content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Cramped versus Uncramped Thermodynamics
18 Cramped versus Uncramped Thermodynamics
18.1 Overview
In this chapter we consider some basic questions about what can be done with thermodynamics. These include:
• Is it possible to define a nontrivial quantitative notion of “heat content” or “thermal energy content” ... | 4 | [
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0.0395507812... | 13,100 | 13100 | |
s P
The Josephus Problem
1. In Massada, in ancient Greece, it was decided that there were too many prisoners and many should be executed. One prisoner was given a sword and all 1000 prisoners were instructed to stand in a
circle... | 4 | [
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Rolling a random walk on a sphere
up vote 36 down vote favorite
10
A ball rolls down an inclined plane, encountering horizontal obstacles, at which it rolls left/right with equal probability. There are regularly spaced staggered gaps that let the ball roll down to
the next, lower obstacle. The pattern resembles a bina... | 5 | [
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Numbers with Large Exponents
Date: 08/22/2001 at 21:11:30
From: T
Subject: Large exponential numbers
I have not been able to figure this out. The problem is:
How many zeros end the number 2^300 * 5^600 * 4^400 ?
I was thinking of the end patterns of the numbers but I could not put
anything together.
Much appreci... | 4 | [
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How quickly is $n\pi$ getting close to integers
up vote 0 down vote favorite
Is there an understandable function $A(\epsilon)$ such that if $q < A(\epsilon)$ then $| q\pi - p| > \epsilon$ for all $p$?
I want to know how quickly $n\pi$ is getting close to integers, e.g., if $n\pi$ is within 0.0001 of an integer then $... | 5 | [
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The Lebesgue differentiation theorem and the Szemeredi regularity lemma
This post is a sequel of sorts to my earlier post on hard and soft analysis, and the finite convergence principle. Here, I want to discuss a well-known theorem in infinitary soft analysis – the
Lebesgue differentiation theorem – and whether there i... | 4 | [
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Bessel Functions
Essentials of Bessel Functions
These very useful special functions are good friends in many investigations
Professor Relton wrote a pleasant short book on Bessel functions (see Reference) that is a model of how to present mathematical results for the practical user, combining gentleness with rigour. ... | 4 | [
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Collected Lambda
Collected Lambda Calculus Functions
The following is a small collection of functions in the untyped lambda calculus which I feel are noteworthy for one reason or another, either by relevance to the foundations of lambda calculus (such
as the combinators and natural numbers) or by utility to people who... | 4 | [
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Ping Pong and Free Group Factors
up vote 7 down vote favorite
1
This question concerns alternative characterizations of free group factors. The ping pong lemma is a well-known criteria for the freeness of a group. I've often wondered if there is a ping pong like
criterion that can be used to determine if a given type ... | 5 | [
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nrich.maths.org
Copyright © University of Cambridge. All rights reserved.
Four people cracked this one: Bella and Andaleeb from Woodhouse Sixth Form College, Sue from Madras College and Alexander from Shevah-Mofet School.
Bella started her answer by trial and error for different triangles
For the triangle of side c ... | 4 | [
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Geodesic path on the unit sphere with the sup norm
up vote 7 down vote favorite
4
Let $X$ be the unit sphere of $\mathbb{R}^n$ with the sup norm, i.e. $X=\{x\in\mathbb{R}^n: \|x\|_{\infty}=1\}$. Let the metric $d$ on $X$ be the geodesic metric induced by the sup norm, i.e for any
two points $x,y\in X$, $$d(x,y)=\inf \... | 4 | [
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Turing-complete primitive blind automata
up vote 3 down vote favorite
2
Let $N$ be the set of natural numbers, $S$ be the set of finite binary sequences, and
$Q = [N \rightarrow N] \times [N \rightarrow N],$
where $[N \rightarrow N]$ is the set of all computable functions on natural numbers.
Then, let us consider t... | 4 | [
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homotopy coherent nerve
Context
$(\infty,1)$-Category theory
Background
Basic concepts
Universal constructions
Local presentation
Theorems
Models
Contents
Idea
The homotopy coherent nerve (also called simplicial nerve) of a simplicially enriched category is a simplicial set which includes information about al... | 4 | [
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Three-Phase
Three-phase AC is not hard to understand if you use a phasor diagram
Most alternating-current (AC) generation and transmission, and a good part of use, take place through three-phase circuits. If you want to understand electric power, you must know something about
three-phase. It is rather simple if you g... | 4 | [
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FFT returning values in wrong order
10-24-2007 #1
FFT returning values in wrong order
Well, you could count this as a continuation of my thread on the GD board, but now my question is MUCH more C# specific, and therefore I decided to go ahead and post it here.
