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|---|---|---|---|---|---|
Topological Spaces
May 19th 2010, 08:07 PM #1
Newbie
Joined
Apr 2009
Posts
11
Topological Spaces
Let X and Y be a topological spaces.
Suppose X is the union of two closed subsets A and B of X .
Let f: A -> Y and g: B-> Y be continuous.
If f(x)=g(x) for every x in the intersection of A and B, ... | 5 | [
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... | 42,600 | 42600 | |
Solving Systems Using Elimination
I need help solving this problem using elimination 2x-2y=61 2x+y=-7 Please help(Nerd)(Nerd)!!
2x+2y=61 2x+y=7 2x+2y=61 -2y -2y __________ 2x = 61 - 2y ___________ 2 -> divide both sides by 2 x = 30.5 - y put this x value into other equation: 2(30.5 -y) +y = 7 61 - 2y + y = 7 -y -y
___... | 4 | [
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Math Forum Discussions
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Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.
Topic: Collinear
Replies: 9 Last Post: May 8, 2013 1:12 P... | 4 | [
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What's the intuition between formal smoothness, etaleness. and unramifiedness?
up vote 17 down vote favorite
17
Let $f: X \to Y$ be a morphism of schemes. Then $f$ is called (EGA IV.17) formally smooth if whenever $T$ is an affine $Y$-scheme and $T'$ a closed subscheme of $T$ defined by a nilpotent ideal (it's
suffic... | 4 | [
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A subring question (revised)
up vote 2 down vote favorite
2
Hello, Let $K/{\mathbb Q}$ be a finite extension which is not necessarily Galois, and ${\mathcal O}$ be the ring of integers of $K$. Let $p$ be a prime in ${\mathbb Q}$ and let $p {\mathcal O}={\
mathfrak p}_1^{k_1} \cdots {\mathfrak p}_r^{k_r}$ be its prime ... | 5 | [
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Is there a nice expression for the number of lattice points on a sphere?
up vote 3 down vote favorite
Possible Duplicate:
Is there a simple way to compute the number of ways to write a positive integer as the sum of three squares?
Is there a nice expression for the number of points in $\mathbb{Z}^3$ which lie... | 5 | [
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How many cubes cover a bigger cube?
up vote 53 down vote favorite
16
How many $n$-dimensional unit cubes are needed to cover a cube with side lengths $1+\epsilon$ for some $\epsilon>0$?
For n=1, the answer is obviously two. For n=2, the drawing below shows that three unit cubes suffice, but it is impossible using... | 5 | [
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help with induction
May 25th 2011, 03:13 PM #46
Member
Joined
May 2011
From
Sacramento, CA
Posts
165
You forget MoeBlee, that we don't know if some number $10^{10^{10}}$ might not be an n such that n = 3j + 8k. That is the point of induction. Therefore, while it is necessary for 13 to fail to be
s... | 5 | [
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u_{xx}-u_{yy}+u_y=0
December 29th 2010, 07:53 PM #1
MHF Contributor
Joined
Mar 2010
From
Florida
Posts
3,093
Thanks
5
u_{xx}-u_{yy}+u_y=0
Using exponential substitution:
$\exp{(rx+sy)}$
$u_{xx}-u_{yy}+u_y=0$
$\exp{(rx+sy)}(r^2-s^2+s)=0$
$r=\pm\sqrt{s^2-s}$
$u=\exp{(\pm x\... | 5 | [
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Nearly constant curvature implies "nearly isometric" to a space form?
up vote 6 down vote favorite
It is well known a Riemannian manifold with constant sectional curvature is a quotient of the Euclidean space, hyperbolic space or sphere. In particular we know how their metric looks like locally.
My question is, is th... | 5 | [
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Math Forum Discussions - Re: A single term formula for calculating the circumference of ellipse
Date: Dec 26, 2011 10:37 PM
Author: thomasinventions@yahoo.com
Subject: Re: A single term formula for calculating the circumference of ellipse
That's fabulous.
Note, as I've used recently in a different fashion, (1-h) coul... | 4 | [
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Natural Frequency
Equation of Motion : Natural Frequency
Figure 2 shows a simple undamped spring-mass system, which is assumed to move only along the vertical direction. It has one degree of freedom (DOF), because its motion is described by a single
coordinate x.
When placed into motion, oscillation w... | 4 | [
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Phase Difference Auto Focusing For Synthetic Aperture Radar Imaging - Patent 4999635
United States Patent: 4999635
( 1 of 1 )
United States Patent
4,999,635
Niho
March 12, 1991
Phase difference auto focusing for synthetic aperture radar imaging
... | 4 | [
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RTe-bookAgDegNormalFormul
RTe-bookAgDegNormalFormul.doc
FORMULATION FOR:
RTe-bookAgDegNormal.xls
This document is a companion to the spreadsheet:
RTe-bookAgDegNorma... | 4 | [
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differential propositional calculus
differential propositional calculus
Contents:
• 1 Casual introduction
• 2 Cactus calculus
• 3 Formal development
1 Casual introduction
Consider the situation represented by the venn diagram in Figure 1.
