content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
.
6. WEAK FIELDS AND GRAVITATIONAL RADIATION
When we first derived Einstein's equations, we checked that we were on the right track by considering the Newtonian limit. This amounted to the requirements that the gravitational field be weak, that
it be static (no time derivatives), and that test particles be moving slo... | 4 | [
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0.01904296875,
-0.05908203125,
0.06201171875,
-0.009948730468... | 11,800 | 11800 | |
Coprime sampling for nonstationary signal in radar signal processing
Abstract
Estimating the spectrogram of non-stationary signal relates to many important applications in radar signal processing. In recent years, coprime sampling and array attract attention for their
potential of sparse sensing with derivative to est... | 4 | [
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Results: Calculate square roots
09-29-2004 #1
Results: Calculate square roots
OK, I' m unable to post the submissions in this thread, for known reasons, but I hope that every contestant can post their submission here for review.
Overview
Most people used the Newton-Rhapson method of solving equations. Yo... | 5 | [
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-0.01519775390625... | 11,802 | 11802 | |
Burnside's lemma and Bell numbers
Burnsideβs lemma and Bell numbers
In this post I am going to show that ${B_n}$, the ${n}$th Bell number, is larger than ${n^n/n!}$.
Our main tool will be Burnsideβs lemma, which states that if a finite group ${G}$ acts on a finite set ${S}$, the average number of fixed points of the ... | 4 | [
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Recusive help
November 21st 2009, 11:55 AM #1
Newbie
Joined
Nov 2009
Posts
18
Recusive help
I am needing help with this
Find f 2, f 3, f 4, and f 5 if f is defined recursively by f 0 = f 1 = 1 and for n = 1,2
f n+1 = ( f n ) 2 + ( f n-1 ) 3
Hello, erinneedshelp!
Just follow the directi... | 4 | [
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Construct a graph from given node degrees
up vote 2 down vote favorite
1
I have to find which of the following values can be the degrees of an undirected graph with 6 vertices:
a) 3 2 2 2 3 3
b) 4 2 2 2 3 2
c) 5 2 2 2 0 3
d) 5 2 2 2 1 2
I only method I found is to try to draw the graph on a sheet of paper and then c... | 4 | [
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-... | 11,805 | 11805 | |
set of subsequential limits
November 13th 2012, 03:30 PM #1
Newbie
Joined
Nov 2012
From
Barcelona
Posts
5
set of subsequential limits
Let A be a closed subset of R. Prove that there exists a sequence of real numbers s.th. if B is the set of all subsequential limits, then B=A.
I know how to do it... | 5 | [
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... | 11,806 | 11806 | |
Category Theory and Haskell 3 : Algebra and Monads
This is the third part of my serie about Haskell and category theory. In the previous post, I described a bit the Hask category and some categorical constructs. The goal of this text is to understand
the meaning of a recursive type like List. For that, we will have to... | 4 | [
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Math Forum: Growing Worms Sample Solutions
Donavan
A four day old worm has 10 isoceles right triangles. A ten day old worm has 24 isoceles right triangles. A 63 day old worm from Trianglia has 128 isoceles right triangles. EXTRA: The worm would
be 15 days old.
I found out that a 4 day old worm from Triang... | 4 | [
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Geometry: arc and angles
Arc Β and Angles
Arc and angles Subtended by them
Some results on angles subtended by arcs of a circle either at the center of the circle or at a point on its circumference.
1) The angle subtended by an arc of a... | 4 | [
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I
Introduction to Population Ecology
Edward B. Radcliffe, Professor Emeritus
Department of Entomology, University of Minnesota
Apunte aquΓ para versiΓ³n en EspaΓ±ol [X]
Background
Thomas Malthus
The first significant contribution to the theory of population ecology was that of Thomas Malthus, an English clergyman... | 4 | [
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Math Forum Discussions
Re: Please help refresh my Algebra skills (factoring & solving)
Posted: Oct 17, 1999 4:33 PM
>If I have some nasty numbers in quadratic form, how do I factor and solve
>for the TWO answers??
>-4.9x^2+5.5x-105=0
>That factors to x(-4.9x+5.5) = -105
>What next??
You can "complete the square"... | 4 | [
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Math Forum Discussions - Re: Why study Egyptian fraction math?
Date: Nov 9, 2012 2:01 PM
Author: Milo Gardner
Subject: Re: Why study Egyptian fraction math?
Arithmetic and geometric proportions offer twoi of the highest forms of Egyptian fraction math. Arithmetic proportions are included in"
http://planetmath.org/enc... | 4 | [
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a library
Cuba - a library for multidimensional numerical integration
The Cuba library offers a choice of four independent routines for multidimensional numerical integration: Vegas, Suave, Divonne, and Cuhre. They work by very different methods, summarized in the
following table:
Routine Basic integration method ... | 4 | [
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0.1... | 11,813 | 11813 | |
Homotopy Equivalences and Induced Correspondences between Fibre Bundles
up vote 2 down vote favorite
Suppose that $f:X\rightarrow Y$ is a homotopy equivalence of manifolds. Given a manifold $F$, the pullback construction for $f$ yields a correspondence between isomorphism classes of fibre bundles
over $X$ with fibre $... | 5 | [
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Unique Values for x, y
Date: 9/10/96 at 16:46:45
From: Anonymous
Subject: Values for x, y Such That...