I am nearly done with the program now...I only h... | 4 | [
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19.5 Integration by Parts
Home | 18.013A | Chapter 19 Tools Glossary Index Up Previous Next
19.5 Integration by Parts
The second useful tool is the backward version of the product rule. The product rule, as we have noted often, tells us
This means that if we seek an anti-derivative of h(x) and we can write h as f... | 5 | [
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Capacitance
What's a capacitor?
A capacitor is a component designed to create and hold an electric field, which means that capacitors can store energy . It takes energy to pull electric charges apart and so establish an electric
field between the separated charges. With the charges held apart, the energy is stored in ... | 4 | [
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strict localization
nLab
strict localization
Given a class $W$ of arrows in a category, the localization $Q_W: C\to C[W^{-1}]$ (if it exists) inverts all the arrows in $W$, i.e. $Q_W(w)$ is an isomorphism in $C[W^{-1}]$ and is universal with
respect to all functors with such a property. The universality makes it a 2-c... | 4 | [
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10.8.2 Wall Functions
Wall functions are a collection of semi-empirical formulas and functions that in effect ``bridge'' or ``link'' the solution variables at the near-wall cells and the corresponding quantities on the
wall. The wall functions comprise
• laws-of-the-wall for mean velocity and temperature (or other s... | 4 | [
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Canceling Interferences for High Data Rate Time Reversal MIMO UWB System: A Precoding Approach
An ultra-high data rate time reversal (TR) multiple-input multiple-output (MIMO) ultra-wideband (UWB) communication system with space-time precoding is proposed. When the symbol duration is set to
approach the duration of UWB... | 4 | [
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Linear dependence and independence.
We consider a vector space V and a set I (this will be a set of indices, generally of the form , but not necessarily).
Definition 5.2.1 A family
of vectors in V is linearly independent if, for any scalars , we have:
If I is a finite set, e.g. , we can write Eq. 7 as follows:
E... | 4 | [
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Octahedron
Talk0
871pages on
this wiki
An octahedron (plural: octahedra) is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.
The octahedron's symmetry group is O[h], of order 48. This group's subgroups include D[3d] (... | 4 | [
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Math Forum Discussions
fom
Posts: 1,968
Registered: 12/4/12
Re: Can addition be defined in terms of multiplication?
Posted: Aug 16, 2013 9:21 PM
On 8/16/2013 7:05 PM, Jim Burns wrote:
> On 8/16/2013 4:54 AM, Peter Percival wrote:
>> Can addition be defined in terms of multiplication? I.e.,
>> is there a formula in th... | 4 | [
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Dividing Square Roots
5.6: Dividing Square Roots
Difficulty Level: At Grade Created by: CK-12
Practice Multiplication and Division of Radicals
The area of a rectangle is $\sqrt{30}$$\sqrt{20}$
Watch This
Watch the first part of this video, until about 3:15.
Khan Academy: How to Rationalize a Denominator
Guidance... | 4 | [
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How to convert dBm to dBi
1. 24th November 2008, 08:54 #1
Member level 3
Join Date
Nov 2008
Posts
57
Helped
0 / 0
Points
1,142
Level
7
dbi to dbm
Hi ,
I have a doubt. Please help me.
Actually, I am testing an patch antenn... | 5 | [
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synthetic differential infinity-groupoid
Context
Cohesive $\infty$-Toposes
Backround
Definition
Presentation over a site
Structures in a cohesive $(\infty,1)$-topos
structures in a cohesive (∞,1)-topos
Structures with infinitesimal cohesion
infinitesimal cohesion?
Models
Differential geometry
$\infty$-Lie th... | 4 | [
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Patent US20040174284 - Method and apparatus for the recovery of signals acquired by an interleaved system of digitizers with mismatching frequency response characteristics
BACKGROUND OF THE INVENTION
[0001] The present invention relates generally to the operation of measurement instruments. More specifically, the inve... | 4 | [
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FOMODEL2: First order languages: syntax, part two; semantics
:: First order languages: syntax, part two; semantics
:: by Marco B. Caminati
::
:: Received December 29, 2010
:: Copyright (c) 2010-2013 Association of Mizar Users
Lm1: for S being Language
for U being non empty set
for f being Interpreter ... | 4 | [
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Find All Pairs of Integer Solutions to a^(2b) = b^a
Date: 02/18/2005 at 18:58:31
From: Jason
Subject: Powers of Powers
Investigate pairs of positive integers (a,b) that satisfy the equation
a^(2b) = b^a.
