content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Thermal Phases of the Interstellar Medium in Galaxies -
M.C. Begelman
2.2. Connection with thermal instability
There is an intimate connection between the existence of thermal phases and the thermal stability of a system: any system exhibiting multiphase equilibria must be thermally unstable over a range of
thermodyna... | 4 | [
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0.... | 42,300 | 42300 | |
1-Dimensional Heat Initial Boundary Value Problems 1: Separation of Variables
Let us consider the following assumptions for a heat conduction problem.
1. The region $\Omega$ is a cylinder of length $L$ centered on the $x$-axis.
2. The lateral surface is insulated.
3. The left end ($x=0$) and the right end ($x=L$) ... | 4 | [
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-0.11279296875... | 42,301 | 42301 | |
Forms
Linear Algebra
This chapter is about several algorithms for matrix algebra over the rational numbers and cyclotomic fields. Algorithms for linear algebra over exact fields are necessary in order to implement the
modular symbols algorithms that we will describe in Chapter Linear Algebra. This chapter partly over... | 5 | [
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0.0073852... | 42,302 | 42302 | |
Computing a polynomial product over roots of unity
up vote 4 down vote favorite
3
I'm trying to compute the coefficients of the following polynomial, where $\omega$ is a primitive $p$-th root of unity, for $p$ prime:
$$a(x) = \prod_{i=0}^{p-1} f(\omega^ix).$$
It turns out that the $i$-th coefficient is always an int... | 5 | [
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0.0461... | 42,303 | 42303 | |
Factorization problem
November 29th 2011, 06:55 PM #1
Newbie
Joined
Nov 2011
Posts
6
Factorization problem
I have a problem factorizing that equation 2x^3-5x^2-6x+8 until now I've found the root x=2 and x=-4/3 and I'm stuck there
Thanks for the help
Re: Factorization problem
Re: Factorization prob... | 4 | [
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0.0034... | 42,304 | 42304 | |
Math Help
$\cos 36^{\circ}=\frac{\sqrt{5}+1}{4}$ $\sin 36^{\circ}=\frac{(\sqrt{5}-1)\sqrt{1+2\sqrt{5}}}{8}$ Then $\tan 36^{\circ}=\frac{(3-\sqrt{5})\sqrt{10+2\sqrt{5}}}{4}$ We have to prove $\sqrt{5}+1>(3-\
sqrt{5})\sqrt{10+2\sqrt{5}}$ Square both members: $6+2\sqrt{5}>(14-6\sqrt{5})(10+2\sqrt{5})$ $17\sqrt{5}>37$ Squ... | 4 | [
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0.06... | 42,305 | 42305 | |
Help, Multiplying binomial radicals
April 10th 2012, 03:17 AM
drmattthew
Help, Multiplying binomial radicals
I've looked through dozens and dozens of questions, and I can't find an example with this format where both numbers in both sides are under the radical sign, and no numbers to the left, please
help. (... | 4 | [
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0.08789062... | 42,306 | 42306 | |
some trignometry simplification
April 10th 2007, 11:43 PM #1
Newbie
Joined
Apr 2007
Posts
7
Solve the following equations if 0<x<2pie (those are 'less than or equal to') answer to 2 decimal places.
a) square root of 2 cos(x = pie/2) + 1 = 0
b) sin(1/2)(x-2pie/9) = 0.6
i would be greatful t... | 4 | [
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Describing the key Sub-algebra of the Bost-Connes System - Part III
Third in a three part series of me trying to describe the Bost-Connes algebra. Part I: $\mathbb{Q}$-Lattices and the Presentation. Part II: Equivalent description in terms of a Hecke Algebra. Part
III: Describing the key Sub-algebra.
In my last post I... | 4 | [
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[SOLVED] Basic probability questions
February 15th 2010, 12:02 AM #1
Senior Member
Joined
Oct 2009
Posts
295
Thanks
9
[SOLVED] Basic probability questions
I'm studying for an exam and am having a few small problems. I wasn't whether it was best to make a thread for each or post everything in one thre... | 4 | [
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Rearranging the quadratic formula
April 14th 2012, 02:26 AM #1
Newbie
Joined
Apr 2012
From
Australia
Posts
4
Rearranging the quadratic formula
Hi guys, I've been tasked with rearranging the quadratic root formula to make "a" the subject. I've been struggling on this one for a little while now and can... | 4 | [
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Random walk on a two-dimensional uniform grid
up vote 2 down vote favorite
Hi,
consider the following random walk on the lattice $\{0,\dots,n\}^2$. It starts at $(0,0)$ and then move either up or right, with probability respectively $p$ and $1-p$. Once it reaches the right
border (respectively the up border), it goes... | 5 | [
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No statistically significant warming since 1995
Because there has been some confusion - and maybe deliberate confusion - among some (alarmist) commenters about the non-existence of a statistically significant warming trend since 1995, i.e. in the
last fifteen years, let me dedicate a full article to this issue.
Update... | 4 | [
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3D Projection Onto a 2D Plane
Date: 7/9/96 at 15:22:57
From: Anonymous
Subject: 3D Projection Onto a 2D Plane
I'm dealing with a theoretical geological problem where I consider a
roughly planar orebody as being 2D. I have drill-hole values and 3D
coordinates for a number of points. Fitting a plane to these points
... | 5 | [
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On Brown representability theorem
up vote 5 down vote favorite
2
The classical Brown representability theorem is for set valued functors. Is there a version for abelian group valued functors, and ring valued functors?