What are unique values for x and y so that x+y and y*x equal the
same number?
Thanks.
Date: 9/10/96 at 19:56:40
From: Doctor Mike
Subject: Re: Values for x, y Such That...
Hello,
I can think of 2 solutions qui... | 4 | [
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0.0183105468... | 11,815 | 11815 | |
Signal Cancellation Improves DDS SFDR
Direct digital synthesizers (DDS) are commonly used for sinusoidal signal generation in RF communication systems and test equipment. An integral component of DDS is the digital-to-analog converter
(DAC). Although a DAC is intended to perfectly reproduce an analog signal from its di... | 4 | [
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... | 11,816 | 11816 | |
Quick question about two-path limit test
October 13th 2010, 09:17 PM
downthesun01
Quick question about two-path limit test
How do you decide what two paths to take? For example:
$\frac{x^{2}y}{x^{4}+y^{2}}$
Can I pick any paths I want? For example:
The line $x=0$
$lim_{x\rightarrow 0}$$\frac{... | 5 | [
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Working with Inverses
May 9th 2009, 02:00 AM #1
Member
Joined
Mar 2009
Posts
133
Working with Inverses
Hi MHF,
I'm having heaps of trouble working out how to solve this question. The text book that I am using is the third addition of Lay's Linear Algebra book and I cant find any examples on this type... | 5 | [
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-0.0327148437... | 11,818 | 11818 | |
A Neighborhood of Infinity
A heavyweight looking title, but this post is really about nothing more than doing arithmetic.
Peano Arithmetic
I've seen
many articles
on
type
level arithmetic. They all seem to share the idea that the Haskell type system can be made to perform computations by treating types as symbols... | 4 | [
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Pascal's Principle
Brightstorm is like having a personal tutor for every subject
See what all the buzz is about
Check it out
Pascal's Principle 8,686 views
According to Pascal's Principle, in a uniform fluid, pressure depends only on height. There can be no pressure gradient except for that caused by liquid pressur... | 5 | [
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Random inequalities V: beta distributions
Iβve put a lot of effort into writing software for evaluating random inequality probabilities with beta distributions because such inequalities come up quite often in application. For example, beta
inequalities are at the heart of the Thall-Simon method for monitoring single-a... | 4 | [
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-0.... | 11,821 | 11821 | |
Homework Help
Posted by John on Sunday, January 17, 2010 at 12:52pm.
Find the exact value of the trigonometric function:
sec(-pi/12)
I am not sure how to answer this off the unit circle.
β’ trig - Reiny, Sunday, January 17, 2010 at 2:05pm
You should know that
sec (-pi/12)
= 1/cos(-pi/12)
= 1/cos(p... | 4 | [
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Messenger, Mercury, and General Relativity
"I think Isaac Newton is doing most of the driving now."
Apollo 8 Lunar Module pilot Bill Anders, when asked who was driving the capsule on the return from the Moon to the Earth, 26 December 1968.
On January 14, 2008, the
Messenger spacecraft
had a spectacular flyb... | 4 | [
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Energy of links and Freedman-He-Wang's conjecture after Ian Agol, Fernando Coda Marques and Andre Neves
Posted by: matheuscmss | August 15, 2012
Energy of links and Freedman-He-Wangβs conjecture after Ian Agol, Fernando Coda Marques and Andre Neves
The solution of a long-standing conjecture normally provokes a lot of... | 4 | [
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Converting Fractions and Decimals
Date: 02/05/97 at 12:04:00
From: Alice
Subject: Fractions and decimals
1. Express 3/5 as a decimal.
2. Express 0.15 as a rational fraction.
Date: 02/06/97 at 20:54:37
From: Doctor Keith
Subject: Re: Fractions and decimals
Hello!
In these explanations, if I make a step that is n... | 4 | [
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inequality
You are currently browsing the tag archive for the βPrekopa-Leindler inequalityβ tag.
One of the fundamental inequalities in convex geometry is the Brunn-Minkowski inequality, which asserts that if ${A, B}$ are two non-empty bounded open subsets of ${{\bf R}^d}$, then
... | 4 | [
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... | 11,826 | 11826 | |
Pinhole Design β what Lord Rayleigh really said
Thoughts from two men on pinhole design. Brian Young investigates the relationship between focal length and the diameter of the pinhole and what Lord Rayleigh thought of this.
Introduction
Many pinholers like to construct their own cameras and, with one exception, there... | 4 | [
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sine wave amplitude calculation
April 27th 2012, 02:35 PM #1
Newbie
Joined
Apr 2012
From
wisconsin
Posts
4
sine wave amplitude calculation
Hi,
I'm having some troubles determining the amplitude/magnitude of the following equation.
