content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
DT (Dowker-Thistlethwaite) Codes
Notice. The Knot Atlas is now recovering from a major crash. Hopefully all functionality will return slowly over the next few days. --Drorbn (talk) 21:23, 4 July 2013 (EDT)
DT (Dowker-Thistlethwaite) Codes
From Knot Atlas
Knots
The "DT Code" ("DT" after Clifford Hugh Dowker and Mor... | 5 | [
-0.060302734375,
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0.007568359375,
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0.04541015625,
0.01324462890625,
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0.032958984375,
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... | 14,100 | 14100 | |
Rational Roots Theorem - Concept
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Rational Roots Theorem - Concept 12,808 views
The rational roots theorem states that all potential roots are in the positive or negative form of the last coefficient s factors d... | 4 | [
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lgorithm
Binary search algorithm
Generally, to find a value in unsorted array, we should look through elements of an array one by one, until searched value is found. In case of searched value is absent from array, we go through all
elements. In average, complexity of such an algorithm is proportional to the length of ... | 5 | [
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Rolling-ball game
up vote 20 down vote favorite
9
The analyses in two recent MO questions, "Rolling a random walk on a sphere" and "Maneuvering with limited moves on $S^2$," suggest a Rolling-Ball Game, as follows.
A unit-radius ball sits on a grid point of a $\delta \times \delta$ regular grid in the plane, with $\d... | 4 | [
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The Case for a Positive Lambda-Term - V. Sahni &
A. Starobinsky
8.2. When may a
Now let us consider the following important question: can a always be described by a minimally coupled scalar field, for any observed behaviour of a(t) or H(a) ? To answer this question let us first
consider the equations of motion describ... | 4 | [
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Math Forum Discussions
Re: Distance Between Lines in R^3 (fwd)
Posted: Jul 26, 2013 7:35 AM
A few notational corrections:
Am 26.07.2013 11:06, schrieb Thomas Nordhaus:
> Am 26.07.2013 05:33, schrieb William Elliot:
>> How do we find the shortest distance between two lines L, L' in R^3 ?
>>
>> 2.
>> http://at.yorku.ca... | 5 | [
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Quadratic Equations: Proficiency Exam
For the quadratic equations in the following problems, specify the values of a,b, a,b, and c. c.
Exercise 1
Solution
a=2,b=β3,c=10 a=2,b=β3,c=10
Exercise 2
Solution
a=10,b=β3,c=0 a=10,b=β3,c=0
For the following problems, use the zero-factor property to solve each quadratic e... | 4 | [
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An expression with an alternating trilinear form, written in terms of the determinant and a symmetric bilinear form
up vote 3 down vote favorite
1
I am trying to understand a line from MacLachlan/Reid's The Arithmetic of Hyperbolic 3-Manifolds (it's in 3.4 if you have the book), that seems it should be elementary but ... | 5 | [
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Intersection of boundary facets of a simplicial complex
up vote 4 down vote favorite
1
Suppose you have an equidimensional $n$-dimensional simplicial complex $\Delta \subseteq \mathbb Q^n$; i.e., $\Delta$ is the union of finitely many $n$-simplices that intersect only along proper
faces. (I really do mean to use the s... | 5 | [
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Medians of Triangles Proof
Date: 05/29/2000 at 10:34:52
From: Jenny
Subject: Medians of triangles
Prove that in any triangle, the sum of medians is more than 3/4 of its
perimeter, but less than the whole perimeter.
Date: 05/29/2000 at 17:49:02
From: Doctor Floor
Subject: Re: Medians of triangles
Hi, Jenny,
Thank... | 5 | [
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How to examine the convexity of a complex function numerically?
up vote 1 down vote favorite
I have a function which does not have a closed form . Large numerical effort should be done to evaluate the function for even a single point. How can I examine the convexity of my function over the
whole domain of function wit... | 5 | [
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Lyapunov stability (idea)
Consider a continuous function f:GβR^N for a non-empty subset GβR^N and an autonomous differential equation dx/dt=f(x(t)), hereafter x'=f(x), with an equilibrium point 0βG - that is, f(0)=0.
The equilibrium 0 is described as being stable in the sense of Lyapunov if βΞ΅>0 βΞ΄>0 such that
If... | 4 | [
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The Pythagorean Theorem
Department of Mathematics Education
J. Wilson, EMT 669
... | 4 | [
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Sphere Tessellation 101:
"The Art of Making Spheres out of Triangles"
Dedication: To My Father, Celebrating his 66th Birthday β June 3rd.
