content
string
quality_label
int64
meta
string
all-MiniLM-L6-v2_embedding
list
doc_id
int64
unique_id
string
Finding the Function Date: 12/17/96 at 11:03:39 From: Bolibar Elourdi, Adolfo Subject: Functions First of all, many thanks for your interest in our problem. We know the dependence of Y with each one of these five variables (a,b,c,d,e) as follows: Y= f(a) = 0.5* a^2 (with b,c,d,e as constants) Y= f(b) = 2*b...
5
[ -0.029296875, 0.0274658203125, 0.05224609375, -0.0576171875, 0.0091552734375, 0.03369140625, -0.05322265625, 0.004058837890625, 0.031005859375, 0.055419921875, 0.054443359375, -0.09765625, -0.0576171875, 0.035400390625, 0.0322265625, 0.039794921875, -0.08203125, 0.04248046875, -0...
13,000
13000
J2 Heat Conversion of work into heat and of heat into work The first main theorem, Impossibility of perpetuum mobile The first main theorem of Ther...
4
[ -0.1044921875, 0.006927490234375, -0.00933837890625, 0.07470703125, -0.036865234375, -0.0274658203125, -0.0084228515625, 0.02978515625, 0.05224609375, 0.0223388671875, 0.007354736328125, -0.017578125, 0.068359375, -0.0028076171875, 0.0234375, -0.0654296875, -0.00173187255859375, 0....
13,001
13001
Long Multiplication Chequer Board   Material Description: A board made up of 36 squares.  The squares are colour-coded to correspond to the categories of the decimal system, green for units, blue for tens, red for hundreds. On the base there is notation in black, right to left for the categories 1 to 100,000,000.  U...
4
[ -0.0257568359375, 0.0693359375, -0.0927734375, -0.03466796875, -0.0576171875, -0.0179443359375, 0.03564453125, 0.04833984375, 0.0128173828125, -0.0791015625, -0.004852294921875, 0.005126953125, 0.0291748046875, -0.03369140625, -0.05419921875, 0.0191650390625, -0.045166015625, 0.031...
13,002
13002
McNemar Tests of Marginal Homogeneity Back to Agreement Statistics page The McNemar test The McNemar test (McNemar, 1947; Sheskin, 2000, pp. 491-508; Somes, 1983) is an extremely simple way to test marginal homogeneity in K×K tables. T...
5
[ -0.0019378662109375, -0.057373046875, 0.00732421875, -0.025390625, 0.0047607421875, 0.0478515625, -0.06591796875, -0.041748046875, 0.0103759765625, 0.0673828125, 0.0634765625, -0.05615234375, 0.0419921875, 0.007415771484375, -0.025390625, 0.015869140625, -0.029052734375, 0.05444335...
13,003
13003
Finding an optimal monotone function? up vote 1 down vote favorite 1 Let $f$ and $g$ be two discrete signals. I want to find a monotone function h such that $h=argmin_{h}\sum_{n\in[0,N]}{(f(n)-h(g(n)))^2}$ I don't really care about finding the global optimum, I just want a good fit. What would be a good representati...
5
[ -0.06298828125, -0.023681640625, 0.04443359375, -0.0185546875, -0.09619140625, 0.020263671875, 0.03955078125, -0.0242919921875, -0.050537109375, -0.03857421875, -0.09814453125, 0.033447265625, 0.036865234375, -0.030029296875, -0.04052734375, 0.0296630859375, 0.08154296875, 0.016723...
13,004
13004
Algebraic equation From Encyclopedia of Mathematics An equation of the type polynomial of degree Here The values of the unknown The roots of a polynomial are related to its coefficients by Viète's formulas (cf. Viète theorem). To solve an equation means to find all its roots contained in the range of values of the...
4
[ -0.1044921875, 0.0294189453125, -0.0301513671875, 0.10693359375, -0.023193359375, 0.029052734375, 0.0203857421875, 0.040283203125, 0.0771484375, -0.0026702880859375, 0.0201416015625, 0.01611328125, 0.004669189453125, 0.04833984375, 0.0216064453125, 0.0279541015625, -0.0947265625, 0...
13,005
13005
A019863 - OEIS A019863 Decimal expansion of sine of 54 degrees. 12 8, 0, 9, 0, 1, 6, 9, 9, 4, 3, 7, 4, 9, 4, 7, 4, 2, 4, 1, 0, 2, 2, 9, 3, 4, 1, 7, 1, 8, 2, 8, 1, 9, 0, 5, 8, 8, 6, 0, 1, 5, 4, 5, 8, 9, 9, 0, 2, 8, 8, 1, 4, 3, 1, 0, 6, 7, 7, 2, 4, 3, 1, 1, 3, 5, 2, 6, 3, 0, 2, 3, 1, 4, 0, 9, 4, 5, 1, 2, 2, 4, 8, 5...
4
[ -0.032958984375, -0.0419921875, -0.1123046875, -0.0859375, -0.0225830078125, -0.037353515625, 0.04443359375, 0.087890625, -0.01434326171875, 0.039794921875, -0.03515625, -0.0035858154296875, 0.00970458984375, 0.0274658203125, -0.0267333984375, -0.01806640625, -0.019287109375, -0.08...
13,006
13006
Use The Formal Defintion Of Derivative To Find ... | Chegg.com formal definition of derivative, solution provided use the formal defintion of derivative to find the derivative of y= 5x^2 at x = -1 what i did: = f(x+h) - f(x) / h = 5(x+h)^2 - 5x^2 / h = 5(x^2 + 2hx + h^2) - 5x^2 / h = 5x^2 + 10hx +5h^2 - 5x^2 / h = 1...
4
[ -0.0245361328125, 0.013671875, 0.0966796875, -0.014892578125, 0.055419921875, -0.0017547607421875, -0.0050048828125, 0.0201416015625, -0.01519775390625, -0.044921875, 0.140625, -0.0240478515625, 0.00119781494140625, 0.0026092529296875, -0.0390625, 0.0625, -0.0458984375, -0.02136230...
13,007
13007
Falling in Water Name: Laura S Status: student Age: 17 Location: N/A Country: N/A Date: 1999 Question: I am trying to conduct an experiment relating to the effect of gravity on things falling in wa...
5
[ -0.051025390625, 0.0179443359375, 0.02001953125, 0.02490234375, -0.0074462890625, -0.0257568359375, 0.02490234375, 0.01202392578125, -0.041259765625, -0.02880859375, -0.014404296875, -0.10302734375, 0.022216796875, 0.1376953125, -0.038330078125, 0.0242919921875, 0.02685546875, 0.14...
13,008
13008
Solving differential equations November 10th 2008, 10:23 AM #1 Newbie Joined Oct 2008 Posts 6 Solving differential equations Find the specific solution for the following differential equations: a) (dy/dx)^2 - x^4 = 0 given the initial value y(1) = 0 b) dy/dx = ysinx given the initial value y(pi)...
4
[ -0.07421875, -0.00518798828125, 0.004852294921875, 0.0283203125, -0.050537109375, 0.05078125, -0.046875, 0.0004253387451171875, -0.031982421875, -0.037841796875, 0.076171875, 0.00022602081298828125, -0.015869140625, 0.0859375, 0.01068115234375, 0.042236328125, -0.03271484375, -0.03...
13,009
13009
Symmetry and the Fourth Dimension (Part 1) Coxeter complexes Though I’m shifting toward applied math, I find myself unable to quit explaining pure math to people—stuff that’s fun purely for its own sake. So, I’ve been posting about symmetry and the fourth dimension over on Google+. Now I want to take those posts, pol...
4
[ -0.0166015625, -0.0036773681640625, -0.0145263671875, -0.0091552734375, -0.06591796875, -0.044921875, -0.042236328125, -0.01104736328125, 0.0235595703125, 0.021728515625, -0.05615234375, -0.042724609375, -0.0189208984375, 0.0235595703125, 0.004241943359375, -0.04150390625, 0.00331115...
13,010
13010
One Chicken, One Day Date: 04/19/2002 at 10:20:39 From: Erryn Bard Subject: Fractions It's the same old chicken and egg question, but with a twist ending: If a chicken and a half lays an egg and a half in a day and a half, how many eggs can one chicken lay in one day? Date: 04/19/2002 at 12:25:12 From: Doctor Pete...
4
[ -0.0166015625, 0.04296875, 0.07080078125, 0.013427734375, -0.06689453125, 0.021240234375, -0.04541015625, -0.025634765625, 0.0213623046875, -0.004547119140625, 0.01373291015625, -0.047119140625, -0.054443359375, 0.046875, 0.0869140625, 0.01055908203125, -0.10205078125, 0.0074768066...