$A\cos(2\omega t+\beta_1)+B\cos(3\omega t+\beta_2)+C\cos(5... | 4 | [
-0.09130859375,
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-0.01019287109375,
0.041015625,
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0.035400390625,
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-0.033203125,
0.032470703125,
0.0751953125,
0.0654296875,
-0.036376953125,
0.0... | 11,828 | 11828 | |
Positive solution for a class of singular semipositone fractional differential equations with integral boundary conditions
Abstract
In this article, by employing a fixed point theorem in cones, we investigate the existence of a positive solution for a class of singular semipositone fractional differential equations wi... | 5 | [
-0.068359375,
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-0.031494140625,
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0.0155029296875,
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0.022705078125,
-0.... | 11,829 | 11829 | |
15-854B: Advanced Approximation Algorithms
For 2a, it should say "expressed as a sum of products of up to k of f's Fourier coefficients".
Thanks to Jonah for pointing this out.
Ok, yeah, part (b) was super-vague, sorry about that. Here is a more precise question, I think.
Consider the matrix $M_2(y)$; if this is ps... | 4 | [
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Math Forum Discussions
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Topic: Plot InverseSurvivalFunction
Replies: 1 Last Post:... | 5 | [
-0.0947265625,
-0.0498046875,
0.02587890625,
0.00250244140625,
0.10302734375,
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0.061279296875,
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-0.0238037109375,
-0.0194091796875,
... | 11,831 | 11831 | |
Are there n polynomials for which all intersection multiplicities are at least m?
up vote 3 down vote favorite
1
I don't know whether this is known or not, but I was thinking of the following problem.
Let $n$ and $m$ be natural numbers. Are there $n$ polynomial $f_1,...,f_n\in \mathbb{C}[x]$, such that all of their i... | 5 | [
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0.004150390625,
-0.044921875,
-0.01165771484375,
-0.03466796875,
0.04882... | 11,832 | 11832 | |
Straight Lines
The equation y = 2x β 1 that we used as an example for graphing functions produced a graph that was a straight line. This was no accident. This equation is one example of a general class of equations
that we call linear equationsΒ in two variables. The two variables are usually (but of course donβt have t... | 4 | [
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-0.12158203125,
-0.04052734375,
... | 11,833 | 11833 | |
How to prove Arnold Conjecture without using S^1 localization?
up vote 7 down vote favorite
1
By the Arnold Conjecture, I mean the following statement:
Let $M$ be a closed symplectic manifold, and $\phi:M\to M$ a Hamiltonian symplectomorphism with nondegenerate fixed points. Then $ \# \operatorname{Fix} (\phi) \g... | 4 | [
-0.0033416748046875,
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0.040283203125... | 11,834 | 11834 | |
Homework Help
Posted by Milly on Monday, September 5, 2011 at 3:30pm.
A ball is thrown off a cliff from a ht of 180 ft above sea level. The ht s of the ball above sea water level at time t is s(t)=-16t2+32t+180. When will the ball strike the water?
β’ Math - Henry, Wednesday, September 7, 2011 at 3:28pm
When th... | 4 | [
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-0.05... | 11,835 | 11835 | |
Minimal Weighings of Ten Coins to Identify the Two Counterfeits
Date: 04/18/2010 at 03:19:13
From: ching
Subject: weighings
Suppose you have a balance scale and 10 similar coins, but 2 of them are
fake. The counterfeits have the same weight, but are lighter than the real
ones.
At least how many weighings on the scal... | 5 | [
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0.0595703125,
... | 11,836 | 11836 | |
Advanced functions question help
March 23rd 2009, 11:54 AM
temour123
Advanced functions question help
I need help with these advanced functions problems
State the Common Ratio of the following Geometric sequence
3/4 , 3/10 , 3/25 , 6/125
2. In the Arithmetic Sequence below, X = ___
100 , ___ , ... | 4 | [
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0.056396484375,
-0.036865234375,
-0.008056640625,
-0.05859375,
-0.06542968... | 11,837 | 11837 | |
cardinalit
cardinality
cardinality
Cardinality
Cardinality is a notion of the size of a set which does not rely on numbers. It is a relative notion. For instance, two sets may each have an infinite number of elements, but one may have a greater
cardinality. That is, in a sense, one may have a βmore infiniteβ number ... | 4 | [
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0.0400390625,
0.030029296875,
-0.047119140625,
-0.05615234375,
-0.0390625,
0.09765625,
-0.0205078125,
0.01104736328125,
0.015380859375,
0.060791015625,
-0.033203125,
... | 11,838 | 11838 | |
The three types of solution sets:
A system of linear equations can have no solution, a unique solution or infinitely many solutions.
