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, -0.040771484375, -0.0032806396484375, 0.007568359375, -0.0242919921875, -0.01312255859375, 0.04541015625, 0.01324462890625, -0.0146484375, -0.0113525390625, 0.032958984375, 0.042724609375, -0.0303955078125, -0.0380859375, -0.111328125, 0.0419921875, -0.08154296875, ...
14,100
14100
Rational Roots Theorem - Concept Brightstorm is like having a personal tutor for every subject See what all the buzz is about Check it out 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
[ -0.05224609375, 0.011962890625, 0.025390625, 0.1396484375, 0.04541015625, 0.09033203125, -0.025634765625, 0.0732421875, 0.056396484375, -0.01416015625, 0.06103515625, 0.0272216796875, 0.05126953125, 0.07373046875, -0.010498046875, 0.05078125, -0.07080078125, 0.006866455078125, -0...
14,101
14101
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
[ 0.0654296875, 0.058837890625, -0.023193359375, -0.00994873046875, 0.061767578125, -0.09326171875, -0.048095703125, 0.0079345703125, 0.044921875, -0.006591796875, -0.05224609375, 0.053466796875, 0.0830078125, -0.0537109375, -0.024169921875, 0.0263671875, -0.0380859375, -0.0634765625...
14,102
14102
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
[ 0.04052734375, -0.0439453125, -0.026611328125, -0.0439453125, -0.031494140625, 0.052978515625, 0.01422119140625, 0.03759765625, 0.09521484375, 0.05712890625, -0.031982421875, 0.03076171875, -0.026611328125, 0.04638671875, -0.0023956298828125, 0.03466796875, 0.0341796875, -0.0072631...
14,103
14103
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
[ -0.0654296875, 0.012939453125, 0.027099609375, 0.07666015625, 0.0234375, 0.0947265625, 0.01190185546875, 0.021240234375, 0.0167236328125, -0.04248046875, 0.059814453125, 0.015869140625, -0.0091552734375, -0.0062255859375, 0.08251953125, -0.016845703125, 0.03662109375, -0.068359375,...
14,104
14104
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
[ -0.09326171875, -0.0128173828125, -0.0517578125, -0.046630859375, 0.056884765625, 0.046630859375, -0.0284423828125, 0.1044921875, -0.0380859375, -0.030517578125, -0.0014190673828125, 0.03857421875, 0.01953125, 0.00732421875, -0.00811767578125, 0.056884765625, -0.056640625, -0.04492...
14,105
14105
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=βˆ’3,c=10 a=2,b=βˆ’3,c=10 Exercise 2 Solution a=10,b=βˆ’3,c=0 a=10,b=βˆ’3,c=0 For the following problems, use the zero-factor property to solve each quadratic e...
4
[ -0.12890625, 0.005340576171875, 0.04638671875, -0.028076171875, 0.0014190673828125, 0.046142578125, 0.00994873046875, 0.025390625, -0.0947265625, 0.01544189453125, 0.0810546875, -0.0208740234375, 0.0260009765625, 0.021484375, -0.0546875, 0.05712890625, -0.048828125, -0.0244140625, ...
14,106
14106
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
[ -0.0791015625, -0.0791015625, 0.02392578125, -0.0625, -0.02880859375, 0.055908203125, -0.0059814453125, -0.09033203125, -0.0198974609375, 0.034912109375, 0.080078125, -0.0341796875, -0.07763671875, -0.018798828125, 0.0439453125, 0.08984375, -0.107421875, 0.033447265625, -0.012939...
14,107
14107
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
[ 0.02294921875, 0.07470703125, 0.07080078125, -0.03369140625, -0.057373046875, 0.0252685546875, 0.0155029296875, -0.037841796875, -0.007049560546875, -0.060302734375, -0.043701171875, -0.10009765625, -0.047607421875, -0.0169677734375, 0.0211181640625, -0.083984375, 0.0235595703125, ...
14,108
14108
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
[ -0.04443359375, 0.049560546875, 0.0126953125, -0.046630859375, 0.01251220703125, -0.010986328125, -0.0189208984375, 0.053466796875, -0.0230712890625, 0.0201416015625, -0.0927734375, -0.0595703125, 0.031494140625, 0.02978515625, 0.0673828125, 0.053466796875, 0.064453125, 0.043701171...
14,109
14109
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
[ -0.041259765625, -0.00897216796875, -0.0498046875, 0.0128173828125, -0.031982421875, -0.09716796875, -0.0220947265625, -0.0196533203125, -0.01025390625, 0.0390625, -0.0908203125, -0.026123046875, 0.004241943359375, -0.0220947265625, -0.04931640625, -0.0252685546875, 0.0233154296875, ...
14,110
14110
Lyapunov stability (idea) Consider a continuous function f:Gβ†’R^N for a non-empty subset GβŠ‚R^N and an autonomous differential equation dx/dt=f(x(t)), hereafter x'=f(x), with an equilibrium point 0∈G - that is, f(0)=0. The equilibrium 0 is described as being stable in the sense of Lyapunov if βˆ€Ξ΅>0 βˆƒΞ΄>0 such that If...