I do not really know where to start, to be honest! I have tried lots
of different values for a and b but have ye... | 5 | [
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0.055908203125,
0.038818359375,
0.11376953125,
0.1708984375,
-0.057373046875,
0.01336... | 13,128 | 13128 | |
Incircles Explained
Copyright © University of Cambridge. All rights reserved.
The largest circle which fits inside a triangle just touching the three sides of the triangle is called the inscribed circle or incircle. This article is about triangles in which the lengths of the
sides and the radii of the inscribed circle... | 5 | [
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0.1083984375,
-0.037353515625,
-0.036376953125,
0.036865234... | 13,129 | 13129 | |
How to: Use Constrained Non-Linear Programming Using the Nelder-Mead Solver
You can use the Nelder-Mead solver (NelderMeadSolver) for some types of constrained non-linear programming. For example, the Nelder-Mead solver can find the local optimum of a general variable
constrained objective function.
One example of th... | 5 | [
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0.05859375,
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0.072265625,
0.03369140625,
-0.03881835... | 13,130 | 13130 | |
algebraic de rham cohomology of a curve
up vote 5 down vote favorite
1
Let $X$ be a smooth projective curve over a field $k$ of characteristic zero. The algebraic de Rham cohomology of $X$ is, by definition, the hypercohomology of the complex of Kähler differentials for
the Zariski topology:
$H^k_{DR}(X)=\mathbb{H}(X... | 4 | [
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-0.045166015625,
0.0118408203125,
0.0615234375,
-0.06640625,
-0.038574... | 13,131 | 13131 | |
The pushout product as an operation
up vote 5 down vote favorite
1
Motivation: In his utterly famous paper, Rezk (here, (pag. 7)) defines a structure called "Quillen ring". I'm wearing my algebraist's hat today, so I was wondering if this definition is chosen to
suggest that somewhere a "true" ring structure is hidden... | 4 | [
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0.081... | 13,132 | 13132 | |
Adventure Games, Permutations Groups, and Spreadsheets
Adventure Games, Permutations, and Spreadsheets
Paul Vodola (PVodola@CAIS.com). Paul Vodola is a Program Scientist and Assistant Program Manager at Systems Planning and Analysis, Inc. in Alexandria, Virginia. He received a Ph.D. in Mathematics at
the University of... | 5 | [
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0.009887695... | 13,133 | 13133 | |
Oscillating reactions and chemical waves by G. Dupuis and N. Berland - Lycée Faidherbe
┌──┬──────────────────────────────────────────┐
│ │ Oscillating reactions - Ch... | 4 | [
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0.00... | 13,134 | 13134 | |
structure of norm one group for quadratic extension of p-adic fields
up vote 4 down vote favorite
Let $F$ be a p-adic field (finite extensions of $\mathbb{Q}_p$ for some prime $p$), and $E/F$ be a quadratic extension. Use $\sigma$ to denote the nontrivial element in the Galois group $Gal(E/F)$.
For any $x\in E$, $N(x)... | 4 | [
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0.042724609375,
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Non-Linear Models in Statsmodels
This blog post is concerned with the milestones achieved and some upcoming features in statsmodels
NONLINEAR MODELS
The model implemented is
y = f(x,θ) + e
where the y is one dimensional endogenous data matrix, f is the nonlinear function, x is exogenous data matrix, θ is parameter... | 4 | [
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Posts about seam carving on Math ∩ Programming
The Problem with Cropping
Every programmer or graphic designer with some web development experience can attest to the fact that finding good images that have an exactly specified size is a pain. Since the dimensions of the
sought picture are usually inflexible, an uncomfo... | 4 | [
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... | 13,137 | 13137 | |
derivation on a group
[For convenience we assume below that is a -module, it does not in general have to be abelian and it suffices to have it a -group.]
Suppose $G$ is a group and $M$ a $G$-module and let $\delta : G \to M$ be a derivation. This means $\delta(g_1g_2) = \delta(g_1) +g_1\delta(g_2)$ for all $g_1, g_2 \... | 5 | [
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0.00994873046875,
0.1... | 13,138 | 13138 | |
simple function
Simple functions
Idea
Simple functions are (almost) the most basic notion of measurable function in measure theory. Given a measure, it's easy to define the integral of a simple function, and we extend this to more
general functions by continuity.
