content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
On general expansion of cos nΘ
Simon Bridge
Equating coefficients of ##cos^{n-2k}\theta## suggests...
$$C_{2k}^n(\cos^2\theta - 1)^k=(-1)^k2^{n-2k}\frac{(n-k-1)!}{k!(n-2k)!}$$... recalling that:$$C_{2k}^n=\frac{n!}{(2k)!(n-2k)!}$$
I still dont know what to make of this - there is no summation over [itex]k[/itex] on... | 4 | [
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Generalization in Adaptation to Stable and Unstable Dynamics
Abstract
Humans skillfully manipulate objects and tools despite the inherent instability. In order to succeed at these tasks, the sensorimotor control system must build an internal representation of both the
force and mechanical impedance. As it is not pract... | 4 | [
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How do I find the value of x?
October 18th 2012, 08:57 AM #1
Junior Member
Joined
Sep 2012
From
canada
Posts
27
question solved - not sure how to delete
---
I'm not sure how to delete this question - I had an error in my calculations but I managed to figure it out and there's no point in keeping ... | 4 | [
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Cannot simplify
Mentallic
When [itex]x>>a[/itex] then you can assume that [tex]x\pm a\to x[/tex] In other words, you just cancel the a when it's in a similar form to the above.
[tex]3x^2-a^2\approx 3x^2[/tex] for example.
You need to be a little more careful. For example, suppose you have something like ##\frac{1}... | 5 | [
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Few q
May 13th 2009, 08:59 PM
foreg0ne
Few q
How do I align the equal signs for working out I have in latex?
With the intergral $\int$ how do I put number at the top and bottom? And how do i also do this for the large brackets $[...]$ ?
May 13th 2009, 09:05 PM
TheEmptySet
Quote:
\int_{a}^{b}f(... | 4 | [
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conjugacy class
Two members of a group, x and y, are said to be "conjugate" if there exists a member of the group, z, such that $zxz^{-1}= y$. That, of course, is the same as saying that $zx= yz$. It is easy to
prove that that is an equivalence relation (refexive: x is conjugate to itself by taking z equal to the group... | 4 | [
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Iq test if i have two tetrahedral pyramids
Galileo
I don't think I understand the question correctly.
You said if you combine the number of balls from two equally sized tetrahedral pyramids and add 20, then you have the number of balls needed to make a pyramid one size larger.
The number of balls needed for a pyramid ... | 4 | [
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determinant problem
November 16th 2006, 04:50 AM #1
Junior Member
Joined
Nov 2006
Posts
26
determinant problem
Assuming that det (AB)= det(A)det(B) for 3 x 3 matrices, prove that
| 3 a+b+c a^3+b^3+c^3 |
| a+b+c a^2+b^2+c^2 a^4+b^4+c^4 |
| a^2+b^2+c^2 a^3+b^3+c^3 a^5+b^5+c^5 |
is equal ... | 5 | [
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Integral with complex denominator
December 9th 2006, 02:30 PM #1
Member
Joined
Jul 2005
Posts
187
Integral with complex denominator
$\int\frac{8x+3}{4x^2+12x+11}dx$
I am not able to solve it using partial fractions because denominator doesn't have real values. What should I do ?
Does it work ou... | 4 | [
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Patent US8086928 - Methods and systems for terminating an iterative decoding process of a forward error correction block
FIELD OF THE INVENTION
The present invention generally relates to communication systems. More specifically, the present invention relates to methods and systems for terminating an iterative decoding... | 4 | [
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Mathematical Characterization of Protein Transmembrane Regions
The Scientific World Journal
Volume 2013 (2013), Article ID 607830, 6 pages
http://dx.doi.org/10.1155/2013/607830
Research Article
Mathematical Characterization of Protein Transmembrane Regions
^1Laboratory of Chemometrics, National Institute of Chemistr... | 4 | [
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Gamma function: Introduction to the Gamma Function (subsection Gamma/05)
The best-known properties and formulas for the gamma function
Values at points
The gamma function can be exactly evaluated in the points . Here are examples:
Specific values for specialized variables
The preceding evaluations can be provided b... | 4 | [
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Upset Prediction in Friction Welding Using Radial Basis Function Neural Network
Advances in Materials Science and Engineering
Volume 2013 (2013), Article ID 196382, 9 pages
http://dx.doi.org/10.1155/2013/196382
Research Article
Upset Prediction in Friction Welding Using Radial Basis Function Neural Network
^1State K... | 4 | [
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How many solutions in 4sin2x=3?
February 21st 2013, 11:30 AM #1
Newbie
Joined
Feb 2013
From
UK
Posts
7
How many solutions in 4sin2x=3?
Hello guys,
I am just wandering how many solution there are to the equation in the title?