4
[ -0.06787109375, -0.050048828125, -0.043212890625, -0.00433349609375, 0.054443359375, 0.0458984375, 0.00201416015625, 0.047119140625, 0.058837890625, 0.009033203125, 0.015869140625, 0.056884765625, 0.061279296875, -0.031005859375, -0.02099609375, 0.0859375, 0.0869140625, -0.07666015...
14,111
14111
The Pythagorean Theorem Department of Mathematics Education J. Wilson, EMT 669 ...
4
[ -0.078125, 0.0791015625, -0.05078125, 0.0419921875, -0.07373046875, -0.045166015625, 0.01104736328125, 0.022216796875, -0.005279541015625, 0.08154296875, 0.04736328125, 0.04736328125, -0.041259765625, 0.08056640625, -0.07470703125, 0.0106201171875, -0.07666015625, 0.064453125, -0...
14,112
14112
Sphere Tessellation 101: "The Art of Making Spheres out of Triangles" Dedication: To My Father, Celebrating his 66th Birthday – June 3rd. Introduction I ...
4
[ -0.016357421875, 0.04052734375, -0.015625, -0.051513671875, -0.037841796875, -0.0849609375, -0.0233154296875, -0.038818359375, -0.01904296875, 0.0654296875, -0.09228515625, -0.040771484375, 0.0220947265625, 0.057861328125, 0.02685546875, -0.015625, 0.038818359375, 0.0308837890625, ...
14,113
14113
bra Narrow Search Earth and space science Mathematics Sort by: Per page: 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
[ 0.005218505859375, 0.0189208984375, 0.046142578125, 0.024658203125, -0.0130615234375, -0.0284423828125, -0.07080078125, 0.0703125, 0.01312255859375, 0.0185546875, 0.0517578125, -0.04150390625, -0.0247802734375, -0.010498046875, -0.021728515625, -0.0625, -0.01953125, 0.050048828125,...
14,114
14114
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
[ -0.00457763671875, -0.011474609375, -0.087890625, -0.08203125, -0.134765625, -0.025390625, -0.04638671875, 0.0247802734375, -0.08984375, -0.01019287109375, 0.08251953125, 0.006317138671875, 0.052490234375, 0.03515625, -0.045654296875, 0.055419921875, -0.0302734375, 0.150390625, -...
14,115
14115
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
[ -0.0024871826171875, -0.0284423828125, -0.0458984375, -0.058349609375, -0.08642578125, 0.004150390625, 0.04931640625, -0.049072265625, 0.0260009765625, 0.0179443359375, -0.013916015625, -0.0927734375, -0.005859375, 0.029052734375, 0.11279296875, 0.0888671875, 0.09228515625, 0.05932...
14,116
14116
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 $$E(N)=\frac{\sum_{k=1}^N PF(k)}{...
4
[ 0.0147705078125, -0.087890625, -0.0257568359375, 0.00616455078125, 0.1015625, -0.048828125, 0.017822265625, 0.1083984375, 0.020751953125, 0.052978515625, -0.0213623046875, 0.0172119140625, 0.023193359375, -0.01116943359375, 0.037109375, -0.005462646484375, -0.032958984375, -0.04980...
14,117
14117
Volume of Cones - Concept Brightstorm is like having a personal tutor for every subject See what all the buzz is about Check it out Volume of Cones - Concept 16,548 views The formula for the volume of cylinders can also be applied to the volume of cones, which occupy only one third of the space of a corresponding c...
4
[ 0.00811767578125, -0.03564453125, 0.02978515625, 0.051513671875, -0.034423828125, -0.0654296875, 0.006591796875, 0.10302734375, 0.119140625, 0.0079345703125, -0.08154296875, 0.01202392578125, 0.051513671875, 0.056884765625, 0.006866455078125, -0.02490234375, -0.0419921875, 0.072753...
14,118
14118
NEWTON: Alloy Component Calculation Alloy Component Calculation Name: Jacey Status: student Grade: 9-12 Location: MA Country: USA Date: Summer 2013 Question: Consider a piece of gold jewelry that w...
4
[ -0.04150390625, 0.0032958984375, 0.000949859619140625, 0.0595703125, -0.0162353515625, -0.10888671875, 0.0849609375, 0.03369140625, -0.05908203125, -0.050048828125, 0.000052928924560546875, -0.080078125, 0.06787109375, 0.07470703125, -0.0133056640625, 0.009765625, 0.03125, 0.058349...
14,119
14119
A NICE necessary and sufficient condition on positive semi-definiteness of a matrix with a special structure! up vote 3 down vote favorite 1 Let $$ 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
[ -0.09521484375, -0.08642578125, 0.046630859375, -0.08837890625, -0.07861328125, 0.0091552734375, 0.00958251953125, -0.072265625, -0.03662109375, 0.0244140625, 0.045654296875, 0.060302734375, -0.005157470703125, 0.0118408203125, -0.011962890625, 0.0093994140625, 0.1474609375, 0.0283...