Introduction
I ... | 4 | [
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bra
Narrow Search
Earth and space science
Mathematics
Sort by:
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Now showing results 1-10 of 12
In this activity, students estimate the size of the visible universe in relation to the size of the Milky Way Galaxy. To do so, students will get a sense of scale and will convert from centimeters to
kilometers... | 4 | [
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Multiplication Methods
Name: Lisa G.
Status: student
Age: N/A
Location: N/A
Country: N/A
Date: N/A
Question: My fourth-grade students are currently learning to multiply two-digit by two-digit numbers. Is there a non-standard algorithm that I can teach my accelerated/gifted students? One that does
not i... | 4 | [
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hypermonoid
Contents
Definition
By removing structure and properties from the notion of hypergroup, a hypermonoid is a set equipped with an associative multivalued multiplication. There are several equivalent ways of making this
more precise:
β’ A hypermonoid is a monoid $M$ in the monoidal Pos-enriched category of... | 4 | [
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What is the growth rate for divisibility of integers
up vote 2 down vote favorite
For a natural number $n\geq 1$, let $PF(n)$ denote the number of prime factors (with multiplicity) of $n$. For example, since $48=2*2*2*2*3$, we have $PF(48)=5$.
For any natural number $N\geq 1$, define $$E(N)=\frac{\sum_{k=1}^N PF(k)}{... | 4 | [
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Volume of Cones - Concept
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Volume of Cones - Concept 16,548 views
The formula for the volume of cylinders can also be applied to the volume of cones, which occupy only one third of the space of a corresponding c... | 4 | [
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NEWTON: Alloy Component Calculation
Alloy Component Calculation
Name: Jacey
Status: student
Grade: 9-12
Location: MA
Country: USA
Date: Summer 2013
Question: Consider a piece of gold jewelry that w... | 4 | [
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A NICE necessary and sufficient condition on positive semi-definiteness of a matrix with a special structure!
up vote 3 down vote favorite
1
Let $$ A = \begin{pmatrix} \sum_{j\ne 1}a_{1j} & -a_{12} & \cdots & -a_{1n}\\ -a_{21} & \sum_{j\ne 2}a_{2j} & \cdots & -a_{2n}\\ \vdots & \vdots & \ddots & \vdots\\ -a_{n1} & -a_... | 4 | [
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What is the different in the cyclotomic tower over a finite ramified extension of Qp?
up vote 6 down vote favorite
2
If $K_n$ is the field $\mathbb{Q}_p(\mu_{p^n})$, then it's easy to see that the relative different $\mathcal{D}(K_n / K_{n-1})$ is $(p)$ for all $n \ge 2$.
What happens if I take an arbitrary, probably... | 5 | [
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dy
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Here's the question you clicked on:
keebler01 Group Title
Determine which, if ... | 4 | [
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Notes
A Fenwick tree is a clever way to represent a list of numbers in an array, which allows arbitrary-length prefix sums to be calculated efficiently. (For example, the list [1,2,3,4,5] has a length-3
prefix [1,2,3] with sum 1+2+3 = 6.) This is useful in various scenarios, most notably to implement arithmetic coding,... | 5 | [
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Mean-Variance Ratio of the Poisson Distribution
Date: 03/27/2001 at 19:08:10
From: Jocelyn
Subject: Proof of mean/variance = 1 for Poisson
I would like to show that V(X)/E(X) = 1 for the Poisson distribution.
In other words, the ratio of the variance and the expected mean equals
one.
I know the formula for the Pois... | 5 | [
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n
This material (including images) is copyrighted!. See my copyright notice for fair use practices.
Now I will apply Newton's laws of motion and gravity to topics more astronomical: objects moving around other objects. What kinds of things can you find out about celes... | 5 | [
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Sedimentation Analysis of Galena Concentrate and Predictability of Effective Particle Depth Based on Settling Time and Particle Diameter
C. I. Nwoye^1, , S. O. Nwakpa^1, I. D. Adiele^2, M. A. Allen^3, S. E. Ede^4, N. E. Idenyi^5
^1Department of Metallurgical and Materials Engineering, NnamdiAzikiwe University, Awka, ... | 4 | [
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Inequality Sign Switch
Date: 01/13/2003 at 00:48:52
From: Devin
Subject: Inequalities
How do you solve the inequality
-1/8w < 3 ?
-1/8w < 3
-8/1 x -1/8w < 3
w < -24
Date: 01/13/2003 at 09:22:58
From: Doctor Rick
Subject: Re: Inequalities
Hi, Devin.
