content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Exponential Cooling Curve Problem
Your model is wrong. The model to use is $T = a (b)^t + 20$ (other models, such as $T = a e^{kt} + 20$, could also be used). Substitute T = 95 at t = 0: 95 = a + 20 => a = 75. Update the model (just
like Ronnie): $T = 75 (b)^t + 20$. Now substitute T = 90 when t = 2 and solve for b.
A... | 4 | [
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0.0673828125,
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0.03271484375,
0.042724609375,
0.0712890625,
0.0703125,
-0.0712890625,
0.054443359375,
0.0458984375,
0.1142578125,
0.058349609375,
-0.0703125,
-0.03515625,
-0.10449... | 37,600 | 37600 | |
Polarizations on intermediate Jacobians
up vote 3 down vote favorite
3
Let $X$ be a Kahler variety of dimension $n$. For each odd number $2k-1 \leq n$ one can consider the $k$-th intermediate Jacobian, that is, the complex torus $$J^{k}X := \frac{H^{2k+1}(X, \mathbb
{C})}{F^k H^{2k+1}(X, \mathbb{C}) + H^{2k+1}(X, \mat... | 4 | [
-0.0751953125,
0.024169921875,
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-0.029541015625,
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0.0859375,
0.0028076171875,
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0.060546875,
0.0244140625,
-0.0245361328125,
-0.048583984375,
0.0402832... | 37,601 | 37601 | |
dimension of D^b(coh( P^1))
up vote 2 down vote favorite
2
Hello,
I am trying to understand Orlov: Remarks on generators of triangulated categories.
Let E be a full subcategory of D^b(coh(P^1)). Let [E] be the smallest full subcategory of D^b(coh(P^1)) such that [E] is closed under direct summands, finite direct sum... | 4 | [
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0.03759765625,
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0.020263671875,
-0.1162109375,
-0.0869140625,
-0.0264892578125,
0.04931640625,
0.060302734375,
-0.02392578125,... | 37,602 | 37602 | |
measurable functions
September 28th 2009, 02:05 AM
robeuler
measurable functions
Let f and g be measurable functions from X to the extended reals. Prove that the sets
A={x:f(x)<g(x)}
and
B={x:f(x)=g(x)}
are measurable.
And then prove that the set of points at which a sequence of measurable ... | 5 | [
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0.0263671875,
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0.0194091796875,
0.0458984375,
-0.... | 37,603 | 37603 | |
Application of similar triangles
November 23rd 2008, 07:06 AM #1
Junior Member
Joined
Nov 2008
From
Vermont, New England, USA, North America, Earth, Sol Solar System, Orion Arm, Milky Way Galaxy
Posts
61
Application of similar triangles
So I have this one problem:
A wall is being supported by a ... | 5 | [
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... | 37,604 | 37604 | |
Determinant of a 3x3 Magic Square
up vote 9 down vote favorite
Hello guys. This is my first question with mathOverflow so I hope my etiquette is up to par here.
My question is regarding a 3x3 magic square constructed using the la Loubere method (see la Loubere method)
Using the method, I have constructed a magic squ... | 5 | [
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0.038330078... | 37,605 | 37605 | |
Determining the asymptotic behavior of a series
up vote 7 down vote favorite
1
I am trying to determine the behavior of the following series as $n\to\infty$. Let $0<\mu<1$ be fixed and for every positive integer $n\geq 1$, consider the function $f_n(t)$ of a real variable $t$
defined by the series $\sum_{k=0}^\infty\m... | 5 | [
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0.0277099609375,
-0.083984375... | 37,606 | 37606 | |
Math Forum: Teacher2Teacher - Q&A #4147
View entire discussion
[<<prev]
From: Pat Ballew (for Teacher2Teacher Service)
Date: Jun 13, 2000 at 00:00:27
Subject: Re: Understanding abbreviation
The teacher who wrote the previous response I spoke of has pointed me to the
message, so I have copied it below. Notice that ... | 4 | [
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... | 37,607 | 37607 | |
THE KONTSEVICH INTEGRAL 1. Introduction The Kontsevich integral
THE KONTSEVICH INTEGRAL
S. CHMUTOV, S. DUZHIN
1. Introduction
The Kontsevich integral was invented... | 4 | [
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0.13964843... | 37,608 | 37608 | |
Pre-algebra: inequality
Suppose $x,y,z$ are any positive real numbers such that $x+y+z=xyz.$ Prove that: $(x-1)(y-1)(z-1) \leq 6\sqrt{3}-10.$ Source: JIPAM
We are looking for $\max_{x>0,y>0,z>0}f_{0}(x,y,z),$ where $f_{0}(x,y,z):=(x-1)(y-1)(z-1)$ under the restriction $g(x,y,z):=x+y+z-xyz=0$. Hence, we set $f_{1}(x,y)... | 5 | [
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... | 37,609 | 37609 | |
Analytic trig question
Hello, bilbobaggins! I think I've guessed what you meant . . . We need a number of double-angle identities: . . $\sin2\theta \:=\:2\sin\theta\cos\theta$ . . $\cos2\theta \:=\:\cos^2\!\theta - \sin^2
\!\theta \:=\:2\cos^2\!\theta -1$ . . $\tan2\theta \:=\:\frac{2\tan\theta}{1 - \tan^2\!\theta}$ $\... | 4 | [
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-0.... | 37,610 | 37610 | |
Cute Numbers
Date: 06/05/2001 at 05:05:16
From: Emily
Subject: Cute numbers
If a square can be cut into n squares of at the most two different
sizes, then n is called a cute number. For example, 4 and 10 are cute
numbers.