14,120
14120
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
[ -0.046142578125, -0.03759765625, 0.026611328125, -0.080078125, 0.09521484375, -0.00054168701171875, -0.047119140625, 0.10888671875, 0.040283203125, -0.1357421875, -0.00579833984375, 0.048583984375, 0.015380859375, -0.0303955078125, -0.051513671875, 0.0206298828125, -0.05078125, 0.0...
14,121
14121
dy Got Homework? Connect with other students for help. It's a free community. β€’ across MIT Grad Student Online now β€’ laura* Helped 1,000 students Online now β€’ Hero College Math Guru Online now Here's the question you clicked on: keebler01 Group Title Determine which, if ...
4
[ -0.045166015625, -0.0213623046875, 0.050537109375, -0.037353515625, -0.021728515625, -0.017822265625, 0.099609375, -0.0079345703125, -0.048095703125, 0.0311279296875, 0.06396484375, -0.130859375, 0.00020503997802734375, 0.038330078125, -0.0390625, 0.00433349609375, 0.01141357421875, ...
14,122
14122
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
[ -0.00167083740234375, 0.006103515625, -0.072265625, -0.003204345703125, -0.056396484375, -0.0732421875, -0.051513671875, 0.005218505859375, 0.004669189453125, -0.007415771484375, -0.06298828125, -0.01025390625, 0.00341796875, -0.005706787109375, -0.07958984375, -0.0155029296875, -0.0...
14,123
14123
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
[ 0.02099609375, 0.0595703125, 0.0771484375, -0.0005950927734375, -0.0303955078125, 0.01043701171875, 0.046630859375, -0.02734375, 0.091796875, -0.01031494140625, 0.034423828125, 0.01409912109375, -0.0235595703125, 0.02490234375, 0.025390625, -0.0361328125, 0.0164794921875, 0.0299072...
14,124
14124
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
[ 0.0478515625, 0.0032806396484375, 0.0238037109375, -0.06396484375, 0.026123046875, -0.01531982421875, 0.00982666015625, 0.01226806640625, 0.08935546875, 0.0654296875, 0.039306640625, -0.007537841796875, -0.03369140625, -0.0498046875, -0.02001953125, -0.02490234375, -0.000224113464355...
14,125
14125
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
[ -0.06591796875, -0.052978515625, 0.03173828125, 0.046142578125, 0.0478515625, -0.059326171875, -0.01422119140625, 0.10107421875, -0.0498046875, 0.01519775390625, -0.04833984375, 0.00103759765625, -0.030517578125, -0.04248046875, -0.0213623046875, -0.060791015625, 0.060791015625, 0....
14,126
14126
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
[ -0.08837890625, 0.00811767578125, 0.031494140625, 0.1103515625, -0.0751953125, -0.0218505859375, -0.04638671875, 0.0576171875, 0.04833984375, -0.0213623046875, 0.0115966796875, -0.0135498046875, 0.07373046875, 0.04833984375, -0.0390625, 0.0849609375, -0.032958984375, -0.05078125, ...
14,127
14127
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
[ -0.044189453125, -0.031494140625, 0.09130859375, 0.049560546875, -0.007110595703125, -0.02294921875, 0.0299072265625, 0.0703125, 0.046875, 0.0654296875, 0.04248046875, 0.015380859375, 0.01092529296875, -0.1064453125, -0.0849609375, 0.019775390625, -0.0732421875, -0.021240234375, ...
14,128
14128
dy Got Homework? Connect with other students for help. It's a free community. β€’ across MIT Grad Student Online now β€’ laura* Helped 1,000 students Online now β€’ Hero College Math Guru Online now Here's the question you clicked on: brookie5150 Group Title 1. Which equation ...
4
[ -0.000186920166015625, -0.0234375, 0.002410888671875, -0.04052734375, -0.0294189453125, 0.04248046875, 0.0291748046875, -0.019287109375, -0.06640625, 0.0035858154296875, 0.10009765625, -0.035400390625, 0.0030059814453125, -0.0244140625, 0.0012054443359375, 0.07861328125, -0.1171875, ...
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
[ -0.109375, 0.053466796875, 0.01324462890625, -0.0220947265625, -0.00811767578125, 0.0185546875, -0.080078125, 0.018798828125, 0.00079345703125, -0.033203125, -0.0220947265625, 0.044189453125, 0.05029296875, -0.10302734375, 0.0252685546875, -0.025634765625, -0.10107421875, -0.024291...
14,130
14130
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
[ 0.06298828125, -0.01007080078125, -0.03857421875, -0.01416015625, 0.07275390625, -0.0400390625, 0.044677734375, 0.015625, -0.044677734375, 0.04443359375, -0.0205078125, -0.0174560546875, -0.01458740234375, 0.09716796875, 0.002960205078125, -0.04150390625, -0.04150390625, 0.05883789...
14,131
14131
dy Got Homework? Connect with other students for help. It's a free community. β€’ across MIT Grad Student Online now β€’ laura* Helped 1,000 students Online now β€’ Hero College Math Guru Online now Here's the question you clicked on: swin2013 Group Title Limit problem? β€’ o...