I believe you mean (-1/8)w < 3, rath... | 4 | [
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Branching Processes and Extinction
Copyright Β© University of Cambridge. All rights reserved.
This is the final destination in our series on population dynamics. Well done for making it this far!
Β
Branching Processes
Β
Following on from the basic branching processes introduction, we now calculate the expected numb... | 5 | [
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1. Which equation ... | 4 | [
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... | 14,129 | 14129 | |
The Magnetized Universe - M. Giovannini
4.6. The dynamo mechanism
According to the naive description of the dynamo instability presented above the origin of large-scale magnetic fields in spiral galaxies can be reduced to the following steps:
β’ during the 30 rotations performed by the galaxy since the protogalactic... | 4 | [
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Using
Task 3: Key Concepts about Using Logistic Regression In NHANES
Logistic regression is used to assess the association between independent variable(s) (X[j]) -- sometimes called exposure or predictor variables β and a dichotomous dependent variable (Y) β sometimes
called the outcome or response variable. Logisti... | 4 | [
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Limit problem?
β’ o... | 4 | [
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Capacitor transient response
Because capacitors store energy in the form of an electric field, they tend to act like small secondary-cell batteries, being able to store and release electrical energy. A fully discharged capacitor
maintains zero volts across its terminals, and a charged capacitor maintains a steady quan... | 5 | [
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Golf Ball Speed
Name: Greg Y.
Status: student
Age: 30s
Location: N/A
Country: N/A
Date: Tuesday, May 21, 2002
Question: I understand from conservation of momentum that after a collision, the total ... | 5 | [
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coherent 2-category
Context
2-Category theory
Definitions
Transfors between 2-categories
Morphisms in 2-categories
Structures in 2-categories
Limits in 2-categories
Structures on 2-categories
Contents
Idea
The generalization of the notion of coherent category from category theory to 2-category theory.
Defini... | 4 | [
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Homann Transfers
Day 1
In order to understand the Hohmann Transfer, students must first know a little about orbits. The Hohmann Transfer consists of two circular orbits and one elliptical orbit.
For circular orbits students should know:
Discuss the radius of the orbit with students. Is the radius constant or does it... | 4 | [
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.
10. HORIZONS, TEMPERATURE AND ENTROPY
One of the remarkable features of classical gravity is that it can wrap up regions of spacetime thereby producing surfaces which act as one way membranes. The classic example is that of Schwarzschild
black hole of mass M which has a compact spherical surface of radius r = 2M th... | 4 | [
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A bullet of mass 20g str... | 4 | [
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New Comic And Some Maths
Posted by
Akano Toa of Electricity
, in
Math/Physics
Oct 22 2011 Β· 123 views
comic diverging numbers sum math
Hi, all,
New comic (and topic) have been posted over in the comics forum! Check it out!
To address the maths in the new comic, the first sum is
1 + 2 + 4 + 8 + ... = Sum(2^n), ... | 4 | [
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Three Factoring Techniques for Quadratic Polynomials
Date: 02/21/2008 at 17:48:06
From: Sarah
Subject: factor the following: 3(40x^3+31x^2+6x)
How would you factor 3(40x^3+31x^2+6x)? There is an exponent to the
3rd power, and the numbers are too large and can not be reduced any more.
The original question was 120x^... | 4 | [
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Do two arbitrary processes have the same central tendency?
7. Product and Process Comparisons
7.3. Comparisons based on data from two processes
7.3.5. Do two arbitrary processes have the same central tendency?
The nonparametric equivalent of the \ By "arbitrary" we mean that we make no underlying assumptions about ... | 5 | [
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Generation, representation and flow of phase information in structure determination: recent developments in and around
Generation, representation and flow of phase information in structure determination: recent developments in and around SHARP 2.0
Volume 59
Part 11
Pages
2023-2030 The methods for treatin... | 4 | [
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C-star-algebra
Context
Algebra
Operator algebra
Noncommutative geometry
Index theory
Contents
Definitions
Abstract $C^\ast$-algebras
Definition
A $C^*$-algebra is a Banach algebra $(A, {\|-\|})$ over a topological field $K$ (often the field $K \coloneqq \mathbb{C}$ of complex numbers) equipped with an involuti... | 4 | [
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The Hardy Weinberg Law and Natural Selection
Introduction.