Definitions
Let $X$ be a measurable space. We may wa... | 4 | [
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0.0... | 13,139 | 13139 | |
Introducution to Algebraic Numbers and Integers
Date: 04/15/2008 at 23:57:56
From: Sujeet
Subject: A different way of classifying Complex Numbers
While researching the classification of Complex numbers on the
internet, I came across the following classification -
[1]. Complex numbers contain -
a. algebraic number... | 4 | [
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-0.0... | 13,140 | 13140 | |
Diagonalizing a Certain Real and Symmetric Toeplitz Matrix
up vote 11 down vote favorite
8
Consider $0\leq \alpha\leq 1$, and let $A_{\alpha}$ be the Toeplitz $n\times n$ matrix given by $$ A_\alpha := \begin{bmatrix} 1 & \alpha & \alpha^2 & \ldots &\alpha^{n-1} \\\ \alpha & 1 & \alpha & \
ddots & \vdots \\\ \alpha^2 ... | 5 | [
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-0.02722167968... | 13,141 | 13141 | |
Treatise On Analysis Vol-Ii
7 ALGEBRAIC PROPERTIES OF CONVOLUTION 275
Let St = Supp(jUj), and suppose that St is compact except possibly for one
index j. Let/6 3CC(G) and let K be the compact support of/. It is enough to
show that the set of points (xl9..., xn) e Gn which belong to the support
n
Y[ S,- of fa... | 4 | [
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T
2. THE PLANCK TIME
The Planck time in cosmology is certainly the most challenging epoch to study, as the framework in which it must be described is still lacking. Though there are several different approaches to this
problem, I will limit myself to that of string/M-theory [5].
Much of the work on string cosmology ... | 4 | [
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0.0615234375,
-0.109375,
-0.... | 13,143 | 13143 | |
maximal element
nLab
maximal element
Maximal elements
Idea
An element of a poset (or proset) is maximal if no other (inequivalent) element is greater. A maximum must be maximal, and a maximal element of a toset must be a maximum. However, it’s easy to find
posets with maximal elements that aren't maxima, or even wit... | 4 | [
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0.0625,
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0.0291748046875,
0.05615234375,
0.033203125,
0.1015625,
0.013916015625,
-0.04809570... | 13,144 | 13144 | |
Physics Archive | October 12, 2008 | Chegg.com
Physics Archive: Questions from October 12, 2008
• Anonymous asked
1 answer
• Anonymous asked
1 answer
• Anonymous asked
2 answers
• sherlock3 asked
1 answer
• AncientRhino2088 asked
1 answer
• stinkypoodagnle asked
0 answers... | 4 | [
-0.03173828125,
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0.03662109375,
0.00060272216796875,
0.008666992... | 13,145 | 13145 | |
dy
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zhiyuan3yu5 Group Title
A particle is movi... | 4 | [
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0.019775390625,
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0.0... | 13,146 | 13146 | |
Sending Surface Waves Along Coaxial Cables, Part 1
Part 1 of this three-part series introduces the concept of surface waves and high-frequency, low-loss propagation along the surface of a single-conductor or high-impedance coaxial line.
Coaxial cables had once been thought to support only a single transverse-electroma... | 4 | [
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0.009765625,
-0.005523681640625,
-0.066894... | 13,147 | 13147 | |
Least squares fitting (linear/nonlinear)
Least squares method is usually mentioned in two contexts. First, its application is widely known in regression analysis. It is used to construct models on the basis of noisy experimental data. At
that, besides constructing a model, it usually performed an estimate of the error... | 4 | [
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0.0478515625,
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0.0257568359375,
0.0615234375,
0.04248046875,
-0.0003795623779296875,
-0.07177734375,
0.00121307373046875,
0.004119873046... | 13,148 | 13148 | |
fiber integration in ordinary differential cohomology
Context
Differential cohomology
Ingredients
Connections on bundles
Higher abelian differential cohomology
Higher nonabelian differential cohomology
Fiber integration
Application to gauge theory
Integration theory
Analytic integration
Cohomological integrat... | 4 | [
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-0.006195068359375,
-0.0208740234375,
0.01... | 13,149 | 13149 | |
Annotated
Annotated SPSS Output
Probit Regression
This page shows an example of probit regression analysis with footnotes explaining the output in SPSS. The data in this example were gathered on undergraduates applying to graduate school and
includes undergraduate GPAs, the reputation of the school of the undergradua... | 4 | [
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0.0751953125,
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0.040283203125,
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0.0556640625,
-0.00860595703125,
0.0150146484375,
-0.016845703125,
0.07275390625,
-0.1396484... | 13,150 | 13150 | |
Magnetism: quantities, units and relationships
If you occasionally need to design a wound component, but do not deal with the science of magnetic fields on a daily basis, then you may become confused about what the many terms used in the data
sheet for the core represent, how they are related and how you can use them ... | 4 | [
-0.06103515625,
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0.06591796875,
0.00830078125,
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0.01202392578125,
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0.10302734375,
0.02685546875,
-0.056396484375,
0.009033203125,
-0.0546875,
0.065... | 13,151 | 13151 | |
regular space
Regular spaces
Idea
A regular space is a topological space (or variation) that has, in a certain sense, enough regular open subsets. The condition of regularity is one the separation axioms satsified by every metric
space (in this case, by every pseudometric space).