A system has no solution if the equations are inconsistent, they are contradictory. for example 2x+3y=10, 2x+3y=12 has no solution. []is the rref form of the matrix for this system. []
... | 5 | [
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0.0361328125,
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0.006561279296875,
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-0.01544189453125,
-0.083984375,
-0.1191406... | 11,839 | 11839 | |
CIRCLES, SQUARES TRIANGLES, POLYHEDRA , LOGARITHMS, AND SPIRALS RELATED TO THE THE QUADRATURE TRIANGLE [ P.Stefanides Interpretation]
About this iReport
Not vetted for CNN
Location
KIFISSIA, Greece
Assignment
This iReport is part of an assignment:
Tech talk
More from PCSTEFANIDES
More iReports you should se... | 4 | [
-0.031982421875,
0.000751495361328125,
-0.0262451171875,
-0.0184326171875,
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0.016357421875,
-0.038330078125,
0.04248046875,
0.001007080078125,
-0.043701171875,
-0.112... | 11,840 | 11840 | |
CHLOND & AKYOL - A Nimatron.
Nim is a two-person game of perfect information thought to be Chinese in origin. The game begins with a number of heaps of objects, usually coins or matchsticks. The players alternate moves by taking
any number of objects from any single pile. The player making the last move is the winner. ... | 4 | [
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0.1059570312... | 11,841 | 11841 | |
Could someone check my answers for limits please?
March 25th 2009, 07:26 AM
anita123
Could someone check my answers for limits please?
Could someone check my calculus answers, please?
1. Find lim x -> 3 (9-x^2)/(x^2-4x+3) I got -3/2
2. Find lim x -> -1 (sqrt(5+x)-2)/1+x, I got 1/4 (Only the 5+x is unde... | 4 | [
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-0... | 11,842 | 11842 | |
Finding optimal k0 values
From Polymath1Wiki
(Difference between revisions)
Xfxie Xfxie
( ... | 4 | [
0.00830078125,
0.04931640625,
0.0225830078125,
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-0.03564453125,
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0.05517578125,
-0.004760742... | 11,843 | 11843 | |
In 1D, is a $W^{1,p}$ function always Lipschitz, for $p\ge1$?
up vote 1 down vote favorite
We know that Morrey's inequality says $W^{1,p} \subset C^{0,\gamma}$ for $\gamma = 1 - n/p$ where $n$ is the dimension. However, in 1D, following the proof of Evans "Partial Differential Equations"
(first edition, pp. 267), we ... | 4 | [
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Zorn's
Context
Foundations
The basis of it all
Foundational axioms
β’ basic constructions:
β’ strong axioms
Removing axioms
Zorn's Lemma
Idea
Zorn's lemma is a proposition in set theory and order theory. It says that: A preorder in which every sub-total order has an upper bound has a maximal element.
Depen... | 4 | [
0.00157928466796875,
0.038818359375,
0.06005859375,
-0.06201171875,
0.09765625,
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0.10009765625,
0.03857421875,
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0.040283203125,
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0.0225830078125,
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0.0184326171875,
-0.009216308... | 11,845 | 11845 | |
Outer Products in Quantum Probability
Example 1: Quantum Logic
1. Start with logic. Something is either true 1 or false 0. No in-betweeners or outsiders today.
2. Now add probability. It hasΒ A%Β chance of being true 1Β and B%Β chance of being false 0. A+B=100%
3. Actually, make that quantum probability. A and B are co... | 4 | [
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... | 11,846 | 11846 | |
Hoping someone can help for once! a^3 = b^3
February 9th 2009, 02:39 PM #1
Newbie
Joined
Jan 2009
Posts
19
Hoping someone can help for once! a^3 = b^3
Show that if a^3 = b^3 if and only if a=b
Suppose a = b
a^3 = (a)(a)(a)
=(b)(b)(b)
=b^3
Prove other direction using contrapositive:... | 4 | [
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0.07568359375,
... | 11,847 | 11847 | |
Exterior powers of the standard representation
up vote 2 down vote favorite
4
For any group character $\chi: G \to \mathbb{C}$, the function $\chi(g^k)$ is an integer-linear combination of other group characters in $\mathrm{Irr}(G)$. There doesn't seem to be a general way of
finding the expansion in terms of the basic... | 4 | [
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0.03173828125,
0.0327148437... | 11,848 | 11848 | |
The elements of Euclid
The elements of Euclid: with dissertations intended to assist and encourage a critical examination of these elements as the most effectual means of establishing a juster taste upon mathematical
subjects than that which at present prevails, Volume 1 (Google eBook)
James Williamson
We haven'... | 4 | [
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-0.1181640625... | 11,849 | 11849 | |
LINEST function
This article describes the formula syntax and usage of the LINEST function (function: A prewritten formula that takes a value or values, performs an operation, and returns a value or values. Use
functions to simplify and shorten formulas on a worksheet, especially those that perform lengthy or complex ... | 5 | [
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0.006988525390625,
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0.09619140625,
0.046630859375,
0.015869140625,
-0.007049560546875,
0.005767822265625,
0.01226806640625,
0.008056640625,
0.005157470703125,
0.07861328125,
-0.12011718... | 11,850 | 11850 | |
Electrical Current
Current
Why Do You Need To Know About Current?