The Hardy Weinberg law of equilibrium is one of the most important concepts in population genetics. First of all for many situations involving complete dominance it provides a way to infer what
proportion of the population consists of homozygous dominant vs. h... | 5 | [
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ing Matrices
Calculating Matrices with the HP-48
Contents
Introduction
The scientific pocket calculator succeeded the slide rule in the 1980's. Not only could it multiply and divide, find trig functions and logarithms, and raise to powers like the slide rule, but it
could add and subtract as well, reducing the tediu... | 4 | [
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monoidal Dold-Kan correspondence
Context
Homological algebra
Higher algebra
Algebraic theories
Algebras and modules
Higher algebras
Model category presentations
Geometry on formal duals of algebras
Theorems
Contents
Idea
The monoidal Dold-Kan correspondence relates simplicial algebras with differential grade... | 4 | [
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Ken Montgomery
EMAT 6690
INSTRUCTIONAL UNIT: Distance, Area, and Volume
ββββββββββ¬βββββββββββ¬βββββ¬ββββββββββββββ¬βββββββ
... | 4 | [
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0.0800781... | 14,147 | 14147 | |
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HELP... Daisy purchased... | 4 | [
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Estimate
Task 1: How to Estimate Mean Food Intakes Using SUDAAN
This section describes how to use SUDAAN to estimate mean food intakes along with standard errors. To illustrate this, consumption of milk is used as an example. As explained in the key concepts
section, there are different ways to group foods for analy... | 4 | [
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An improved empirical bayes approach to estimating differential gene expression in microarray time-course data: BETR (Bayesian Estimation of Temporal Regulation)
Abstract
Background
Microarray gene expression time-course experiments provide the opportunity to observe the evolution of transcriptional programs that cel... | 4 | [
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nrich.maths.org
Copyright Β© University of Cambridge. All rights reserved.
'Maths Filler 2' printed from http://nrich.maths.org/
The first 6 marks are filled one every half minute.
Then for mark 7 we first fill up to 6 completely:
$M+ = 1+3+1 = 5$
$A+ = \frac{3.5+4}{2} \times 2 +4 - \frac{1+2}{2} \times 2 +2 = 10.5... | 4 | [
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Non-Faithfully Flat Quantum Homogeneous Spaces
up vote 2 down vote favorite
3
Let $G$ and $H$ be two Hopf algebras, and $\pi: G \to H$ a Hopf algebra map. We will call an algebra of the form $$ M:= \lbrace m \in G ~ | ~ m_{(1)} \otimes \pi(m_{(2)}) = m \otimes 1 \rbrace $$ a
quantum homogeneous space.
There are many ... | 4 | [
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-... | 14,152 | 14152 | |
Is there an interpretation of the "anticommutative" symmetric monoidal structure on $\mathbb{Z}$-graded abelian groups in terms of $\mathbb{G}_m$ actions?
up vote 4 down vote favorite
2
The category of $\mathbb{Z}$-graded abelian groups is equivalent to the category of comodules over the commutative Hopf algebra (over... | 4 | [
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holographic principle of higher category theory
Context
Higher category theory
Basic concepts
Basic theorems
Applications
Models
Morphisms
Functors
Universal constructions
Extra properties and structure
1-categorical presentations
Functorial quantum field theory
Contents
The general abstract principle
In ... | 4 | [
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0... | 14,154 | 14154 | |
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KE8717504 Group Title
Solve the following ... | 4 | [
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0.109375,
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0.0089111328125,
-0.0008583068847... | 14,155 | 14155 | |
s razor
Occam's razor
Occamβs razor
The following example in statistics illustrates the principle of Occamβs razor. See Article on Occamβs Razor on Wikipedia for a thorough discussion, mathematical or not, of this principle, which is
also known as the principle of parsimony.
Given the following ten pairs of hypothet... | 5 | [
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Patent US7272620 - Frequency divider with low harmonics
BACKGROUND OF THE INVENTION
1. Claim of Priority
This application is a continuation-in-part of copending U.S. utility application entitled βProgrammable Frequency Divider,β Ser. No. 09/370,099, filed on Aug. 6, 1999, now U.S. Pat. No. 6,707,326 and
is incorporat... | 4 | [
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0.061279296875,
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0.04638671875,
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0.045654296875,
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0.01184082... | 14,157 | 14157 | |
Formula for Nim
Date: 02/22/2002 at 15:20:56
From: Kentaro Miura
Subject: NIM
Hi.