13,011
13011
of Drinfel'd module From Encyclopedia of Mathematics 2010 Mathematics Subject Classification: Primary: 11G09 Secondary: 11F7011R3922E55 [MSN][ZBL] A Drinfel'd $A$-module, (where $A$ is an appropriate ring) over a field $L$ of characteristic $p>0$ is an exotic $A$-module structure on the additive group $\def\Ga{\ma...
4
[ -0.1455078125, -0.05712890625, -0.039794921875, 0.07373046875, 0.0654296875, -0.04052734375, -0.022216796875, 0.0296630859375, 0.053466796875, -0.1201171875, 0.0267333984375, 0.034912109375, -0.049560546875, 0.00421142578125, 0.03515625, -0.08837890625, -0.048583984375, 0.110839843...
13,012
13012
Binary Multiplication http://www.exploringbinary.com/binary-multiplication/ This is the third of a four part series on “pencil and paper” binary arithmetic, which I’m writing as a supplement to my binary calculator. The first article discusses binary addition; the second article discusses binary subtraction; this art...
4
[ -0.0137939453125, -0.0106201171875, -0.08251953125, -0.06640625, -0.056640625, -0.08740234375, -0.01806640625, 0.04736328125, -0.005401611328125, 0.03662109375, -0.004547119140625, 0.0009002685546875, 0.07470703125, 0.0186767578125, -0.05029296875, 0.021240234375, -0.11669921875, 0...
13,013
13013
Integration with variable limits "Sanaa" wrote in message <kuim31$gkn$1@newscl01ah.mathworks.com>... > "Torsten" wrote in message <kuih1o$c4g$1@newscl01ah.mathworks.com>... > > "Sanaa" wrote in message <kuig3n$9d$1@newscl01ah.mathworks.com>... > > > "Steven_Lord" <slord@mathworks.com> wrote in message <ktb57u$el8$1@new...
5
[ -0.03173828125, 0.029052734375, -0.023681640625, -0.01123046875, -0.09033203125, 0.004974365234375, 0.022705078125, -0.01092529296875, 0.0234375, 0.034912109375, 0.046630859375, -0.045166015625, 0.09033203125, -0.0198974609375, -0.048583984375, 0.054443359375, -0.043701171875, 0.00...
13,014
13014
Sampling from a torus by Joseph Rickert One of the key ideas in topological data analysis is to consider a data set to be a sample from a manifold in some high dimensional topological space and then to use the tools of algebraic topology to reconstruct the manifold. It turns out that the converse problem of taking a r...
5
[ -0.078125, 0.001678466796875, -0.01953125, -0.005828857421875, 0.006622314453125, -0.0096435546875, 0.031005859375, -0.0341796875, 0.087890625, 0.0216064453125, -0.0037994384765625, -0.0230712890625, 0.08349609375, 0.0169677734375, 0.031494140625, -0.080078125, 0.01031494140625, 0....
13,015
13015
Pascal's Triangle - Concept Brightstorm is like having a personal tutor for every subject See what all the buzz is about Check it out Pascal's Triangle - Concept 16,613 views Pascal's triangle is a geometric arrangement of the binomial coefficients in the shape of a triangle. In Pascal's triangle, each number in t...
4
[ -0.043701171875, 0.04052734375, -0.053466796875, 0.068359375, -0.02490234375, 0.00176239013671875, 0.034912109375, -0.039306640625, 0.0260009765625, 0.01446533203125, -0.055419921875, -0.0228271484375, -0.0260009765625, -0.01300048828125, 0.078125, 0.0927734375, -0.07470703125, 0.0...
13,016
13016
Stable Marriages and Designing Markets Here is a fun puzzle. Suppose we have a group of 10 men and 10 women, and each of the men has sorted the women in order of their preference for marriage (that is, a man prefers to marry a woman earlier in his list over a woman later in the list). Likewise, each of the women has s...
5
[ -0.033203125, 0.016357421875, -0.0264892578125, -0.01007080078125, -0.031494140625, 0.032470703125, 0.005889892578125, 0.022216796875, 0.0311279296875, 0.052001953125, -0.01287841796875, 0.035400390625, 0.0277099609375, 0.031494140625, 0.0064697265625, 0.004974365234375, 0.0422363281...
13,017
13017
Searle's Bar for a good heat conductor Thermal Conductivity of a good conductor. Object Measure the thermal conductivity of Copper using the Searle's bar method. SAFETY WARNING This experiment uses steam heating. Be careful to avoid touching the hot surfaces of the steam generator, tubing and the Searle's bar appa...
4
[ -0.14453125, 0.01239013671875, -0.0634765625, -0.000698089599609375, -0.078125, 0.0019989013671875, -0.0242919921875, 0.0303955078125, -0.0059814453125, -0.05322265625, 0.0308837890625, -0.140625, 0.01220703125, -0.039794921875, -0.1171875, -0.091796875, -0.03271484375, 0.047607421...
13,018
13018
2010 The eruption of Mt. Pinatubo in the Philippines on June 15, 1991 provided a natural test of the climate system to radiative forcing by producing substantial cooling of global average temperatures over a period of 1 to 2 years. There have been many papers which have studied the event in an attempt to determine th...
4
[ -0.052978515625, 0.0133056640625, 0.10498046875, 0.11181640625, 0.054931640625, -0.1103515625, -0.08544921875, 0.07763671875, -0.03173828125, 0.040283203125, -0.01019287109375, -0.06396484375, 0.0247802734375, -0.02099609375, -0.03271484375, 0.01068115234375, -0.056640625, 0.013305...
13,019
13019
The Mechanism Of Population Doubling Malthus - The Principle Of Population In England in 1798, as the world population approached 1 billion, Malthus wrote "An Essay On The Principle Of Population". The principle was mathematical in nature, and stated that populations always tend towards exponential g...
4
[ -0.051025390625, -0.0194091796875, 0.05419921875, 0.05615234375, -0.04736328125, 0.00482177734375, -0.06982421875, 0.02392578125, -0.0537109375, 0.05908203125, 0.1083984375, 0.0595703125, -0.0179443359375, -0.042236328125, 0.01953125, -0.01116943359375, -0.06787109375, 0.0034179687...
13,020
13020
Jack's Blackboard The definitions of pseudoprimes The idea behind the AKS primality tests is not an original idea from its authors, but it can be traced back to Pierre de Fermat , in the 1600. The fundamental idea that Fermat had, and that is used in the AKS test, but also in the Miller-Rabin and Solovay-Strassen p...
4
[ -0.10107421875, -0.036865234375, -0.10546875, -0.00193023681640625, 0.06884765625, -0.01190185546875, 0.068359375, 0.06884765625, -0.01318359375, -0.025634765625, -0.06298828125, 0.054443359375, 0.01507568359375, 0.0263671875, -0.058837890625, -0.08203125, -0.0257568359375, -0.0086...
13,021
13021
Math Forum Discussions Math Forum Ask Dr. Math Discussions Internet Newsletter MathTools Teacher2Teacher Teacher Exchange Workshops Search All of the Math Forum: Views expressed in these public forums are not endorsed by Drexel University or The Math Forum. Topic: exponential regression Replies: 1 Last Post: Feb 3...
4
[ -0.06884765625, 0.023681640625, -0.0257568359375, 0.021240234375, 0.0017852783203125, -0.05078125, 0.048583984375, 0.0225830078125, 0.01708984375, 0.044677734375, 0.083984375, -0.00811767578125, 0.0947265625, 0.05029296875, 0.052001953125, 0.046630859375, -0.08935546875, -0.0590820...
13,022
13022
The Product Rule - Concept Brightstorm is like having a personal tutor for every subject See what all the buzz is about Check it out The Product Rule - Concept 18,702 views Use the product rule to find the derivative of the product of two functions--the first function times the derivative of the second, plus the se...
5
[ -0.043701171875, -0.08154296875, 0.06787109375, -0.01275634765625, -0.0303955078125, -0.01226806640625, 0.0615234375, 0.07373046875, 0.023193359375, 0.057861328125, 0.01611328125, 0.044189453125, 0.06640625, -0.0022125244140625, 0.023193359375, 0.09619140625, -0.040771484375, 0.137...
13,023
13023
For The Vector Matrix Difference Equation: X(k+1)=A ... | Chegg.com Vector Matrix Difference Equation, Zero State Response Image text transcribed for accessibility: For the vector matrix difference equation: x(k+1)=A x(k) + B r(k): A = : B=[1 0] y(k) = C x(k) + D r(k) rightarrow C = [ 1 2] : D = 3 Take the Z Transform...