Facts About Current
Current
Current Units
Measuring Current
Problem & Links to Other Lessons
You are at: Basic Concepts - Quantities - Current
Return to Table of C... | 4 | [
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-0.0400390625,
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0.037109375,
-0.02709... | 11,851 | 11851 | |
Confidence Intervals for Misbehaved Functionals
Larry Wasserman
Suppose you want to estimate some quantity ${\theta}$ which is a function of some unkno... | 4 | [
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0.030517578125,
-0.08544921875,
0.052978515625... | 11,852 | 11852 | |
.
7. THE PHYSICS OF THE PHASE DIAGRAM
7.1. Energy densities in the two phases
At temperature much larger than the transition temperature, we expect the particles of the glue to behave as free particles, ignoring completely the presence of the color force. Thus, as for a photon
gas, we expect the energy density to be... | 4 | [
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-0... | 11,853 | 11853 | |
Given an integer, how do I find the next largest power of two using bit-twiddling?
up vote 31 down vote favorite
13
If I have a integer number n, how can I find the next number k > n such that k = 2^i, with some i element of n by bitwise shifting or logic.
Example: if I have n = 123, how can I find k = 128, which is ... | 5 | [
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Gene selection with multiple ordering criteria
Abstract
Background
A microarray study may select different differentially expressed gene sets because of different selection criteria. For example, the fold-change and p-value are two commonly known criteria to select
differentially expressed genes under two experimenta... | 4 | [
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-0.0167236328... | 11,855 | 11855 | |
LOSCHMIDT'S NUMBER
(Science Progress, v. 27, 1933, pp. 634-649)
LOSCHMIDT'S NUMBER
... | 4 | [
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0.0042724609375,
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-0.064453125,
-... | 11,856 | 11856 | |
Smooth submanifolds defined by Subrings
up vote 3 down vote favorite
5
To be honest, I don't really know, whether or not the following is a research level question:
Let $M$ be a smooth manifold, $C^\infty(M)$ the smooth function ring on $M$ and suppose $R\subset C^\infty(M)$ is a subring. What are conditions, such th... | 4 | [
-0.095703125,
-0.031494140625,
-0.02685546875,
-0.006622314453125,
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-0.0277099609375,
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0.10791015625,
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0.037109375,
-0.0279541015625,
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0.03759765625,
0.003875732421875... | 11,857 | 11857 | |
Solving Proportions
Solving proportions
Solving proportions by using cross product to find unknown terms is what this lesson is about
We will also show somes principles, special techniques or shortcuts that can be used to quickly solve a proportion
Terms to know:
x, y, or any other letter is used to stand for an ... | 4 | [
0.000010251998901367188,
0.00775146484375,
0.0040283203125,
-0.045166015625,
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0.06396484375,
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0.04052734375,
0.12353515625,
0.04931640625,
0.0712890625,
-0.02722167968... | 11,858 | 11858 | |
RouchΓ©'s theorem
May 12th 2011, 12:13 PM
MathMan170
RouchΓ©'s theorem
I have a question that is as follows,
Let $p(z)=z^{2}-ce^{-z}$ where $0<c<1$
Use Rouches Theorem to show that if $c<{\frac{1}{e}}$ then there are two zeros of p(z) within the unit circle.
Now i chose $g(z)=z^{2}$ and $h(z)=-ce^{-... | 5 | [
-0.0458984375,
0.091796875,
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0.0908203125,
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-0.0181884765625,
-0.058349609375,
-0.11083984375,
-0.00408935546875,
-0.08349609375... | 11,859 | 11859 | |
Kinematics with Quaternions
I haven't been able to find any satisfactory pages on Google on this subject, but maybe I wasn't looking correctly. I'm trying to find the equivalent kinematic equations for use with quaternions. If
I had to guess, I would think that you take the regular formulas and where you normally mult... | 4 | [
-0.09521484375,
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0.06298828125,
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0.048095703125,
-0.05224609375,
0.18945312... | 11,860 | 11860 | |
Failure devices prob.
September 11th 2009, 10:40 AM #1
Failure devices prob.
There are 30 devices, it is known that 20 of them are failure and 10 are ok. There are chosen 4 of them. What is the probability that the chosen devices are not all of them failure/ok?