The boundary is 0_<X_<360(degrees) (_< meaning less than or equal to... | 4 | [
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Linear transformations and matrices
April 26th 2005, 12:57 AM
Mathman24
Linear transformations and matrices
Hi
I got a question regarding the matrix of linear transformation.
If a linear transformation T: R^3 -> R^2 implies that T(1,2-1) = (1,4) ; T(-1,2,1) = (5,9) and T(2,2,1) = (2,1).
Is the mos... | 5 | [
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Machine Learning Notes—Locally Weighted Regression
by Tadas Vilkeliskis, September 8, 2013
In the previous post I covered linear regression which can be used to predict continuous values. This post is a sequel to simple linear regression and will talk about weighted linear regression.
Locally Weighted Regression
On... | 4 | [
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Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 562140, 13 pages
http://dx.doi.org/10.1155/2013/562140
Research Article
Numerical Solution of the Fractional Partial Differential ... | 5 | [
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Cauchy Integral #2
July 14th 2009, 07:49 AM #1
Junior Member
Joined
Oct 2008
Posts
33
Cauchy Integral #2
Evaluate the following closed contour integral
1)
$\oint\frac{zdz}{z-1}$
with $|z|=2$
Since $z =1$ is inside $|z| =2$
Let $f(z) = z$
And by the Cauchy Integral formula
... | 5 | [
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Brevet US4975961 - Multi-layer neural network to which dynamic programming techniques are applicable
BACKGROUND OF THE INVENTION
This invention relates to a multi-layer neural network or net.
Neural networks of various types are described in an article contributed by Richard P. Lippmann to the IEEE ASSP Magazine, Apr... | 4 | [
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Integral of e
Hi, I've to show that $\int_0^{2\pi}e^{-i(k+n)\theta}d\theta=0$ Thanks for any help.
$\int_0^{2\pi}{e^{-i(k + n)\theta}\,d\theta} = -\frac{1}{i(k + n)}\left[e^{-i(k + n)\theta}\right]_0^{2\pi}$ $= -\frac{1}{i(k + n)}\left[e^{-2\pi i(k + n)} - e^{0i(k + n)}\right]$. Assuming that $-(k
+ n)$ is an integer,... | 5 | [
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general solution of a differential equation
December 2nd 2009, 12:59 PM #1
Newbie
Joined
Dec 2009
Posts
7
general solution of a differential equation
Find the general solution of the differential equation
dy/dx = y^4 ( (x+1) / (x-2)(x^2 + 5)) and any other solutions if they exist.
The DE is sep... | 4 | [
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An Experiment Consists of Pulling a Heavy Wooden Block Across a Level Surface...
jli10
1. The problem statement, all variables and given/known data
An experiment consists of pulling a heavy wooden block across a level surface with a spring force meter. The constant force for each try is recorded, as is the accelerat... | 4 | [
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Trig Equation
Can anyone please show me how to do 2cos2x=7cosx. I have no clue. Thanx in advance.
cos2x=2(cos^2)x-1 (double angle)...that is how Mr Fantastic got his result. Rearranging into a quadratic in cos x should yield... (4cosx +1)(cosx -2) = 0 (4cosx) + 1 = 0 and (cosx) - 2 = 0 ....now
solve for x in both
| 4 | [
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Complexifying Lie algebras (footnote to group thread)
Astronomy
Sci Advisor
PF Gold
P: 23,103
C will stand for the complexnumbers
Let V be a vectorspace over the reals.
V x V is the cartesian product, the set of ordered pairs (u,v)
We can turn that into a vectorspace over the complexnumbers
in what I guess is a... | 4 | [
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GOLDEN RATIO WORKSHEET
This worksheet can be used to record your answers for the various exercises in this lesson. This lesson is meant as an introduction to this topic and not at all exhaustive. You will, however, come
away with a sense of some of the significance the Golden Ratio has in our world and a good basic und... | 4 | [
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Direct product of faithful representations into direct sum
rkrsnan
Direct product of two irreducible representations of a finite group can be decomposed into a direct sum of irreducible representations. So, starting from a single faithful irreducible representation,
is it possible generate every other irreducible re... | 5 | [
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Fundamental Theorem of Calc.!
April 16th 2008, 10:28 AM #1
Member
Joined
Nov 2007
Posts
112
Fundamental Theorem of Calc.!
Oil leaks out of a tanker at a rate of r = 0.5t + 4 gallons per minute, where t is in minutes.