4
[ -0.09228515625, 0.060302734375, -0.0576171875, -0.0078125, 0.007354736328125, -0.01043701171875, 0.00390625, 0.00665283203125, 0.024169921875, 0.06689453125, 0.044921875, -0.025390625, 0.056396484375, -0.042236328125, -0.01312255859375, 0.06591796875, -0.04541015625, -0.03930664062...
13,024
13024
Mastering Physics Solutions: Suspending Charged Particles Using Electric Fields Stopping the Proton Solution Below: Part A What must the charge (sign and magnitude) of a particle of mass 1.43 g be for it to remain stationary when placed in a downward-directed electric field of magnitude 660 N/C? Use 9.81 m/s ^2 f...
4
[ -0.04248046875, 0.0712890625, -0.0040283203125, 0.0181884765625, -0.043701171875, 0.019287109375, -0.01519775390625, 0.0308837890625, -0.091796875, 0.0024261474609375, 0.0186767578125, -0.002777099609375, -0.005828857421875, -0.053466796875, -0.06591796875, 0.0458984375, 0.0305175781...
13,025
13025
Eigenfaces, for Facial Recognition This post assumes familiarity with the terminology and notation of linear algebra, particularly inner product spaces. Fortunately, we have both a beginner’s primer on linear algebra and a follow-up primer on inner products. The Quest We are on a quest to write a program which recog...
4
[ -0.0537109375, 0.00506591796875, -0.0244140625, -0.09716796875, -0.03125, 0.002349853515625, -0.0172119140625, -0.0654296875, -0.07275390625, 0.0123291015625, 0.04248046875, -0.080078125, 0.0186767578125, 0.01806640625, 0.023193359375, -0.0732421875, 0.00170135498046875, 0.01098632...
13,026
13026
Is it possible to solve the argument maximization problem $\arg\max_x \langle x,l \rangle −f_1(x)−f_2(x)$ via convex duality? up vote 4 down vote favorite I am attempting to solve the argument maximization problem $$\arg\sup_x \{ \langle x,l \rangle − f_1(x)−f_2(x) \} \ \ \ \ \ \ \ \ \ \ (1)$$ where the functions $f...
4
[ -0.0732421875, -0.0791015625, 0.02197265625, -0.0986328125, -0.0019989013671875, -0.05322265625, 0.01507568359375, 0.0262451171875, -0.05517578125, 0.03564453125, -0.08984375, 0.0181884765625, 0.057861328125, -0.0030975341796875, 0.032470703125, 0.08056640625, 0.0098876953125, 0.02...
13,027
13027
Existence of a smooth function with nowhere converging Taylor series at every point up vote 12 down vote favorite 11 By Borel's theorem, for any sequence of real numbers $a_n,$ there is a $C^{\infty}$-function $f:\mathbb{R}\to\mathbb{R}$ whose Taylor series at 0 is $\sum a_nx^n.$ In particular, there are $C^{\ infty}$...
5
[ -0.11376953125, -0.06591796875, -0.07373046875, 0.126953125, 0.0250244140625, 0.048583984375, 0.0111083984375, -0.0299072265625, 0.0230712890625, -0.010009765625, 0.037109375, 0.01239013671875, -0.0067138671875, -0.032958984375, -0.05908203125, -0.038330078125, -0.0289306640625, -0...
13,028
13028
Rat Population Date: 04/27/99 at 14:09:33 From: Kimberly Cook Subject: Rat population This is a word problem. Help! Two rats, one male and one female, scampered on board a ship anchored at a local dock. The ship set sail across the ocean. When it reached a deserted island in late December, the two rats abandoned ...
4
[ 0.01422119140625, -0.0279541015625, -0.00653076171875, 0.056884765625, 0.008544921875, 0.01129150390625, -0.006591796875, -0.06005859375, -0.1044921875, 0.09619140625, 0.060546875, -0.08642578125, -0.0439453125, 0.0101318359375, -0.0201416015625, 0.007659912109375, -0.0294189453125, ...
13,029
13029
Is Your A/B Testing Tool Finding Differences That Aren't? Is Your A/B Testing Tool Finding Differences That Aren’t? You may not know it, your A/B testing tool may be finding differences that really aren’t. The tool may tell you that version 2 performs better than version 1 because it found statistically significant d...
5
[ 0.031494140625, -0.032958984375, 0.01153564453125, -0.046630859375, 0.00360107421875, -0.1357421875, -0.07275390625, 0.004058837890625, 0.0576171875, -0.04248046875, -0.02587890625, -0.025146484375, -0.034912109375, -0.0311279296875, 0.0615234375, 0.022216796875, 0.130859375, -0.06...
13,030
13030
Darwin's approach to X-ray diffraction on lateral crystalline structures Volume 70 Part 1 Pages 64-71 January ^aKomi Research Center, Ural Division, Russian Academy of Sciences, 167982, Syktyvkar, Russian Federation,^bSchool of Science and Technology, University of New England, NSW 2351, 2014 ...
4
[ -0.021484375, -0.040283203125, 0.07177734375, -0.033447265625, -0.039306640625, -0.06005859375, -0.0693359375, 0.103515625, -0.059814453125, 0.045654296875, -0.0247802734375, -0.0159912109375, 0.0272216796875, 0.06494140625, 0.0306396484375, -0.055419921875, -0.06640625, 0.01196289...
13,031
13031
Homework Help Posted by Hannah on Tuesday, July 7, 2009 at 8:15am. a sequence {an} is given by a1 = (3)^1/2 , an+1 = (3+an)^1/2. Show that {an} is monotonic and bounded, and calculate the limit if it exists • Math - Reiny, Tuesday, July 7, 2009 at 9:10am A(n) = √(3 + √(3 + √(3 + ...))..) to infinity let x ...
4
[ -0.06591796875, -0.0233154296875, -0.02783203125, -0.000720977783203125, -0.0927734375, 0.0069580078125, -0.0194091796875, 0.029296875, 0.0859375, -0.0098876953125, 0.03173828125, -0.02587890625, 0.0235595703125, 0.037841796875, -0.0216064453125, 0.008056640625, -0.01251220703125, ...
13,032
13032
Physics Archive | May 21, 2010 | Chegg.com Physics Archive: Questions from May 21, 2010 • Anonymous asked 0 answers • Anonymous asked 1 answer • Anonymous asked Three point charges are located at the corners of an equilateraltriangle as in the figure below. Fin... Show more Three poi...
5
[ -0.018310546875, 0.033447265625, -0.08251953125, -0.00762939453125, 0.0238037109375, -0.04248046875, 0.03662109375, 0.0537109375, 0.06298828125, 0.01239013671875, 0.07373046875, -0.123046875, 0.0169677734375, 0.0771484375, 0.0164794921875, -0.052490234375, -0.02197265625, -0.087402...
13,033
13033
Bundles of wood - Math Central Hi Darcy, If each bundle was 1 cubic foot it would take 128 of them to make a cord so each would be one, one hundred and twenty-eighth of a cord. If each bundle was 2 cubic foot it would take 128/2= 64 of them to make a cord so each would be one sixty fourth of a cord. If each bundle w...
4
[ -0.044189453125, -0.00933837890625, -0.07470703125, -0.01708984375, -0.0146484375, -0.0859375, -0.044189453125, 0.087890625, -0.040771484375, 0.046142578125, 0.01361083984375, -0.0186767578125, 0.052978515625, 0.10693359375, -0.07470703125, 0.03125, -0.0537109375, 0.051025390625, ...
13,034
13034
Symmetry and the Fourth Dimension (Part 4) Last time I posed a puzzle: figure out the Coxeter diagrams of the Platonic solids. When you do this, it’s hard to help noticing a cool fact: if you take a Platonic solid and draw a dot in the center of each face, these dots are the vertices of another Platonic solid, called...
4
[ -0.03466796875, -0.025390625, 0.01092529296875, 0.0164794921875, -0.055908203125, -0.0169677734375, -0.02001953125, -0.036376953125, 0.031494140625, -0.00360107421875, -0.052978515625, -0.0185546875, -0.039306640625, 0.0264892578125, 0.00164031982421875, -0.048583984375, -0.048583984...
13,035
13035
the Mean Aerodynamic Chord To Locate the Mean Aerodynamic Chord on a Tapered or Delta Wing Measure the root and tip chord. Then draw the following lines on the plans: • At the root of the wing, draw a line parallel to the centerline of the fuselage extending forward from the leading edge and rearward from the tra...