_______
| | |
|___|___|
| | |
|___|___|
_______
|_|_| |
|_|_|___|
|_|_| |
|_|_|_... | 4 | [
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0.095703125,
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0.01153564453125,
0.00866699218... | 37,611 | 37611 | |
How much of ZFC do I need to construct this cofinal, order-preserving class function?
up vote 3 down vote favorite
EDIT: I'm bumping this, because while Joel ruled out some naive options, my question in bold below is not yet answered.
Suppose I have a directed partially ordered set $(\Gamma,\leq)$ with a bottom eleme... | 5 | [
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0.1030... | 37,612 | 37612 | |
Law of cosine Help!!
July 29th 2006, 12:31 PM #1
Senior Member
Joined
Jul 2006
From
Shabu City
Posts
381
Law of cosine Help!!
Cud u give me the formula of Law of Cosine on how to solve a triangle w/ 3 sides
given?
Im kind of confused with this problem:
a = 5, b = 6, c = 9
find all 3 ... | 4 | [
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0.00537109375,
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0.0103759765625,
0.033203125,
0.0022430419921875,
-0.04150390625,
0.007568... | 37,613 | 37613 | |
Two ways to solve log problem.
May 1st 2009, 11:05 PM
craigmain
Two ways to solve log problem.
Hi,
I show two workings to solve the equation below using the simplification rules for logs.
My textbook does not indicate how and when solutions are lost using the log simplification rules. Clearly if we use ... | 4 | [
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0.05078125,
-0.1... | 37,614 | 37614 | |
Euler's Theorem
May 5th 2008, 01:38 PM #1
Junior Member
Joined
Feb 2007
Posts
70
Euler's Theorem
I'm supposed to prove that $a^{37} \equiv a(mod\ 1729)$ for any integer $a$ using Euler's theorem. I'm trying to first prove it under the assumption that $gcd(a, 1729)=1$, which allows me to
apply Euler's... | 5 | [
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-0.027587890625,
-0.103515625,
0.050537... | 37,615 | 37615 | |
Line intercepting curve
August 27th 2010, 10:15 PM
caramelcake
Line intercepting curve
Quote:
A straight line of gradient $m$ is drawn through the point $A(2, -4)$ on the curve $y = x^2 - 4x$. Find, in terms of $m$, the coordinates of the point $B$ at which the line intercepts the curve
again.
Thes... | 4 | [
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0.1845703125,
0.02685546875,
0... | 37,616 | 37616 | |
Trouble calculating residues
June 25th 2009, 04:08 AM
vsywod
Trouble calculating residues
Hello,
I'ld like to calculate the reside of $f(z):=\frac{z^{n-1}}{\sin^n(z)}$ at $z_0=0$.
Using the definition I get $\text{res}_{0}f = \frac{1}{2\pi i} \int_\kappa \frac{z^{n-1}}{\sin^n(z)} dz$, but I cant comput... | 5 | [
-0.076171875,
0.04736328125,
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0.04833984375,
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0.0247802734375,
0.00811767578125,
-0.0279541015625,
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0.0281982421875,
-0.06640625,
-0.01287841796875,
0.044189453125,
-0.0380... | 37,617 | 37617 | |
The orbit $(G\cdot X) \cap \mathfrak{t}$ for $X\in \mathfrak{t}$ singular
up vote 1 down vote favorite
This question may be a simple problem for experts. Let $G$ be a connected compact Lie group and $T$ be its maximal torus. Let $\mathfrak{g}$ and $\mathfrak{t}$ be the corresponding Lie algebras. We
know that $\mathfr... | 5 | [
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Multi-scale modeling of the caro
Multi-scale modeling of the carotid artery
G. Rozema, A.E.P. Veldman, N.M. Maurits University of Groningen, University Medical Center Groningen The Netherlands
University of Groningen Computational Mechanics & Numerical Mathematics
Area of inter... | 4 | [
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-0.08251953125,
... | 37,619 | 37619 | |
Why does bosonic string theory require 26 spacetime dimensions?
up vote 22 down vote favorite
21
I do not think it is possible really believe or experimentally check (now), but all modern physical doctrines suggest that out world is NOT 4-dimensional, but higher. The least sophisticated
candidate - bosonic string theo... | 4 | [
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-0.0341796875,
0.003829... | 37,620 | 37620 | |
Distance to an apartment of the affine building of GL(N)
up vote 13 down vote favorite
4
Here $F$ is a locally compact non-archimedean non-discrete field.
Let $X$ be the reduced (affine) Bruhat-Tits building of ${\rm GL}(n,F)$. Fix a maximal split torus $T$. Let $B$ be a Borel subgroup containing $T$ and write $U$ fo... | 5 | [
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0.06640625,
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-0.0986328125,... | 37,621 | 37621 | |
Sequence of function.
June 5th 2010, 02:16 AM #1
Sequence of function.
Let $(f_n)^\infty_{n=1}$ be a sequence of functions which are defined on $[a,b]$, and uniformly converges there to bounded function $f$. Let $\Phi\in C(\mathbb{R})$ which is continuous function
on all $\mathbb{R}$.
