0.032958984375, -0.07470703125, 0.01177978515625, -0.0419921875, 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, 0.05712890625, 0.047607421875, 0.037109375, 0.046875, 0.037841796875, -0.025146484375, 0.06201171875, -0.0400390625, 0.028564453125, 0.06689453125, -0.0306396484375, -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, -0.006103515625, 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, 0.01470947265625, -0.0234375, -0.0712890625, -0.0859375, 0.014404296875, -0.038818359375, -0.006378173828125, -0.09521484375, -0.01513671875, -0.06689453125, 0.072265625, -0.04638671875, -0.0036773681640625, -0.11865234375, 0.0206298828125, -0.044189453125, 0.10058...
36,490
36490
12.3 Calculus Video Textbook Interactive Download PDFs Additional Resources 12.3 Calculus GET IN LINE • 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
[ -0.0546875, 0.034912109375, -0.016357421875, 0.01336669921875, -0.041015625, 0.036376953125, -0.025634765625, 0.003387451171875, 0.06640625, 0.01556396484375, 0.0625, 0.05419921875, 0.03515625, 0.064453125, 0.01513671875, 0.0546875, -0.06396484375, 0.078125, -0.06396484375, 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
[ 0.056640625, 0.0201416015625, 0.00011396408081054688, 0.07470703125, -0.07373046875, -0.00115203857421875, 0.0225830078125, 0.00970458984375, -0.025634765625, 0.0194091796875, -0.06640625, -0.0267333984375, 0.019287109375, 0.05126953125, 0.01171875, 0.00909423828125, -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
[ -0.054443359375, -0.006866455078125, -0.016357421875, 0.00189208984375, -0.05029296875, -0.0098876953125, -0.018798828125, 0.036865234375, -0.0242919921875, -0.052978515625, 0.0164794921875, 0.0380859375, -0.0062255859375, -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
[ -0.1533203125, -0.03759765625, -0.0213623046875, 0.0283203125, -0.0218505859375, 0.05517578125, -0.0159912109375, 0.033935546875, 0.003753662109375, -0.039794921875, 0.002838134765625, 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
[ -0.0859375, 0.0120849609375, -0.0888671875, -0.03857421875, -0.12158203125, 0.02392578125, 0.01092529296875, -0.1220703125, 0.0289306640625, -0.0294189453125, 0.03564453125, 0.02880859375, -0.0419921875, -0.002899169921875, 0.010986328125, 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
[ -0.11865234375, -0.021728515625, 0.004791259765625, 0.033203125, 0.0145263671875, 0.059326171875, 0.1142578125, 0.040283203125, -0.00921630859375, -0.006500244140625, 0.02978515625, 0.054931640625, 0.083984375, -0.01806640625, -0.016845703125, -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
[ -0.07958984375, 0.0966796875, 0.0595703125, -0.0262451171875, 0.10693359375, 0.0206298828125, -0.036376953125, 0.0166015625, -0.0146484375, 0.0712890625, 0.11181640625, -0.12060546875, 0.0250244140625, 0.051025390625, -0.04345703125, 0.0673828125, -0.051513671875, -0.0205078125, ...
36,497
36497
construct a square when the sum of its diagonal and side is given Word Problem Answers (8,110) Statistics Answers (2,579) Calculus Answers (5,182) Trigonometry Answers (2,299) Geometry Answers (4,541) Algebra 2 Answers (9,339) Algebra 1 Answers (22,541) Pre-Algebra Answers (11,111) Assuming we're familiar with ways ho...
4
[ 0.040283203125, 0.07275390625, -0.016357421875, -0.057373046875, -0.05419921875, 0.0076904296875, -0.055908203125, 0.043212890625, -0.00750732421875, -0.025390625, 0.0235595703125, -0.0009613037109375, 0.03076171875, 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
[ -0.0341796875, 0.0194091796875, 0.0294189453125, 0.0303955078125, 0.1376953125, 0.00634765625, 0.0206298828125, 0.1328125, -0.035888671875, 0.0045166015625, -0.11328125, -0.00183868408203125, 0.01708984375, 0.038330078125, -0.00677490234375, -0.02587890625, -0.06591796875, -0.00527...
36,499
36499