4
[ -0.0028533935546875, 0.064453125, -0.001068115234375, -0.10986328125, -0.040771484375, 0.01263427734375, -0.0732421875, 0.15234375, -0.005950927734375, -0.0322265625, 0.06689453125, -0.0390625, -0.056884765625, -0.0230712890625, -0.06787109375, -0.00982666015625, -0.03955078125, -0...
13,036
13036
How to calculate the inverse of the sum of two eigen-decomposed matrices up vote 2 down vote favorite The are two eigen-decomposed matrices $A$ = $U_1$$V_1$$U_1$$^H$, $B$ = $U_2$$V_2$$U_2$$^H$, in which $V_1$ and $V_2$ are the eigen-matrices formed by the non-negative eigenvalues and the eigenvalues are all less than ...
5
[ -0.0255126953125, 0.003875732421875, -0.103515625, -0.037353515625, -0.0262451171875, -0.07275390625, 0.031494140625, -0.146484375, -0.06689453125, -0.03271484375, 0.034423828125, -0.0155029296875, -0.0267333984375, -0.029541015625, -0.01177978515625, 0.049560546875, 0.0089111328125,...
13,037
13037
nrich.maths.org Copyright © University of Cambridge. All rights reserved. David from Mount Carmel School sent us his working to one of the problems: The numbers which can be divided by five but leave a remainder of four are: 4, 9, 14, 19, 24, 29, 34, 39, 44, 49, 54, 59, 64, 69, 74, 79, 84, 89, 94 and 99. The number...
4
[ 0.0220947265625, 0.08935546875, 0.041259765625, -0.0830078125, 0.0050048828125, 0.054931640625, 0.064453125, 0.07763671875, -0.0299072265625, -0.0130615234375, -0.068359375, -0.04052734375, 0.0274658203125, 0.047119140625, -0.0089111328125, -0.00096893310546875, -0.0400390625, 0.09...
13,038
13038
[SciPy-dev] Updated generic optimizers proposal dmitrey openopt@ukr.... Wed Apr 25 12:25:18 CDT 2007 Check for the case: objFun(x) = sum(x) x0 = [0 0 0 0 0 0 0 0 0 1] (or very small numbers instead of zeros, smaller than typicalDeltaX/50 for example) lb = zeros ub = ones (or any other) so if you use random shift for...
4
[ -0.0517578125, -0.06494140625, 0.0064697265625, -0.0184326171875, 0.0400390625, -0.0771484375, 0.06201171875, -0.0103759765625, -0.01458740234375, -0.00090789794921875, 0.076171875, -0.0361328125, -0.0034942626953125, -0.05859375, -0.015869140625, -0.01177978515625, 0.00836181640625,...
13,039
13039
Lower bound on number of tetrahedra needed to triangulate a knot complement up vote 8 down vote favorite 4 Following along a similar line to the question asked here: Is there an explicit bound on the number of tetrahedra needed to triangulate a hyperbolic 3-manifold of volume V? Let $K$ be a (hyperbolic) knot in $S^3...
4
[ 0.011474609375, 0.0164794921875, -0.08837890625, -0.0654296875, -0.0966796875, -0.0228271484375, -0.038818359375, 0.0301513671875, 0.003662109375, 0.04736328125, 0.0074462890625, -0.0634765625, -0.00127410888671875, -0.0703125, 0.000583648681640625, -0.0308837890625, 0.05322265625, ...
13,040
13040
sound (physics) :: Beats An important occurrence of the interference of waves is in the phenomenon of beats. In the simplest case, beats result when two sinusoidal sound waves of equal amplitude and very nearly equal frequencies mix. The frequency of the resulting sound (F) would be the average of the two original freq...
4
[ -0.004974365234375, -0.0390625, -0.0033721923828125, 0.0087890625, -0.0576171875, 0.03515625, -0.048828125, -0.068359375, 0.1201171875, -0.0194091796875, -0.00360107421875, -0.0439453125, 0.012939453125, -0.1181640625, 0.04345703125, 0.01312255859375, 0.06787109375, 0.041015625, ...
13,041
13041
Hodge star operator Context Riemannian geometry Basic definitions Further concepts Theorems Applications Differential geometry Contents Idea Given a finite dimensional (pseudo)-Riemannian manifold $(X,g)$, the Hodge star operator “completes” a $k$-differential form to the volume form of $(X,g)$. Definition L...
4
[ -0.10888671875, 0.0281982421875, 0.09716796875, -0.07861328125, -0.08203125, 0.047119140625, 0.031982421875, -0.049560546875, -0.01397705078125, -0.01153564453125, 0.0026092529296875, -0.0015869140625, 0.00848388671875, -0.060791015625, 0.0400390625, 0.0269775390625, -0.046875, 0.0...
13,042
13042
Is it possible to generate 40,000+ element of Fibonacci recursively in Lisp? up vote 2 down vote favorite 1 I'm trying to solve Project Euler question 2 with Lisp. This recursive solution blows the stack on execution, but I thought Lisp (using clisp) would recognize the tail recursion. This is being entered into the t...
5
[ -0.04638671875, -0.01507568359375, -0.01507568359375, -0.0712890625, 0.00872802734375, -0.06640625, 0.0111083984375, 0.08935546875, -0.009765625, 0.051025390625, -0.0128173828125, -0.0634765625, -0.03173828125, 0.012451171875, -0.07958984375, -0.008544921875, -0.001953125, -0.00665...
13,043
13043
Electronics Fundamentals 4A and 4B 4A Fundamentals of Electronics IA (3 units) CSU Lecture 3 hours. Recommended Corequisite: Electronics 4B. The first class for electronics majors. Atomic theory, voltage, resistance, current, energy and power, Ohm's law, series-parallel circuits, voltage and current dividers. Networ...
4
[ -0.023681640625, 0.072265625, -0.00469970703125, -0.064453125, -0.07421875, 0.01318359375, -0.050537109375, 0.048828125, -0.045166015625, 0.05126953125, 0.023681640625, -0.072265625, 0.10107421875, -0.021240234375, -0.027099609375, 0.028564453125, -0.0419921875, -0.01519775390625, ...
13,044
13044
Calculating pi with AGM and mpmath This post gives an algorithm based on the arithmetic-geometric mean that rapidly converges to pi. I’ll use it to illustrate multiple precision arithmetic using Python’s mpmath module. Given two non-negative numbers a and b, their arithmetic mean is (a + b)/2 and their geometric mean...
5
[ -0.061767578125, -0.060546875, -0.072265625, -0.0002803802490234375, -0.07421875, -0.058349609375, -0.0267333984375, 0.083984375, 0.0103759765625, 0.0115966796875, 0.00848388671875, 0.078125, 0.1064453125, -0.01495361328125, -0.007568359375, -0.0189208984375, 0.0186767578125, -0.00...
13,045
13045
MathFiction: Eye of the Beholder (Alex Kasman) Shortly after a stunning success in her research, personal tragedy forces a math professor to change careers and begin work at the NSA where her work on cryptography involves some difficult ethical decisions. This is one of the stories in my collection Reality Conditions a...
4
[ -0.0029754638671875, -0.060546875, -0.04736328125, -0.0289306640625, -0.0654296875, 0.045654296875, 0.057373046875, 0.0311279296875, 0.0966796875, 0.0252685546875, -0.078125, 0.09765625, -0.005889892578125, 0.060546875, -0.035400390625, -0.0299072265625, -0.07373046875, 0.060546875...
13,046
13046
How Many Possible Combinations Are There On A 5 Digit Lock Combination Lock On A Suitcase Has 5 Wheels, Each Labeled With Digits 1 To 8. ? Combination lock on a suitcase has 5 wheels, each labeled with digits 1 to 8. ? - how many possible combinations are there on a 5 digit lock 5 How a combination lock code two digit...
4
[ -0.041015625, -0.0068359375, 0.01275634765625, -0.03662109375, 0.025390625, 0.1376953125, 0.04052734375, 0.0008087158203125, 0.02783203125, 0.06640625, 0.0498046875, 0.0279541015625, 0.0213623046875, -0.0029754638671875, -0.038818359375, 0.0751953125, -0.1142578125, -0.006988525390...
13,047
13047
If two projections are close, then they are unitarily equivalent up vote 5 down vote favorite Given two projections $p,q\in B(H)$, it is well-known that if $\|p-q\|<1$, then there exists a unitary $u\in B(H)$ with $q=upu^*$. The proof that immediately occurs to me uses comparison of projections (the inequality forces...