Prove that the seque... | 5 | [
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-0.00811767578125,
-0.... | 37,622 | 37622 | |
Difficulty with a math word problem. Help me out here please.
March 18th 2012, 08:38 PM #1
Newbie
Joined
Mar 2012
From
Bartow, FL
Posts
9
Difficulty with a math word problem. Help me out here please.
Ok, I'm getting ready to go to school this summer, and in the meantime, I'm trying to learn as much ... | 4 | [
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0.07470703125,
0.0361328125,
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0.0308837890625,
0.039794921875,
-0.07763671875,
-0.033203125,
0.044433... | 37,623 | 37623 | |
URGENT MATH HELP: Differntial Equations and Applications of Intergration
May 25th 2009, 06:15 PM #1
Junior Member
Joined
Sep 2008
Posts
28
URGENT MATH HELP: Differntial Equations and Applications of Intergration
2. A culture starts with 200 bacteria and grows at a rate proportional to its size. After 3 h... | 5 | [
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0.08251953125,
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-0.00921630859375,
0.00008058547973632812,
0.023193359375,
-0.02221... | 37,624 | 37624 | |
Problem with Complex numbers.
I have (z^(3))+2i=0 and the second is (z^(2))-2i.z-2i=1 Pls show me the right direction with these problems,10x
z^3 = -2i => z = the three cube roots of -2i. Have you been taught how to find the three cube roots of a complex number using de Moivre's Theorem? z^2 - 2i z - 2i = 1 => (z - i)... | 4 | [
-0.08837890625,
0.0556640625,
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0.1181640625,
0.03564453125,
-0.044921875,
-0.060546875,
0.04833984375,
-0.... | 37,625 | 37625 | |
Basic Arithmetic Conundrum.
July 20th 2011, 02:50 AM #1
Newbie
Joined
Mar 2011
Posts
8
Basic Arithmetic Conundrum.
Hi all
I stumbled upon the following :
A bottle filled with water ( density 1 kilo per Litre (1000 cm3) weighs 950 grammes, filled with alcohol ( density 800 grammes ) this bottle ... | 4 | [
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0.026611328125,
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0.125,
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-0.03076171875,
-0.00616455078125,
0.0722656... | 37,626 | 37626 | |
Help with evaluating a sum
October 9th 2011, 07:51 AM #1
Newbie
Joined
Sep 2008
Posts
13
Help with evaluating a sum
Hello everyone,
I'm not sure if this is the best category for my post, but i will try asking anyways. I've spent quite a bit of time trying to figure it out.
Basically, the proble... | 5 | [
-0.041015625,
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0.0458984375,
0.0274658203125,
-0.0161132812... | 37,627 | 37627 | |
Please Reada::...
June 26th 2007, 04:55 PM #1
Please Reada::...
Hey, i've decided to give myself some things to work out., in preparation for my Exam. Obviously it's not any questions from the exam, how would i have got a hold of them? They may seem easy, but
some people do happen to be Dyslexic:
I origin... | 4 | [
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0.06494140625,
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... | 37,628 | 37628 | |
Short lattice vectors orthogonal to a random vector
up vote 5 down vote favorite
1
Let $N$ be some prime number. Suppose I draw $s$ elements $g_1,..., g_s$, where each $g_i\in [N]$ is taken uniformly from some interval $I_i$ of size, say $\sqrt{N}$.
Is it possible to provide a lower-bound (which works on average, or ... | 5 | [
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0.02294921875,
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0.025146484375,
... | 37,629 | 37629 | |
Lie groups vs. algebraic groups and deformations
up vote 12 down vote favorite
4
I am interested in deformations of (discrete subgroups of) Lie groups. But, as I understand it, deformation theory, as a theory, prefers to speak schemes.
At least the classical Lie groups can be turned into group schemes, allowing for a... | 4 | [
-0.1318359375,
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0.029541015625,
0.059814453125,
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0.101562... | 37,630 | 37630 | |
Finding cos (pi / 5)
March 1st 2008, 11:40 PM #1
Junior Member
Joined
Feb 2008
Posts
60
Finding cos (pi / 5)
Hello. Sorry to be a nuisance to you guys but you've all been very helpful. This is going to be my last question.
-----
If:
sin(3pi / 10) = (1 + squareroot 5) / 4
Find the exac... | 4 | [
-0.1279296875,
0.018798828125,
0.033447265625,
-0.0067138671875,
0.03369140625,
0.02783203125,
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0.055908203125,
0.02294921875,
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0.1005859375,
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0.08056640625,
0.02783203125,
-0.0556640625,
-0.03271484375,
0.0615234375,
... | 37,631 | 37631 | |
Why Does a Negative Times a Negative Make a Positive?
Date: 11/25/2003 at 11:36:37
From: Brea
Subject: negative integers
Why is a negative times a negative a positive? When you answered this
question to other people, the way you explained it was over my head.