res. p = 0.611
OK so I tried finding the pr... | 5 | [
0.0810546875,
0.045654296875,
0.032958984375,
-0.039794921875,
0.0033111572265625,
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0.059326171875,
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-0.0218505859375,
-0.0703125,... | 11,861 | 11861 | |
Inequality 3
Hi, firstly, we can notice that $f(x)=\frac{1}{x^2-x+3}$ is concave on $[0,\frac{3}{2}]$ (by 2 derivations). So, if a,b, and c are in $[0,\frac{3}{2}]$, we can apply the inegality of convexity, and
the result is obvious. Now, if at least one of the 3 numbers is $> \frac{3}{2}$. Then, the 2 others are $< \f... | 5 | [
0.015625,
-0.050048828125,
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0.01031494140625,
0.025146484375,
0.0751953125,
-0.05029296875,
-... | 11,862 | 11862 | |
Voronoi Diagrams
Subsections
Voronoi Diagrams
An ordinary Voronoi diagram is formed by a set of points in the plane called the generators or generating points. Every point in the plane is identified with the generator which is closest to it by
some metric. The common choice is to use the Euclidean distance metric
... | 4 | [
-0.02099609375,
0.04541015625,
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0.00146484375,
-0.0439453125,
-0.03125,
0.0029602050781... | 11,863 | 11863 | |
Final post on the Wang-Landau and the Flat Histogram criterion
Hey,
With Robin Ryder we wrote a paper titled The Wang-Landau Algorithm Reaches the Flat Histogram in Finite Time and it has been accepted in Annals of Applied ProbabilityΒ (arXiv preprintΒ here). Iβm
especially happy about it since it was the last remaini... | 4 | [
-0.08837890625,
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-0.068359375,
-0.004302978515625,
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0.15234375,
-0.01177978515625,
0.002105712890625,
-0.05419921875,
0.12109375,
-0.047119140... | 11,864 | 11864 | |
nrich.maths.org
Copyright Β© University of Cambridge. All rights reserved.
'Curved Square' printed from http://nrich.maths.org/
We had some really great, clear and detailed solutions for this one. It's a shame we can only write about a few of them!
Mowada and Megan used only clever coordinate geometry and the area of... | 5 | [
0.033935546875,
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0.1142578125,
0.038818359375,
-0.09716796875,
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0.0296630859375,
-0.032470703125,
0.06494140625,
0.01043701171875,
-0.01300048828125,
-0.0211181640625,... | 11,865 | 11865 | |
Is my answer right? Function problem
January 1st 2011, 08:59 PM #1
Junior Member
Joined
Nov 2010
From
NY
Posts
64
Is my answer right? Function problem
Find f(x) if f(x+1) = x^2-5x+3. Hint: let u =x+1 and find f(u). (ps do you think the author of this question is curseing at me? haha)
I got f(x)=... | 4 | [
-0.0625,
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0.0267333984375,
-0.002044677734375,
0.04345703125,
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-0.0186767578125,
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-0.07275390625,
0.0028228759765625,
0.03662109375,
-0.0164794921875,
-0.0322265625,
-0.0458984375,
-0.03222... | 11,866 | 11866 | |
Return of the simplest climate model
The
simplest climate model
balances the energy leaving the earth to space with the energy coming in from the sun. If the climate is not changing, these two will be the equal. As long as climate is not changing rapidly, a
modifier we can make quantitative, they'll be very nearly eq... | 4 | [
-0.0006256103515625,
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0.0908203125,
0.05029296875,
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-0.031494140625,
0.0546875,
-0.056396484375,
0.0267333984375,
-0.... | 11,867 | 11867 | |
Model PAs With Wideband Signals
Comparing conventional and orthogonal polynomial models with and without memory effects shows how these models can be used to emulate the nonlinear behavior of power amplifiers.
Chokri Jebali, Noureddine Boulejfen, Ali Gharsallah, and Fadhel M. Ghannouchi
Effective modeling of power am... | 4 | [
0.0380859375,
-0.01348876953125,
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0.025390625,
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0.1044921875,
0.06640625,
0.042236328125,
-0.007537841796875,
... | 11,868 | 11868 | |
Snubber Circuit Design Calculators
See our other Electronics Calculators.
Driving inductive loads with transistor switches, whether they be flyback transformers, relays or motors often result in the high voltage resonant spikes when the coils are interrupted from their
current current source by the transistor. There ... | 4 | [
-0.08056640625,
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0.0908203125,
-0.01556396484375,
0.043212890625,
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-0.020263671875,
0.0556640625,
0.02099609375,
0.07... | 11,869 | 11869 | |
time-shifted ODEs/volume of polytopes
up vote 3 down vote favorite
1
Hello,
I'm looking for help with the following ODE:
f'(t) = x f(1 - at)
for 0 < a < 1, x in any interval (though 0 < x < 1 would be best), and f(0) = 1. There should be a solution for $0 \leq t \leq 1$...
My rather weak repertoire of techniques f... | 5 | [
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0.06494140625,
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0.045166015625,
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0.0308837890625,
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0.0115966796875,
-0.0223388671875,
-0... | 11,870 | 11870 | |
the
You are currently browsing the tag archive for the βproduct theoremsβ tag.