5
[ -0.08056640625, 0.0272216796875, -0.045654296875, -0.046142578125, -0.07861328125, 0.0732421875, 0.01519775390625, -0.026123046875, -0.010986328125, -0.068359375, -0.06201171875, -0.02978515625, 0.0791015625, 0.03466796875, -0.00008153915405273438, -0.003753662109375, 0.068359375, ...
13,048
13048
A conjecture on intersection of some intervals. up vote 9 down vote favorite It was proved here that if $a\in \mathbb{N}_{\geq3}$ then $$\bigcap_{i = 1}^{a} \bigcup_{j = 0}^{i-1} \left[\frac{1+aj}{i},\frac{a(j+1)-1}{i}\right] = \varnothing \tag{1}$$ It may be conjectured that forcing $i\ne b$, where $1\leq b< a$, re...
5
[ -0.031005859375, 0.0206298828125, 0.03662109375, -0.0205078125, -0.0098876953125, -0.0140380859375, 0.08740234375, -0.041259765625, -0.0023040771484375, -0.01483154296875, -0.06982421875, -0.04345703125, 0.08740234375, 0.015380859375, 0.00164031982421875, -0.005584716796875, 0.012939...
13,049
13049
Detection of rare functional variants using group ISIS Abstract Genome-wide association studies have been firmly established in investigations of the associations between common genetic variants and complex traits or diseases. However, a large portion of complex traits and diseases cannot be explained well by common v...
4
[ 0.0019683837890625, -0.041015625, 0.015625, 0.006195068359375, 0.038818359375, -0.0159912109375, 0.04296875, -0.0267333984375, -0.01531982421875, -0.07470703125, 0.07470703125, -0.00567626953125, -0.0263671875, -0.016845703125, -0.053466796875, 0.0164794921875, -0.0712890625, 0.003...
13,050
13050
Time: Seconds, 24-hour Clock and Duration The second is a unit of measurement of time. It is smaller than the minute. We use the second to tell a moment of time more accurately or precisely. We use h to denote hour, min to denote minute and s to denote second. 1 minute = 60 seconds 1 min = 60 s We use h to denote hour...
4
[ 0.0673828125, 0.0966796875, 0.037109375, -0.0289306640625, -0.038818359375, 0.00250244140625, -0.01177978515625, 0.095703125, 0.0634765625, -0.000736236572265625, 0.047607421875, 0.01190185546875, 0.046875, 0.007171630859375, -0.005828857421875, -0.042724609375, -0.04833984375, 0.0...
13,051
13051
Ship's Bearing Associated Topics || Dr. Math Home || Search Dr. Math Ship's Bearing Date: 8/22/96 at 13:7:3 ...
4
[ -0.024169921875, 0.05224609375, 0.046630859375, 0.022705078125, -0.046875, 0.022705078125, -0.1015625, 0.06982421875, -0.0498046875, -0.009521484375, 0.0341796875, 0.047607421875, -0.03662109375, 0.01470947265625, -0.0810546875, 0.00927734375, -0.00689697265625, -0.0302734375, 0....
13,052
13052
Number Bases As pointed out in the discussion Why Study Math various schemes were used to represent numbers throughout the ages. All of these systems did not support fundamental operations such as addition and subtraction. It was not until the idea of a base to define a number system was developed that number represent...
4
[ -0.043212890625, -0.01708984375, -0.01202392578125, -0.099609375, -0.0225830078125, 0.0218505859375, -0.04052734375, 0.1259765625, 0.1435546875, 0.031982421875, -0.0400390625, 0.0303955078125, 0.054931640625, 0.054443359375, -0.0235595703125, -0.10693359375, -0.1064453125, 0.043212...
13,053
13053
How can I perform a Mantel test in R? R FAQ: How can I perform a Mantel test in R? A Mantel test measures the correlation between two matrices typically containing measures of distance. A Mantel test is one way of testing for spatial autocorrelation. Using functions in the ade4 library, we can perform a Mantel test ...
5
[ -0.002716064453125, -0.0250244140625, -0.0673828125, 0.053955078125, -0.00762939453125, -0.038818359375, -0.06591796875, -0.00982666015625, -0.052978515625, -0.00994873046875, -0.0028076171875, -0.0277099609375, -0.0478515625, 0.05517578125, 0.047119140625, -0.06494140625, -0.0070190...
13,054
13054
Systems of Linear Equations March 30th 2008, 06:13 AM #1 Newbie Joined Mar 2008 Posts 2 Systems of Linear Equations x + 3y - z = 13 2x -5z = 23 4x - y -2z = 14 I have no idea how to start this. please help me! thanks. Re: Systems of Linear Equations Solution: Given x + 3y - z = 13...
4
[ -0.09130859375, 0.03369140625, -0.06884765625, -0.0390625, 0.03173828125, 0.0045166015625, 0.00096893310546875, -0.038330078125, -0.09521484375, -0.00151824951171875, 0.0390625, 0.0216064453125, 0.06884765625, -0.0106201171875, -0.04931640625, 0.0272216796875, -0.08740234375, 0.006...
13,055
13055
Declination In astronomy Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth... , declination (abbrev. dec or δ ) is one of the two coordinates of the equatorial coordinate system The equatorial coordinate system is a wid...
4
[ 0.0269775390625, -0.0140380859375, 0.00439453125, -0.080078125, -0.030029296875, -0.08935546875, -0.0390625, 0.017822265625, 0.1474609375, 0.007720947265625, 0.0291748046875, 0.0024566650390625, 0.00457763671875, -0.02099609375, 0.003265380859375, -0.1123046875, -0.0390625, 0.01892...
13,056
13056
Hypergeometric Calculator Hypergeometric Calculator: Online Statistical Table The Hypergeometric Calculator makes it easy to compute individual and cumulative hypergeometric probabilities. For help, read the Frequently-Asked Questions or review the Sample Problems. To learn more, read Stat Trek's tutorial on the hype...
5
[ 0.08740234375, 0.017333984375, 0.07861328125, -0.033447265625, -0.078125, -0.06298828125, 0.0145263671875, 0.01025390625, 0.001312255859375, 0.0194091796875, -0.000942230224609375, -0.08349609375, 0.052490234375, -0.041748046875, 0.0712890625, -0.0050048828125, 0.00604248046875, -0...
13,057
13057
Information Geometry (Part 1) I’d like to provide a bit of background to this interesting paper: • Gavin E. Crooks, Measuring thermodynamic length. which was pointed out by John F in our discussion of entropy and uncertainty. The idea here should work for either classical or quantum statistical mechanics. The paper...
4
[ -0.041748046875, -0.039794921875, 0.03515625, 0.0235595703125, -0.036376953125, 0.000827789306640625, 0.04541015625, 0.01324462890625, 0.0712890625, -0.03466796875, -0.0074462890625, -0.056396484375, 0.05126953125, 0.025146484375, -0.035400390625, -0.0269775390625, 0.06591796875, -...
13,058
13058
a.e. convergence of the powers of an operator built from rotations up vote 7 down vote favorite 1 Consider two numbers $a,b\in R/Z$ and some integer $p\geq 1$. Let $T:L^p(R/Z)\rightarrow L^p(R/Z)$ be the operator given by $$T(f)(x)=1/2(f(x+a)+f(x+b))$$ For which values of $a,b$ do we have almost everywhere convergenc...
4
[ -0.0244140625, -0.0284423828125, -0.06884765625, -0.0166015625, 0.0206298828125, 0.0791015625, 0.091796875, -0.01019287109375, -0.00010728836059570312, -0.0247802734375, 0.0233154296875, 0.052490234375, 0.0216064453125, -0.0281982421875, 0.008056640625, -0.052490234375, -0.0088500976...
13,059
13059
dy Got Homework? Connect with other students for help. It's a free community. • across MIT Grad Student Online now • laura* Helped 1,000 students Online now • Hero College Math Guru Online now Here's the question you clicked on: onegirl Group Title Find an equation of th...
4
[ -0.036865234375, 0.0032958984375, -0.001922607421875, -0.01007080078125, 0.0478515625, 0.021728515625, 0.050048828125, 0.04150390625, -0.033935546875, 0.044189453125, 0.107421875, -0.06396484375, -0.00836181640625, -0.0247802734375, 0.02392578125, 0.059326171875, -0.06494140625, -0...
13,060
13060
Sum of Fibonacci Series Date: 05/23/2000 at 04:40:14 From: Edward Barton Subject: Fibonacci sequence Is there any formula for the sum of the first n numbers in the Fibonacci sequence? I've been looking for one without success. I did find a quartic equation that worked for the first few (five or six), but it got prog...