When you have a negative integer, in order to multiply b... | 4 | [
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0.0576171875,
0.08837890625,
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-0.0250244140625,
0.025634765625,
0... | 37,632 | 37632 | |
Invariant functionals on C(R) and amenable groups
up vote 2 down vote favorite
Since there seems to be no progress in this interesting question, I took the liberty to reformulate it in a way, that is easier to understand. Moreover, my answer shows that the question is related
to amenable groups. Therefore I changed t... | 5 | [
-0.06787109375,
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0.0211181640625,
0.0235595703125,
-0.01446533203125,
0.... | 37,633 | 37633 | |
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Topic: binary search with arbitrary or random split
Repli... | 4 | [
-0.115234375,
-0.06689453125,
0.046875,
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0.034423828125,
-0.0076904296875,
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0.05322265625,
-0.025146484375,
0.03564453125,
0.005401611328125,
-0.044677734375,
-0.010559... | 37,634 | 37634 | |
Area of Parallelogram
April 16th 2009, 11:42 AM #1
Area of Parallelogram
A Parallelogram has area 85 $cm^2$. The side lengths are 10 cm and 9 cm. What are the measures of the interior angles
Given the area is 85cm^2. Use the base as 10 cm, so $10 \cdot h = 85 \, \Rightarrow h = 8.5$
This gives one angle... | 4 | [
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0.050537109375,
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-0.0218505859375,
... | 37,635 | 37635 | |
A.e Convergent Problem.
December 9th 2011, 08:46 PM
younhock
A.e Convergent Problem.
Suppose i have $\sum_{n=1}^{\infty} ||f_n||_2 < \infty$. How to show that the $\sum_{n=1}^{\infty} f_n$ converges absoutely almost everywhere ,
f= $\sum_{n=1}^{\infty} f_n \in L^2$ , and $||f||_2 <= \sum_{n=1}^{\infty}||f_n|... | 5 | [
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-0.061767578125,
0.035888671875,
-0.035644531... | 37,636 | 37636 | |
final proof involving real functional equation
April 17th 2007, 06:53 PM #1
Junior Member
Joined
Jul 2006
Posts
73
final proof involving real functional equation
Suppose that f:R->R is a continuous function such that f(x+y) = f(x) +f(y) for all x, y element of R. Prove that there exists k element of R su... | 4 | [
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-0.0206298828125... | 37,637 | 37637 | |
Field Theory Proof -- Please Help
September 17th 2009, 02:49 PM
amm345
Field Theory Proof -- Please Help
Let X,Y,Z be sets. Prove that X union (Y intersecting Z) = (X union Y) intersecting (X union Z).
The proof would start off by showing that each side is a subset of the other, I believe... But there would... | 4 | [
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-0.033935546... | 37,638 | 37638 | |
Complex Line Integrals
November 18th 2008, 03:47 PM
robeuler
Complex Line Integrals
Here I go again...
All of these line! integrals are on the circle |z|=2, with counterclockwise orientation.
1. int(z^104)dz
2. int(z*conjugate(z))d|z|
3. int(conjugate(z))dz
4. int(cos(z)/z^3)dz
5. int(s... | 5 | [
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... | 37,639 | 37639 | |
Creating a Parity Check Matrix
make-ldpc: Make a low density parity check matrix, by random generation.
make-ldpc pchk-file n-checks n-bits seed method
where method is one of the following:
evencol checks-per-col [ no4cycle ]
evencol checks-distribution [ no4cycle ]
... | 5 | [
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-0.05712890625,
-0.1083984375,
-0.0220947265625,
0.036376953125,
0.003463745117... | 37,640 | 37640 | |
Deformations of semisimple Lie algebras
up vote 12 down vote favorite
6
In the questions Is "semisimple" a dense condition among Lie algebras? and What is the Zariski closure of the space of semisimple Lie algebras?, something equivalent to the following is mentioned: if
you have a smoothly varying family of semisimpl... | 4 | [
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0.08496... | 37,641 | 37641 | |
Surface Integral Help
November 20th 2009, 08:16 AM #1
Junior Member
Joined
Mar 2009
Posts
63
Surface Integral Help
The figure shows the surface created when the $cylinder\ y^2 + z^2 = 1\ intersects\ the\ cylinder\ x^2 + z^2 = 1\ Find\ the\ area\ of\ this\ surface.$
I think to find the surface integr... | 4 | [
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0.05712890625,
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-... | 37,642 | 37642 | |
Large Numbers and Congruences
Date: 03/05/2002 at 12:42:43
From: Boris Dusek
Subject: Last three digits of large number
Find the last three digits of the number 11^(11^(11^(11^(11^11))))
written in base seven.
Date: 03/09/2002 at 06:57:06
From: Doctor Pete
Subject: Re: Last three digits of large number
Hi Boris,
... | 5 | [
-0.06494140625,
0.04541015625,
-0.058837890625,
-0.08203125,
0.01177978515625,
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0.0615234375,
0.047119140625,
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0.044189453125,
-0.036865234375,
-0.08056640625,
0.06835... | 37,643 | 37643 | |
Homotopy groups of the blow-ups and monotone symplectic manifolds
up vote 3 down vote favorite
I want to calculate the second homotopy group of the blow-up of the unit cotangent disk bundle of a closed surface $\Sigma$, i.e $\pi_2\left(D^*T\Sigma\#\overline{\mathbb{C}P^2}\right).$ Actually, I
want to understand whethe... | 5 | [
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... | 37,644 | 37644 | |
Math Tools Discussion: All Tools on Computer, Generating a graph curve from 2 known points and a middle reference point.
Discussion: All Tools on Computer
Topic: Generating a graph curve from 2 known points and a middle reference point.