In other words say we have an abelian group valued functor F on the category of CW top. spaces, sati... | 4 | [
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_SAS_ Congruence IF two sides and included angle of ... - TeacherWeb
Section 4.4 Use the SAS Congruence Postulate
Posutlate 20 Side-Angle- Side (SAS) Congruence
IF two sides and included angle of one triangle
are congruent to two sides and the included
angle of a second trian... | 4 | [
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Are All Infinitely Long Repeating Numbers Even?
Date: 06/06/2000 at 17:53:50
From: Richard Huggins
Subject: All infinitely long numbers of repeating form are even?
Take any infinitely long repeating series:
x = 1234123412341234...
This one repeats after a section of length 4.
Multiply the number by 10^(secti... | 4 | [
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The limits of parallelism
up vote 3 down vote favorite
1
Is it possible to solve a problem of O(n!) complexity within a reasonable time given unlimited number of processing units and infinite space?
The typical example of O(n!) problem is brute-force search: trying all permutations.
I have asked this question on Sta... | 5 | [
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Algorithm of the Week: Shortest Path in a Graph
Introduction
Since with graphs we can represent real-life problems it’s almost clear why we would need an efficient algorithm that calculates the shortest path between two vertices. Getting back to our example of
a road map we can use such an algorithm in order to find ... | 5 | [
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Nonstandard Hessian approximations in Gauss-Newton
up vote 1 down vote favorite
The Gauss-Newton algorithm optimizes functions
$$ E(x) = \sum f(x)^2 $$
by approximating f as (locally) linear, in which case the Hessian of $E$ is approximated as
$$ H = 2 \sum {J_f}^T J_f $$
Now if I introduce a robust cost function ... | 4 | [
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Can we change the Lebesgue measure by forcing?
up vote 9 down vote favorite
1
Suppose $M$ is a model of ZFC, and $\mu^M$ is the Lebesgue measure on $\mathbb R^M$ such that $\mu^M(\mathbb R^M)=1$. It is known that if $r$ is a Cohen real over $M$ and $N=M[r]$ then $\mu^N(\mathbb
R^M)=0$.
This is a very strong transitio... | 5 | [
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0.06... | 42,320 | 42320 | |
The Inverse Spanning Tree Problem
June 24, 2009
What graphs have a given number of spanning trees
Gustav Kirchhoff is famous for his work on electrical circuits: his rules, called Kirchhoff’s laws, are widely used in electrical engineering. He also proved a theorem that allows the number of
spanning trees to be com... | 4 | [
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Benchmark for Maxwell - Monique Dauge
Benchmark computations for Maxwell equations
for the approximation of highly singular solutions
The aim of this benchmark is to provide Maxwell problems whose solution has a strong unbounded singularity. Most of these problems can be solved alternatively by a scalar boundary value... | 5 | [
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Logarithms for Physics Help
By
Stan Gibilisco
— McGraw-Hill Professional
Updated on Sep 17, 2011
Introduction
A logarithm (sometimes called a log ) is an exponent to which a constant is raised to obtain a given number. Suppose that the following relationship exists among three real numbers a , and x , and y
:
a ... | 4 | [
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Galois Field Division Check
March 24th 2012, 01:03 PM
taskforce141
Galois Field Division Check
Hello. I worked through a Galois field problem and I just wanted to see if I have done everything correctly.
The question follows,
Compute in GF(2^8):
(x^4 + x + 1)/(x^7 + x^6 + x^3 + x^2)
where the ir... | 5 | [
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Composite Material
Materials Science on CD-ROM User Guide
Mechanics of Composite Materials
Version 2.1
Bill Clyne, University of Cambridge
Boban Tanovic, MATTER
It is assumed that the student is familiar with simple concepts of mechanical behaviour, such as the broad meanings of stress and strain. It would be an ad... | 4 | [
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0.008117675781... | 42,325 | 42325 | |
The proof of Cheeger's splitting theorem for almost nonnegative Ricci curvature manifolds
up vote 1 down vote favorite
1
Cheeger's splitting theorem says "Let $\left( {M_i^n,{p_i}} \right)\mathop \to \limits^{G - H} \left( {X,p} \right)$ with $Ric\left( {{M_i}} \right) \ge - \left( {n - 1} \right){\varepsilon _i}$ $\
... | 4 | [
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Homework Help
Posted by Kyo on Monday, May 17, 2010 at 12:19am.
It takes bromine vapor 4.73 min to effuse through a pinhole of a container. How long will it take CH4 gas to effuse under the same temperature and pressure?
Okay so, I tried using Graham's law for this problem. Rate A was 4.73. Molar Mass of bromine was ... | 4 | [
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Sum of First Four Digits Equals Units Digit
Date: 10/20/2001 at 17:15:03
From: James
Subject: Mathcounts Workout 8 1995-96
How many even five-digit numbers have the property that the sum of the
first four digits is the units digit?
I tried to solve it by patterning.