5
[ -0.07958984375, -0.0184326171875, 0.03759765625, 0.00063323974609375, -0.0201416015625, -0.0003643035888671875, -0.043701171875, 0.00750732421875, 0.09521484375, 0.08203125, -0.04248046875, -0.012451171875, -0.08349609375, 0.07861328125, -0.08251953125, 0.021484375, -0.12109375, -0...
13,061
13061
Gaussian elimination From CFD-Wiki (Difference between revisions) Jasond (Talk | contribs) Jasond (Talk | contribs) ← Older edit Newer edit → Line 1: ...
4
[ -0.10400390625, -0.017822265625, 0.0201416015625, -0.0208740234375, 0.0230712890625, -0.046142578125, 0.1279296875, -0.0791015625, 0.00634765625, 0.0341796875, 0.07080078125, 0.1064453125, 0.0908203125, -0.10205078125, -0.046875, 0.007568359375, -0.00909423828125, -0.0576171875, ...
13,062
13062
. 5. BIAS AND HIERARCHICAL CLUSTERING The biggest stumbling-block for attempts to confront theories of cosmological structure formation with observations of galaxy clustering is the uncertain and possibly biased relationship between galaxies and the distribution of gravitating matter. The idea that galaxy formation m...
4
[ -0.052978515625, -0.1015625, 0.025390625, 0.09521484375, 0.037109375, 0.0020751953125, -0.046875, 0.036376953125, 0.11376953125, -0.020751953125, -0.0101318359375, -0.047607421875, 0.0556640625, -0.03857421875, 0.052978515625, -0.06298828125, 0.06396484375, -0.0810546875, -0.0732...
13,063
13063
Chebyshev wavelets method for solving Bratu’s problem Abstract A numerical method for one-dimensional Bratu’s problem is presented in this work. The method is based on Chebyshev wavelets approximates. The operational matrix of derivative of Chebyshev wavelets is introduced. The matrix together with the collocation met...
5
[ -0.062255859375, 0.057373046875, -0.033935546875, -0.142578125, -0.041259765625, -0.005126953125, -0.0191650390625, 0.08447265625, -0.0069580078125, -0.022705078125, 0.027587890625, 0.05126953125, -0.0257568359375, -0.09521484375, -0.0169677734375, -0.024658203125, -0.09765625, -0....
13,064
13064
Algebra Hence, if (x, y) be the co-ordinates of P, as w* varies continuously from - oo to +00, P will describe continuously the right-hand branch A'AA" of the rectangular hyperbola, whose semi-axis-major is OA = a, in the direction indicated by the arr...
4
[ 0.00726318359375, 0.01165771484375, 0.000012159347534179688, -0.004180908203125, 0.026123046875, -0.11474609375, 0.0625, -0.01104736328125, 0.08837890625, -0.023681640625, 0.115234375, -0.0191650390625, -0.04931640625, -0.0091552734375, 0.007354736328125, -0.0230712890625, -0.0722656...
13,065
13065
Power and rate allocation for video conferencing in cellular networks Abstract We consider resource allocation for semi-elastic applications such as video conferencing. We propose to model user utility as a sigmoid function of the average bit rate over multiple time slots. The goal is to maximize the total expected us...
4
[ 0.0123291015625, -0.007110595703125, 0.0155029296875, -0.10400390625, -0.052001953125, -0.03564453125, 0.0615234375, 0.05419921875, 0.052490234375, 0.0260009765625, -0.08447265625, 0.046630859375, 0.033203125, 0.018798828125, -0.0203857421875, 0.0595703125, 0.091796875, -0.01806640...
13,066
13066
Inverting a covariance matrix numerically stable up vote 4 down vote favorite 1 Given an $n\times n$ covariance matrix $C$ where $n$ around $250$, I need to calculate $x\cdot C^{-1}\cdot x^t$ for many vectors $x \in \mathbb{R}^n$ (the problem comes from approximating noise by an $n$-dimensional Gaussian distribution)....
4
[ -0.04931640625, -0.08056640625, 0.0201416015625, -0.051513671875, 0.057861328125, -0.072265625, -0.046875, -0.015625, -0.06689453125, 0.04248046875, -0.0177001953125, 0.072265625, -0.01275634765625, -0.0191650390625, -0.060791015625, 0.06103515625, 0.0693359375, 0.046142578125, 0...
13,067
13067
Double integral change of variable examples Example 1 Compute the double integral \begin{align*} \iint_\dlr g(x,y) dA \end{align*} where $g(x,y)=x^2+y^2$ and $\dlr$ is disk of radius 6 centered at origin. Solution: Since computing this integral in rectangular coordinates is too difficult, we change to polar coordinat...
5
[ -0.07421875, -0.050537109375, -0.037353515625, -0.1298828125, 0.05126953125, -0.0167236328125, -0.037353515625, 0.0224609375, -0.0230712890625, 0.0615234375, 0.004058837890625, 0.08740234375, -0.0233154296875, 0.005401611328125, 0.021728515625, -0.0093994140625, -0.052001953125, 0....
13,068
13068
Invertible STFT and ISTFT in Python up vote 25 down vote favorite 11 Is there any general-purpose form of short-time Fourier transform with corresponding inverse transform built into SciPy or NumPy or whatever? There's the pyplot specgram function in matplotlib, which calls ax.specgram(), which calls mlab.specgram(),...
5
[ -0.11376953125, -0.025390625, -0.09326171875, -0.00421142578125, 0.0166015625, -0.011474609375, 0.00167083740234375, 0.037353515625, -0.011474609375, -0.03857421875, -0.006500244140625, 0.00067138671875, -0.0186767578125, 0.0025482177734375, 0.0791015625, -0.0281982421875, 0.03637695...
13,069
13069
Jamie Craane's Blog Out of interest I am familiarizing myself in genetic algorithms, in short GA. My interest in GA came when I first heard about the JGAP project. As mentioned on the project's site "JGAP (pronounced "jay-gap") is a Genetic Algorithms and Genetic Programming component provided as a Java framework.". Fo...
5
[ -0.15234375, 0.030517578125, -0.04638671875, 0.0191650390625, -0.01416015625, -0.0021209716796875, 0.029541015625, -0.000518798828125, -0.10009765625, -0.041015625, -0.0732421875, 0.0289306640625, 0.044921875, -0.058349609375, -0.07421875, -0.0157470703125, 0.0419921875, 0.00098419...
13,070
13070
Duration Philippe Jorion's Orange County Case: 2.1 Duration Definition Duration is a characteristic of a bond. For fixed-coupon bonds, duration can be intuitively defined as the average maturity of all bond payments, where each payment is weighted by its value. In the fixed-income market, duration is an essenti...
4
[ 0.013427734375, 0.04736328125, -0.0172119140625, 0.0294189453125, 0.0223388671875, -0.02294921875, -0.0830078125, 0.0037384033203125, 0.09521484375, -0.03369140625, 0.038330078125, -0.00885009765625, -0.0198974609375, 0.00107574462890625, -0.004150390625, -0.02685546875, -0.040283203...
13,071
13071
Primes and $x^2+2y^2+4z^2$ up vote 13 down vote favorite 3 A few months ago, I have asked a question about primes represented by ternary quadratic forms. I got two wonderful answers, which showed me how the theory was way richer and more complex that I naively expected from the case of binary forms. I was also given a...
5
[ -0.044189453125, -0.03173828125, 0.00811767578125, 0.0225830078125, 0.0186767578125, 0.0257568359375, 0.05908203125, 0.0267333984375, 0.0157470703125, -0.0027923583984375, -0.0235595703125, 0.0693359375, 0.033203125, 0.0269775390625, 0.0269775390625, -0.0084228515625, 0.0240478515625...
13,072
13072
Solving by Interpolation Date: 05/30/2001 at 05:04:47 From: Rosly Subject: Exponential equation Dear Dr. Math, Given y = 10 and b = 1.419, find X from this equation: y = ( b^(-0.25X)) + 0.84X I have X, but when I replaced in the equation above, I couldn't get y = 10. I really appreciate your consultation. D...
5
[ -0.0654296875, 0.0019378662109375, 0.0203857421875, 0.007537841796875, -0.004119873046875, -0.050537109375, 0.0595703125, 0.052734375, -0.00604248046875, -0.0120849609375, 0.018310546875, 0.01190185546875, 0.06787109375, 0.0830078125, 0.12060546875, 0.1279296875, -0.083984375, -0.0...
13,073
13073
Simplifying algebraic expressions Simplifying algebraic expressions with one or more variables by combining like terms is what this lesson will show you. We will show you first how to simplify numerical expressions. Let's say you are adding 5 + 5 + 5 + 5. What is a quick way to get the answer? You can do 4 × 5 and...