4
[ -0.080078125, 0.01953125, 0.004852294921875, -0.0380859375, -0.0003337860107421875, -0.016357421875, 0.04931640625, -0.00360107421875, 0.06298828125, -0.06787109375, 0.039306640625, -0.1455078125, 0.0145263671875, -0.00982666015625, -0.00518798828125, -0.08544921875, -0.0064697265625...
14,132
14132
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
[ -0.0015106201171875, 0.0400390625, 0.00151824951171875, 0.057373046875, 0.0419921875, 0.0159912109375, 0.0137939453125, 0.031494140625, 0.109375, 0.044189453125, 0.06982421875, 0.00159454345703125, 0.057373046875, 0.0284423828125, -0.06884765625, -0.07861328125, -0.0302734375, 0.01...
14,133
14133
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
[ 0.0986328125, 0.052978515625, -0.03173828125, -0.0947265625, 0.0152587890625, -0.00762939453125, -0.057861328125, 0.04345703125, 0.01373291015625, 0.056640625, 0.076171875, 0.059814453125, -0.0235595703125, 0.01239013671875, 0.0556640625, 0.030517578125, 0.041259765625, 0.006591796...
14,134
14134
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
[ 0.06298828125, -0.07861328125, 0.00004935264587402344, 0.06591796875, 0.0274658203125, -0.0267333984375, -0.0294189453125, 0.001617431640625, 0.029052734375, -0.020751953125, -0.01409912109375, -0.047607421875, -0.031494140625, 0.021240234375, 0.06396484375, 0.0712890625, 0.020385742...
14,135
14135
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
[ 0.07080078125, 0.0693359375, -0.0771484375, -0.058349609375, 0.0150146484375, -0.0478515625, 0.018798828125, -0.044677734375, 0.06396484375, 0.01446533203125, 0.15625, 0.008056640625, -0.0216064453125, -0.0017242431640625, -0.036865234375, -0.044921875, 0.007080078125, 0.0224609375...
14,136
14136
. 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
[ -0.031494140625, 0.006256103515625, -0.018798828125, 0.043212890625, 0.041748046875, 0.0135498046875, 0.0179443359375, -0.00848388671875, 0.123046875, -0.01422119140625, -0.078125, -0.055419921875, -0.0703125, 0.01324462890625, 0.02490234375, -0.09716796875, 0.002166748046875, -0.0...
14,137
14137
dy Got Homework? Connect with other students for help. It's a free community. β€’ across MIT Grad Student Online now β€’ laura* Helped 1,000 students Online now β€’ Hero College Math Guru Online now Here's the question you clicked on: ashna Group Title A bullet of mass 20g str...
4
[ -0.04150390625, 0.134765625, 0.042724609375, -0.0009918212890625, 0.040283203125, 0.006500244140625, -0.01806640625, 0.07666015625, -0.0341796875, 0.031005859375, 0.048095703125, -0.04052734375, -0.0303955078125, 0.025390625, -0.045654296875, 0.01318359375, 0.0172119140625, 0.09179...
14,138
14138
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
[ -0.1103515625, 0.01507568359375, 0.0179443359375, 0.08447265625, 0.0308837890625, -0.0311279296875, 0.018310546875, 0.0791015625, 0.0673828125, 0.05419921875, -0.076171875, -0.03125, 0.0218505859375, 0.0206298828125, -0.04638671875, -0.00994873046875, -0.006805419921875, -0.0344238...
14,139
14139
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
[ -0.047607421875, 0.0159912109375, 0.0537109375, 0.014404296875, 0.01275634765625, 0.00628662109375, 0.0289306640625, -0.0302734375, -0.0238037109375, 0.0267333984375, 0.06396484375, 0.01080322265625, 0.06982421875, -0.03759765625, 0.06201171875, 0.10693359375, -0.07177734375, 0.084...
14,140
14140
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
[ -0.023193359375, -0.1201171875, 0.00714111328125, -0.0859375, 0.01202392578125, -0.048583984375, -0.050048828125, 0.03759765625, 0.01806640625, 0.03515625, -0.00665283203125, 0.00811767578125, 0.0517578125, -0.040283203125, -0.03466796875, -0.072265625, 0.01416015625, -0.046875, ...
14,141
14141
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
[ -0.07958984375, -0.00408935546875, 0.04296875, 0.042724609375, 0.06396484375, -0.05517578125, -0.04833984375, 0.01904296875, 0.0218505859375, -0.040771484375, 0.00909423828125, -0.01068115234375, -0.0093994140625, 0.030517578125, 0.00762939453125, -0.0947265625, -0.0615234375, 0.06...
14,142
14142
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
[ -0.06494140625, 0.01519775390625, -0.0478515625, 0.0281982421875, -0.1455078125, 0.02587890625, 0.03271484375, -0.016845703125, 0.00072479248046875, -0.03955078125, -0.01165771484375, -0.022705078125, 0.000156402587890625, -0.00421142578125, 0.00153350830078125, 0.039794921875, 0.006...
14,143
14143
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
[ -0.0084228515625, 0.0211181640625, 0.0145263671875, 0.08349609375, 0.017333984375, 0.057861328125, -0.046630859375, 0.04931640625, -0.004913330078125, 0.052734375, 0.07080078125, -0.033203125, -0.0517578125, -0.01263427734375, 0.026611328125, 0.028564453125, -0.027099609375, 0.0241...