Even numbers means that it end with 0, 2, 4, 6, ... | 4 | [
0.037841796875,
0.0296630859375,
0.058837890625,
-0.04638671875,
-0.0634765625,
0.1015625,
0.011962890625,
0.0111083984375,
-0.006011962890625,
-0.0262451171875,
-0.0216064453125,
0.0101318359375,
0.035400390625,
0.06787109375,
-0.1171875,
0.04833984375,
-0.02099609375,
0.032470703... | 42,328 | 42328 | |
Normal distribution question
October 29th 2008, 12:34 PM #1
Newbie
Joined
Oct 2008
From
Ca, USA
Posts
2
Normal distribution question
I can't seem to be able to understand word problems
an applicant take a test . The time it normally distributed with mean time 60 minutes and standard deviation 8 ... | 5 | [
0.0498046875,
0.07470703125,
0.072265625,
0.0242919921875,
-0.01556396484375,
-0.028076171875,
-0.027099609375,
0.138671875,
-0.0247802734375,
0.048095703125,
0.0517578125,
-0.04931640625,
0.01275634765625,
0.021728515625,
0.0064697265625,
-0.038330078125,
0.0228271484375,
-0.03027... | 42,329 | 42329 | |
Polymath1Wiki
Imo 2010
From Polymath1Wiki
This is the wiki page for the mini-polymath2 project, which seeks solutions to Question 5 of the 2010 International Mathematical Olympiad.
The project will start at 16:00 UTC July 8, and is hosted at the polymath blog. A discussion thread is hosted at Terry Tao's blog.
Rul... | 4 | [
-0.041259765625,
0.06787109375,
0.08740234375,
0.00689697265625,
0.032958984375,
-0.01153564453125,
0.00390625,
0.0140380859375,
-0.0306396484375,
0.054443359375,
-0.050048828125,
-0.06494140625,
0.01153564453125,
0.051513671875,
-0.035400390625,
0.03857421875,
0.036376953125,
-0.0... | 42,330 | 42330 | |
Conserved quantity
July 22nd 2009, 07:54 AM #1
Newbie
Joined
Jul 2009
Posts
2
Conserved quantity
I have read a paper recently in which the authors consider a system of differential equations show below.
$<br /> x'=x+a-y$
$<br /> y'=x(b-2y)/c<br /> <br />$
Where
a,b,c are constants.
... | 5 | [
-0.0947265625,
-0.026123046875,
0.04345703125,
-0.005523681640625,
0.035888671875,
0.0966796875,
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0.0107421875,
0.0255126953125,
0.0113525390625,
0.0595703125,
-0.053466796875,
-0.0081787109375,
-0.0135498046875,
-0.013671875,
0.09912109375,
-0.0322265625,
-0.00595092... | 42,331 | 42331 | |
tion
Appendix 2
Calculation of sample size
Chapter 5 introduced the issue of calculating the sample size needed to estimate the population mean with a reasonable level of confidence.
The optimum sample size is based formally on calculation from the following equation (Proctor and Meullenet, 1998):
where
x = s... | 5 | [
0.068359375,
0.053955078125,
0.001495361328125,
0.05859375,
-0.044921875,
-0.0240478515625,
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0.1455078125,
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0.038818359375,
-0.060791015625,
-0.0277099609375,
-0.052001953125,
-0.035888671875,
-0.051025390625,
0.1064453125,
-0.005340576... | 42,332 | 42332 | |
Calc BC(2?) Series Question
March 15th 2012, 03:16 PM
Xeritas
Calc BC(2?) Series Question
My high school teacher gave us the following problem:
The coefficients of the power series (starting at n=0 and continuing for all real numbers) a[n](x-2)^n satisfy a[0] = 5 and a[n ]= ((2n+1)/(3n+1))a[n-1] for all n≥1... | 5 | [
-0.059814453125,
-0.03564453125,
-0.0089111328125,
0.0693359375,
-0.032470703125,
0.01348876953125,
-0.052978515625,
-0.02783203125,
0.06982421875,
0.0269775390625,
0.038818359375,
-0.060302734375,
-0.01220703125,
0.0027008056640625,
-0.059814453125,
-0.01483154296875,
-0.05688476562... | 42,333 | 42333 | |
an example of a semigroup with solvable word problem but unsolvable power problem
up vote 5 down vote favorite
4
We say that a semigroup $S$ has solvable power problem if there is an algorithm that takes as input an element $s \in S$ and decides whether or not there exist $m,n \in \mathbb{N}$ with $m \neq n$
and $s^m=... | 5 | [
-0.0556640625,
0.056396484375,
-0.07373046875,
0.0703125,
-0.0159912109375,
-0.0194091796875,
0.002227783203125,
-0.11865234375,
-0.0308837890625,
0.0252685546875,
-0.0150146484375,
-0.00174713134765625,
0.09326171875,
0.00604248046875,
0.0673828125,
0.0546875,
-0.00946044921875,
0... | 42,334 | 42334 | |
Piecewise Notation and Absolute Value
Date: 9/9/96 at 13:25:22
From: Anonymous
Subject: Piecewise Notation and Absolute Value
Using piecewise notation, write x in terms of y for the following
equation: "y = 2x + abs(2-x)". I have graphed the equation and I
think part of the answer is x = y-2 for y in the range of ... | 4 | [
-0.004638671875,
0.023193359375,
-0.0048828125,
-0.045654296875,
0.023681640625,
-0.05712890625,
-0.03515625,
0.10546875,
-0.058837890625,
-0.019775390625,
0.05224609375,
-0.051513671875,
0.03759765625,
0.06005859375,
0.0869140625,
0.036865234375,
0.032470703125,
-0.111328125,
0.... | 42,335 | 42335 | |
Is Dependent Choice all we really need?