(a) Write a definite integral for the total gallons of oil that leak out of the tan... | 5 | [
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Ordinary Differential Equations problems
February 15th 2009, 10:40 AM #1
Senior Member
Joined
Jul 2007
Posts
290
Ordinary Differential Equations problems
I'm having trouble figuring out which method I should be using on some of these problems. Any help in figuring out which methods would be best is much ... | 5 | [
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0.0220947265625,
0.03857421875,
0.033935546875,
-0.03564453125,
-0... | 20,427 | 20427 | |
An example of a beautiful proof that would be accessible at the high school level?
up vote 40 down vote favorite
57
The background of my question comes from an observation that what we teach in schools does not always reflect what we practice. Beauty is part of what drives mathematicians, but we rarely talk about
beau... | 5 | [
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0.013671875,
0.065... | 20,428 | 20428 | |
Apps of differentiation
December 16th 2007, 10:26 AM #1
Member
Joined
Nov 2006
From
San Francisco
Posts
145
Apps of differentiation
I don't have a problem solving these problems but i cant seem to find the equation(s) of this problem. A right triangle is formed in the first quadrant by the x and y ax... | 4 | [
-0.00830078125,
0.023681640625,
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0.11669921875,
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0.0673828125,
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0.0244140625,
0.02099609375,
-0.01470947265625,
0.10107421875,
-0.06201171875,
-0.1040039... | 20,429 | 20429 | |
Power Series&Function Series Questions
January 18th 2010, 11:56 PM
WannaBe
Power Series&Function Series Questions
I'll be delighted to get Some help in these questions:
1. Determine whether the next function series uniformly converges:
SIGMA_ (1-x)^2 * x^n in [0,1]
2. Determine where the next serie... | 5 | [
-0.0230712890625,
-0.0302734375,
0.0439453125,
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-0.043701171875,
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0.02099609375,
-0.03564453125,
0.01544189453125,
-0.0263671875,
-0.08447265625,
-0.00994873046875,
0.0751953125,
-0.07421875,
-0.048583984375,
-0.037841796875,
0.0164794921875,
-0.1376... | 20,430 | 20430 | |
Generalizing the Replacement Theorem
June 5th 2011, 05:17 PM #1
Generalizing the Replacement Theorem
Let $\beta$ be a basis for a vector space $V$ and let $S$ be a linear independent subset of $V$. Prove there exists a subset of $\beta$, $S_1$, such that $S\cup{S_1}$ is a basis for $V$
Proof
Let $S_1$ be... | 5 | [
-0.040283203125,
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0.11572265625,
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-0.00518798828125,
-0.0703125,
0.017578125,
0.0458984375,
-0.0303955078125,
0.004119873046875,
-0.0294189453125,
0.0216064453125,
0.0... | 20,431 | 20431 | |
Challenge Problem
July 12th 2010, 08:43 AM
Chris11
Challenge Problem
This is a challenge problem. It has been approved by Mr Fantastic.
This problem is from some putnam comptition. I got the problem out of a book that I have. It's fun.
Problem:
let $A\subseteq R$ be a set that is closed under mult... | 5 | [
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0.0205078125,
0.00183868408203125,
... | 20,432 | 20432 | |
standard error of estimate
June 7th 2008, 10:48 PM
Judi
standard error of estimate
standard error of estimate=
square root of sum of squares of difference of y and y hat divided by n-2
how does this become--------->
square root of sum of y square minus a times sum of y minus b times sum of xy and di... | 4 | [
-0.031982421875,
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0.051025390625,
-0.043212890625,
-0.... | 20,433 | 20433 | |
Polynomial Time Approximation Schemes for the Constrained Minimum
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 394721, 8 pages
http://dx.doi.org/10.1155/2012/394721
Research Article
Polynomial Time Approximation Schemes for the Constrained Minimum Spanning Tree Problem
Department of Computer Science... | 5 | [
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integrate a numerical function
Hi
I browsed the forums but could not find a solution to my problem. Ii have a system of differential equations; however, I have the solution to one of the functions as an integral of another function
in the system, but since the solutions are all numerical I don't know how to implement ... | 4 | [
-0.0859375,
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0.06103515... | 20,435 | 20435 | |
Field Enhancement in a Grounded Dielectric Slab by Using a Single
Advances in OptoElectronics
Volume 2012 (2012), Article ID 439147, 9 pages
http://dx.doi.org/10.1155/2012/439147
Research Article
Field Enhancement in a Grounded Dielectric Slab by Using a Single Superstrate Layer
^1Department of Radio Science and Eng... | 4 | [
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... | 20,436 | 20436 | |
help with polynomials
March 6th 2007, 11:13 AM #1
Junior Member
Joined
Mar 2007
Posts
36
help with polynomials
Im stuck on the following questions and need some help. Sorry I dont know how to do X squared on the keyboard so X^2 means X squared and etc.