14,144
14144
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
[ -0.0615234375, 0.064453125, -0.1044921875, -0.036865234375, -0.09716796875, -0.03662109375, -0.11328125, 0.0257568359375, -0.054931640625, 0.039306640625, 0.083984375, 0.0615234375, -0.01611328125, 0.06591796875, 0.0179443359375, 0.01080322265625, -0.09033203125, 0.0908203125, -0...
14,145
14145
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
[ -0.08837890625, 0.0146484375, 0.014892578125, -0.0712890625, -0.056396484375, -0.04833984375, -0.03759765625, 0.056396484375, 0.103515625, -0.02392578125, 0.0016326904296875, -0.0615234375, -0.059814453125, 0.032470703125, 0.126953125, -0.013427734375, 0.050048828125, 0.08447265625...
14,146
14146
Ken Montgomery EMAT 6690 INSTRUCTIONAL UNIT: Distance, Area, and Volume β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”¬β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”¬β”€β”€β”€β”€β”¬β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”¬β”€β”€β”€β”€β”€β”€β” ...
4
[ 0.04052734375, -0.01953125, -0.0157470703125, -0.04443359375, 0.004425048828125, -0.07421875, 0.021240234375, 0.060302734375, 0.003997802734375, -0.046630859375, -0.0152587890625, -0.0869140625, 0.006591796875, 0.051513671875, 0.03466796875, -0.048583984375, -0.025390625, 0.0800781...
14,147
14147
dy Got Homework? Connect with other students for help. It's a free community. β€’ across MIT Grad Student Online now β€’ laura* Helped 1,000 students Online now β€’ Hero College Math Guru Online now Here's the question you clicked on: JamenS Group Title HELP... Daisy purchased...
4
[ -0.0228271484375, 0.012451171875, 0.041259765625, 0.0296630859375, -0.07421875, -0.01495361328125, -0.00604248046875, -0.0108642578125, -0.002593994140625, 0.083984375, 0.09912109375, -0.02734375, -0.003204345703125, 0.055908203125, 0.04736328125, 0.06103515625, -0.10546875, -0.061...
14,148
14148
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
[ 0.049560546875, 0.028564453125, 0.0439453125, 0.051513671875, -0.017822265625, 0.0024871826171875, 0.0322265625, 0.0869140625, -0.03271484375, -0.00885009765625, -0.005584716796875, -0.09814453125, -0.01318359375, 0.00823974609375, -0.006988525390625, -0.1142578125, 0.064453125, -0...
14,149
14149
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
[ -0.10986328125, -0.064453125, 0.024658203125, 0.0250244140625, 0.1064453125, -0.00087738037109375, -0.0189208984375, -0.044677734375, 0.0888671875, -0.035888671875, -0.072265625, -0.0012664794921875, -0.024658203125, 0.060302734375, -0.01080322265625, 0.0281982421875, -0.09228515625,...
14,150
14150
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
[ -0.01171875, 0.048828125, 0.0205078125, -0.04541015625, -0.04541015625, 0.00982666015625, 0.008056640625, 0.10009765625, -0.04541015625, 0.037841796875, -0.0152587890625, -0.095703125, 0.05419921875, -0.0169677734375, -0.056396484375, -0.02392578125, -0.0267333984375, 0.00509643554...
14,151
14151
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
[ -0.064453125, -0.068359375, -0.05419921875, 0.04150390625, -0.078125, 0.05810546875, -0.0361328125, -0.053466796875, -0.053466796875, -0.047607421875, 0.054931640625, -0.056396484375, -0.031982421875, 0.03173828125, 0.08447265625, 0.038818359375, 0.0230712890625, 0.07275390625, -...
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
[ -0.10693359375, 0.0238037109375, 0.03515625, 0.0289306640625, -0.0859375, -0.01513671875, 0.00909423828125, -0.068359375, -0.068359375, 0.005950927734375, 0.047119140625, -0.0703125, -0.040283203125, -0.02490234375, 0.00567626953125, 0.0751953125, 0.0947265625, -0.0013885498046875,...
14,153
14153
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
[ 0.00897216796875, -0.0250244140625, 0.0257568359375, -0.032958984375, -0.020751953125, 0.007110595703125, -0.0419921875, -0.0164794921875, 0.06494140625, -0.033203125, -0.0189208984375, -0.04541015625, -0.146484375, 0.0184326171875, 0.1318359375, -0.040771484375, 0.0169677734375, 0...
14,154
14154
dy Got Homework? Connect with other students for help. It's a free community. β€’ across MIT Grad Student Online now β€’ laura* Helped 1,000 students Online now β€’ Hero College Math Guru Online now Here's the question you clicked on: KE8717504 Group Title Solve the following ...
4
[ -0.002105712890625, 0.109375, 0.01434326171875, 0.00689697265625, -0.0201416015625, 0.046142578125, -0.032958984375, 0.0283203125, 0.0052490234375, 0.0634765625, 0.051513671875, -0.09326171875, 0.0286865234375, -0.00136566162109375, -0.0306396484375, 0.0089111328125, -0.0008583068847...