up vote 12 down vote favorite
4
http://en.wikipedia.org/wiki/Axiom_of_dependent_choice
Is DC sufficient for the understanding of objects that are countable in some suitable sense? For example, is DC sufficient for the full development of the theory of von Neumann algebras on a
... | 5 | [
-0.0615234375,
-0.095703125,
-0.05712890625,
0.00421142578125,
-0.00750732421875,
0.09814453125,
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0.07470703125,
-0.001434326171875,
-0.003753662109375,
0.0025787353515625,
-0.039794921875,
0.0284423828125,
0.0556640625,
0.02783203125,
0.0167236328125,
0.039794921875,... | 42,336 | 42336 | |
induction proof
November 1st 2008, 04:03 PM
NidhiS
induction proof
I need some help with this induction proof.I'm like stuck at a crucial point and don't know how to get past it and complete the proof (Thinking)
The question says:
Suppose $b1,b2,b3...$
is a sequence defined as follows : $b1= 4 , b2... | 4 | [
-0.06689453125,
0.03173828125,
-0.007049560546875,
-0.061767578125,
0.000213623046875,
0.0269775390625,
0.015869140625,
0.0216064453125,
-0.046630859375,
-0.06689453125,
-0.07373046875,
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0.04541015625,
-0.045654296875,
-0.037109375,
0.06982421875,
0.02197265625,
0... | 42,337 | 42337 | |
Does a finite-dimensional Lie algebra always exponentiate into a universal covering group
up vote 9 down vote favorite
5
Hi,
I am a theoretical physicist with no formal "pure math" education, so please calibrate my questions accordingly.
Consider a finite-dimensional Lie algebra, A, spanned by its d generators, X_1,... | 4 | [
-0.146484375,
-0.007781982421875,
-0.0537109375,
0.08203125,
-0.037109375,
0.041015625,
0.0712890625,
-0.138671875,
0.053955078125,
-0.0308837890625,
0.05224609375,
-0.02685546875,
-0.058837890625,
0.00946044921875,
0.048583984375,
0.053466796875,
-0.039306640625,
0.1044921875,
-... | 42,338 | 42338 | |
Do coproducts in categories of algebras preserve monos?
up vote 4 down vote favorite
1
Even if the answer is no, I am interested in a more specific question.
Let $\Sigma$ be a set of operations of finite arity, $E$ be a set of equations over $\Sigma$ and $\mathcal{A}(\Sigma,E)$ be the respective category of algebras ... | 5 | [
-0.0194091796875,
-0.047607421875,
0.0341796875,
0.03076171875,
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0.07177734375,
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0.0142822265625,
-0.033203125,
0.0361328125,
0.00958251953125,
-0.1611328125,
-0.0115966796875,
0.0238037109375,
0.07763671875,
0.0654296875,
0.003997802734375,
0.0043640136... | 42,339 | 42339 | |
Math Help
February 6th 2009, 09:05 PM #1
Junior Member
Joined
Nov 2007
Posts
58
Unbiasedness
A sample of size 1 is drawn from the uniform pdf defined over the interval [0, theta]. Find an unbiased estimator for theta^2. Hint: is theta hat = Y^2 unbiased?
Use the hint!
$E(Y^2) = k \theta^2$ the... | 5 | [
0.041748046875,
0.056640625,
0.006683349609375,
0.0016021728515625,
0.052001953125,
0.0137939453125,
0.0022735595703125,
-0.031494140625,
0.007415771484375,
0.054443359375,
0.02099609375,
0.049072265625,
0.0260009765625,
-0.00897216796875,
-0.095703125,
0.02197265625,
0.0143432617187... | 42,340 | 42340 | |
Homework Help
2. A 5-committee is to be chosen from 4 teachers and 4 students. What is the probability that
Is question correct? I am not sure...
• Math - MathMate, Sunday, March 6, 2011 at 7:15pm
1a
3∪6 represent 2 successful event out of 6 possible outcomes. If the numbers chosen were 2 and 4 instead of ... | 4 | [
0.0693359375,
-0.044921875,
0.049560546875,
-0.038818359375,
-0.041259765625,
0.04248046875,
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0.0167236328125,
0.00164794921875,
0.07470703125,
-0.00445556640625,
-0.0361328125,
-0.035888671875,
-0.0030670166015625,
-0.07666015625,
0.0361328125,
-0.001220703125,
-0.0... | 42,341 | 42341 | |
Equation with Two Exponential Terms
Date: 06/27/2009 at 15:34:36
From: Dan
Subject: find ordered pair (a,b) for 3^a + 7^b giving a perfect square
Any perfect square can be expressed as n^2, find all ordered pairs
for 3^a + 7^b which result in a perfect square answer.
I'm not sure where to begin. I have an idea that... | 5 | [
-0.10302734375,
0.0269775390625,
-0.048583984375,
0.09228515625,
-0.04443359375,
0.07568359375,
0.034423828125,
-0.0263671875,
0.018798828125,
-0.00341796875,
-0.01953125,
-0.0341796875,
0.041015625,
0.07373046875,
0.0673828125,
-0.017333984375,
-0.10791015625,
-0.048583984375,
0... | 42,342 | 42342 | |
differentiating a rational quadratic
March 28th 2012, 12:43 PM #1
Member
Joined
Nov 2010
Posts
93
differentiating a rational quadratic
Hello, I am trying to differentiate this function so I work out where it is increasing or decreasing.
What is the best procedure to do this. I tried using quotient ru... | 5 | [
0.012939453125,
-0.023193359375,
0.0546875,
0.01953125,
-0.016357421875,
0.031494140625,
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0.0252685546875,
0.0419921875,
0.016357421875,
0.099609375,
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0.06298828125,
-0.01611328125,
-0.07763671875,
0.025390625,
0.056396484375,
0.049072265625,
0.0252... | 42,343 | 42343 | |
Sets with equal positive measure in every interval
up vote 10 down vote favorite
Hi,
I want to write a proof that relies on the fact that:
There are Borel Sets $A$ and $B$ contained in $\mathbb{R}$ such that
$A \cap B = \emptyset$ and $\lambda(A \cap (x,y)) = \lambda(B \cap (x,y)) > 0$.