1. Simplify 4X^5 + 16X / 4X
b. Simplify 2X^... | 4 | [
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0.04248046875,
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0.052978515625,
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0.00683593... | 20,437 | 20437 | |
2013 Lewis meditation results
A small group of Quantified Selfers tested themselves daily on arithmetic and engaged in a month of meditation. I analyze their scores with a multilevel model with per-subject grouping, and find
the expect result: a small decrease in arithmetic errors which is not statistically-sig... | 4 | [
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0.0... | 20,438 | 20438 | |
Calculus Help
February 5th 2013, 05:03 AM #1
Newbie
Joined
Oct 2012
From
Lancaster
Posts
20
Calculus Help
This question looks really simple and thats whats worrying me a liittle.
Show that if f = f(x, y) and f[yy]=0, then f(x, y) = g(x)y + h(x) for some funcions g, h.
I simply show that f[y... | 5 | [
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-0.0439453... | 20,439 | 20439 | |
Blahut-Arimoto algorithm in Matlab
For a discrete memoryless channel
where
Given a channel transition matrix whose
Reference: Chapter 9 in the book Information Theory and Network Coding by Raymond Yeung.
function [C r] = BlahutArimoto(p)
% Capacity of discrete memoryless channel
% by Blahut-Arimoto algorithm
% Inp... | 5 | [
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... | 20,440 | 20440 | |
Finding a composite inverse function.
May 1st 2010, 10:11 PM #1
Junior Member
Joined
Jan 2010
Posts
66
Finding a composite inverse function.
Hey guys! I need to find:
$tan(cot^{-1}(\frac{-1}{\sqrt{3}}))$
Here's how I'm going about finding the answer:
I read this as, "Tangent of the angle w... | 4 | [
-0.0634765625,
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0.059814453125,
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0.003997802734375,
-0.015991210937... | 20,441 | 20441 | |
Convert an integral from Cartesian to Polar coordinates and evaluate it.
$r^2 = x^2 +y^2$ $y = r\sin \theta$ $x = r \cos \theta$ lets convert the boundaries $x = \sqrt{4y-y^2 }$ $x^2 = 4y -y^2 \Rightarrow x^2+y^2 = 4y$ $r^2 = 4r\sin \theta$ $r = 4 \sin \theta$ r changes
from 0 to $4\sin \theta$ and theta from 0 to pi/2... | 5 | [
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0... | 20,442 | 20442 | |
Uncertainty in the parameters A and B for a linear regression
I'm working through John Taylor's An Introduction to Error Analysis and so far this is the only problem I haven't been able to solve. I was hoping someone could lend me some insight.
The problem asks you to use error propagation to verify that the uncertain... | 4 | [
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0.04101... | 20,443 | 20443 | |
Vectors question
April 29th 2011, 01:12 PM #1
Junior Member
Joined
Apr 2011
Posts
56
Vectors question
I'm not sure where you'd ask vector questions, but since this one involved $\cos$ I decided to ask it here:
Two vectors, a and b, have a common starting point with an angle of 120 degrees between th... | 4 | [
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0.0186767578125,
-0.0771484... | 20,444 | 20444 | |
Analysis of Stability of Traveling Wave for Kadomtsev-Petviashvili Equation
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 230871, 3 pages
http://dx.doi.org/10.1155/2013/230871
Research Article
Analysis of Stability of Traveling Wave for Kadomtsev-Petviashvili Equation
^1College of Mathematics and Info... | 5 | [
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... | 20,445 | 20445 | |
complex number
May 29th 2011, 04:52 AM #1
Junior Member
Joined
Jul 2009
Posts
68
complex number
for any two complex no. z1 and z2 prove that re(z1 z2) = re(z1) * re(z2) - im(z1) * im(z2)
my incomplete soln-
don't have any idea about it.
Last edited by saha.subham; May 29th 2011 at 07:00 AM. ... | 4 | [
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-0.04443359375,... | 20,446 | 20446 | |
PinkMonkey.com Calculus Study Guide - Section 2.4 Left Hand And Right Hand Limits
2.4 Left Hand And Right Hand Limits ( One-sided Limits )
While defining the limit of a function f as x tends to 'a', we consider values of f (x) when x is very closed to 'a'. The values of x may be greater or lesser than a. If we restric... | 4 | [
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Patent US4434490 - Spectrophone stabilized laser with line center offset frequency control
ORIGIN OF INVENTION
The invention described herein was made in the performance of work under a NASA contract and is subject to the provisions of Section 305 of the National Aeronautics and Space Act of 1958, Public Law
85-568 (7... | 4 | [
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Summary: ON DYNAMICAL SYSTEM THEORY APPLICATION TO EARTH-SATELLITE PITCH
AUTHOR: Emmanuel Osei-Frimpong - KNUST
ABSTRACT: In this paper, an analytic method for solving a differential equation which represents
the dynamics of Pitch Attitude librations of an orbiting earth-satellite is discussed. This highly non linear
e... | 4 | [
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0.03833007... | 20,449 | 20449 | |
Patent US6193607 - Random number generator for electronic applications
SPECIFICATION
This application is a Continuation-in-Part of application Ser. No. 08/665,699, filed Jun. 18, 1996, entitled “Random Number Generator for Electronic Applications, now U.S. Pat. No. 5,871,400.