<< see all messages in this topic
< previous message | next message >
Subj... | 4 | [
-0.1484375,
-0.0062255859375,
-0.002410888671875,
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0.072265625,
0.08642578125,
-0.087890625,
-0.0... | 37,645 | 37645 | |
Parabola Word Problem
April 3rd 2006, 03:59 AM #1
Newbie
Joined
Mar 2006
Posts
10
Parabola Word Problem
Hello,
This is only my 3rd post here I'm pretty sure. I want to say thanks again to those who helped me with my first post in the two questions I listed. I have another question on how to set up t... | 4 | [
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-0.021240234375,
-0.09521484375,... | 37,646 | 37646 | |
Banach spaces or not?
March 30th 2011, 03:55 PM #1
Dear MHF members,
I have two questions on Banach spaces,
and I would really appreciate if you help me with a complete answer.
Let $[a,b]$ be a interval and $c\in[a,b]$.
1. Denote by $\Omega_{c}([a,b],\mathbb{R})$ the set of all real valued bounde... | 5 | [
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0.0546875,
0.053466796875,
-0.0476074218... | 37,647 | 37647 | |
Reference for subsemigroups of $\mathbb{N}^n$
up vote 4 down vote favorite
2
A well known result about the natural numbers $\mathbb{N}$ says that for any finite subset $A \subset \mathbb{N}$ there exists $R \ge 0$ such that if $n$ is in the subgroup of $\mathbb{Z}$ generated
by $A$ and if $n \ge R$ then $n$ is in the ... | 4 | [
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0.00860595703125,
... | 37,648 | 37648 | |
Is $x \, \tan(x)$ integrable in elementary functions?
up vote 15 down vote favorite
4
I'm teaching Calculus and my students asked me to calculate the integral of $x \, \tan(x)$.
I spent quite a lot of effort to do this, but I'm now even not sure if the integral could be presented in elementary functions.
Does anybod... | 5 | [
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... | 37,649 | 37649 | |
Partial derivative
$3x^2 \ln(1-xy)$ the partial derivatvie with respect to y is $\frac{x}{1-xy}$ is that right?
but i thought you treat x as a constant so its derivative is 0?
Yes, it is treated like a constant. What do you do to differentiate a constant times a function? It's the constant times the derivative of tha... | 5 | [
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-0.1259765625,
... | 37,650 | 37650 | |
Ways to prove the fundamental theorem of algebra
up vote 76 down vote favorite
95
This seems to be a favorite question everywhere, including Princeton quals. How many ways are there?
Please give a new way in each answer, and if possible give reference. I start by giving two:
1. Ahlfors, Complex Analysis, using Liou... | 4 | [
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0.003753662109375,
-0.01385498046875,
-0.03125,
-0.071289062... | 37,651 | 37651 | |
Tangent Line Question
October 31st 2006, 03:58 PM #1
Newbie
Joined
Mar 2006
Posts
17
Tangent Line Question
Hi, I have a quick question about finding the equation of a tangent line to the graph of y = (3x+5)e^x at x=0
so far I have Point (0,5)
Code:
(3(x+h) +5)e^(x+h) - (3x+5)e^x
------... | 5 | [
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0.03564453125,
-0.10400390625,
-0.05... | 37,652 | 37652 | |
qua
September 17th 2007, 05:45 AM #1
Equation
I have two questions:
The first is that I can't seem to get the answer to the attached equation. The book says x = 1, or x = 1/2. Though this is probably because of my second question:
The second question is, is there a method to work out how to factorise? S... | 4 | [
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... | 37,653 | 37653 | |
Trig simplification issues
October 22nd 2010, 08:07 PM
abzolutezero
Trig simplification issues
I'v been sick in my college math class and have been a bit behind. I really could use some help and have been slamming my head against my text book trying to figure some of these simplifications
out.(Headbang) One ... | 4 | [
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-0.0234375,... | 37,654 | 37654 | |
Recursion and Closed Formulas
March 2nd 2010, 08:44 PM #1
Newbie
Joined
Jul 2009
Posts
18
Recursion and Closed Formulas
Hello!
I've be scanning different help forums and I have a come across two different questions involving finding closed formulas. I have attempted to answer them with no luck and n... | 5 | [
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0.03515625,
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-0.07666015... | 37,655 | 37655 | |
How to count symmetry factors of Feynman diagrams?
up vote 11 down vote favorite
6
I have enough fears that this question might get struck down. Still let me try.
I shall restrict myself to $\frac{\lambda \phi^4}{4!}$ perturbed real scalar quantum field theory and call as "symmetry factor" of a Feynman diagram to be... | 4 | [
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0.05078125,
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0.00363... | 37,656 | 37656 | |
Trigonomertric identities
$cos20°cos100°+cos100°cos140°-cos140°cos200°$ = $cos20°cos100°+cos100°cos140°+cos140°cos20°$ Now, see $<br /> sec\frac{\pi}{9},sec\frac{5\pi}{9},sec\frac{7\pi}{ 9}<br />$ are the roots of equation $
<br /> sec^{3}\theta+6sec^{2}\theta-8=0<br />$ see thread: http://www.mathhelpforum.com/math-he... | 5 | [
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0.04931... | 37,657 | 37657 | |
[SOLVED] Differential equation
Find the function http://hosted.webwork.rochester.edu/...2d857fb531.png that satisfies the differential equation and the condition http://hosted.webwork.rochester.edu/...0ef732ac51.png. So first of
all I found integration factor which is http://hosted.webwork.rochester.edu/...09c1189e41.p... | 5 | [
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-0.00... | 37,658 | 37658 | |
Question on $Ext$
up vote 3 down vote favorite
1
Let $S$ be the polynomial ring $k[x_0,\ldots,x_n]$, $x$ one of the variables $x_i$, $I\subseteq S$ a homogeneous ideal which has a generating set $f_1,\ldots,f_r$ where $\deg_x f_i=0$ for all $i$.