Note that $x < y \in \mathb... | 5 | [
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0.10498046875,
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-0.0537109375,
0.037353515625,
-0.0286865234375,
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0.0208740234375,
0.0230712890625,
0.0693359375,
0.07177734375,
-0.0009307861328125,
0.08837890625,
-0.10058593... | 42,344 | 42344 | |
Comparing heights of rational points on curves through covers
up vote 2 down vote favorite
1
Let $a$ be a closed point in $\mathbf{P}^1_{\overline{\mathbf{Q}}}$.
Let $Y \cong \mathbf{P}^1_{\overline{\mathbf{Q}}} $ and let $\pi:Y\to \mathbf{P}^1_{\overline{\mathbf{Q}}}$ be a finite morphism which is unramified above $... | 4 | [
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0.045654296875,
0.0634765625,
0.0277099609375,
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0.05419921875,
0.025390625,
0.059326171875,
0.033935546875,
0.0135498046875,
... | 42,345 | 42345 | |
Design of Linear-Phase FIR Filters by General Interpolation
If the desired interpolation points are not uniformly spaced between 00 and π then we can not use the DFT. We must take a different approach. Recall that for a Type I FIR filter, Aω=hM+2∑n=
0M−1hncos(M−n)ω A ω h M 2 n 0 M 1 h n M n ω For convenience, it ... | 4 | [
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0.03125,
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0.010498046875,
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0.01129150390625,
0.08203125,
-0.08447265625,
0.003997802734375,
... | 42,346 | 42346 | |
Which method is used to solve this ODE?
May 3rd 2014, 12:50 PM #1
Newbie
Joined
Oct 2012
From
Germany
Posts
19
Which method is used to solve this ODE?
Hi, I am trying to solve an assignment in chemistry which involves an ODE. The equation is:
$\frac{d[I]}{dt}+k_{b}[I]=k_{a}[A]_{0}e^{-k_{a}(t)}$
... | 5 | [
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0.021240234375,
-0.045654296875,
0.02893... | 42,347 | 42347 | |
ESDNOTES
ELEMENTARY STRUCTURAL DESIGN
Elementary Structural Design (CIV131) is a module taught to Master of Engineering and Bachelor of Engineering students at Newcastle University. This page is intended primarily for those students. ... | 5 | [
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-0.02587890625,
-0.0294189453125,
-0.0277099609375,
-0.013427734375,
0.037597... | 42,348 | 42348 | |
Removable base loci for non-projective varieties
up vote 5 down vote favorite
2
The theorem of Zariski-Fujita says the following: Given a line bundle $L$ with base locus $B$ on a projective variety $X$. If $L_{|B}$ is ample on $B$, then $L$ is semiample, i.e. $L^{\otimes m}$ is
generated by global sections for some $m... | 4 | [
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0.1162109375,
0.08935546875,
-0.06982421875,
-0.01025390625,
-0.035... | 42,349 | 42349 | |
Trying to apply matrices in Physics but having trouble
March 22nd 2011, 02:34 PM
s3a
Trying to apply matrices in Physics but having trouble
Here is the original matrix:
matrix([20,10,0,0,549/100],[0,-10,30,30,41/50],[20,0,30,30,467/100],[1,-1,-1,0,0])
Here is the matrix in its echelon form:
matrix([... | 5 | [
-0.035400390625,
0.00072479248046875,
-0.09326171875,
-0.054931640625,
0.0458984375,
-0.0091552734375,
-0.02392578125,
-0.029541015625,
-0.09814453125,
-0.01416015625,
0.0615234375,
-0.01416015625,
0.03515625,
-0.024658203125,
0.00653076171875,
0.06591796875,
-0.0732421875,
0.00646... | 42,350 | 42350 | |
Inference for Regression Using Technology for AP Statistics
Inference for Regression Using Technology for AP Statistics (page 2)
By
Duane C. Hinders
— McGraw-Hill Professional
Updated on Feb 4, 2011
All of the mechanics needed to do a t-test for the slope of a regression line are contained in this printout. You n... | 5 | [
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0.0252685546875,
-0.0186767578125,
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0.01708984375,
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0.0252685546875,
0.0164794921875,
-0.08... | 42,351 | 42351 | |
Geometric Proofs
April 29th 2012, 08:02 AM
ZombieOverlord
Geometric Proofs
https://www.connexus.com/content/med...2092712682.jpg
Make a two-column proof showing statements and reasons to prove that triangle ABD is similar to triangle ABC.
(10 points)
17.
Look at the figure shown below.
... | 4 | [
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0.00677490234375,
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-0.09375,
-0.0090... | 42,352 | 42352 | |
Basis in dual space
February 15th 2008, 05:38 PM
tttcomrader
Basis in dual space
Let $V = \mathbb {R} ^{3}$, define f, g, h in V* by $f(x,y,z) = x-2y ,g(x,y,z)=x+y+z , h(x,y,z)=y-3z$.
Prove that {f,g,h} is a bsis for V*, then find a basis for V.