BACKGROUND OF THE INVENTION
1. Field of ... | 4 | [
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-0.026... | 20,450 | 20450 | |
A Nonlinear Finite Element Method for Magnetoelectric Composite and the Study on the Influence of Interfacial Bonding
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 197940, 14 pages
http://dx.doi.org/10.1155/2013/197940
Research Article
A Nonlinear Finite Element Method for Magnetoelectric Compos... | 4 | [
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-0.03759765625,
-0... | 20,451 | 20451 | |
Application of derivatives, to an aircraft landing.
February 26th 2013, 09:56 PM
Goku
Application of derivatives, to an aircraft landing.
An approach path for an aircraft landing is shown in the figure and satisfies the following conditions:
( i ) The cruising altitude is when descent starts at a horizon... | 4 | [
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... | 20,452 | 20452 | |
Chain Rule with Three Nested Square Roots
February 13th 2011, 02:24 PM
joatmon
Chain Rule with Three Nested Square Roots
This one makes my brain spin:
Find the derivative:
$y = \sqrt{x + \sqrt{x + \sqrt{x}}}$
I see four composed functions here (sorry I'm running out of letters at the end):
$y ... | 5 | [
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0.0167236328125,
-0.0380859375,
0.00866699... | 20,453 | 20453 | |
Double Angle Question
March 7th 2009, 01:14 AM #1
Junior Member
Joined
Sep 2008
Posts
49
Double Angle Question
Show that sin S - sin T = 2.cos (S + T / 2) .sin (S - T / 2)
(By the way, am I right in saying that you are not allowed to expand the RHS when the question asks to 'show'?)
Thanks !
... | 4 | [
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-0.019775390625,
0.01239013671875,
-... | 20,454 | 20454 | |
Solve this function
August 13th 2008, 08:07 AM #1
Newbie
Joined
Aug 2008
Posts
4
Solve this function
Hey guys!
2f(x)-3f(1/x)=x^2, x not = 0, find f(2). options are
1. -7/4, 2.5/2, 3.-1, 4.none
Please solve it asap...i'm unable to solve it........thanks
plug in x=2 and x=1/2, you obtain ... | 4 | [
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0.07861328125,
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-0.04541015625,
0.028564453125,
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Rearranging Annuitie formula to find R
October 10th 2007, 10:58 PM #1
Newbie
Joined
Oct 2007
Posts
4
Rearranging Annuitie formula to find R
Hey everyone I need help really badly.
I have a formula that looks like this
A=PR^n + Q(R^n-1)/R-1
But i need to rearrange it to make R the subject. Ive... | 5 | [
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Method of External Potential in Solution of Cauchy Mixed Problem for the Heat Equation
ISRN Mathematical Analysis
Volume 2013 (2013), Article ID 640985, 5 pages
http://dx.doi.org/10.1155/2013/640985
Research Article
Method of External Potential in Solution of Cauchy Mixed Problem for the Heat Equation
Institute of M... | 5 | [
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Patent US5694342 - Method for detecting signals in non-Gaussian background clutter
BACKGROUND OF THE INVENTION
The present invention relates to the field of signal processing, and more particularly to a method for detecting weak signals in a non-Gaussian, non-stationary background.