I have been attempting to figure out a formula for the game called
the Chip Game. You can play with any number of chips. Each player
takes turns to eliminate up to three coins at a time. The person to
take the last chip loses the game... | 4 | [
-0.0220947265625,
0.03076171875,
-0.041259765625,
-0.099609375,
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0.061767578125,
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0.01611328125,
-0.00799560546875,
0.0009918212890625,
0.02978515625,
0.0033111572265625,
0.... | 14,158 | 14158 | |
Sierpinski Gasket
Date: Tue, 29 Aug 1995 08:05:54 -0500 (CDT)
From: Anonymous
Subject: sierpinski's gasket
We are 8th grade algebra students from Oshkosh, Wisconsin. We are stumped
by this problem: A Sierpinski Gasket is formed by removing successfully
smaller equilateral triangles. What is the area of a Sierpinsk... | 5 | [
-0.0029449462890625,
0.095703125,
0.017333984375,
0.006378173828125,
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0.0703125,
0.07275390625,
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-0.0189208984375,
-0.0028533935546875,
-0.037841796875,
-0.056884765625,
-0.... | 14,159 | 14159 | |
dy
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marissapaige Group Title
It's silly that I... | 4 | [
-0.00494384765625,
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0.01019287109375,
0.0023956298828125,
-0.03857421875,
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0.06884765625,
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0.0031890869140625,
-0.044189453125,
-0.0299072265625,
0.0189208984375,
0.0820... | 14,160 | 14160 | |
Consistency Techniques
Guide to Constraint Programming Β© Roman BartΓ‘k, 1998
Contents Prev Up Next
Constraint Sa... | 4 | [
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0.0093994140625,
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0.0023040771484375,
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0.045654296875,
-0.05810546875,
0.00994873046875,
0.056884765625... | 14,161 | 14161 | |
Automorphism Group of Paley Graph
up vote 2 down vote favorite
Hello all,
I would like an explanation as to the structure description of the automorphism group of a Paley graph.
Paley graphs are a specific case of Cayley graphs where the group is $Z_q$ (q is a prime power for some prime p = 1 mod 4) and the connecti... | 4 | [
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0.0888671875,
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0.045166015625,
-0.06689453125,
-0... | 14,162 | 14162 | |
Does there exist a pure recurrence formula with polynomial coefficients for Fibonacci(2^n)?
up vote 9 down vote favorite
1
Let F(n) be the Fibonacci sequence as defined by F(1)=1, F(2)=1, F(n)=F(n-1)+F(n-2) for n>=3. I'm looking for a pure recurrence formula for the function X(i)=F(2^i) whose coefficients may be
polyn... | 5 | [
-0.1064453125,
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0.048583984375,
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0.036376953125,
0.0225830078125,
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0.0205078125,
0.031494140625,
0.031494140625,
-0.064453125,
-0.0... | 14,163 | 14163 | |
Shades of Fermat's Last Theorem
Copyright Β© University of Cambridge. All rights reserved.
'Shades of Fermat's Last Theorem' printed from http://nrich.maths.org/
The familiar Pythagorean relationship $3^2+ 4^2=5^2$ is one solution to$$(x - 1)^n + x^n = (x + 1)^n$$ so what about other solutions for $x$ an integer and $... | 5 | [
-0.04052734375,
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0.05615234375,
-0.05419921875,
-0.02587890625,
-0.038818359375,
-0.0329... | 14,164 | 14164 | |
Combining Rates of Work
Date: 08/30/98 at 17:05:34
From: REGINA
Subject: Combining Rates of Work
It takes me 3 hours to paint a house. It takes you 5 hours to paint a
house. How long will it take for both of us to paint a house? I first
added. Then I changed and multiplied instead. What should I do?
Date: 08/31/98... | 4 | [
0.0810546875,
0.05224609375,
0.035400390625,
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0.10693359375,
0.055908203125,
0.048095703125,
-0.0123901367187... | 14,165 | 14165 | |
Monads are Elephants Part 3
In this series I've presented an alternative view on the old parable about the blind men and the elephant. In this view, listening to the limited explanations from each of the blind men eventually
leads to a pretty good understanding of elephants.
So far we've been looking at the outside of... | 4 | [
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-0.0096435546875,
0.03271484375,
0.01092529296875,
-0.0252685546875... | 14,166 | 14166 | |
dy
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BrizyBaby16 Group Title
A restaurant charg... | 4 | [
-0.03173828125,
0.01348876953125,
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0.0096435546875,
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0.03125,
-0.1015625,
-0.0181884765625,
0.01068115234375,
-0.00171661376953125,
-0.020263671875,
0.04614257... | 14,167 | 14167 | |
Does local triviality in the fppf topology imply local triviality in the etale topology?
up vote 7 down vote favorite
1
Given an algebraically closed field $k$, a smooth group scheme $G$ over $k$ and a principal $G$-bundle $X \rightarrow Y$, which is locally trivial in the fppf topology.