Definitions
Fix a topological space... | 4 | [
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-0.06689453125,
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0.0126953125,
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-0.029541015625,
-0.003173828125,
-0.00299072265625,
0.052001953125,
-0.06640625,
0.002044677734375,
-0.0380... | 13,152 | 13152 | |
Permutations - Concept
Brightstorm is like having a personal tutor for every subject
See what all the buzz is about
Check it out
Permutations - Concept 20,561 views
In statistics, in order to find the number of possible arrangements of a set of objects, we use a concept called permutations. There are methods for ca... | 4 | [
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0.0225... | 13,153 | 13153 | |
MOND
7. MOND AS MODIFIED INERTIA
Most people seem to prefer modifying gravity to modifying inertia; perhaps because the latter seems to be less drastic; perhaps because it is a game that has been much played before. I personally
feel, without concrete evidence, that there is more potential in modified inertia as the ... | 4 | [
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0.057373046... | 13,154 | 13154 | |
Derivations of Pi and a Polygon of Degree n
Date: 4 Mar 1995 18:05:14 -0500
From: MRS MAUREEN C HAMILTON
Subject: area of a polygon of degree n
I am curious about the derivation of pi. I figured out it
was probably derived by computing the limit of the area of a
polygon of degree n as n approaches infinity. For th... | 4 | [
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0.046875,
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0.004119873046875,
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-0.012... | 13,155 | 13155 | |
es
#include <boost/math/special_functions/beta.hpp>
namespace boost{ namespace math{
template <class T1, class T2, class T3>
calculated-result-type ibeta_inv(T1 a, T2 b, T3 p);
template <class T1, class T2, class T3, class Policy>
calculated-result-type ibeta_inv(T1 a, T2 b, T3 p, const Policy&);
template <class T1... | 4 | [
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-0.060546875,
0.0... | 13,156 | 13156 | |
reduced suspension
nLab
reduced suspension
Context
Homotopy theory
Background
Variations
Definitions
Paths and cylinders
Homotopy groups
Theorems
Reduced suspension
Idea
If we take a pointed space $(X,x_0)$, then its reduced suspension $\Sigma X$ is obtained by taking the cylinder $I\times X$ and identifying... | 4 | [
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0.126953125,
0.02294921875,
-0.00433349609375,
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0.036376953125,
0.00970458984375,
-0.04296875,
-0.006011962890625,
-0.06396484375,
0.... | 13,157 | 13157 | |
A graphic explanation of the Bayes
I enjoyed how the 3.16 section of the Stanford Artificial Intelligence class presented the Bayes theorem. Instead of giving a formula and expecting the alumni to apply it, they gave us a problem that
the Bayes theorem would solve and expected, I believe, that we figured it out oursel... | 4 | [
-0.0244140625,
0.07421875,
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0.045166015625,
-0.042724609375,
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-... | 13,158 | 13158 | |
Uniqueness of super godel numbers of $\varphi$ and $\neg \varphi$
up vote 2 down vote favorite
Let $e_{0},e_{1},...,e_{n}$ be a sequence of wffs or other expressions. Code each $e_{i}$ by a regular godel number $g_{i}$, to yield a sequence of numbers $g_{0},g_{1},...,g_{n}$. Then encode this
sequence of regular godel ... | 5 | [
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Damn Cool Algorithms: Homomorphic Hashing
Posted by Nick Johnson | Filed under homomorphic-hashing, damn-cool-algorithms, fountain-codes
In the last Damn Cool Algorithms post, we learned about Fountain Codes, a clever probabilistic algorithm that allows you break a large file up into a virtually infinite number of sm... | 4 | [
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0.036865234375,
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unit
For special kinds of units see also unit of an adjunction and unit of a monad. Different (but related) is physical unit.
Units
Idea
A unit is a quantity $u$ such that every other quantity (of a certain type) is a multiple (in a certain sense) of $u$.