Many signal detection schemes in us... | 4 | [
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Patent US7650272 - Evaluation of Bayesian network models for decision support
BACKGROUND OF THE INVENTION
(1) Technical Field
The present invention relates to a method and software tool for evaluation of Bayesian Network (BN) models for decision support. More specifically, the present invention relates to a technique... | 4 | [
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Patent US7969120 - Method for calculating power capability of battery packs using advanced cell model predictive techniques
CROSS-REFERENCE TO RELATED APPLICATIONS
The present application is a divisional application of U.S. patent application Ser. No. 11/963,307, filed on Dec. 21, 2007, which is a continuation of U.S.... | 4 | [
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Patent US5260673 - π/4 differential encoding for digital cellular mobile systems
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention generally relates to digital cellular mobile communications systems and, more particularly, to a scheme for π/4 phase shift differential encoding which reduces t... | 4 | [
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Relativistic Electron
strangequark
3. The attempt at a solution
a) [tex]q_{e} \Delta V = \Delta K = \frac{1}{2}m_{e}c^{2}[/tex]
[tex]\Delta V =\frac{m_{e}c^{2}}{2q_{e}}=255,499 Volts[/tex]
This is fine. (If you have learned about masses of particles expressed in electron-volts, you'll see that this value makes s... | 5 | [
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-0.... | 20,462 | 20462 | |
Creation/annihilation operators
P: 527
For a system of N non-interacting bosons we start with the tensor product of single particle states [itex]\otimes_{n=1}^N | \alpha_i \rangle[/itex] and then, due to the indistinguisability of the
particles, symmetrize to obtain the occupation number state
[itex]| n_1,n_2,\ldots,... | 4 | [
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Math Help
July 26th 2007, 01:35 PM #1
Newbie
Joined
Jul 2007
Posts
6
Circles
In circle O and circle P, AP is equal to 10 and AC is equal to 8. Line segment CB is also perpendicular to line segment AP. Find the measure of DP.
Here's what I have so far : Since all radii of a circle are congrue... | 4 | [
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The K-Theoretic Formulation of D-Brane Aharonov-Bohm Phases
Advances in High Energy Physics
Volume 2012 (2012), Article ID 920486, 10 pages
http://dx.doi.org/10.1155/2012/920486
Research Article
The K-Theoretic Formulation of D-Brane Aharonov-Bohm Phases
Department of Mathematics, Physics, and Statistics, Purdue Uni... | 4 | [
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Linear Algebra: Sub-Space!
February 6th 2009, 09:31 PM #1
Linear Algebra: Sub-Space!
For the vectors in R^3, determine whether the first vector can be expressed as a linear combination of the other two.
a) (-2,0,3), (1,3,0), (2,4,-1)
b) (1,2,-3), (-3,2,1), (2,-1,-1)
If you could please help me solvi... | 4 | [
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Help to understand 4th order Runge-Kutta alternative implementation
March 19th 2012, 05:54 AM #1
Newbie
Joined
Mar 2012
From
Spain
Posts
1
Help to understand 4th order Runge-Kutta alternative implementation
Hi,
I have been given a code that uses fourth order RK method for solving a PDE system.
... | 4 | [
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0.037... | 20,467 | 20467 | |
Basis of a Dual Space
November 21st 2009, 02:55 AM #1
Basis of a Dual Space
If I have a vector space $U$ and a dual space $U^*$, with $e_1,...,e_n$ a basis of $U$ and $e^1,....,e^n$ a basis of $U^*$, does the basis of $U^*$ always have to have this form:
$e^i(e_j)=\delta_{ij}=\begin{cases} 1 \ \ \ \ if \ i=j... | 4 | [
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0.... | 20,468 | 20468 | |
Please give me some hints:
I need to find the integral of: (2*x^(1/2))/(b+x^(1/2)), where b is a constant real number. thanks a lot, T
topsquark, if we let $y = b + \sqrt{x}$, then we have $\dfrac{dy}{dx} = \dfrac{1}{2\sqrt{x}}$ $dx = 2\sqrt{x} dy = 2(y - b) dy$, right? (We could also write $y = b + \sqrt{x} \implies ... | 5 | [
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Patent US4218749 - Apparatus and method for digital noise synthesis
BACKGROUND OF THE INVENTION
This invention relates to noise generators and, more particularly, to an apparatus and method for generating pseudo-random parallel bits and for utilizing the generated bits to obtain Gaussian
distributed noise and Poisson ... | 4 | [
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A method to compute roots other than sqrt.
loop quantum gravity
is there a method to compute roots other than sqrt?, like 10th root or 13th root of a number?
and, what are they?
This one is a good candidate for
Newton's method
. We choose an arbitrary value x
[0]
, then use:
[tex]x_{n + 1} = x_n - \frac{f(x_{n}... | 5 | [
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0.... | 20,471 | 20471 | |
invertible and diagonalized matrix
September 24th 2012, 07:17 AM #1
Junior Member
Joined
Sep 2012
From
ohio
Posts
68
invertible and diagonalized matrix
Given the matrix A=[29,18][-50,-31] explain why there is no invertible matix P that diagonalizes A.
So I've solved for the eigenvalue and found ... | 5 | [
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DeMoivre's Theorem
December 15th 2008, 09:55 AM #1
Newbie
Joined
Dec 2008
Posts
2
DeMoivre's Theorem
I was asked to find both sin4() and cos4() in terms of sin() and cos()
using DeMoivre's Theorem.
I couldnt figure out how to type the actual symbol for theta on here so i just used ()....
I... | 5 | [
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Calculus HELP!!!!