4
[ 0.0089111328125, 0.0654296875, 0.00634765625, -0.01092529296875, 0.0074462890625, 0.0361328125, -0.042724609375, -0.0390625, 0.03271484375, 0.0458984375, 0.007659912109375, 0.003082275390625, -0.056396484375, 0.0286865234375, -0.027099609375, 0.0137939453125, -0.11474609375, 0.1523...
13,074
13074
Checkerboard Squares Date: 09/29/97 at 18:40:08 From: Tasha Gibson Subject: Checkerboard squares My teacher gives us a problem of the week and I haven't really been able to figure out this last one. Here's the question: Say you have an 8x8 checkerboard. There are many other little and big squares inside of that so ...
4
[ 0.142578125, 0.0201416015625, -0.004913330078125, -0.018310546875, -0.0155029296875, 0.0673828125, -0.046630859375, 0.0201416015625, -0.02294921875, -0.00013828277587890625, -0.033935546875, 0.06689453125, -0.051025390625, 0.04150390625, -0.12890625, -0.049560546875, -0.0025634765625...
13,075
13075
Cycling Motion Problem Associated Topics || Dr. Math Home || Search Dr. Math Cycling Motion Problem Date: 6/26/96...
4
[ 0.05810546875, 0.0888671875, -0.003082275390625, -0.06982421875, -0.05126953125, 0.0294189453125, -0.04541015625, 0.11865234375, -0.076171875, -0.017822265625, -0.01312255859375, -0.055419921875, 0.018310546875, 0.034423828125, 0.0172119140625, 0.05810546875, -0.0390625, 0.09179687...
13,076
13076
nrich.maths.org Copyright © University of Cambridge. All rights reserved. Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. Choose several different sets of four consecutive whole numbers and do the same. What do you notice? Can you explain wha...
4
[ -0.01019287109375, 0.037841796875, 0.01116943359375, -0.0771484375, -0.02587890625, 0.021484375, -0.0028533935546875, 0.0034637451171875, 0.072265625, -0.0888671875, -0.041015625, 0.05078125, 0.0361328125, -0.00107574462890625, -0.032470703125, -0.0654296875, -0.0184326171875, -0.0...
13,077
13077
Entropy conjecture for distributions over $\mathbb{Z}_n$ up vote 7 down vote favorite 1 Suppose we have two independent random variables $X$ (with distribution $p_X$) and $Y$ (with distribution $p_Y$) which take values in the cyclic group $\mathbb{Z}_n$. Let $Z = X +Y$, where the addition is done modulo $n$. Distribut...
4
[ -0.08837890625, 0.003204345703125, 0.0211181640625, 0.00701904296875, 0.06982421875, 0.019775390625, 0.09521484375, 0.005706787109375, -0.032470703125, -0.0274658203125, 0.0272216796875, 0.049072265625, 0.047119140625, 0.0361328125, 0.0167236328125, -0.0098876953125, -0.0033874511718...
13,078
13078
Formal Schemes Mittag Leffler up vote 16 down vote favorite 3 Here is a question that I'm just copying from Math Stack Exchange that I asked awhile ago. It has just been sitting there unanswered, and although I haven't really thought about it since I posted it, I'm still very interested in a nice example if it exists....
4
[ -0.142578125, -0.0196533203125, 0.041015625, -0.0218505859375, 0.10986328125, -0.09619140625, 0.1044921875, 0.01171875, -0.0038299560546875, -0.103515625, 0.08447265625, 0.0234375, 0.049560546875, -0.08056640625, -0.031982421875, 0.056396484375, 0.07470703125, 0.002105712890625, ...
13,079
13079
dy Got Homework? Connect with other students for help. It's a free community. • across MIT Grad Student Online now • laura* Helped 1,000 students Online now • Hero College Math Guru Online now Here's the question you clicked on: aboveit Group Title A 120-foot-long rope i...
4
[ -0.045654296875, 0.045654296875, 0.0024871826171875, -0.0291748046875, -0.03857421875, 0.026611328125, 0.060791015625, -0.000942230224609375, -0.08837890625, 0.048095703125, 0.0625, -0.0164794921875, 0.0289306640625, -0.037109375, -0.026123046875, 0.09326171875, -0.11083984375, 0.0...
13,080
13080
Separation of Variables January 5th 2011, 01:41 PM #1 MHF Contributor Joined Mar 2010 From Florida Posts 3,093 Thanks 5 Separation of Variables $u_{xyz}-xyzu=0$ $\varphi'(x)\psi'(y)\omega'(z)-xyz\varphi(x)\psi(y)\omega(z)=0$ $\displaystyle\frac{\varphi'(x)}{\varphi(x)}=\frac{ xyz\psi(y)...
5
[ -0.10546875, -0.0172119140625, 0.041748046875, 0.0322265625, -0.030517578125, 0.053955078125, 0.03564453125, -0.09619140625, -0.044921875, 0.006683349609375, 0.09765625, 0.038818359375, 0.00921630859375, -0.003143310546875, 0.0859375, 0.0478515625, -0.053955078125, -0.10107421875, ...
13,081
13081
Pi-algebra Context Homotopy theory Background Variations Definitions Paths and cylinders Homotopy groups Theorems Contents Idea A $\Pi$-algebra is an algebraic model for the homotopy groups $\pi_*X$ of a pointed topological space, $X$, together with the action of the primary homotopy operations on them, in th...
4
[ -0.04638671875, -0.00830078125, -0.0267333984375, 0.000537872314453125, -0.10205078125, 0.09912109375, 0.0228271484375, 0.038330078125, 0.04443359375, 0.00185394287109375, -0.0257568359375, -0.00933837890625, -0.0096435546875, 0.0230712890625, 0.08642578125, -0.0595703125, -0.0121459...
13,082
13082
Computing the Factoradic Rank of a Permutation (N choose K) up vote 3 down vote favorite 2 I've recently learnt about CNS and FNS, and since they look so elegant to me, I decided to try and implement methods to generate combinations and permutations using those techniques. I finished my method to convert from n choose...
5
[ -0.047119140625, -0.07373046875, -0.059326171875, -0.06201171875, -0.0174560546875, 0.076171875, 0.042236328125, -0.0181884765625, 0.013916015625, 0.03076171875, 0.0216064453125, 0.031494140625, 0.068359375, -0.04345703125, -0.0693359375, 0.05029296875, -0.047119140625, 0.030395507...
13,083
13083
Are there countable index subrings of the reals? up vote 17 down vote favorite 7 1. Does ${\mathbb R}$ have proper, countable index subrings? By countable I mean finite or countably infinite. By subring I mean any additive subgroup which is closed under multiplication (I don't care if it contains $1$.) By index, ...
5
[ -0.000713348388671875, -0.06201171875, -0.08544921875, 0.07373046875, -0.04345703125, 0.00083160400390625, 0.029296875, 0.027099609375, 0.072265625, -0.10986328125, -0.06591796875, 0.0106201171875, 0.040283203125, 0.0341796875, -0.0849609375, -0.057373046875, 0.0037994384765625, -0...
13,084
13084
Equations, Inequalities and Basic Logic 1.5 QUADRATIC INEQUALITIES In Section 1.3 we solved inequalities of the type In this section we shall learn about procedures for solving First, let us consider the simple quadratic inequality x^2 b. Since x^2 ≥ 0, if b < 0, there is no solution for this inequality. Here, we mu...
4
[ -0.08251953125, 0.05712890625, 0.064453125, 0.0198974609375, -0.052978515625, 0.0274658203125, 0.019287109375, 0.04150390625, 0.054443359375, -0.02294921875, 0.05078125, 0.00732421875, 0.0849609375, 0.0004138946533203125, 0.05029296875, 0.05810546875, -0.03662109375, -0.08251953125...
13,085
13085
ion Decimal To Hex Conversion A recent project required a decimal to hex conversion. In LotusScript, this is very basic. But this needed to be done in formula language for this particular application. So we wrote a decimal to hex conversion using looping in the R6 formula language. Since just about every calculator o...
4
[ 0.01483154296875, 0.099609375, -0.0157470703125, -0.0255126953125, -0.076171875, 0.028076171875, 0.045654296875, 0.07958984375, -0.0025482177734375, -0.00628662109375, 0.01416015625, -0.040771484375, -0.01904296875, 0.031982421875, -0.00482177734375, -0.04833984375, -0.1005859375, ...
13,086
13086
B-Tree B-Trees: Balanced Tree Data Structures Introduction Tree structures support various basic dynamic set operations including Search, Predecessor, Successor, Minimum, Maximum, Insert, and Delete in time proportional to the height of...