14,155
14155
s razor Occam's razor Occam’s razor The following example in statistics illustrates the principle of Occam’s razor. See Article on Occam’s 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
[ 0.0299072265625, -0.0260009765625, -0.06884765625, 0.076171875, 0.0576171875, 0.0235595703125, -0.032958984375, 0.10400390625, 0.06982421875, 0.01953125, 0.1025390625, 0.0751953125, 0.0303955078125, 0.02783203125, -0.0045166015625, -0.0017852783203125, 0.0157470703125, -0.022583007...
14,156
14156
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 β€œProgrammable Frequency Divider,” Ser. No. 09/370,099, filed on Aug. 6, 1999, now U.S. Pat. No. 6,707,326 and is incorporat...
4
[ -0.1396484375, 0.061279296875, 0.004364013671875, -0.02978515625, -0.04150390625, -0.0093994140625, -0.033203125, -0.0004425048828125, -0.00138092041015625, 0.01708984375, -0.0230712890625, -0.0203857421875, 0.04638671875, -0.037109375, 0.045654296875, -0.0021209716796875, 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, -0.0272216796875, 0.02099609375, 0.08056640625, 0.035888671875, 0.0123291015625, 0.061767578125, -0.04248046875, -0.009765625, 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, -0.01434326171875, -0.12890625, 0.055419921875, 0.0703125, 0.07275390625, -0.0133056640625, -0.044921875, -0.03466796875, -0.0419921875, -0.0189208984375, -0.0028533935546875, -0.037841796875, -0.056884765625, -0....
14,159
14159
dy Got Homework? Connect with other students for help. It's a free community. β€’ across MIT Grad Student Online now β€’ laura* Helped 1,000 students Online now β€’ Hero College Math Guru Online now Here's the question you clicked on: marissapaige Group Title It's silly that I...
4
[ -0.00494384765625, -0.026611328125, 0.01019287109375, 0.0023956298828125, -0.03857421875, 0.020751953125, -0.0576171875, 0.07568359375, -0.01287841796875, -0.01556396484375, 0.06884765625, -0.051025390625, 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
[ -0.029052734375, 0.0093994140625, -0.05126953125, 0.0023040771484375, -0.00860595703125, -0.00119781494140625, -0.005767822265625, -0.05810546875, -0.11328125, -0.103515625, -0.046875, 0.0030975341796875, 0.12158203125, 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
[ -0.07666015625, 0.07568359375, -0.0036773681640625, 0.0101318359375, -0.052978515625, 0.01611328125, 0.059326171875, 0.0299072265625, -0.017822265625, 0.0284423828125, 0.0791015625, -0.0732421875, 0.011962890625, 0.0888671875, -0.0035858154296875, 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, -0.06689453125, -0.04736328125, 0.048583984375, -0.006866455078125, -0.0284423828125, -0.046630859375, -0.0101318359375, 0.036376953125, 0.0225830078125, -0.048095703125, -0.123046875, -0.0299072265625, 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, 0.0067138671875, -0.0078125, 0.0791015625, 0.049560546875, 0.03173828125, 0.0201416015625, -0.00994873046875, 0.03857421875, -0.07373046875, -0.051025390625, -0.0205078125, -0.00153350830078125, 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, -0.0036163330078125, -0.0068359375, -0.06298828125, -0.061279296875, -0.0201416015625, -0.055908203125, 0.00433349609375, -0.0186767578125, -0.057861328125, 0.004913330078125, 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
[ -0.0751953125, -0.052734375, 0.058837890625, 0.0076904296875, -0.055419921875, -0.0091552734375, -0.03466796875, -0.034912109375, -0.01409912109375, -0.0037384033203125, 0.00909423828125, -0.064453125, -0.0791015625, -0.0096435546875, 0.03271484375, 0.01092529296875, -0.0252685546875...
14,166
14166
dy Got Homework? Connect with other students for help. It's a free community. β€’ across MIT Grad Student Online now β€’ laura* Helped 1,000 students Online now β€’ Hero College Math Guru Online now Here's the question you clicked on: BrizyBaby16 Group Title A restaurant charg...