Figure $1.$ Local Habitations, And Names
The area of the rectangle r... | 4 | [
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Nth root of a matrix as an analytic function?
up vote 2 down vote favorite
Let $A$ be a $k \times k$ invertible matrix over complex numbers.
If it possible to write its nth root as an analytic function (i.e. power series in $A$)?
EDIT: Complex coefficients can be functions of $A$.
Notes
If a matrix $A$ has only on... | 4 | [
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Finite T-uples and the axiom of Regularity
up vote 1 down vote favorite
Let V be the universe of sets (the class of all sets). Let U(0)=V, U(1)=V*V, the class that is cartesian product of the class V=U(0) with V, and for n>=1, let U(n+1)=U(n)*U(0); For every natural
integer n, let T(n)=U(n+1)/U(n) be the class that is... | 5 | [
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Some problems...
June 4th 2006, 09:22 AM
ReadingChick
Some problems...
I've been having some trouble with some trig problems. It would be great if someone could help me to do them. I'm not very sure how to put in symbols such as pie, etc. so I apologize in advance
for having to write it out. :o
*Using a... | 4 | [
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Projectile Motion
February 14th 2011, 12:15 PM
Darkprince
Projectile Motion
I have the following problem:
A projectile of mass m is launched from the origin at time t=0, with speed U, at an angle of elevation a+b to the horizontal. The launch site lies on a ramp that makes an angle b to the
horizontal (Y... | 4 | [
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About digits in a number
March 12th 2008, 01:34 AM
san4unall
About digits in a number
Hi,
Could anyone please tell me if there is any formula or method to find the number of digits in the result of multiplication of 2 numbers?
For e.g. if a 12 digit number is multiplied by a 16 digit no. then how many d... | 4 | [
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Very basic topology question
June 15th 2011, 09:18 PM
BWilson
Very basic topology question
Hello, I am having some difficulty on problem 17 of chapter 2 in Rudin's Principles of Mathematical Analysis. The problem reads: "Let E be the set of all x in [0,1] whose decimal expansion
contains only the digits 4 an... | 5 | [
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Anything special (historical?) about surface $x\cdot y\cdot z\ +\ x+y+z=0$?
up vote 11 down vote favorite
1
QUESTION
I wanted to introduce and develop the complex logarithm from scratch. As the result I've arrived a couple of months ago at the following identity after which the road to complex logarithm is wide
ope... | 4 | [
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Calculate Vapor Pressure Change Using Raoult's Law
This example problem demonstrates how to use Raoult's Law to calculate the change in vapor pressure by adding a nonvolatile liquid to a solvent.
Problem:
What is the change in vapor pressure when 164 g of glycerin (C[3]H[8]O[3]) is added to 338 mL of H[2]O at 39.8 °C... | 4 | [
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Extending finite morphisms of curves to finite morphisms of arithmetic surfaces
up vote 4 down vote favorite
1
Let $\pi:Y\longrightarrow X$ be a finite morphism of smooth projective geometrically connected curves over a number field $K$. Let $h:\mathcal{X}\longrightarrow \textrm{Spec} \ O_K$ be a regular
integral flat... | 4 | [
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Higher dimensional Bezout via Hilbert polynomials: a reference
up vote 3 down vote favorite
2
For the purposes of teaching my elementary course in algebraic geometry I am looking for a reference (or notes) that contains a complete proof of a higher-dimensional weak Bezout theorem. I only want
to learn about a proof th... | 4 | [
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Touring China and Thailand
Date: 5/30/96 at 1:49:34
From: Eric Liu
Subject: How long is the tour?
Hi! This is Cristian. I have two math questions:
1. A tour to China is twice as long as a tour to Thailand. If both
tours last 5 weeks and 1 day altogether, how long is the tour to
China?
2. The total of the a... | 4 | [
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-0.031494140625... | 42,625 | 42625 | |
Need help on this tricky question
August 20th 2010, 05:16 AM
JohnLord123
Need help on this tricky question
Find the sum: Cos^2 (0) + Cos^2 (2) + Cos^2 (4) + Cos^2 (356) + Cos^2 (358) + Cos^2 (360)
Thanks in advance.