In the previous set of notes, we saw that one could derive expansion of Cayley graphs from three ingredients: non-concentration, product theorems, and quasirandomness. Quasirandomness was discussed
in Notes 3. In the current set of notes, w... | 5 | [
-0.06787109375,
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0.0625,
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0.0078125,
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0.04345703125,
-0.0... | 11,871 | 11871 | |
Complex Numbers in Second Degree Equation
Date: 9/15/96 at 15:4:53
From: Anonymous
Subject: Complex Numbers in Second Degree Equation
Solve the equation z^2+(4-2i)z-8i = 0
How I tried to solve it:
z = -(4-2i)/2 +- sqr( ( (4-2i)/2)^2 + 8i)
... and after some simplification:
z = -2+i +- sqr(3+4i)
But I don't know... | 5 | [
-0.0703125,
0.060546875,
0.0238037109375,
0.06201171875,
-0.061767578125,
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-0.0159912109375,
-0.03515625,
0.0213623046875... | 11,872 | 11872 | |
round
Frictionless trajectories on a merry-go-round
ββ―β―ββββββββββββββββββββββββββββββ
βββLegend: β
βββ β
βββ β’ paint on merry-go-round β
βββ β
βββ β’ Coriolis force β
βββ β
βββ β’ centrifugal force ... | 4 | [
0.03173828125,
0.007293701171875,
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-0.01141357421875,
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-0.0179443359375,
-0.01055908203125,
0.0113525390625,
-0.078125,
-0.051513671875,... | 11,873 | 11873 | |
Formula for Triangular Numbers
Date: 08/29/98 at 17:32:48
From: Tobin Huff
Subject: Formula for triangular numbers
Is there a formula to figure out triangular numbers? With square
numbers, the formula is the number of dots on one side squared:
...
...
...
is 3^2 = 9.
If my question isn't clear enough, pl... | 4 | [
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-0.060... | 11,874 | 11874 | |
Numerical Analysis
Interpolation in Digital Signal Processing and Numerical Analysis
Β
Saeed Babaeizadeh
... | 4 | [
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0.046630859375,
0.00823974609375,
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0.04541015625,
-0.04150390625,
0.0106201171875,
-0.003448486328125,
-0.08789... | 11,875 | 11875 | |
adjoint functor
Context
Category theory
Concepts
Universal constructions
Theorems
Extensions
Applications
Contents
Definition
We say that two functors $L:C\to D$ and $R:D\to C$ are adjoint if they form an adjunction $L \dashv R$ in the 2-category Cat of categories. This means that they are equipped with natura... | 4 | [
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0.0284423828125,
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0.01287841796875,
0.0019378662109375,
0.04... | 11,876 | 11876 | |
limit proof
December 2nd 2010, 01:41 PM
pflo
limit proof
One way determine the deriveative of $e^x$ is to use inverse functions (natural logs). Another way is to use the definition of a derivative. Thus, $\frac{d}{dx}e^x=\lim_{h\rightarrow0}\frac{e^
{x+h}-e^x}{h}$. When simplified, this results in the equati... | 5 | [
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-0.020751953125,
... | 11,877 | 11877 | |
Pr
VII. Production in the Early Universe
A. Review of Big Bang Cosmology
To understand how dark matter particles could have been created in the early universe, it is necessary to give a brief review of the standard model of cosmology. The standard model of cosmology, or
the "Big Bang Theory" in more colloquial langu... | 4 | [
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-0.1337890625,
0.03979492... | 11,878 | 11878 | |
Intro 23. Iteration
>> << Usr Pri JfC LJ Phr Dic Rel Voc !: Help Dictionary
23. Iteration
The repetition of a process, or of a sequence of similar processes, is called iteration. Much iteration is implicit, as in */b and a*/b, and a*b ; explicit iteration is provided by the power
conjunction (^:), by agenda (@.) with ... | 5 | [
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-0.00994873046875,
-0.050048828125,
-0.... | 11,879 | 11879 | |
Mathematical And Physical Papers - Iii
ON THE MOTION OF PENDULUMS.
117
lation, and in fact T~l loge (a0O differs veiT sensibly from A' Making now this substitution in (174), integrating, and after integration restoring a in the last term by means of (175), we get
g log a2 - log a0
0 being an arbitra... | 4 | [
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... | 11,880 | 11880 | |
[SOLVED] Z18 Calculation
http://img91.imageshack.us/img91/7874/61804661.jpg $\frac{2}{7}+\frac{7}{13}=\frac{[2]X[13]+[7]X[7]}{[7]X[13]}$ Im not sure how to multiply this out please show steps on how to do this. Thanks
Hi as you mentioned it's not 3 mod 17, actually it is 3 mod 18. take 75 and when you try to divide 75... | 5 | [
-0.08056640625,
0.103515625,
-0.0031280517578125,
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0.03125,
-0.052490234375,
-0.0289306640625,
-0.0859375,
0.06494140625,
... | 11,881 | 11881 | |
A Neighborhood of Infinity
Generalising Monoids
The word 'monad' is derived from the word 'monoid'. The explanation usually given is that there is an analogy between monoids and monads. On the surface, this seems a bit unlikely. The
join
operation in a monad is supposed to correspond to the binary operator in the mo... | 4 | [
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0.04296875,
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0.0634765625,
0.0234375,
0.0174560546875,
0.0030059814453125,
0.02648925... | 11,882 | 11882 | |
Graphs of Hyperbolic Functions
The graphs and properties such as domain, range and asymptotes of the 6 hyperbolic functions: sinh(x), cosh(x), tanh(x), coth(x), sech(x) and csch(x) are explored using an applet. The six hyperbolic
fun... | 4 | [