My work so far:
I first show that {f,g,h} is a linea... | 4 | [
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0.026611328125,
-0.0123291015625,
-0.0810546875,
-0.0... | 42,353 | 42353 | |
Introduction to Projection Methodology
Content of appendix A
Since its inception in 1964, the Projections of Education Statistics series has been providing projections of key education statistics to policy makers, educators, researchers, the press, and the
general public. This edition of Projections of Education Stat... | 4 | [
0.049560546875,
0.005035400390625,
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0.125,
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-0.045166015625,
0.05... | 42,354 | 42354 | |
Piecewise Differentiability
September 17th 2009, 06:08 PM #1
Junior Member
Joined
Sep 2009
Posts
71
Piecewise Differentiability
Let f be the piecewise defined function given by f(x)=ax+b x≤2. 2-x^2 2<x. Find a and b so that f is differentiable at x=2.
I actually solved this problem a couple of minut... | 4 | [
0.0284423828125,
0.00579833984375,
0.0272216796875,
-0.10107421875,
-0.0240478515625,
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0.059326171875,
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0.06787109375,
-0.0693359375,
0.0294189453125,
0.004730224609375,
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0.08203125,
-0.059814453125,
-0.... | 42,355 | 42355 | |
Optimization Involving A Cylinder
April 16th 2009, 02:33 PM #1
Junior Member
Joined
Nov 2008
Posts
53
Optimization Involving A Cylinder
I am not sure how to go about doing this question:
A cylindrical can needs to hold 500cm^3 of apple juice. The height of the can must be between 6cm and 15cm, incl... | 4 | [
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0.12890625,
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0.08642578125,
-0.0242919921875,
-0.00138092041015625,
0.050537109375,
0.0527... | 42,356 | 42356 | |
Module-2_Lesson-3
Module
2
Stresses in machine
elements
Version 2 ME, IIT Kharagpur
Lesson
3
Strain analysis
Version 2 ME, IIT Kharagpur
Instructional Objectives
At the end of this lesson, the... | 5 | [
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-0.0834960937... | 42,357 | 42357 | |
Trig
March 1st 2009, 05:14 AM
sa87uk
Trig
Could do with some help, thanks in advance.
The sloping sides of a factory gable roof make angles of 39o and 52o with the horizontal. The longer sloping side is 75m from top to bottom edge. Find the corresponding length of the shorter
side, and the vertical heig... | 4 | [
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0.0520019531... | 42,358 | 42358 | |
Possible Paths across a Rectangular Grid
Date: 02/16/2005 at 21:59:13
From: Wenying
Subject: How many different paths from A to B are possible?
Consider a grid that has 3 rows of 4 squares in each row with the
lower left corner named A and upper right corner named B.
Suppose that starting at point A you can go one s... | 4 | [
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-0.0169677... | 42,359 | 42359 | |
Linear Algebra Proof Regarding Linear Transformations
February 28th 2013, 11:51 PM #1
Newbie
Joined
Dec 2012
From
Davis
Posts
22
Linear Algebra Proof Regarding Linear Transformations
Given the following vectors in R^2:
a(sub 1) = (1; -1), a(sub 2) = (2; -1), a(sub 3) = (-3;2),
b(sub 1) = (1;0... | 5 | [
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0.032... | 42,360 | 42360 | |
Converging sequence
July 19th 2012, 09:54 AM #1
Member
Joined
Apr 2010
Posts
116
Thanks
1
Converging sequence
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit.
$a_n = \left(1 + \frac{1}{n^2}\right)^n$
I was never ver... | 5 | [
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... | 42,361 | 42361 | |
Finding lattice with short basis-vectors containing given lattice
up vote 0 down vote favorite
Hello
While working on understanding the space spanned by certain integer relations of real numbers I have come across the following problem. Given $v_1,\dots, v_n \in \mathbb{Z}^m$ I am would like to find
$w_1, \ldots w_n ... | 4 | [
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0.078613... | 42,362 | 42362 | |
Math Forum Discussions
Re: Problem with Cantor's diagonal argument
Posted: Feb 14, 2002 1:44 PM
In article <a4gvml$7ud9$1@ID-110648.news.dfncis.de>,
Herman Jurjus <h.jurjus@hetnet.nl> wrote:
>"Dave Seaman" <dseaman@seaman.cc.purdue.edu> wrote in message
>news://a4gf7t$2or@seaman.cc.purdue.edu...
>> We don't have t... | 5 | [
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Modulus of negative numbers
May 10th 2008, 02:38 PM
MrSteve
Modulus of negative numbers
Hello
I really hope someone can help me with this.
I am reading lecture notes and it says the following -
-12 mod 11 = 10
-1 mod 11 = 10
When I do -12 mod 11 and -1 mod 11 on my calculator I get -1 for... | 4 | [
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Riemann integral
November 28th 2011, 06:35 AM
mechaniac
Riemann integral
$f(x)=\begin{cases}& \sin(x) , x\leq \pi /2 \\ & \1 , x> \pi /2\end{cases}$
Determine the riemann integral for every $x\in R$
$I(x)=\int_{0}^{x}f(t)dt$
I dont know if i do this right, but this is how i tried:
$I'(x)=f(... | 5 | [
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Solving the Cubic, Part TwoSolving the Cubic, Part Two
A while back I I began a discussion about deriving formulas for solving polynomial equations. We saw that linear and quadratic polynomials did not pose much of a challenge. But cubic polynomials are
considerably more complex. The set-up was that we had a polynomial... | 4 | [
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0.00... | 42,366 | 42366 | |
When does a probability measure take all values in the unit interval?