August 20th 2010, 10:02 AM
earboth
Quote:
1. I assume that the argument of the... | 4 | [
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For which rings does there exist an invertible Vandermonde matrix?
up vote 2 down vote favorite
2
Suppose $R$ is a commutative ring, and $S \subset R^{n\times n}$ is an $R$-module. We are given $H_0,\dots,H_n \in R^{n\times n}$, and we know that for all $r \in R$, $$H_0 + r H_1 + \dots r^n H_n \
in S$$ The question is... | 5 | [
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0.039794921875,
0.0286865234375,
... | 42,627 | 42627 | |
Lens Tutorial
This note gives a tutorial on lenses and gives some common lens formulas. I attempted to make it between an FAQ (just simple facts) and a textbook. I generally give the starting point of an idea, and
then skip to the results, leaving out all the algebra. If any part of it is too detailed, just skip ahea... | 4 | [
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... | 42,628 | 42628 | |
Polynomial representing all nonnegative integers
up vote 186 down vote favorite
98
Lagrange proved that every nonnegative integer is a sum of 4 squares.
Gauss proved that every nonnegative integer is a sum of 3 triangular numbers.
Is there a 2-variable polynomial $f(x,y) \in \mathbf{Q}[x,y]$ such that $f(\mathbf{Z} ... | 4 | [
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... | 42,629 | 42629 | |
seemingly simple derivative
October 17th 2009, 05:51 PM #1
Newbie
Joined
Oct 2009
Posts
14
seemingly simple derivative
hello all. my friend has asked me for help on a derivation but i've come up blank.
the derivation in question is:
$\frac{d}{dx}lnx^{lnx}$
i thought $lnx$
he thought $... | 5 | [
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Dimension of central simple algebra over a global field "built using class field theory".
up vote 13 down vote favorite
2
If $F$ is a global field then a standard exact sequence relating the Brauer groups of $F$ and its completions is the following:
$$0\to Br(F)\to\oplus_v Br(F_v)\to\mathbf{Q}/\mathbf{Z}\to 0.$$
The... | 4 | [
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Too long equation
Add tags Information and discussion about LaTeX's math and science related features (e.g. formulas, graphs).
7 posts • Page 1 of 1
Hello everybody,
I have a very long equation and this causes me some problems. I want it to look the following way:
left side = right side\\
+continuation of right si... | 4 | [
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0.01904296875... | 42,632 | 42632 | |
Line Integral over Curve
April 27th 2010, 10:00 PM #1
Newbie
Joined
Apr 2010
Posts
5
Line Integral over Curve
Calculate $\int_{C} z dx+x dy+y dz$
where C is the curve obtained by intersecting surfaces $z=x^2$ and $x^2+y^2=4$, oriented so that the z-coordinate increases along C.
That C has to be... | 4 | [
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0.090... | 42,633 | 42633 | |
Standard deviation
1. April 13th 2009, 08:51 AM #1
IM using my brothers account with his permission of course
thanks
Last edited by osmosis786; April 14th 2009 at 04:58 AM.
2. April 13th 2009, 06:33 PM #2
3. April 14th 2009, 03:44 AM #3
I dont need someone to read my ans... | 4 | [
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-0.038... | 42,634 | 42634 | |
Group problem with Abelian
Prove that a group G is Abelian iff $(ab)^{-1} = a^{-1}b^{-1}$.
We have $(ab)^{-1}=b^{-1}a^{-1}$ Then the equality becomes $a^{-1}b^{-1}=b^{-1}a^{-1}$. Multiply both sides at left by $a$: $aa^{-1}b^{-1}a=ab^{-1}a^{-1}a\Rightarrow b^{-1}a=ab^{-1}$ Now, multiply
both sides by $b$ $bb^{-1}ab=ba... | 4 | [
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0.076171875,
-0.111816... | 42,635 | 42635 | |
Average Rate of Change
October 27th 2008, 07:44 AM #1
MHF Contributor
Joined
Jul 2008
From
NYC
Posts
1,489
Average Rate of Change
For the function given below, answer (a) through (c).
(a) For each function below, find the average rate of change
of f from 1 to x:
[f(x) - f(1)]/(x - 1), w... | 4 | [
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-0.01556396484375,
0.01904296875,
-0.0966796875,
-0.04... | 42,636 | 42636 | |
Noether's Theorem in Quantum Mechanics
up vote 10 down vote favorite
10
In classical mechanics:
If a Lagrangian L is preserved by an infinitesimal change in the state space variables q[i] -> q[i] + εK[i](q) leads to only second order change in the Lagrangian: $$ 0 = \frac{dL}{d\epsilon} = \
sum_i \left( \frac{\partia... | 4 | [
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10.2 Arch and Chords
Bell work
Find the value of radius, x, if the diameter
of a circle is 25 ft.
25 ft
x
Bell work Answer
Radius, x, is 12.5 ft
Unit 3 : Circles:
10.2 Arcs and Chords
Objectives: Students ... | 4 | [
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Is \sqrt{1-x^2} uniformly continuous?
May 3rd 2009, 01:52 PM #1
Is \sqrt{1-x^2} uniformly continuous?
Is $f(x)=\sqrt{1-x^2}$ uniformly continuous?
Here is my proposed solution.