Definitions
Exactly what this means depends on context.... | 4 | [
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... | 13,161 | 13161 | |
Special Killing Vector Fields
up vote 4 down vote favorite
1
Consider $(M^{n},g)$ to be a Riemannian manifold and suppose that $X$ is a smooth non-trivial Killing vector field on $M$. Away from the zeros of $X$ we have a natural distribution $D$ of $(n-1)
$-planes defined so that $D_p$ is orthogonal to $X_p$. If the d... | 4 | [
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-0.048583984375,
0.0263671875,
0.0224609375,
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Division by zero
Name: chris j stella
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: N/A
Question: What happens when you divide a number by 0? (9/0). Do you get infinity, or just a null-set... | 4 | [
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On a difference scheme of second order of accuracy for the Bitsadze-Samarskii type nonlocal boundary-value problem
Abstract
In this study, the Bitsadze-Samarskii type nonlocal boundary-value problem with integral condition for an elliptic differential equation in a Hilbert space H with self-adjoint positive definite
o... | 5 | [
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-0.011474609375,
-0.... | 13,164 | 13164 | |
Predicting Your Firm's Future with Least Squares, Part II
Linear least squares lets you find the line that best fits a set of data points but sometimes the points don't lie along a line. The second part of this two-part article explains how you can use
polynomial least squares to find curves that fit your data. As the
... | 4 | [
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0.06494140625,
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-0.037353515625,... | 13,165 | 13165 | |
20 Degree Isosceles Triangle
Problem: 20 Degree Isosceles Triangle
Given the isosceles triangle below with AC = BC, angle C = 20 degrees, angle ABD = 60 degrees and angle BAE = 50 degrees, determine the measure of angle EDB.
Solution 1
The first thing I will do is draw segment DG parallel to AB. Then construct segm... | 4 | [
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0.019... | 13,166 | 13166 | |
The
In order to explain why the numbers are suggesting that it is better to switch, it's necessary to describe how the game is played. If you have never seen Monty Hall's Let's Make A Deal game show,
then let me catch you up to speed.
Let's Make A Deal
I can only assume Monty Hall's game show Let's Make A Deal took ... | 4 | [
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Concavity and Inflection Points - Problem 1
Brightstorm is like having a personal tutor for every subject
See what all the buzz is about
Check it out
Concavity and Inflection Points - Problem 1 5,878 views
Find the second derivative of the function (do this by calculating the first derivative, then calculating the ... | 4 | [
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-0.0184326171... | 13,168 | 13168 | |
Differentiation problems (please solve with steps)
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,401
Re: Differentiation problems (please solve with steps)
Omar Desoky
Guest
Re: Differentiation problems (please solve with steps)
All is ok for me no problem about the final resu... | 5 | [
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0.03979... | 13,169 | 13169 | |
Math Forum Discussions
Math Forum
Ask Dr. Math
Discussions
Internet Newsletter
MathTools
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Teacher Exchange
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Search All of the Math Forum:
Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.
Topic: Operations with algebraic fractions assistance ple... | 4 | [
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-0.009521484375... | 13,170 | 13170 | |
homotopy dimension
Context
$(\infty,1)$-Topos Theory
Background
Definitions
Characterization
Morphisms
Extra stuff, structure and property
Models
Constructions
structures in a cohesive (∞,1)-topos
Contents
Definition
This appears as HTT, def. 7.2.1.1.
Definition
An (∞,1)-topos $\mathcal{X}$ is locally of ... | 4 | [
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0.01953125,
... | 13,171 | 13171 | |
Position From Depth 3: Back In The Habit
A friend of mine once told me that you could use “back in the habit” as the subtitle for any movie sequel. I think it works.
So a lot of people still have trouble with reconstructing position from depth thing, judging by the emails I get and also the threads I see in the gamed... | 4 | [
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0.119... | 13,172 | 13172 | |
sigma-model -- exposition of classical sigma-models
Context
Quantum field theory
Phyiscs
$\infty$-Chern-Simons theory
Ingredients
Definition
Examples
This is a subentry of sigma-model. See there for background and context.
Contents
Exposition of classical $\sigma$-models
We survey, starting from the very ... | 4 | [
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-0.03173828125,
-0.000926971435546875,
-0.05004882812... | 13,173 | 13173 | |
Physics Archive | October 13, 2008 | Chegg.com
Physics Archive: Questions from October 13, 2008
• Anonymous asked
1 answer
• shwanky asked
1 answer
• Anonymous asked
=1.79 A. The figure below is an endview of the c... Show more
Three long, parallel conductors carry currents of
I... | 5 | [
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-0.08837890625,... | 13,174 | 13174 | |
Completing the Square: Alternate Method
Date: 02/06/98 at 12:30:16
From: Han-Han Wang
Subject: New method for solving by completing the square
I have come up with a new method for solving quadratic equations by
ccompleting the square. Instead of dividing by the coefficient of the
quadratic term (and getting complica... | 4 | [
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0.0029449462890625,
0.083984375,
... | 13,175 | 13175 | |
cyclic polynomials and their solutions
up vote 4 down vote favorite
I'll call a polynomial in $z_1,..,z_N$ cyclic if it is invariant under cyclic permutation of the indices. I hope that's standard terminology.