-0.000492095947265625,
0.00799560546875,
-0.006378173828125,
-0.048095703125,
0.025146484375,
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-0.006072998046875,
0.0634765625,
-0.068359375,
-0.04760742187... | 11,883 | 11883 | |
Least-squares fitting of data
This applet determines a linear or polynomial function that is least-squares fitted to a discrete set of data points. Functions of one variable, Y(x), can be plotted. Such functions are: linear of
degree... | 4 | [
-0.02587890625,
0.005401611328125,
0.00384521484375,
-0.03564453125,
0.029296875,
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-0.022216796875,
-0.03271484375,
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-0.016357421875... | 11,884 | 11884 | |
parabolic equation
parabolic equation, any of a class of partial differential equations arising in the mathematical analysis of diffusion phenomena, as in the heating of a slab. The simplest such equation in one
dimension, u[xx] = u[t], governs the temperature distribution at the various points along a thin rod from mo... | 4 | [
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Short Comings of the Planetary Spin-Orbit Coupling Model
SIMPLE TIDAL TORQUING MODEL
(UPDATED 20/03/2012)
... | 4 | [
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Fundamentals of Physics, Part 3
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Overview
This 8th edition of Fundamentals of Physics inc... | 5 | [
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Determining homotopy classes [T^2, RP^2]
up vote 9 down vote favorite
6
So I've been interested in computing homotopy classes of maps $T^2=S^1\times S^1$ to $\mathbb{R}\mathbb{P}^2$. So first, we can decompose $T^2$ into a cell complex with one zero cell, $S^1\vee S^1$
and a disc $D^2$ glued down to $S^1\vee S^1$ usi... | 4 | [
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Another Isosceles Triangle
Date: 10/27/1999 at 02:49:07
From: Imaad Dalal
Subject: Geometry
A triangle has sides of length 29, 29, and 40 cm. Find another
isosceles triangle with the same perimeter and area that also has
sides of integral length.
I tried creating a pair of simultaneous equations but that did not
wo... | 4 | [
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Why Does Cross Multiplication Work?
Date: 05/09/2002 at 18:27:43
From: Kimberly Geisler
Subject: Why does cross multiplication work?
I am a sixth grade teacher in PA. We just started working on
proportions in math and a few students want to know why we cross
multiply to solve a proportion like:
3/15 = n/30
where ... | 4 | [
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How does the Death Star Deal with all of its Surplus Heat?
While I can't say why I'm on his bent of posting about thermally related posts something that has bounced around in my brain for a while, is how can the death star manage to not liquefy itself when
it fires its super laser.
For background, according to some ca... | 4 | [
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.
6. DISSIPATIONLESS GALAXY FORMATION
6.1. Dissipationless collapse and violent relaxation
Several authors (Sandage, Freeman and Stokes, 1970; Gott and Thuan, 1976) have discussed the possibility that the key process in determining whether a protogalactic cloud becomes an elliptical or
spiral galaxy is the amount of... | 4 | [
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Best possible sieves for the jacobsthal problem, linear programming, and the prime 2
up vote 7 down vote favorite
Background/Motivation
Gerhard Paseman asked a question about bounds on the Jacobsthal function a while ago, which made me curious about whether the known bounds are best possible. Briefly, the Jacobsthal ... | 4 | [
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chemistry (NEED HELP)
Posted by Jessie on Tuesday, April 19, 2011 at 8:35pm.
In a series of decays (hypothetical), the nuclide Ra-227 beomes Pb-203. How many alphas and how many betas are emitted in this series? Give two answers: first, give the number of alpha decays; then,
the number of beta decays.
I know that the... | 4 | [
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Tangent to the Curve
November 12th 2010, 03:21 PM #1
MHF Contributor
Joined
Mar 2010
From
Florida
Posts
3,093
Thanks
5
Tangent to the Curve
Greetings,
This should be a relatively easy question, but, unfortunately, I am struggling with solving it. I understand the forum is used purely for gui... | 5 | [
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free monad
Context
Higher algebra
Algebraic theories
Algebras and modules
Higher algebras
Model category presentations
Geometry on formal duals of algebras
Theorems
Free monads
Definition
A free monad is a free object relative to a forgetful functor whose domain is a category of monads.
This general concept ... | 4 | [
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Economics: Cost & Revenue - Problem 1
Brightstorm is like having a personal tutor for every subject
See what all the buzz is about
Check it out
Economics: Cost & Revenue - Problem 1 3,175 views
As we will see later, derivatives can have economic applications. But first, we must learn the terminology used when discu... | 4 | [
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Homework Help
Posted by Anonymous on Friday, March 15, 2013 at 5:45pm.
Given the following quadratic equation find.
a) the vertex
b) the axis of symmetry
c) the intercepts
d) the domain
e) the range
f) the interval where the function is increasing
g) the interval where the function is decreasing
h) graph the f... | 4 | [
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Parabolic Bridges
From Math Images
Real Life Parabolas
Field: Algebra
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