Break $[-1,1]$ into three partitions: $[-1,-4/5]\cup(-4/5,4/5)\cup[4/5,1]$
On $[-1,-4/5]$, $f(x)$ is defined on a compact ... | 5 | [
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0.06201171875,
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-0.017... | 42,639 | 42639 | |
Class number of non-maximal order in imaginary quadratic function field?
up vote 7 down vote favorite
2
It is well known that for $K=\mathbb{Q}(\sqrt{D})$, $D < 0$, the non-maximal order of squarefree conductor $f$, relatively prime to $D$, has class number $$h_K \prod_{p|f} (p-(\frac{D}{p}))$$
What is the class numb... | 4 | [
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Nikon MicroscopyU
CCD Resolution for Optical Microscopy
The ultimate resolution of a CCD is a function of the number of photodiodes and their size relative to the image projected onto the chip's surface by the microscope optics. When att... | 4 | [
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0.044921875... | 42,641 | 42641 | |
Given a graph embedded on a torus, how many edges are necessary for noncontractible loops to be long?
up vote 11 down vote favorite
6
If we are given a graph embedded on a torus, with the following properties, what is the minimum number of edges it can have?
• Any noncontractible loop is comprised of at least n edg... | 4 | [
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Fermat's Theorem
March 3rd 2011, 01:32 PM
mathematic
Fermat's Theorem
I was wondering if someone might be able to look over my proof's involving Fermat's Theorem.
When n = 2p, where p is an odd prime, then a^(n-1)= a (mod n) for any integer a.
So let n=2p
We have a^(2p-1)
a^(2p)*1/a
a^2a^p*1... | 4 | [
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Short Term Decision Making-Limiting Factor (Part 1)
August 20th, 2006 Comments off
One part of managerial accounting is the need to understand limiting factor for short term decision. As a result of limited supply of resources constraint, a company normally cannot produces as many
products as it wish.
The limited sup... | 4 | [
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[SOLVED] Show that 2 + 8x - 2x^3 = 0 has three real solutions
August 1st 2009, 07:08 AM #1
Junior Member
Joined
Aug 2009
Posts
29
[SOLVED] Show that 2 + 8x - 2x^3 = 0 has three real solutions
Hi
How do I show that 2 + 8x - 2x^3 = 0 has three real solutions?
I know you can say it has at most thr... | 5 | [
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Explanation and Test Case for Pick's Theorem
Date: 06/13/2006 at 02:47:54
From: Anelisa
Subject: the use of area theorems to check validity of Pick's theorem
I want to be able to test Pick's Theorem for the area of polygons. I
want to accompany each polygon with a detailed test of the formula.
But I don't really un... | 4 | [
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Dirichlet Inverse Problem
June 27th 2011, 02:16 PM #1
Junior Member
Joined
Jun 2010
Posts
59
Dirichlet Inverse Problem
The Dirichlet Convolution is this:
$(f * g)(n) = \sum\limits_{d \mid n} f(d)g(\frac{n}{d})$
The $\iota(n)$ function:
$\iota(n) = \begin{cases} 1 & \text{if } n = 1 \\ 0 & ... | 4 | [
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-0.00668... | 42,647 | 42647 | |
tangent sphere bundle over sphere
up vote 3 down vote favorite
2
are there some general description about tangent sphere bundle over sphere? (it is a special $S^{n-1}$bundle over $S^n$)
say for n=1,it is trivial,$S^0\times S^1$,for n=2,it is $SO(3)\cong \mathbb{R}P^3$, for n=3,it is trivial again,so it is for n=7. ho... | 4 | [
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0.00433349609375,
0... | 42,648 | 42648 | |
Computing the function field of a curve given as a subvariety of the Jacobian of its cover or merely the degree of the covering
up vote 0 down vote favorite
I read following paragraph from:
G. Tamme, Teilkörper höheren Geschlechts eines algebraischen Funktionenkörpers, Arch. Math. 23 (1972), 257--259
Here $C$ is a c... | 4 | [
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... | 42,649 | 42649 | |
prove by induction 6 divides n^3 -n
May 31st 2008, 05:08 PM
robocop_911
prove by induction 6 divides n^3 -n
Hello there!
I don't get it - what to assume in the following problem for solving by induction
Prove that 6 divides n^3 - n whenever n is a nonnegative integer
I tried following:
assume... | 4 | [
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0.049... | 42,650 | 42650 | |
Fermat's Last Theorem
June 16th 2010, 10:02 AM #1
Newbie
Joined
Jun 2010
Posts
11
Fermat's Last Theorem
I am having troubles showing that if you could prove Fermat's Last Theorem for n = 4 and you knew it held for any odd prime then Fermat's Last Theorem holds.