From the short exact sequence $$0\to S/I(-1)\xrightarrow{f} S/I \to S/(x... | 5 | [
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0.0556... | 37,659 | 37659 | |
Choosing 5 balls from 10 black, 20 white, 40 red.
June 10th 2011, 06:39 PM #1
Newbie
Joined
Mar 2011
Posts
2
Choosing 5 balls from 10 black, 20 white, 40 red.
10 black, 20 white, 40 red
The question is what is probability when we reach 5 of them, and we have 2 white, 2 red, 1 black.......
And so... | 4 | [
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0.150390625,
-0.004089355... | 37,660 | 37660 | |
Continouty of a mapping, need help
November 29th 2008, 03:09 PM #1
Newbie
Joined
Nov 2008
Posts
3
Continouty of a mapping, need help
Hi,
I'm having trouble with an assignment of mine. I hope someone here can help me. It should be trivial - I just think I've overseen something... Well, here goes:
... | 5 | [
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0.045166015625,
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-0.128... | 37,661 | 37661 | |
Voltage Comparator and Multiplier make stable Sine Wave
Voltage Comparator and “Q” Multiplier make a stable
Sine Wave Oscillator
Ramón Vargas Patrón
rvargas@inictel.gob.pe
... | 4 | [
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0.01... | 37,662 | 37662 | |
Infinite sets and Countable sets
I don't understand what (c) and (d) are and how do their elements look like.
For c). The characteristic function is ${1_A}(x) = \left\{ {\begin{array}{rl} {1,}&{x \in A} \\ {0,}&{x otin A} \end{array}} \right.$. Look at the collection $\left\{1_{\{k\}}:k\in\mathbb{N}\right\}$
For d) de... | 4 | [
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More on universal homeomorphisms
up vote 2 down vote favorite
I would like to understand this notion better; where could I find some examples? In particular, I am interested in the following questions (and references for the answers).
1. Is a universal homeomorphism of connected regular (excellent finite dimensional... | 5 | [
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Asymptotic Distribution of Primes
up vote 5 down vote favorite
3
Given an integer $n$ and let $1\leq m\leq n$ be such that $n$ and $m$ are coprimes define $$ \mathcal{N_{n,m}}:=\text{the set of primes $p$ such that $p\equiv{m}\hspace{0.1cm}\mathrm{mod}(n)$}. $$
Let $\mathcal{P}$ be the set of all primes. I seem to rec... | 4 | [
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-0.0473632812... | 37,665 | 37665 | |
I need help with more factorizaing...
March 21st 2009, 09:44 PM #1
Newbie
Joined
Jan 2009
Posts
13
I need help with more factorizaing...
factorization is not my thing
anywayz here are the two questions
x^2 +3x(x+3y)+2(x+3y)^2
and
3(2x-y)^2 +2y(2x-y)-5y^2
steps would be nice
th... | 4 | [
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0.0385742187... | 37,666 | 37666 | |
Beyond Locality-Sensitive Hashing
This is an extended version of (the only) post in my personal blog.
In this post I will introduce locality-sensitive hashing (for which Andrei Broder, Moses Charikar and Piotr Indyk have been recently awarded Paris Kanellakis Theory and Practice Award) and sketch
recent developments ... | 4 | [
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0.0... | 37,667 | 37667 | |
cohomology and Eilenberg-MacLane spaces
up vote 12 down vote favorite
4
This question is related to this question from Dinakar, which I found interesting but don't yet have the background to understand at that level.
Unless I'm mistaken, the rough statement is that H^n(X;G) (the n-dimensional cohomology of X with coe... | 4 | [
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0.023803710... | 37,668 | 37668 | |
Combinatorial meaning of the functional equation for logarithm
up vote 14 down vote favorite
2
If we set $\exp(x)=\sum x^k/k!$, then $\exp(x+y)=\exp(x)\cdot \exp(y)$. In terms of coefficients it means that $(x+y)^n=\sum \frac{n!}{k!(n-k)!} x^ky^{n-k}$, i.e. just binomial expansion.
Now consider logarithm. Set $L(x):=... | 5 | [
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Conservative differential equations "in the wild"
up vote 5 down vote favorite
Dear MO world,
I'm teaching an undergraduate course on "fun with chaos". As part of a test (on bifurcations in differential equations), I asked students to sketch phase portraits for a family of (2d) differential
equations. While preparing... | 5 | [
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How do I simplify the following equation?
March 20th 2012, 10:30 PM #1
Junior Member
Joined
Oct 2007
Posts
52
How do I simplify the following equation?