1. March 11th 2006, 11:49 AM #1
2. March 11th 2006, 03:38 PM #2
FrozenFlames
Is there time R'(t)=0
Yes, notice that $R(t)$ is a differenciable function, and $R(0)=R(24)$ thus, by Rolle's Theorem (or Mean-Value theorem) there exists a real number, $0<t<24$ such as,
... | 5 | [
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-0.04858398437... | 20,474 | 20474 | |
A field with polynomials and gcd.
March 27th 2007, 06:02 PM #1
Super Member
Joined
Mar 2006
Posts
705
Thanks
2
A field with polynomials and gcd.
Let F be a field and let f(x),g(x),h(x) and d(x) be polynomials in F[x]. Prove if gcd( f(x),g(x) ) = 1_{F} and f(x) divides g(x)h(x), then f(x)|h(x).
A... | 5 | [
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0.... | 20,475 | 20475 | |
Acute Angled Triangle...difference of two sides
November 19th 2011, 02:42 AM #1
Junior Member
Joined
Nov 2011
From
Karachi
Posts
34
Acute Angled Triangle...difference of two sides
I am totally clueless on this. I have tried Pythagoras theorem and tried taking a lot of ratios but don't seem to get any... | 4 | [
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Symbolic Logic Help
April 6th 2010, 06:59 AM #1
Newbie
Joined
Apr 2010
Posts
2
Symbolic Logic Help
Hey guys,
I've been studying this book "Introduction to Logic" and have come across 3 tough questions I was hoping I could get explained to me as I have no clue where to start. They deal with the rules... | 5 | [
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0.0195312... | 20,477 | 20477 | |
Parametric equations of a general equation of parabola
April 20th 2010, 01:34 AM #1
Newbie
Joined
Nov 2009
Posts
21
Parametric equations of a general equation of parabola
A parabola passes thorough the points (1,0) & (0,1) and x & y axes are tangent at these points respectively. How to find the parametri... | 4 | [
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Finding distance, given velocity with cos.
September 6th 2008, 07:50 AM #1
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Joined
Sep 2008
Posts
7
Finding distance, given velocity with cos.
What a wonderful website this is. Thank you all in advance for any help or guidance you can give me.
So, okay.
Find the distance traveled in 15 se... | 5 | [
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0.04541015625,
0.087890625,
... | 20,479 | 20479 | |
6 Trigonometry Questions needing help...
August 12th 2007, 05:12 PM #1
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Joined
Aug 2007
Posts
9
6 Trigonometry Questions needing help...
So I have like 6 problems right now left or so on my Calculus homework sheet (somewhere around like 150 problems total) and I'm having trouble showing these solut... | 5 | [
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0.012... | 20,480 | 20480 | |
Working out the units?
Register to reply
by tommyboo
Tags: units, working
P: 10 I am having a problem finding the correct SI unitsfor the quantity A?
In the equation
A=√(R/TY)
... | 4 | [
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0.076660... | 20,481 | 20481 | |
word problem, Maximum
May 1st 2009, 06:31 AM #1
Super Member
Joined
Sep 2008
Posts
607
word problem, Maximum
You have a given length of fence. Using the wall of a house as one side of a rectangular fence, how would you place the fence around the other three sides in order to enclose the largest possible
... | 4 | [
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0.0272216796875,
-0.0001392364501953125,
0.0... | 20,482 | 20482 | |
PDE Initial Condition Question
November 30th 2010, 02:46 AM #1
Newbie
Joined
Aug 2010
Posts
7
PDE Initial Condition Question
Hello,
I have the following PDE:
$u_t = k u_xx$
with $u(x,0) = f(x), u_x(0,t) = u_x(L,t) = 0$
which I solve using separation of variables by letting $u = XT$.
... | 4 | [
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Solutions for sin and cos equations
Really need help with how to figure these out. Attachment 28428 Thanks James
For the first one, rewrite the equation using the double-angle identity for sine, to get: $2\sin(x)\cos(x)=\sqrt{2}\cos(x)$ Now, divide through by $\sqrt{2}$ then subtract $\cos(x)$ from both sides,
factor ... | 4 | [
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Photon is electromagnetic field, right?
Barry_G
Maxwell's equations do not explain how can photon have electric and magnetic field and yet we can not bend a beam of light by external electric or magnetic fields.
Yes they do. They do precisely that. This is absolutely obvious, but lets walk through it. Let [itex]E_{... | 4 | [
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Temperature change with altitude
Alright guys, just looking for a point in the right direction for a tutorial question.
GIVEN VALUES:
Temperature change with increasing altitude: 0.0065 K/m
Temp at sea level: 15ºC
Pressure at sea level: 101.5 kPa
FIND:
Atmospheric pressure at 7500m.