Is this bundle also locally t... | 5 | [
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0.1005859375,
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0.01141357421875,
... | 14,168 | 14168 | |
In which commutative algebras does any derivation possess a flow?
up vote 7 down vote favorite
3
Definitions
Suppose $A$ is a commutative algebra over $\mathbb{R}$ with unity. $\mathbb{R}$-linear map $\xi\colon A\to A$ is a derivation of $A$ iff $\xi(ab)=a\xi(b)+\xi(a)b$ for any $a,b\in A$. If $\gamma\colon
\mathbb{R}... | 5 | [
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-0.04150390625,
0.01452636718... | 14,169 | 14169 | |
Fluid Mechanics program help
03-08-2008 #1
Registered User
Join Date
Mar 2008
Posts
19
Fluid Mechanics program help
Hey all, I have programming assignment in school.I need some mathematical help in it.
I dont want you to do the whole programming assignment to me.I just have problem how is the calcula... | 5 | [
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0.03369140625,
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-0.0306396484375,
... | 14,170 | 14170 | |
Sums of Squares and Sums of Cubes
Copyright Β© University of Cambridge. All rights reserved.
Let $n$ be a whole number. When is it possible to write $n$ as a sum of two squares, say $n=a^2+b^2$, or as a sum of three squares, say $n=a^2+b^2 +c^2$, or as a sum of four squares, and so on? Of
course, $a$, $b$, $c$, $\ldots... | 4 | [
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0.0791015625... | 14,171 | 14171 | |
Quaternions and Reflections
Copyright Β© University of Cambridge. All rights reserved.
'Quaternions and Reflections' printed from http://nrich.maths.org/
Quaternions are 4-dimensional numbers of the form $(a,x,y,z)= a+x{\bf i}+y{\bf j}+z{\bf k}$ where $a, x, y$ and $z$ are real numbers, ${\bf i, j}$ and ${\bf k}$ are ... | 4 | [
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-0.1171875,
0.029541015625,
-0.04638671875,
0.0... | 14,172 | 14172 | |
Gauss linking integral and quadratic reciprocity
up vote 16 down vote favorite
7
In the setting of Mazur's "primes and knots" analogy, prime ideals $\mathfrak p\subset\mathcal O_K$ correspond to "knots" $\operatorname{Spec}\mathcal O_K/\mathfrak p$ inside a "3-manifold" $\
operatorname{Spec}\mathcal O_K$. The law of q... | 4 | [
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0.00994873046875,
0.0283203125,
... | 14,173 | 14173 | |
Multiple Regression and Excel
Multiple Regression and Excel (Overview)
In the lectures, you have been introduced to the idea of regression based on a two quantitative variables. We usually label the explanatory variable X and the response variable Y. With such data,
regression allows you to predict Y values based on X... | 4 | [
-0.0208740234375,
0.00848388671875,
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0.033447265625,
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0.0791015625,
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0.0419921875,
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-0.037109375,
0.0301513671875,
-0.041... | 14,174 | 14174 | |
The Relevance of History - Keplerian Finance
History is philosophy teaching by examples.Β ~Thucydides
Several years ago a manager pitched Β his algorithmic bond trading fund to a networking group that I was a member of. As someone who had been professionally involved with creating similar systems, my
questions naturall... | 4 | [
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0.055908203125,
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0.009521484375,
-0.06494140625,
-0.06787109375,
-0.036376953125,
-0... | 14,175 | 14175 | |
pe
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Spectrum Group Title
Which of the followin... | 4 | [
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0.047119140625,
0.01531982421875,
-0.01300048828125,
-0.032470703125,
0.006072998046875,
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0.00372314453125,
-0.014892578125,
0.038818359375,
0.07861328125,
-0.08349609375,
0.0184326171875,
0.00762939453125,
0.013427734375,
-0.01312255859375,
-0.0205078125,
-0.0... | 14,176 | 14176 | |
The competition between inertia and
10.301. Introduction to Fluid Mechanics
Animations from CD for understanding HW 1
Since showing animations on the overhead in class is problematic, I have prepared this summary that you can use with the CD in the front jacket of your textbook. Animations can be quite useful in
unde... | 4 | [
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... | 14,177 | 14177 | |
Dynamical degrees (after Blanc and Cantat)
Posted by: matheuscmss | May 31, 2013
Dynamical degrees (after Blanc and Cantat)
About one week ago (May 23, 2013), I saw a very nice talk of Serge Cantat on Dynamical degrees at the seminar of the Topology and Dynamics team of Orsay.