I have N complex numbers $(z_1,...,z_N)$. I want to be able to compute what they are up to cyclic permutatio... | 4 | [
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... | 13,176 | 13176 | |
Statistics and the Treatment of Experimental Data
2.2 The Poisson Distribution
The Poisson distribution occurs as the limiting form of the binomial distribution when the probability p -> 0 and the number of trials N -> µ = Np, remains finite. The probability of observing r
events in this limit then reduces to
(16)
L... | 4 | [
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-0.05419921875,
0.002655029296875,
-0.0859... | 13,177 | 13177 | |
Writing Equations for Word Problems
Date: 09/01/98 at 18:25:24
From: Tigger
Subject: Writing Equations for Word Problems
In Algebra 1 we need to write equations for these word problems and
then solve them:
1. An oil painting is 16 years older than a watercolor by the same
artist. The oil painting is also three t... | 4 | [
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... | 13,178 | 13178 | |
[Lowerbounds, Upperbounds]
On Geomblog, Piotr mentioned a problem that I think many of us can share: if we really have to pick just one to teach (as in his case), do we go with 2-4 trees or red-black trees?
For the most part, the pros and cons of the two approaches are quite, urr, balanced.
There is a fascinating ... | 4 | [
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-0.049560546875,
0.0791... | 13,179 | 13179 | |
Last One Standing
Copyright © University of Cambridge. All rights reserved.
'Last One Standing' printed from http://nrich.maths.org/
Many wonderful solutions have been received and here are a few selected ones. Enjoy!
Anon from Horrington Primary experimented with the simulator and arrived at an answer:
The mean a... | 5 | [
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0.004150390625,
0.052734375,
-0.07958984375,
-0.043701171875,
0.013427734375,
-0.0869140625,
0.024... | 13,180 | 13180 | |
Beam Pointing Direction of Traveling-Wave Arrays
A series of curves for dielectric-filled waveguide arrays illustrate how the beam direction is dependent on various array parameters. Example problems consider the various tradeoffs available.
Appendix
Download this article in .PDF format
This file type includes high... | 4 | [
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-0.07568359375,
0.04931640625,
0.0166015625,
-0.08642578125,
-0.084472... | 13,181 | 13181 | |
Find the Function (fog)(x)
Date: 07/02/2003 at 19:44:55
From: Pamela
Subject: Functions
Let f(x) = 2x-1 and g(x) = (x+5)/2. Find the function (fog)(x).
Simplify your answer.
g(x) = (x+5)/2
= 2[(x+5)/2]-1
= x+5-1
= x+4
Date: 07/03/2003 at 11:02:27
From: Doctor Mike
Subject: Re: Functions
... | 4 | [
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indecomposable object
Context
Category theory
Concepts
Universal constructions
Theorems
Extensions
Applications
Topos Theory
Could not include topos theory - contents
Indecomposable objects
Definition
An object $X$ of a category $C$ is indecomposable if it cannot be expressed as a non-trivial coproduct of ob... | 5 | [
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0.08984375,
... | 13,183 | 13183 | |
Need Help!!
i have a problem with this maths question: How many squares are on a chess board, including 2 x 2 squares etc. can anyone help??????
1x1 squares : 8x8 =64 2x2 squares : 8x8 - 15 = 49 3x3 squares : 8x8 - 15 - 13 = 36 ... 8x8 squares : 8x8 - 15 - 13 - ... = 1 The number os positions for 1x1 squares is 64 All... | 4 | [
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0.01684570312... | 13,184 | 13184 | |
problem
November 12th, #4
2012, 07:27 PM
Math Team Re: Ladder sliding down wall problem (Implicit Diff)
... | 5 | [
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-0.0649414062... | 13,185 | 13185 | |
A Bayesian model for gene family evolution
Abstract
Background
A birth and death process is frequently used for modeling the size of a gene family that may vary along the branches of a phylogenetic tree. Under the birth and death model, maximum likelihood
methods have been developed to estimate the birth and death ra... | 4 | [
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0.00622558593... | 13,186 | 13186 | |
The Erdos-Mordell Theorem
Date: 10/13/2000 at 14:33:11
From: Rayna Zacks
Subject: Related to Fermat Point in Triangle
Let P be a point in a triangle. Let D be the sum of the distances from
P to the 3 vertices, and let E be the sum of the shortest distances
from P to the edges (trilinear coordinates of P). Prove that... | 4 | [
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-0.004730224609375,
0.015441894531... | 13,187 | 13187 | |
What's new
You are currently browsing the tag archive for the ‘van der Corput lemma’ tag.