$2log_{e}(y)=-log(x+e^x)+c$, to be in the form y=? where c is the constanf of the integration I have just done (not needed for the simplification)
T... | 5 | [
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0.0898... | 37,671 | 37671 | |
Cauchy Mean Value Theorem Consequence problem
November 25th 2008, 01:14 PM #1
Super Member
Joined
Mar 2006
Posts
705
Thanks
2
Cauchy Mean Value Theorem Consequence problem
Suppose that the function $f: \mathbb {R} \rightarrow \mathbb {R}$ has two derivatives, with $f(0)=f'(0)=0$ and $|f''(x)| \leq 1$... | 4 | [
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GRAPH
GRAPH ALGORITHMS
Definitions (background):
Graph: nodes/vertices, and edges/arcs as pairs of nodes. {V, E}
e12=(v1, v2, l12)
The third term l12, if present, could be a label or the weight of an
edge.
Directed graph: edges are ordered pairs of nodes.
Weighted graph: each ed... | 4 | [
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Non-finite version of Nakayama's lemma?
up vote 1 down vote favorite
Let $A$ be a local ring with nilpotent maximal ideal $\mathfrak{m}$ (i.e., some power of $\mathfrak{m}$ vanishes), and $M$ an $A$-module (not necessarily finitely generated). Let $\bar{S}\subset M/\
mathfrak{m}M$ be a set of generators and $S$ a set ... | 5 | [
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... | 37,674 | 37674 | |
Ma
Simple Interest Made Simple!
• The formula for simple interest is I = Prt
• In order to determine any of the variables (I, P, r, t) you only need the other 3
• When you know three of the four values, here's how you calculate the unknown.
□ To find principal (P) P = I/rt
□ To find the interest rate... | 4 | [
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Irreducible polynomials with constrained coefficients
up vote 16 down vote favorite
8
Over at the Cafe, after reading about TWF 285, I asked more-or-less
About how many polynomials with coefficients in $\{\pm 1\}$ and of degree $d$ are irreducible?
and that's what I want to ask here.
The first no-go analysis: s... | 5 | [
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-0.00010538101196289062,
0.0148315... | 37,676 | 37676 | |
Number of spanning subgraphs of $K_n$ with given number of edges and connected components
up vote 1 down vote favorite
Given some positive integers $n,e$ and $c$, I would like to know the number of spanning subgraphs of $K_n$ having $e$ edges and $c$ connected components.
Essentially, what I am asking for here is th... | 4 | [
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0.057861328125,
-0.01025390625,... | 37,677 | 37677 | |
Dini condition and integrability condition
up vote 1 down vote favorite
Assume that $A$ is an arbitrary positive integrable function on $[0,1]$. Whether exists a convex function $f_A(x)=x g(x)$ of $(0,+\infty)$ into itself (depending on $A$) such that $\lim_{x\to +\
infty} g(x)=+\infty $ and $$\int_0^1 A(x) g(1/x^2) d... | 5 | [
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0.00411987304687... | 37,678 | 37678 | |
Is independence meaningful for commutative $C^*$-algebras?
up vote 4 down vote favorite
3
I don't know very much about spectral theory so probably the answer to my question has a basic reference which I would appreciate.
Let's say I have two self-adjoint operators on a Hilbert space and that they commute. I know that... | 5 | [
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-0.039794921875,
0.065917... | 37,679 | 37679 | |
binomial transform, Hurwitz zeta function
up vote 1 down vote favorite
For $j,n\in\mathbb Z_+$, let $$ L_{j,n}^{(t)}= \sum_{m=0}^{n} \Bigl(-\frac 12\Bigr)^{n-m}{n\choose m}{m+j+1\choose m+1} \left( \frac {1}{t+\frac 12}\right)^{m+j+2} $$ and $$ L_{j,n} =\sum_{t=1}^\
infty L_{j,n}^{(t)} $$
We would like to show that f... | 4 | [
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0.035400390625,
0.0358886... | 37,680 | 37680 | |
Homework Help
Posted by chris on Wednesday, November 30, 2011 at 11:08pm.
The height (in feet) attained by a rocket t seconds into flight is giving by the function
h(t)= -1/3t^3 + 16t^2 + 33t + 10
When is the rocket rising?
When is the rocket decreasing?
when does it reach its maximum height above the ground?
wha... | 4 | [
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-... | 37,681 | 37681 | |
Example: Representing Sets
Next: Example: Huffman Encoding Trees Up: Symbolic Data Previous: Example: Symbolic Differentiation
Example: Representing Sets
In the previous examples we built representations for two kinds of compound data objects: rational numbers and algebraic expressions. In one of these example... | 4 | [
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The Hundred Fowls
Date: 09/29/2001 at 16:14:28
From: Yana
Subject: Word Problem
A Chinese puzzle found in the sixth-century work of mathematician
Chang Chiu-chen called the "hundred fowls" problem asks:
If a rooster is worth five coins, a hen three coins, and three
chickens together are worth one coin, how many roo... | 4 | [
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law of total probability
January 30th 2010, 01:21 AM #1
Newbie
Joined
Jan 2010
Posts
8
law of total probability
use the law of total probabilty to prove that
a. if P (A l B) = P (A l B,) then A and B are independent
b. if P (A l C ) > P (B l C) and P (A l C' ) > P( B l C' ), then P (A) > P (B)
... | 4 | [
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L1 Poincare Inequality
The L1 Poincare inequality – bounding the 1-norm of a function by the 1-norm of it’s derivative – can be understood as a consequence of applying the isoperimetric inequality to the function’s level
sets. Let f be a smooth function that passes through zero at least once on a sufficiently nice (co... | 4 | [
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Prove log of eigenvalues are dense in R?