I am not entirely sure where to start.... | 5 | [
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... | 42,651 | 42651 | |
Emirps
November 2, 2010
We give three solutions. The first uses a function emirp? to identify emirps and enumerates them by testing each n in range:
(define (rev n) (undigits (reverse (digits n))))
(define (palin? n) (= n (rev n)))
(define (emirp? n) (and (prime? n) (prime? (rev n)) (not (palin? n))))
(define (emirp... | 4 | [
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0.03... | 42,652 | 42652 | |
need homework help
March 28th 2007, 07:34 PM
mimi
need homework help
Here's the two questions i'm having problems with:
1. Complete 1300 cm2 = ____m2.
2. given a right triangle with b=4 and c =11, find a approximated to three decimal places.
thank you so much in advance...Mimi
March 28th 2007, 07:... | 4 | [
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Can any countably generated k-algebra occur as the ring of global sections of some variety?
up vote 5 down vote favorite
1
In the answer to this question we saw that there exists a nonsingular quasi-projective threefold over a field with non-finitely generated global sections.
I was talking about this previous questi... | 5 | [
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sample size
Sample Size
Chapter 13
Two Ways to Classify Techniques
• Fixed or sequential sampling
• Sample size logic is based on traditional
(such as Neyman-Pearson) or Bayesian
inferential methods
Sample Size Affected by Practical
Issues
• Time pressure
... | 5 | [
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0.044677734375,
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0.052978515625,
0.06396484375,
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0.076171875,
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0.04638671875,
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0.029052734375,
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-0.0546875,
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0.024658203125,
-0.0168457... | 42,655 | 42655 | |
Sphere inscribed in pyramid
1. September 21st 2012, 10:53 AM #1
2. September 21st 2012, 02:44 PM #2
Re: Sphere inscribed in pyramid
Hi, aleschio.
I don't think we need to know $\beta.$ I will use $m$ to denote the measure of a length. My idea is something like this:
1) Since the base i... | 4 | [
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0.1... | 42,656 | 42656 | |
Exotic functions
In my generative 2d art such as Aleph Null and dbCinema, a virtual ‘brush’ moves around the screen ‘painting’. So I have need of functions that aren’t particularly predictable but buzz around the
screen–and stay on screen. Ideally, they’d look like a human scrawl. Like the graphics in this article.
Wh... | 4 | [
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a number proof or disproof question
if a>0 then we can write $a^3=b^2-c^2$$b,c\in\mathbb{Z}$ how can ı prove the truthness this equation
Don't you see that $\forall a \in \mathbb{N}^{*},\ a^{3}=\left( \frac{a^{2}+a}{2}\right)^{2}-\left( \frac{a^{2}-a}{2} \right)^{2}$ ? Actually, you can write $a^{3}=(b+c)(b-c)$, and a... | 5 | [
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0.0947265625,
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0.07128... | 42,658 | 42658 | |
Exchangeable of the limitation
$\lim_{x\rightarrow1-0}\sum_{n=1}^{\infty}\frac{x^{n-1}}{nln(n+1)} = \sum_{n=1}^{\infty}\lim_{x\rightarrow1-0}\frac{x^{n-1}}{nln(n+1)}$ Is the above equation right? in the other words, can we take
the limitation into the summation?
Yes, as long as the quantity considered is positive. The... | 5 | [
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Shapes of torus and modular group
In June 2012, I emphasized that the Higgs field was the first experimentally observed elementary scalar field – the Higgs boson is the first elementary spinless particle we know – and because string
theory loves to predict scalar fields and gives them many roles while many alternative ... | 4 | [
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Supervised Clustering for Spam Detection in Data Streams
Ulf Brefeld Peter Haider and Tobias Scheffer
Technical University Berlin, Germany u
... | 4 | [
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bound on sum of logarithms
November 29th 2011, 10:45 AM #1
Newbie
Joined
Nov 2011
Posts
12
bound on sum of logarithms
I have that
$\prod_{i,j} (1-y_{ij}) \geq l$, where $1> y_{ij}\geq 0$
I need to bound the following using $l$
$\prod_{i,j} (1-a_{ij}y_{ij}) \geq ?$, where $1> y_{ij}\geq 0$ ... | 4 | [
0.01336669921875,
-0.0712890625,
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0.064453125,
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0.0011138916015625... | 42,662 | 42662 | |
Parabola word problem about a suspension bridge
July 19th 2010, 11:38 AM
iluvpigs1991
Parabola word problem about a suspension bridge
The two towers on either end will be 50 feet high and 300 feet apart. The two supporting cables are connected at the top of the towers and hang in a curve that is a parabola. Ther... | 4 | [
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-0.0419921875... | 42,663 | 42663 | |
[SOLVED] Hyperbola
April 16th 2010, 04:50 PM #1
Junior Member
Joined
Apr 2010
Posts
29
[SOLVED] Hyperbola
Hello.