4
[ -0.03173828125, 0.01348876953125, -0.00421142578125, -0.0791015625, 0.005340576171875, -0.01220703125, -0.0035247802734375, 0.0096435546875, -0.0023345947265625, 0.059326171875, 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
[ 0.01043701171875, 0.0260009765625, 0.035400390625, -0.04296875, 0.09521484375, -0.01116943359375, 0.06591796875, 0.015869140625, -0.003997802734375, -0.03955078125, 0.06982421875, -0.0042724609375, -0.0693359375, 0.00653076171875, 0.1005859375, -0.003814697265625, 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
[ -0.09228515625, -0.036865234375, 0.00811767578125, -0.0220947265625, -0.0269775390625, 0.09619140625, 0.09912109375, 0.005859375, 0.0458984375, -0.03564453125, 0.0556640625, 0.006805419921875, 0.00390625, -0.029052734375, 0.0128173828125, 0.0751953125, -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
[ -0.06005859375, 0.0263671875, -0.01312255859375, -0.0712890625, -0.056640625, -0.041259765625, -0.048583984375, 0.1474609375, -0.043701171875, -0.029296875, -0.0712890625, 0.022216796875, 0.07666015625, 0.03369140625, -0.08740234375, 0.03662109375, -0.1298828125, -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
[ -0.0341796875, 0.0390625, -0.0208740234375, 0.0888671875, -0.01171875, 0.060546875, -0.015869140625, -0.032958984375, 0.09765625, -0.07568359375, -0.06689453125, 0.047119140625, -0.043701171875, 0.0478515625, -0.068359375, -0.072265625, 0.060302734375, 0.03271484375, 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
[ -0.10986328125, 0.029541015625, 0.036865234375, -0.049072265625, -0.12060546875, -0.01068115234375, 0.0167236328125, -0.06591796875, -0.01153564453125, -0.06201171875, 0.0810546875, -0.0057373046875, 0.0146484375, 0.00101470947265625, -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
[ -0.052490234375, -0.0380859375, 0.002899169921875, -0.00921630859375, 0.0150146484375, -0.0478515625, 0.078125, 0.076171875, 0.042236328125, -0.039794921875, 0.08837890625, 0.055419921875, 0.020751953125, 0.02734375, -0.08251953125, 0.062255859375, 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, -0.036376953125, 0.033447265625, 0.050537109375, 0.1298828125, -0.044677734375, -0.0137939453125, 0.0791015625, 0.0272216796875, 0.078125, 0.03515625, 0.048828125, 0.02783203125, 0.0419921875, 0.0732421875, -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
[ -0.031494140625, 0.0712890625, -0.07177734375, -0.03369140625, -0.0274658203125, -0.06640625, -0.0849609375, 0.055908203125, -0.02783203125, -0.005828857421875, -0.005340576171875, 0.03759765625, -0.01312255859375, 0.009521484375, -0.06494140625, -0.06787109375, -0.036376953125, -0...
14,175
14175
pe Got Homework? Connect with other students for help. It's a free community. β€’ across MIT Grad Student Online now β€’ laura* Helped 1,000 students Online now β€’ Hero College Math Guru Online now Here's the question you clicked on: Spectrum Group Title Which of the followin...
4
[ -0.03125, 0.047119140625, 0.01531982421875, -0.01300048828125, -0.032470703125, 0.006072998046875, 0.08203125, 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
[ -0.07421875, -0.0157470703125, 0.02001953125, -0.064453125, 0.03076171875, 0.005706787109375, 0.01239013671875, 0.08984375, 0.01043701171875, -0.029052734375, 0.0206298828125, -0.0174560546875, -0.006256103515625, -0.06591796875, -0.08837890625, -0.03955078125, -0.005401611328125, ...
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
[ -0.08984375, 0.0018768310546875, -0.015869140625, 0.031494140625, -0.060302734375, 0.05224609375, 0.02734375, 0.013916015625, 0.10009765625, -0.0791015625, -0.064453125, -0.01226806640625, 0.0081787109375, 0.043701171875, 0.04296875, -0.04736328125, 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
[ -0.0294189453125, -0.08984375, 0.01611328125, -0.03759765625, -0.0654296875, -0.04248046875, -0.035400390625, 0.0615234375, -0.003814697265625, 0.06884765625, 0.05322265625, -0.0203857421875, 0.0045166015625, -0.07666015625, -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
[ -0.005279541015625, -0.0169677734375, 0.002593994140625, 0.00750732421875, -0.0859375, -0.046630859375, 0.008056640625, 0.041259765625, -0.055908203125, 0.0869140625, 0.01507568359375, -0.0220947265625, 0.064453125, -0.026611328125, -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. β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€...