Before entering on the details of Serge... | 4 | [
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0.06005859375,
-0.0179443359375,... | 14,178 | 14178 | |
vibration
5.5 Introduction to vibration of systems with many degrees of freedom
The simple 1DOF systems analyzed in the preceding section are very helpful to develop a feel for the general characteristics of vibrating systems.Β Β They are too simple to approximate most real
systems, however.Β Β Real systems have more t... | 5 | [
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-0.01220703125,
-0.0174560546875,
0.06298828125,
-0.00034... | 14,179 | 14179 | |
Comparing Observed Values with Expected Values
My last two blog entries described two helper methods which programmatically compute Chi-square values and Normal values. I wrote them to create a C# method which compares a set of observed values
with a set of expected values using the G test. The G test is very similar ... | 5 | [
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0.064453125,
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-0.02734375,
-0.0400390625,
0.037841796875,
-0.04... | 14,180 | 14180 | |
geometric mean of similar triangles
Geometric Mean of Similar TrianglesΒ
Geometric Mean of Similar Triangles : The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle.
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββ... | 4 | [
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0.0654296875,
0.04443359375,
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-0.0390625,
-0.010864257812... | 14,181 | 14181 | |
Queueing Theory
Queues are waiting lines.
Basic Structure of Queueing Models
The Basic Queueing Process
The basic process assumed by most queueing models is the following. Customers requiring service are generated over time by an input source (arriving process). These customers enter the queueing
system and join a q... | 5 | [
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-0.072265625,
0.08935546875,
-0.12890625,
... | 14,182 | 14182 | |
quantum anomaly
Context
Physics
Differential cohomology
Ingredients
Connections on bundles
Higher abelian differential cohomology
Higher nonabelian differential cohomology
Fiber integration
Application to gauge theory
Contents
Idea
There are at least two things that are called quantum anomalies in the contex... | 4 | [
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0.0123291015625,
-0.041015625,
... | 14,183 | 14183 | |
Efficient Cutting
Copyright Β© University of Cambridge. All rights reserved.
'Efficient Cutting' printed from http://nrich.maths.org/
Ysanne and Joanna from Central Newcastle High School sent us their thoughts:
Roughly half of the paper should be used to make the circles and roughly half to make the rectangle as the ... | 4 | [
-0.045166015625,
0.09619140625,
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0.07421875,
-0.054931640625,
-0.057373046875,
-0.003021240234375,
0.07177734375,
... | 14,184 | 14184 | |
Derangements and Generalizations
Given any sequence of n distinct objects, in how many ways can those
objects be rearranged so that none of the objects is in its original
position? This is known as the number of "derangements" of n,
denoted by D(n). Obviously D(1)=0 and D(2)=1.
One way (not the most efficient) of d... | 5 | [
-0.005279541015625,
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0.04150390625,
... | 14,185 | 14185 | |
Cup products of connected sum
up vote 1 down vote favorite
2
Hej,
I am interested in the cohomology ring of the connected sum $M \# N$ of two oriented manifolds $M$ and $N$ in terms of the corresponding cohomology rings of $M$ and $N$.
Mayer-Vietoris shows that in dimensions $0<k<n$ the additive structure is given b... | 4 | [
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0.033447265625,
-0.0153... | 14,186 | 14186 | |
nrich.maths.org
Copyright Β© University of Cambridge. All rights reserved.
'Immersion' printed from http://nrich.maths.org/
To begin, we can work out the volume of each solid:
Solid 1) A sphere of radius $1 \ \mathrm{cm}$ :
$$\textrm{[Volume]} = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi \ \mathrm{cm^3}$$
Solid 2) A solid... | 5 | [
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-0.0174560546875,... | 14,187 | 14187 | |
Fuel Left in an Ellipsoidal Tank
Date: 10/19/2002 at 01:33:03
From: Chris Wells
Subject: How much fuel is left in a tank at any depth, given that the
tank is ellipsoidal?
While working for an oil company 25 years ago, I was encamped in the
desert in western Argentina. It was about 6 hrs round-trip to the
nearest gas ... | 5 | [
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-0.03515625,
0.027099609375,
-0.057861328... | 14,188 | 14188 | |
nrich.maths.org
Copyright Β© University of Cambridge. All rights reserved.