For this question - Show how to determine a point P of the hyperbola xy = c^2 such that the asymptotes cut off a segment of length 6c in the tangent at P,
I've equated 6c^2= sqrt[a^2... | 5 | [
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Please help! (Area)
August 28th 2008, 10:58 AM #1
Newbie
Joined
Aug 2008
Posts
5
A central angle of a circle with radius 10 has a measure of 1.35 radians. The secant line between the end points of the arc of the angle divides the sector swept by the arc into two regions, one
a triangle and the other b... | 4 | [
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When to use L'Hospital's Rule...
I'm having some issues determining when I can and cannot use L'Hospital's Rule. Tips? Suggested approaches?
You can use it when you have the following typical cases: #1 Indetermination of the form $\frac00.$ #2 Indetermination of the form $\frac\infty\infty.$ Of course, if you're solvi... | 5 | [
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-0.080078... | 42,666 | 42666 | |
The Twelve-Step Cycle of 4/sin(x)
Beginning with any real number x, the sequence of values produced by iterating the function x → -4/sin(x) invariably converges on the twelve-step cycle
[]
or else the cycle consisting o... | 4 | [
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Chapter 9 – Solids and Fluids
This chapter deals with properties of solids and fluids (liquid and gases). One of the
properties of a material is its elasticity, which is a measure of the extent to which a force
can deform the material. In particular, ... | 5 | [
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Mandelbrot set and analytic functions such that $f(az)=f(z)^2+c$
up vote 5 down vote favorite
1
It is well known that the function $f(z)=2\cos(\sqrt {-z})$ (or more accurately the entire function $f(z)=2\sum_{n=0}^\infty \frac{z^n}{(2n)!}$) satisfies such a functional equation, i.e. $f(4z)= f
(z)^2-2$ ; it is not hard... | 4 | [
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0.01513671875,
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Are surface bundles over a surface with non-zero signature necessarily complex (or algebraic)?
up vote 12 down vote favorite
6
By "surface bundle over a surface" I mean a compact, oriented 4-manifold $X$ which is the total space of an oriented fiber bundle $X\to B $ over an oriented 2-manifold $B$. Assume that the sig... | 4 | [
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0.011779785156... | 42,670 | 42670 | |
A urn contain N white
December 29th 2009, 09:02 PM #1
Banned
Joined
Dec 2008
From
Mauritius
Posts
523
A urn contain N white
Question : A urn contain N white and M black balls. Balls are randomly selected, one at a time , until a black one is obtained . It we assume that each selected ball is replace... | 5 | [
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0.00909423828125,
-0.0029449462890625,
0.0693359375,
0.0673828125,
-0.077... | 42,671 | 42671 | |
Designing Cycloidal Gears
Hugh Sparks
April 26, 2013
http://www.csparks.com
Watches and clocks traditionally use cycloidal gearing. This page will show you how to design these gears and the cutters used to make them. The focus will be on the design described in British
Standard 978 Part 2: Cycloidal Type Gears. This ... | 4 | [
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0.00411987304687... | 42,672 | 42672 | |
Coordinate Systems
April 27th 2008, 08:30 PM
geton
Coordinate Systems
I've two question, please help me to solve.
Question 1:
A line with gradient 4 touches the parabola with equation y^2 = 4x. Find the coordinates of the point of contact of this tangent with the parabola and an equation of the normal t... | 4 | [
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0.0625,
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0.0294189453125,
0.0272216796875,
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-0.0126953125,
... | 42,673 | 42673 | |
Differentiating y
May 4th 2013, 02:38 AM
Paze
Differentiating y
I can't seem to wrap my head around differentiating y or f(x). For example: x^2+xy^2=2.
I understand the product rule and everyone keeps saying that ''it's just the product rule'' when I'm differentiating implicitly like that, but I don't have ... | 5 | [
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0.042236328125,
0.03759765625,
0.08447265625,
-0.0751953125,
-0.0147705078... | 42,674 | 42674 | |
Math Problems need hELP!!
September 23rd 2007, 12:38 PM
lemontea
Math Problems need hELP!!
Can anyone help me with these two problems! THank You!!!
1) Evaluate:
http://img.photobucket.com/albums/v3...athproblem.jpg
2.) a and b are two integers, and a>b. The sum of a and b is 5, but their product is ... | 4 | [
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0.06005859375,
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0.1435546875,
-0.053466796875,
-0.006... | 42,675 | 42675 | |
Spheres over rational numbers and other fields
up vote 6 down vote favorite
1
Let K be an ordered field. Define the n-sphere:
$$S^n(K) := \{ (x_1,x_2,\dots,x_n+1) \in K^{n+1} \mid \sum_{i=1}^{n+1} x_i^2 = 1 \}$$
A set of vectors $v_1, v_2, \dots, v_r \in S^n(K)$ is orthonormal if the dot product of any two of them i... | 5 | [
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0.039794921875,
... | 42,676 | 42676 | |
Lucas Sequences, Revisited
January 21, 2014
Lucas sequences are important both to the study of prime numbers and in cryptography, and we’ve used Lucas sequences in several previous exercises, most recently just a few months ago; unfortunately,
some of the code given in some of those exercises was incorrect, and looki... | 4 | [
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-0.05517578125,
-0.0... | 42,677 | 42677 | |
4 ?'s Help Me Please!!!