4
[ -0.07763671875, 0.07421875, 0.0255126953125, -0.043701171875, -0.0240478515625, 0.02490234375, -0.037353515625, 0.023681640625, -0.018798828125, 0.01397705078125, 0.041748046875, -0.09130859375, 0.041015625, 0.0654296875, 0.04443359375, -0.0201416015625, -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
[ -0.061279296875, -0.07080078125, -0.04443359375, -0.00701904296875, -0.0634765625, -0.06591796875, 0.10888671875, -0.0213623046875, 0.10546875, 0.00946044921875, 0.058837890625, 0.05810546875, 0.0791015625, -0.0322265625, 0.0303955078125, -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
[ -0.0908203125, -0.03515625, 0.0247802734375, 0.07373046875, -0.0703125, 0.01416015625, 0.03662109375, 0.03173828125, 0.0120849609375, -0.02197265625, 0.030029296875, 0.0308837890625, -0.087890625, 0.0164794921875, -0.007080078125, -0.00775146484375, 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, -0.0179443359375, -0.0245361328125, -0.017822265625, -0.078125, -0.044189453125, 0.10302734375, -0.03125, -0.01025390625, -0.0654296875, -0.01123046875, 0.013427734375, 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, -0.041259765625, 0.07080078125, -0.01043701171875, -0.0322265625, 0.04345703125, 0.01385498046875, -0.052490234375, 0.0693359375, 0.06982421875, -0.006622314453125, -0.04736328125, -0.041259765625, -0.0262451171875, -0.04296875, -0.0084228515625, 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
[ 0.0087890625, 0.078125, 0.02880859375, 0.0072021484375, 0.021728515625, 0.0654296875, 0.052490234375, -0.02783203125, 0.00628662109375, -0.150390625, 0.056640625, -0.060546875, 0.025146484375, -0.034423828125, 0.0152587890625, 0.12060546875, -0.0283203125, 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
[ 0.049560546875, -0.0244140625, -0.0201416015625, -0.048583984375, -0.0205078125, -0.05126953125, -0.00811767578125, 0.08935546875, -0.0087890625, -0.0032501220703125, -0.12255859375, -0.06689453125, 0.0198974609375, 0.056884765625, -0.0218505859375, -0.054931640625, -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
[ -0.0235595703125, 0.08740234375, -0.054931640625, 0.03076171875, 0.0869140625, -0.051513671875, 0.0164794921875, 0.041748046875, 0.00689697265625, -0.072265625, -0.02490234375, -0.0042724609375, -0.017578125, 0.037353515625, -0.04248046875, -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
[ -0.00982666015625, 0.06591796875, 0.1240234375, 0.043701171875, -0.0654296875, -0.0211181640625, 0.01373291015625, 0.054931640625, -0.0341796875, 0.01806640625, 0.0029754638671875, -0.0576171875, 0.032958984375, 0.0771484375, -0.0390625, -0.00634765625, 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
[ -0.00860595703125, -0.00469970703125, 0.0947265625, -0.07958984375, 0.04833984375, 0.01708984375, -0.033203125, 0.060302734375, 0.05908203125, 0.01104736328125, 0.041015625, 0.01611328125, -0.00872802734375, 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
[ -0.08056640625, 0.00360107421875, -0.018310546875, 0.028076171875, 0.00714111328125, 0.03515625, 0.09423828125, 0.007659912109375, 0.07373046875, -0.003143310546875, 0.048095703125, -0.080078125, -0.00994873046875, 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
[ 0.0098876953125, 0.0189208984375, -0.0186767578125, -0.02490234375, 0.006927490234375, -0.01318359375, -0.03564453125, 0.076171875, -0.050048828125, -0.036376953125, 0.007415771484375, -0.00714111328125, -0.05126953125, 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 it’s 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
[ -0.02197265625, -0.040283203125, 0.072265625, 0.027587890625, -0.00518798828125, 0.007415771484375, 0.00732421875, -0.05078125, -0.026611328125, -0.00341796875, 0.0625, -0.078125, -0.05908203125, -0.01202392578125, 0.04833984375, 0.05126953125, 0.0123291015625, 0.05322265625, 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 I’m going to write about here ...
4
[ -0.05419921875, -0.0458984375, -0.008544921875, 0.0125732421875, 0.08203125, 0.072265625, 0.0361328125, -0.020751953125, 0.01226806640625, 0.0194091796875, 0.053466796875, -0.0771484375, 0.057373046875, 0.006500244140625, -0.0301513671875, 0.0093994140625, 0.003204345703125, -0.004...
14,194
14194
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
[ -0.0908203125, -0.042236328125, 0.0196533203125, 0.038818359375, 0.0096435546875, -0.052978515625, -0.0225830078125, -0.032958984375, 0.060546875, -0.0115966796875, 0.02685546875, 0.01904296875, 0.020751953125, 0.006744384765625, -0.002166748046875, -0.0732421875, -0.034912109375, ...
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
[ 0.00006341934204101562, 0.0198974609375, -0.00099945068359375, 0.0291748046875, 0.0208740234375, 0.0194091796875, -0.048095703125, 0.099609375, -0.015625, 0.0181884765625, -0.0216064453125, 0.09814453125, 0.0400390625, 0.005615234375, -0.050048828125, -0.06298828125, -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
[ -0.10986328125, 0.05615234375, 0.03369140625, 0.058349609375, 0.0218505859375, -0.0223388671875, 0.04443359375, -0.0198974609375, 0.0029754638671875, -0.0169677734375, 0.0859375, -0.126953125, 0.0177001953125, 0.0732421875, 0.0654296875, -0.040771484375, -0.034912109375, 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
[ 0.0732421875, 0.055419921875, -0.02587890625, -0.0164794921875, -0.0712890625, 0.031494140625, -0.006927490234375, 0.01080322265625, -0.006927490234375, 0.0026092529296875, -0.050537109375, -0.0230712890625, -0.034912109375, -0.01123046875, -0.0133056640625, 0.06396484375, -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
[ -0.083984375, -0.025390625, -0.0380859375, -0.041259765625, -0.1279296875, 0.04833984375, -0.01953125, 0.1171875, 0.0230712890625, 0.00396728515625, 0.0166015625, 0.12890625, 0.006744384765625, -0.032958984375, -0.061767578125, 0.1171875, -0.06396484375, -0.0021820068359375, -0.0...
14,199
14199