up vote 7 down vote favorite
4
Let $\mathbb{P}$ be a probability measure on some probability space $(\Omega,\mathcal{A})$. Are there conditions on the $\sigma$-algebra $\mathcal{A}$ such that for every real number $c\in [0,1]$ we
find a set $A\in\ma... | 5 | [
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Cech nerve as homotopy colimit?
up vote 3 down vote favorite
5
Given a category $\mathcal{C}$ with a notion of covering $\{ U_{i} \rightarrow X \}$ for an object $X$ (say $\mathcal{C}$ is a Grothendieck site), we can form the Cech nerve
$$ \cdots \coprod_{i}{U_{ijk}} \overrightarrow{\overrightarrow{\rightarrow}}\copr... | 4 | [
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Posts from July 7, 2009 on Programming Praxis
Modular arithmetic is a branch of number theory that is useful in its own right and as a tool in such disciplines as integer factorization, calendrical and astronomical calculations, and
cryptography. Modular arithmetic was systematized by Carl Friedrich Gauss in his book D... | 4 | [
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-0... | 42,369 | 42369 | |
Real x, y verify relation arctg x+arctg y=pi/2. How show x*y=1? - Homework Help - eNotes.com
Real x, y verify relation arctg x+arctg y=pi/2. How show x*y=1?
You should move one member to the right side, such that:
`arctan x = pi/2 - arctan y`
You need to take the tangent function both sides, such that:
`tan(arctan ... | 4 | [
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-0.... | 42,370 | 42370 | |
Related Rates (Story Problems)
October 6th 2009, 02:18 PM #1
Member
Joined
Oct 2008
Posts
80
Related Rates (Story Problems)
1) A ball is dropped from a height of 20 meters, 12 meters away from the top of a 20-meter lamppost. The ball's shadow, caused by the light at the top of the lamppost, is moving alo... | 5 | [
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bond with 10 years left to maturity
March 18th 2007, 09:41 AM #1
Junior Member
Joined
Nov 2006
Posts
62
bond with 10 years left to maturity
This is a two part question, I understood the first part but now I am at a standstill. Here is the question: We are asked what is the price of the bond if the yield ... | 4 | [
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Scissors Congruence The Birth of Hyperbolic Volume
Scissors Congruence: The Birth of Hyperbolic Volume
Gregory Leibon
Department of Mathematics
Dartmouth College
Scissors... | 4 | [
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-0.04... | 42,373 | 42373 | |
Math Forum Discussions
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Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.
Topic: How would you find the parabolas determined by poi... | 4 | [
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0.... | 42,374 | 42374 | |
Countability of Primes and Composites
Date: 05/18/2002 at 11:25:37
From: Robin
Subject: Countability of Primes and Composites
I know that the union of a countable number of countable sets is
countable, but I was wondering if you take a countable set that is
the union of two infinite sets, is it possible that one of t... | 5 | [
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-0... | 42,375 | 42375 | |
Prove... pi
Associated Topics || Dr. Math Home || Search Dr. Math
Prove... pi
Date: 7/5/96 at 20:2:1
... | 5 | [
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... | 42,376 | 42376 | |
Integration by substitution
February 23rd 2013, 06:09 AM #1
Junior Member
Joined
Aug 2012
From
The Earth
Posts
71
Thanks
1
Integration by substitution
∫√(1-x^2 ) dx
Letting x = sin θ,
dx/dθ = cos θ
∫√(1-x^2 ) dx
=∫√(1-sin^2θ ) cos θ dθ
=∫cos^2 θ dθ
=∫ (1-sin^2θ) dθ
... | 5 | [
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Thales theorem converse
November 24th 2012, 07:34 PM
juvenchan
Thales theorem converse
Hi everyone,
I need some help.
How many Thales Theorem Converse (inscribe Circle) are there?
Can anyone show me different proofs of Thales Theorem Converse (have to be inscribe Circle)
Thanks a lot.
I a... | 5 | [
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... | 42,378 | 42378 | |
Order of Integer Questions
October 21st 2010, 03:34 PM #1
Member
Joined
Nov 2008
Posts
152
Order of Integer Questions
1) Show that if n is a positive integer and a and b are integers relatively prime to n such that $(ord_{n}a, ord_{n}b)$ = 1, then $ord_{n}(ab)$ = $ord_{n}a * ord_{n}b$
2) Let p be a ... | 5 | [
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-0.057861328... | 42,379 | 42379 | |
Convexity and integrals
December 29th 2010, 07:23 AM #1
Junior Member
Joined
Sep 2010
Posts
43
Convexity and integrals
I need help in three basic problems. (But unfortunatelly I can't solve them!)
1. Where is the following function convex/concave? +infection points
$y=\frac{1}{\ln(x)}$
2.Wh... | 4 | [
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0.0393066406... | 42,380 | 42380 | |
Cuspidal automorphic representations as the space of $K$-finite vectors in a unitary cuspidal automorphic representation.
up vote 5 down vote favorite
The definition I know of for a cuspidal automorphic representation of, say, $G=\mathrm{GL}_2$ over a number field $F$ (relative to a choice of compact open subgroup $K_... | 4 | [
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... | 42,381 | 42381 | |
Monte Carlo Simulation: Election Forecasting and Exit Poll Modeling
Richard Charnin
Updated: July 8, 2012
2004 Monte Carlo Electoral Vote Simulation (pre-election and exit polls)
The simulation model consists of 200 election trials based on pre-election state polls and post-election exit polls. It is strong circums... | 4 | [
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An Annoying Open Problem
October 8, 2011
How do we tell if two groups are isomorphic?