Lane 1. Find the 3 cofactors of the second row of: $<br /> A=\left [ \begin{array}{ccc}<br /> {-7}& {-5}&{6}\\<br /> {9}& {4}&{-3}\\<br /> {8}&{-1}&{2}<br /> \end{array} \right]<br />$ The cofactor
$C_{i,j}$ is $(-1)^{i+j}$ times the determinant of the matrix obtained from $A$ by deleting the $i... | 5 | [
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-0.06640625,
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0.01287841796875,
-0.0272216796875,
-0.0... | 42,678 | 42678 | |
Error to sum of Euler phi-functions
up vote 12 down vote favorite
4
The number theory identity $\phi(1) + \phi(2) + \dots + \phi(n) \approx \frac{3n^2}{\pi^2}$ can be interpreted as counting relatively prime pairs of numbers $0 \leq \{ x,y \} \leq n$ .
Has anyone studied the distribution of error term? $\displaystyle... | 4 | [
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-0.10693359375,
0.0230712890625,
-0.04... | 42,679 | 42679 | |
Continuous Strictly Positive Measures on Countable Boolean Algebras
up vote 4 down vote favorite
This is a followup to:
Strictly Positive Measures on Countable Boolean Algebras
Suppose a countable Boolean algebra B is a subalgebra of the power set of the reals. (For example, let B be the Boolean algebra of definable... | 5 | [
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-0.022... | 42,680 | 42680 | |
Vector Proof - Dot and Cross Products
February 25th 2009, 10:53 AM #1
Junior Member
Joined
Jul 2008
Posts
74
Vector Proof - Dot and Cross Products
Hello everyone,
I am having some trouble with the following problem and would appreciate help. Thank you!
---
16. For any vectors $\vec{a}, \ve... | 4 | [
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-0.0283203125,
0.05297851... | 42,681 | 42681 | |
Meromorphic 1-form and Picard's theorem
up vote 13 down vote favorite
5
Let $D$ be the open unit disk in the complex plane and $U_1,U_2,\,\ldots\,,U_n$ be an open cover of the puntured disk $D^*= D\setminus\{0\}$. Suppose on each open set $U_j$ there is an injective
holomorphic function $f_j$ such that $df_j=df_k$ on ... | 5 | [
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0.00019359588623046875,
-0.1083984375,
-0.1591796875... | 42,682 | 42682 | |
Extension Fields
Date: 12/03/98 at 08:49:17
From: Andy Ullom
Subject: Modern Algebra Problems
I have looked at these problems and do not know where to start. Could
you give me a little help?
We are working with Extension Fields.
1) Show that Q(sqrt(2), sqrt(3)) = Q(sqrt(2) + sqrt(3))
2) Find the splitting field o... | 5 | [
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0.0103759765625,
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0.022216796875,
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-0.024169921... | 42,683 | 42683 | |
Is the transcendence degree of a domain over a subfield the same as that of the fraction field of that domain?
up vote 3 down vote favorite
1
Consider the inclusion $k\subset A$ of the field $k$ in the domain $A$ and the fraction field $K=Frac(A)$ of $A$.
Obviously if a family $(a_i)_{i\in I}$ of elements $a_i \in A$ ... | 5 | [
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... | 42,684 | 42684 | |
Tutorial
One of the most striking features of QOCA is its simple interface. To understand the interface design, consider a simple application, that of a constraint-based graphics editor. The editor
essentially provides three operations: the user may add objects or constraints, the user may delete an object or constrain... | 4 | [
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0.07470703125,
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0.014892578125,
-0.0603027343... | 42,685 | 42685 | |
Area Between Curves
Date: 01/11/97 at 00:40:11
From: Anonymous
Subject: The Application of integrals
I have no trouble finding the area between curves when there are only
two curves, but this problem involves three. I get an answer, but it
is off by .02. The book states it as a fraction, so I assume that my
number s... | 5 | [
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-0.0971679687... | 42,686 | 42686 | |
Expressing fiber product of affines via an ideal
up vote 1 down vote favorite
Let $X$ (resp. $Y$) be the affine $k$-scheme defined by the ideal $I$ (resp. $J$) in the polynomial ring $k[x_1,...x_n]$ (resp. $k[y_1,...,y_m]$). Let $Z$ be the affine scheme defined by the ideal
$L$ in $k[z_1,...z_s]$, and let $f^\*:k[z]/L... | 4 | [
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... | 42,687 | 42687 | |
Does each finite morphism of curves have a model whose minimal resolution is semi-stable
up vote 2 down vote favorite
Let $\pi:Y\to X$ be a finite morphism of smooth projective geometrically connected curves over a number field $K$.