4
[ -0.0400390625, 0.052001953125, -0.052001953125, 0.027587890625, -0.005096435546875, -0.0712890625, -0.043212890625, 0.0546875, 0.0289306640625, 0.030517578125, -0.038818359375, 0.06103515625, 0.047607421875, -0.037109375, -0.01416015625, 0.09521484375, -0.057373046875, 0.0130615234...
13,087
13087
Statics eBook: Introduction to Distributed Loads STATICS - THEORY In many static problems, applied loads are given as distributed force loads. This is similar to stacking sand bags on a beam so that the load is...
4
[ -0.048583984375, -0.01556396484375, -0.045166015625, -0.00604248046875, -0.0220947265625, -0.04833984375, -0.021484375, 0.0198974609375, 0.032958984375, 0.07177734375, -0.0264892578125, 0.031005859375, 0.021240234375, 0.03662109375, -0.035400390625, 0.01385498046875, -0.0041198730468...
13,088
13088
Solar for Heat... Ouch! - Wood, Gas, Oil, Geothermal and Other Heating Units Came across this site that gives you a formula to determine the amount of solar panels you would need to replace current needs: http://www.solar-electric.com/solar_system_costs.htm # First, take number of KWH shown on your bill. Divi...
4
[ 0.0595703125, 0.014404296875, 0.0751953125, 0.0341796875, -0.006500244140625, -0.0810546875, 0.031005859375, -0.0208740234375, -0.0228271484375, 0.0225830078125, -0.056884765625, -0.080078125, 0.01531982421875, 0.0228271484375, 0.052978515625, 0.0238037109375, 0.000484466552734375, ...
13,089
13089
Linear interpolation From Encyclopedia of Mathematics A method for the approximate calculation of the value of a function $f(x)$, based on the replacement of $f(x)$ by a linear function \[ L(x)=a(x-x_1)+b,\] the parameters $a$ and $b$ being chosen in such a way that the values of $L(x)$ coincide with the values of ...
4
[ -0.13671875, -0.048095703125, 0.0634765625, -0.06201171875, 0.035400390625, -0.00970458984375, -0.0203857421875, 0.007293701171875, 0.00909423828125, 0.01190185546875, 0.0189208984375, -0.0211181640625, 0.10498046875, -0.078125, 0.0576171875, 0.0888671875, -0.095703125, 0.014404296...
13,090
13090
Prime Surrogates for Demented Denormalization So here's the issue. I've got a code translation / lookup table that's denormalized with three values, like so: A B C AB AC BC ABC Each combination has its own description. And the values are always ordered lowest-to-highest (always ABC, not CBA). The objects have normal...
4
[ 0.007415771484375, -0.03466796875, -0.0869140625, -0.1005859375, -0.07763671875, -0.017822265625, -0.0361328125, 0.0260009765625, -0.011474609375, 0.040771484375, -0.10693359375, 0.049072265625, -0.00147247314453125, -0.0133056640625, 0.00041961669921875, 0.05029296875, -0.0341796875...
13,091
13091
Groups — A Primer The study of groups is often one’s first foray into advanced mathematics. In the naivete of set theory one develops tools for describing basic objects, and through a first run at analysis one develops a certain dexterity for manipulating symbols and definitions. But it is not until the study of group...
4
[ 0.003997802734375, 0.000820159912109375, -0.0302734375, 0.062255859375, -0.034912109375, -0.06689453125, -0.0272216796875, -0.01123046875, 0.099609375, -0.0040283203125, -0.003997802734375, 0.00543212890625, -0.03466796875, -0.0106201171875, -0.004364013671875, -0.0213623046875, -0.0...
13,092
13092
Frobenius homomorphism Frobenius homomorphism Let $F$ be a field of characteristic $p>0$. Then for any $a,b\in F$, $\displaystyle(a+b)^{p}$ $\displaystyle=$ $\displaystyle a^{p}+b^{p},$ $\displaystyle(ab)^{p}$ $\displaystyle=$ $\displaystyle a^{p}b^{p}.$ Thus the map $\begin{matrix}\phi:F&\to&F\\ a&\mapsto&a^{...
4
[ 0.05859375, 0.0228271484375, -0.0238037109375, 0.045654296875, 0.004180908203125, 0.0240478515625, 0.00897216796875, 0.02734375, 0.0299072265625, 0.0159912109375, 0.06591796875, 0.056396484375, -0.0908203125, 0.045654296875, 0.0147705078125, 0.08251953125, -0.107421875, -0.03173828...
13,093
13093
geometric realization of categories Context Homotopy theory Background Variations Definitions Paths and cylinders Homotopy groups Theorems Category theory Concepts Universal constructions Theorems Extensions Applications Contents Definition Write $N : Cat \to sSet$ for the nerve functor from Cat to sS...
4
[ -0.004302978515625, -0.01953125, -0.022705078125, -0.087890625, -0.07568359375, 0.011962890625, -0.035888671875, 0.0947265625, 0.002838134765625, 0.01202392578125, -0.0181884765625, -0.04052734375, -0.0169677734375, 0.022216796875, 0.05224609375, -0.024169921875, 0.0294189453125, 0...
13,094
13094
dy Got Homework? Connect with other students for help. It's a free community. • across MIT Grad Student Online now • laura* Helped 1,000 students Online now • Hero College Math Guru Online now Here's the question you clicked on: Edutopia Group Title in simple harmonic mo...
4
[ -0.05224609375, 0.109375, 0.1318359375, 0.03564453125, -0.01434326171875, 0.06298828125, -0.0400390625, 0.0023651123046875, 0.046875, 0.049560546875, 0.1416015625, -0.0244140625, -0.0111083984375, -0.06787109375, 0.01318359375, 0.044189453125, -0.045166015625, 0.0478515625, -0.03...
13,095
13095
Electric Power Single and Three Phase Power Active Reactive Apparent Complex Power It is very conceptual and essential to understand. For establishing the expression of complex power, we have to first consider a single phase network that's voltage and current can be represented in complex form as V.e^jα and I.e^jβ. Wh...
4
[ -0.056640625, 0.0595703125, -0.045166015625, 0.10400390625, -0.00018596649169921875, 0.041748046875, 0.0595703125, 0.039306640625, 0.1279296875, 0.0230712890625, 0.032470703125, -0.03662109375, 0.07177734375, 0.04248046875, 0.0458984375, 0.003021240234375, -0.115234375, 0.047607421...
13,096
13096
smooth structure from submanifolds This can be interpreted in several ways mathematically. We start with two smooth manifolds, $M$ and $N$, and a bijection $\Phi \colon M \to N$. We want to learn something about what $\Phi$ must or can be by testing it on submanifolds. Ideally, we would like a condition equivalent to $...
4
[ -0.028076171875, -0.040283203125, 0.09814453125, 0.00970458984375, 0.01373291015625, 0.044189453125, 0.0390625, 0.0299072265625, 0.01361083984375, -0.0255126953125, 0.03271484375, -0.00592041015625, 0.033203125, -0.0137939453125, 0.0021209716796875, -0.0223388671875, 0.0286865234375,...
13,097
13097
Angular and Linear Fields of View of Galilean Telescopes and... : Optometry & Vision Science The Galilean telescope is widely used in low-vision prescriptions. As is common in compound optical instruments, its field of view (FOV) is greatly limited. Consequently, for telescopes of a given magnification (all other thing...
4
[ 0.018798828125, -0.040283203125, -0.12890625, -0.08056640625, 0.01043701171875, -0.08154296875, 0.0213623046875, 0.087890625, 0.040771484375, 0.0791015625, 0.0089111328125, 0.006591796875, -0.0390625, -0.020263671875, -0.07275390625, -0.031494140625, -0.0291748046875, 0.00370788574...
13,098
13098
. 4. ENERGETIC PARTICLE ACCELERATION IN COLLISIONLESS SHOCKS The reflected ions with a gyro-radius exceeding the width of the shock transition region can then be efficiently accelerated, via the Fermi mechanism, by converging plasma flows carrying magnetic inhomogeneities and MHD waves. In perpendicular shock a net t...
4
[ -0.0196533203125, -0.02587890625, 0.0927734375, -0.02880859375, 0.04541015625, 0.04296875, 0.021240234375, 0.054931640625, -0.056640625, -0.0262451171875, 0.0211181640625, -0.018310546875, 0.023193359375, -0.050537109375, -0.017578125, -0.03271484375, 0.05322265625, 0.0245361328125...
13,099
13099