Vikraman Arvind and Jacobo Torán are both complexity theorists, both with wide interests, but both who have worked extensively on the graph isomorphism problem. See their survey here, for example.
Today I want to talk about about... | 4 | [
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Where are the limits of this question?
Question 7
At first I thought it was polar co-ordinates but it was parametric so I used the arc length formula to try and find the length of the curve in ONE of the quadrants. I would later times this by 4
to get the length of the curve all together. So arc length = ... | 4 | [
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Vanishing Nets
August 8, 2010 by scienceofdoom
Many commenters have expressed the opinion that the net radiation at the earth’s surface is quite small and therefore radiation doesn’t play a big part in establishing the temperature of the lower
atmosphere. The lower atmosphere, for reference, is usually known as the t... | 4 | [
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How do you prove this inequality?
March 11th 2014, 11:19 PM #1
Newbie
Joined
Mar 2014
From
Singapore
Posts
1
How do you prove this inequality?
Prove that a/b + b/a is greater or equal to 2, give that a and b >0. Your help is appreciated.
Love,
numbertheoryboy
Re: How do you prove this inequ... | 4 | [
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Probability of Success with Random Guessing
Date: 07/12/2008 at 12:44:54
From: Tom
Subject: Probability: Why 75%
I'm reading a book called "The Drunkard's Walk" by Dr. Leonard
Mlodinow. It's an entirely readable look at the history of
probability and the misconceptions of probability.
I have come to a part that I d... | 5 | [
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prime and jacobson radical, please help
August 28th 2008, 04:21 AM #1
Member
Joined
Aug 2008
Posts
97
prime and jacobson radical, please help
I want to find prime and jacobson radical radicals in Z[T]/(T^3), here Z = integers.
My definition of jacobson radical is that it is intersection of maximal id... | 5 | [
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Direction Field
Direction Field, n=2
This applet draws solution curves in the phase plane of a 2x2 autonomous system of Ordinary Differential Equations over the systems direction field. The system is of the form:
... | 4 | [
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Cute problem solution
Yesterday I posed the following problem: If $S$ is the set of positive integers whose decimal expansion does not contain a 3, does
\[ \sum_{n\in S}\frac{1}{n} \]
converge or diverge? My solution is after the break.
The sum converges. To see this, we’ll partition $S$ into subsets $S_k$ so that ... | 5 | [
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... | 42,390 | 42390 | |
Deductive geometry, tangents
September 1st 2009, 07:42 AM #1
Member
Joined
May 2008
Posts
101
Deductive geometry, tangents
Hi, I have a problem which I am having trouble solving.
Let $ABC$ be a right-angled triangle. A circle $T$ having side $AC$ as its diameter meets hypotenuse $AB$ at point $E$. A... | 4 | [
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Calculate XIRR in SQL Server
Posted Tuesday, May 11, 2010 10:26 AM
Hello All,
SSC-Enthusiastic Is there any way to calculate XIRR in SQL server using T-SQL.
Kindly suggest.
Thankx
Group: General Forum
Members
Last Login: Mon... | 5 | [
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Make 'N' the Subject
February 27th 2008, 11:16 AM #1
GreenStreet
Guest
Make 'N' the Subject
Hey, before I start I just want to say that yes I am new, this is my first ever post but I've tried to look for help on questions in this book which ask to make 'N' or 'X' the subject so I
decided to look at a maths fo... | 4 | [
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A question about a one-form on Riemannian manifold
up vote 1 down vote favorite
2
Let M be a Riemannian Manifold, $X$ is a smooth vector field on M with isolated zeros. Is there a one-form $\omega$ with isolated zeros such that $\omega(X)$ has nontrivial zeros? (nontivial zero
means that the piont is neither in $X$'s ... | 5 | [
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A GENERALISED ALGORITHM FOR THE DEMAND PREDICTION OF A SHORT LIFE CYLCLE PRODUCT SUPPLY CHAIN AND ITS IMPLEMENTAION IN A BAKED PRODUCT
International Journal of Engineering and Technology (IJMET), ISSN 0976
INTERNATIONALMechanical Volume 4, Issue 1, January - Februar... | 5 | [
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Interpolation
From Sutherland_wiki
Linear Interpolation
A linear function may be written as \(f(x) = a_0 + a_1 x.\) Given any two data points, \(( x_1, y_1 )\), and \((x_2,y_2)\), we can determine a linear function that exactly passes through these
points. We can do this by solving for \(a_0\) and \(a_1\). Since the... | 5 | [
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On a discusssion of the Peano axioms
September 7th 2013, 05:12 PM #1
MHF Contributor
Joined
Mar 2011
From
Tejas
Posts
3,310
Thanks
687
On a discusssion of the Peano axioms
so 1+1 = 1+1?
You haven't defined the successor function. You only defined it for 1 and 2. What is your definiton of the... | 4 | [
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on a sphere
How can I generate points randomly distributed on a sphere?
• That is, how can I generate points that are equally distributed over the area of the sphere? It won't work, for example, to generate (uniformly distributed) random latitudes and (uniformly
distributed) random longitudes, because any speci... | 4 | [
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is this correct?
October 7th 2009, 06:39 PM #1
Member
Joined
Sep 2009
Posts
162
is this correct?
Today in math I learned new concepts. However, I am unsure if these three questions are correct. This is what I did:
Solve by considering all cases. Show each solution on a number line.
$x^2-2x-15<0$... | 4 | [
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