Question. Does there exist a finite field extension $L/K$ and a regular model $\mathc... | 5 | [
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0.04052734375... | 42,688 | 42688 | |
H^4 of the Monster
up vote 32 down vote favorite
11
The Monster group $M$ acts on the moonshine vertex algebra $V^\natural$.
Because $V^\natural$ is a holomorphic vertex algebra (i.e., it has a unique irreducible module), there is a corresponding cohomology class $c\in H^3(M;S^1)=H^4(M;\mathbb Z)$ associated to this
... | 4 | [
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0.006072998046875... | 42,689 | 42689 | |
Symmetric Matrix proof !
December 11th 2009, 05:27 AM
Avi06
Symmetric Matrix proof !
Given that A is a n x n symmetric matrix and $\lambda_{1} \geq \lambda_{2} \geq .... \geq \lambda_{n}$ , where $\lambda_{i}$ are eigenvalues of A.
Show that:
$<br /> \lambda_{1}\|x\|^{2} \geq x^{T}Ax \geq \lambda_{n}\|x... | 5 | [
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0.08251953125... | 42,690 | 42690 | |
Tensor product and basis
January 21st 2011, 02:57 PM #1
Member
Joined
Oct 2010
Posts
131
Tensor product and basis
Hello,
Let V,W be some finite dim. vector spaces and denote $(e_i)_{i=1,..,n}, (g_j)_{j=1,..,m}$ the bases of V,W respectively.
Now i want to show that $(e_i \otimes g_j) ,1\leq i,j... | 5 | [
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0.06494140625... | 42,691 | 42691 | |
A Group-Delay Interpretation of Polyphase Filters
Previously, polyphase interpolation and decimation were derived from the Noble identities and motivated for reasons of computational efficiency. Here we present a different interpretation of the
(ideal) polyphase filter.
Assume that HzHz is an ideal lowpass filter wit... | 4 | [
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0.0537... | 42,692 | 42692 | |
Ring Isomorphism
November 1st 2008, 01:50 PM #1
Ring Isomorphism
Let R and S be rings and let I ▹R, J ▹S be ideals. Prove that
$(R\times S)/(I\times J) \simeq (R/I) \times (S/J)$
I think
$(R\times S)/(I\times J)$ is of the form $(a,b) + (I,J) : a \in R, b \in S$ that is also of the form $(a + I, b + J... | 4 | [
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The Riemann's Zeta Function represented as a continued fraction and a question of convergence.
up vote 9 down vote favorite
6
The Riemann's zeta function can be expressed as a continued fraction as follows \begin{align*} \zeta(z)=\newcommand{\bigk}{\mathop{\Huge\vcenter{\hbox{K}}}}\left(1-\bigk_{k=1}^{\infty }\frac{-e... | 4 | [
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0.0546875,
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Perfect Square Trinomial
September 30th 2008, 04:23 AM #1
Member
Joined
Dec 2007
Posts
96
Find two values of b that will make [tex]9x^2+bx+25[tex] a perfect square trinomial.
The formulas for Perfect Square Trinomial are:
[tex](a+b)^2=a^2+2ab+b^2[tex]
[tex](a-b)^2=a^2-2ab+b^2[tex]
As I s... | 4 | [
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0... | 42,695 | 42695 | |
Acyclic models via model categories?
up vote 12 down vote favorite
5
Recall the acyclic models theorem: given two functors $F, G$ from a "category $\mathcal{C}$ with models $M$" to the category of chain complexes of modules over a ring $R$, a natural transformation
$H_0(F) \to H_0(G)$ induces a natural transformation ... | 4 | [
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0.0673828125,
-0.... | 42,696 | 42696 | |
Center for Science Education:
SOLUTIONS TO THE SECOND HOUR EXAM
1. Newtons's first law states that an object at rest stays at rest unless acted on by outside forces; an object in motion stays in constant motion unless acted on by outs... | 4 | [
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0.08447265625,
0.07470703125... | 42,697 | 42697 | |
kinetic energy
January 6th 2009, 12:50 PM #1
Junior Member
Joined
Feb 2008
Posts
71
kinetic energy
Okay so i'll go right to it (been sitting about 2 hours with this question);
An icecube is sliding 3 meters friction free off the ledge of a house roof which has the angle of 27 degrees. What speed wil... | 4 | [
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Genus computation
up vote 1 down vote favorite
2
What is the smartest way to compute the genus of a hyperelliptic curve $C: y^2 = f(x)$ (with $f$ a separable polynomial of degree $n> 3$ over a field $k = \bar{k}$ of characteristic $0$ (prob.
characteristic unequal $2$ is enough). (Just to be precise, I am referring to... | 5 | [
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0.02490... | 42,699 | 42699 |