So what I've done is found the t... | 5 | [
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Practical Foundations of Mathematics
Paul Taylor
7.7 Gluing and Completeness
To complete the equivalence between syntax and semantics, it rema... | 4 | [
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Parametric Equations!!
April 7th 2008, 06:23 PM #1
Member
Joined
Nov 2007
Posts
112
Parametric Equations!!
At time t, the position of a particle moving on a curve is given by
(a) Find the exact value of t at which the curve has a horizontal tangent.
t =
(b) Find dy/dx in terms of t.
d... | 5 | [
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-0.004974365234... | 20,488 | 20488 | |
Shape-Free Finite Element Method: Another Way between Mesh and Mesh-Free Methods
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 491626, 14 pages
http://dx.doi.org/10.1155/2013/491626
Research Article
Shape-Free Finite Element Method: Another Way between Mesh and Mesh-Free Methods
^1Department of... | 4 | [
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Patent US4876509 - Image restoration process for magnetic resonance imaging resonance imaging
This is a Continuation-in-Part of a patent application filed Dec. 17, 1986, in the name of Robert J. Perlmutter entitled "Image Restoration Process for Magnetic Resonance Imaging," and bearing Serial
No. 942,604.
FIELD OF THE... | 4 | [
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acceleration with respect to time
April 8th 2008, 11:41 AM
thermalwarrior
acceleration with respect to time
Could anyone help with this?
a(t)= -g/b^2(v(t)^2 - b^2)
i need to find t in terms of v, b, g, vo,
I think I need to separate the variables but not sure how to progress.
Thanks.
April 8... | 5 | [
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Patent US6943571 - Reduction of positional errors in a four point probe resistance measurement
FIELD OF THE INVENTION
The invention disclosed broadly relates to the field of resistance measurement probes and more specifically to four point probes for resistance measurements in semiconductor wafers.
BACKGROUND OF THE ... | 4 | [
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Multidimensional Taylor Series and Symmetric Tensors
As a warm up post, I’m going to talk about an important generalization of something that should be familiar to anyone’s who has made through a semester of calculus: Taylor series! (And if you
haven’t seen these guys before, or are perhaps feeling a bit rusty, then ... | 4 | [
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[SOLVED] Collision of particles - coefficient of restitution
July 4th 2008, 01:35 AM #1
Member
Joined
Jun 2007
Posts
131
[SOLVED] Collision of particles - coefficient of restitution
If there is a particle X of mass 3m which is moving with velocity Ui on a smooth horizontal table and it collides with a pa... | 4 | [
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Integration of functions of Complex Variables
Let's try this. We'll extend k to a+ib, and see what happens to our integral:
[tex]e^{-(a+ib)x} = e^{-a x} e^{-i b x} = e^{-a x} cos(b x) - i e^{-a x} sin(b x)[/tex]
Integrating this, we get the following two integrals:
[tex]\int_0^\infty e^{-a x} cos(b x) dx = \frac{a}{... | 5 | [
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help me with solving this..
October 6th 2005, 05:55 AM #1
Newbie
Joined
Sep 2005
Posts
4
help me with solving this..
Ive got this DE: 8(du/dx)+4(du/dy)=9u
I separate it with u=X(x)Y(y)
Let me give you my thoughts:
8*X' + k^2*X = 0
4*Y' - (k^2 + 9)*Y = 0
These yields:
solving... | 4 | [
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0.01721... | 20,496 | 20496 | |
Derivate f(x)=x^2*e*(-3x)
January 6th 2010, 03:57 AM #1
Newbie
Joined
Jan 2010
Posts
4
Derivate f(x)=x^2*e*(-3x)
Hi guys
I've been trying to solve this for a little while now but I feel kinda lost and I thought you could maybe help me out.
so
f(x)=x^2*e^(-3x)
f '(x)=?
Thank you.
... | 5 | [
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subgroups of the group <x,y:x²=y³=(xy)¹²>
December 13th 2010, 01:58 AM #1
Newbie
Joined
Dec 2008
Posts
12
subgroups of the group <x,y:x²=y³=(xy)¹²>
Can anybody help me in finding the all possible subgroups of the group
<x,y:x²=y³=(xy)¹²>. Actually i want to find the the number of all subgroups of th... | 5 | [
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-0... | 20,498 | 20498 | |
Trig subtitution
The point of "trigonometric substitution" is to use trig identities such as
sin^2(θ)= 1- cos^2(θ) so that
sin(θ)= √(1- cos^2(θ))
sec^2(θ)= 1+ tan^2(θ) so that
sec(θ)= √(1+ tan^2(θ))
tan^2(θ)= sec^2(θ)- 1 so that
tan(θ)= &ra... | 5 | [
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0... | 20,499 | 20499 |