up vote 3 down vote favorite
Suppose you have the set of all possible $n$ x $n$ square adjacency matrices where $n$={1,2,3,4...}. For each matrix, compute the logarithm of the largest eigenvalue. Is it true that the set of
logarithms you obtain is dense in $\mathbb{R}$? How do ... | 5 | [
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[SOLVED] nth root in a simple calculator
May 16th 2010, 05:02 AM
rohankg88
[SOLVED] nth root in a simple calculator
I came across this trick to find n th root of any number on a calculator that does not have nth root function or logs !! problem is I can't figure out why it works ...
To find : nth root of x.... | 5 | [
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... | 37,687 | 37687 | |
absolute value..2 different answer
December 7th 2009, 10:58 AM
Candy101
absolute value..2 different answer
absolute value
I getting a different answer...don't know why
|3-4x|≥2
what i did was=====> i made it in to 2 parts ===>3 - 4x ≥ 2 and 3 - 4x ≥-2
my final answer that i got is
1/4≥x (... | 4 | [
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Fluid flow in pipe.
May 18th 2010, 07:16 AM #1
Newbie
Joined
May 2010
Posts
1
Hi,
I have what I'm sure is an easy question for a maths genius. However I need to know the answer for an insurance claim:-
"How much water in litres will flow through a 20mm pipe in one hour with the water pressure at... | 4 | [
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0.0092773... | 37,689 | 37689 | |
Error in thought:How many onto functions there from a set of 4 element to 2 elements?
August 14th 2011, 09:10 AM
x3bnm
Error in thought:How many onto functions there from a set of 4 element to 2 elements?
There's a math problem in the book Discrete Mathematics with Applications(2nd Edition) by Susanna S. Epp is ... | 5 | [
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Determining the simplices in freudenthal triangulation
up vote 0 down vote favorite
HI,
I have a doubt on Freudenthal Triangulation. I want to partition a simplex into finer simplices.
The FT gives me the vertices of the simplices which partition my original simplex into finer simplices.
I am interested in enumerat... | 4 | [
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Solve the equation
$\lfloor x \rfloor =x^2(x^2-2)$ where $\lfloor x \rfloor$ denotes the floor function.
With the floor on the left, the right side must be integer valued which, in turn means $x^2$ must be integer valued. x is either an integer or the square root of an integer. So just try some
integers. If x= 0, this... | 4 | [
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0.0009918212... | 37,692 | 37692 | |
GENERAL SOLUTION f(x,t) please help
April 10th 2010, 02:38 PM #1
Newbie
Joined
Apr 2010
Posts
2
hello,
im having difficulty answering this question, please could somebody spare sometime answering it.. it starts off an exam paper and is putting me off the whole thing..
wats da general solution of
... | 5 | [
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-0.0... | 37,693 | 37693 | |
Kontsevich's formality theorem from an explicit homotopy
up vote 10 down vote favorite
5
Suppose that $X$ is a smooth manifold, whose $C^{\infty}$-functions we denote by $A$. Let $D_{poly}^*(A):=\bigoplus_{n\geq -1}Hom(A^{\otimes n+1},A)$ be the Lie algebra of polydifferential operators
with the Hochschild differentia... | 4 | [
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Math Help
February 18th 2006, 03:42 PM #1
Global Moderator
Joined
Nov 2005
From
New York City
Posts
10,616
Thanks
9
Finite>Infinite
Proof that if $S$ is any finite set and $T$ is any infinite set then $|S|<|T|$. In mathematical words prove that there exists a surjection $\phi:S\to T$ which is no... | 5 | [
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Limits of piecewise function
September 16th 2011, 12:55 PM
habibixox
Limits of piecewise function
Lim where f (x) = 2 (x+1) if x <3
x->2 4 if x=3
x^2 - 1 if x> 3
please tell me you have to write out what the left and right limits are to find out if they are equal?
:(
left limit is 6 and r... | 4 | [
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Permutations.
January 25th 2009, 09:14 PM
Big-K
Permutations.
10C2
i know the answer is 45.
but for some reason, i can't get THAT answer. i keep getting something else....
anyone help me please?
thank you in advance!
January 25th 2009, 09:19 PM
andreas
Quote:
10 C 2= $\frac{10!}{8!... | 4 | [
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... | 37,697 | 37697 | |
Roots related question
November 1st 2008, 05:45 AM #1
Newbie
Joined
Sep 2008
Posts
7
Roots related question
Hey guys I was having trouble with this question can someone plesase explain it to me in detail. thanks much appreciated.
$x^3 - 3^3 = (x - 3)(x^2 + 3x + 9)$.
Therefore the roots of $x^3 ... | 4 | [
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Trig iden: Quadruple angle formulas
July 23rd 2007, 06:51 PM
andrewsx
Trig iden: Quadruple angle formulas
How do you tackle these?
1. 2cos^2 4x-1
sin4xcos4x
2. 1-4sin^2x+4sin^4x
The answers to the first is 2cot8x and the second is cos^22x. I would like to see the step by step process.
H... | 4 | [
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