The following result is due independently to Furstenberg and to Sarkozy:
Theorem 1 (Furstenberg-Sarkozy theorem) Let ${\delta > 0}$, and suppose that ${N}$ is sufficiently large depending on ${\delta}$. Then every subset ${A... | 4 | [
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Distributing points with respect to a concave function
up vote 5 down vote favorite
2
Suppose I have a concave function defined on the unit interval such that $f(0) = f(1) = 0$ and $\int_0^1 f(t) dt = \alpha$, where $\alpha$ is "small" (say $0.01$ or thereabouts). Say I distribute $n$
points $x_1,\dots,x_n$ on the uni... | 5 | [
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-0.03173828... | 13,189 | 13189 | |
A038458 - OEIS
A038458 Consider the equation q^x-p^x=1 where p,q are successive primes; solve for x; the smallest such x is 0.567148... which occurs when p=113, q=127. Sequence gives decimal expansion of this 5
value of x. Sometimes called the Smarandache constant.
5, 6, 7, 1, 4, 8, 1, 3, 0, 2, 0, 2, 0, 1... | 5 | [
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Expansion
Sizing Expansion
Sizing the Expansion Tank
In closed loop systems, expansion tanks must be appropriately sized for the system to operate properly. For expansion tanks the acceptance volume must be sufficient to accommodate expansion of the
heat transfer fluid when the solar loop goes into stagnation. Prov... | 5 | [
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0.00007581710815429688,
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Mathematical formulation of quantum mechanics
One of the remarkable facts of
quantum mechanics
in its current formulations is its abstractness. Prior to the emergence of quantum mechanics as a separate
theory
, the mathematics used in physics consisted mainly of
differential geometry
and
partial differential eq... | 4 | [
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. C
2. COSMOLOGY WITH A COSMOLOGICAL CONSTANT
2.1 Cosmological parameters
From the Friedmann equation (5) (where henceforth we take the effects of a cosmological constant into account by including the vacuum energy density [] into the total density H there is a critical
value of the energy density such that the spat... | 4 | [
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-0.... | 13,193 | 13193 | |
ib
#include <boost/math/distributions/inverse_chi_squared.hpp>
namespace boost{ namespace math{
template <class RealType = double,
class Policy = policies::policy<> >
class inverse_chi_squared_distribution
{
public:
typedef RealType value_type;
typedef Policy policy_type;
inverse_chi_squared_d... | 4 | [
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Polynomial function from $S^3$ to $S^3$ and quaternions
up vote 9 down vote favorite
I am searching the polynomial functions from $S^3$ to $S^3$.
($S^3$ is the set of vectors $x$ in $\mathbb{R}^4$ such that $\|x\|=1$)
We say $g$ is a polynomial function from $S^3$ to $S^3$, if there exists $f_1,f_2,f_3,f_4 \in \math... | 4 | [
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0.048583984375,
-0.0498046875,... | 13,195 | 13195 | |
Probability that a word in the free group becomes (much) shorter?
up vote 12 down vote favorite
3
Let $w$ be a word of length $2\ell$ chosen at random on the alphabet $\{x_1,x_1^{-1},x_2,x_2^{-1},\dotsc,x_k,x_k^{-1}\}$. By the reduction $\rho(w)$ I mean what you obtain by deleting substrings of
the form $x_i x_i^{-1}$... | 5 | [
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-0... | 13,196 | 13196 | |
PCMI@MathForum: Circle Packing: A Directed Investigation of Descartes' Circle Theorem
Circle Packing: A Directed Investigation
of Descartes' Circle Theorem
... | 5 | [
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dy
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Here's the question you clicked on:
klewis1 Group Title
Find an equation of th... | 5 | [
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-0.02783203125,
-0.014404296875,
0.0673828125,
-0.05712890625,
-0.04638671... | 13,198 | 13198 | |
Congruent Triangles Worksheet
1.
Which of the following cannot be used to prove that two triangles are congruent?
a. AAS congruence postulate
b. SAS congruence postulate
c. SSS congruence postulate
d. AAA congruence postulate
Solution:
AAA congruence postulate cannot be used to prove that two triangles a... | 4 | [
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... | 13,199 | 13199 |