'Andy's Marbles' printed from http://nrich.maths.org/
Several very well reasoned solutions came in for this problem about Andy's marbles. Katherine from Treffos, North Wales, pupils from Wigginton Primary and Stephen from Frisby School all went... | 4 | [
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0.009033203125,
0.083984375,... | 14,189 | 14189 | |
Past Events and Probability
Date: 04/05/2000 at 06:05:46
From: Peter
Subject: Probability (Past affects the future?)
Hi,
I will break up millions of tosses into groups of tens. I toss a fair
coin 10 times and so overall heads and tails will show about 5 times
each, or 50%.
Runs will occur through these tens, e.g. ... | 5 | [
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0.01104736328125,
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0.0130615234375,
-0.0023956298828125,
-0.048583984375,
-0.00665283203125,
... | 14,190 | 14190 | |
Tetration
From TORI
Tetration (or Tetrational) ${\rm tet}_b$ to base $b \in \mathbb R$, $b\!>1$
is the $\mathbb C \mapsto \mathbb C$ function, which is solution of equations
${\rm tet}_b(z\!+\!1) = \exp_b\!\big( {\rm tet}_b(z) \big)$
${\rm tet}_b(0) = 1$
such that, at least for $b\!>\!1$, is holomorphic at ... | 4 | [
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0.0113525390625,
0.008056640625,
-0.06591796875,
-0.0732421875,
-0.... | 14,191 | 14191 | |
nrich.maths.org
Copyright Β© University of Cambridge. All rights reserved.
'Quick Route' printed from http://nrich.maths.org/
The solution below was sent in by Taryn from Kerang Technical High School. The quickest route takes $14$ minutes walking exactly one quarter of the way along the edge and then in a straight lin... | 5 | [
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0.01220703125,
-0.04736328125,
0.029296875,
-0.0419921875,
-0.... | 14,192 | 14192 | |
Spans and Vector Spaces - pt 3
Well, I was out of town for a weekend, and then had a miserable cold that went away but only after sleeping about 4 extra hours per day for a few days. So itβs been a while since I continued the
story here.
To recap: I first explained how to turn a span of sets into a linear operator bet... | 4 | [
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0.0625,
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0.0... | 14,193 | 14193 | |
The Limit Assumption and Quantified Counterfactual Logic
I spent last weekend at the Rutgers Semantics Workshop, which was a great success. Thanks to Angela Harper and Jason Stanley for putting on such a good conference. I learned a few things there, some
of which quite surprised me. What Iβm going to write about here ... | 4 | [
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Deconvolution
Fourier Deconvolution
Fourier deconvolution is the converse of Fourier convolution in the sense that division is the converse of multiplication. If you know that mx equals n, where m and n are known but x is unknown, then
x equals n/m. Conversely if you know that m convoluted with x equals n, where ... | 5 | [
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... | 14,195 | 14195 | |
Two Primes Make One Square
Copyright Β© University of Cambridge. All rights reserved.
'Two Primes Make One Square' printed from http://nrich.maths.org/
This question has been very well answered - thank you to everyone who sent us solutions. David, Jack and Matthew, and Beth, Harry and Henry from St. Nicolas CE Junior ... | 4 | [
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-0.015625,
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0.0400390625,
0.005615234375,
-0.050048828125,
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-0.053955078125,... | 14,196 | 14196 | |
Verify Trigonometric Identities
How to verify trigonometric identities? Several examples with detailed solutions are presented. Since we will make use of the basic trigonometric identities, a list of these Trigonometric Identities
is a... | 4 | [
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0.0732421875,
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0.09179687... | 14,197 | 14197 | |
Card Game Probability Question
Date: 5/22/96 at 15:21:51
From: Anonymous
Subject: Card Game Probability Question
Given a regular deck of 52 cards, what is the probability of getting
the following combination: a spade, a queen, a diamond. The cards
taken are not to be placed back into the deck.
Date: 6/1/96 at 19:... | 4 | [
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-0.0133056... | 14,198 | 14198 | |
Mathematical Description: P01
Note: If some equations do not display properly, then they may be fixed by one of the following: reload this page using your browser's "reload" button or click on the equation itself
Mathematical Description: P01 - Universal Joint
by David W. Henderson and Daina Taimina
The universal ... | 5 | [
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-0.0... | 14,199 | 14199 |