Reduction Definition and 447 Threads

Hey guys, I'm doing some experimenting recently with some primality tests, and I need help figuring out how to automate the following: Given an even number N, divide by 2k (k \in \mathbb{N}). If N/2k is an integer, reduce mod 2k+1. (If N/2k is not an integer, simply move on to the next one.)...

Hello, I have come across this sentence in a paper: "For a metal, the introduction of a finite temperature T can be of a more technical use: the Fermi surface of the system is no longer a sharp feature in the Brillouin zone, and the number of electronic wave vectors "k points" needed to...

Homework Statement t^2y''-4ty'+6y=0 t>0, y1(t)=t^2 find the 2nd solution using method of reduction of order.Homework Equations The Attempt at a Solution Let y=v(t)t^2 y'=2tv+v't^2 y''=2v+2tv'+v''t^2+2tv' put in back into eq and solving reduces to (checked it twice) t^4*v''=0 v''=0 Then I...

I don't know what to do with the x^3*e^x on the left side of the page. In the example the instructor gave for a different problem, you couldn't solve for x. In this problem you can so what does that mean I need to do with it?

see image http://i.imgur.com/OCj7Q5f.jpg

When you do the 1st and 2nd derivatives of y2, you're supposed to get u' and u'' in your answer. My question is why can't you do it the way I've started to do it? Or, why are my answers for y2' and y2'' wrong? http://i.imgur.com/OarDiuW.jpg

Homework Statement Use the method of reduction of order to find another independently linear solution y2(x) when given one solution. x^2y'' - x(x+2)y' + (x+2)y = 0 y_1(x) = x The Attempt at a Solution Hopefully y2(x) will take the form of v(x)y1(x) or I have no idea how to solve the ODE...

I think I have this right, its just its an online assignment and I don't want to lose any points on it.(1/4 my grade) Question: Find y2 if y1= x^(-1) and the equation: x^2y"+3ty'+y=0. I solved(using Abel's) for it: ln(x)/x but I am not entirely sure. Wondering if I am spot on or...

A panel put out over 30.7 volts, say 34 volts and I have a micro-inverter that require a voltage of 11-30 to work. Other than shading some of the panel, is there a way to half the voltage from the panel without as much loss from shading some of the cells to work the inverter?

When something is oxidized, it gains oxygen, loses hydrogen or loses electron. However, if the substance gains something else other than oxygen then it won't be considered oxidation anymore? For instance H+ +OH- -->H2O so in this case it seems that the H+ gained oxygen from OH- but actually the...

Homework Statement prove the following reduction formula, n>0 ∫((1+x^2)^n) dx=(x(1+x^2)^n)(1/(2n+1)) +2n/(2n+1)∫(1+x^2)^(n-1) dx Homework Equations none The Attempt at a Solution one of many attempts, i get close, but no cigar. Huge blow to the calculus ego. Any help would be greatly...

Hi I have a question I was wondering if y'all could clear up. Let's say I have two metal cations, Iron (III) and Manganese (II). Will binding them to an anionic ligand lower their reduction potentials (making each a better redundant) and if so why? Is it because the anionic charge of the...

Friction causes a torque that opposes angular momentum. It gets reduced. how can we derive a relation connecting these. friction starts with maximum and becomes zero. angular velocity and its corresponding momentum decreases maximum in the beginning and increases towards the end. the radial...

Hi, this seems like the right section to post, I have a few questions, three fractions that I know the answer for but I just can't figure out how they were arrived at (the middle step). The only way I can think of solving them is expanding it all out etc. which would result in a 100 term cubic...

I'm developing a 2 Dimensional iOS war game, so think guns bullets damage hit points etc. I'm trying to write a function that calculates the Velocity of a bullet at a certain distance, so that I can calculate the force of the bullet at a certain distance. So let's say the that Rifle A is...

This is not a homework problem, I just want to understand some theory behind this mathematical method. Specifically, if we know that one solution is y1(t), then why is the second solution in the form y2(t) = v(t) * y1(t)? Where v(t) is the function that you need to solve for. Why does...

use method of reduction of order to find second solution: t2y''-4ty+6y = 0 , y1(t)= t2 Attempt: So I've done all the steps, up to the substitution, but I'm having problems with what appears to be a simple linear equation but I can't solve it: Any ways, with w = v' I arrive at...

I am new to the forums and need help with something. I have been using a spreadsheet that somebody else made in order to help me design an electric motorcycle. I have been inputing my own data using most of his calculations and I have noticed that he did not calculate any aerodynamic parameters...

Legendre polynomials I have one solution to $(1-x^2)y''-2xy'+\lambda^2 y=0$ and that is $$ \lambda^2a_0 - (2 - \lambda^2)xa_1 + 2a_2 + 6xa_3 + \sum_{k = 2}^{\infty}\left[a_k\left(\lambda^2 - k - k^2\right) + a_{k + 2}\left(k^2 + 3k + 2\right)\right]x^k = 0. $$ From this equation, we can conclude...

I have a problem with differential equations - 2nd order - reduction of order my problem is as follows: (x − 1)y" − xy' + y = 0 , x > 1 ; y_1(x) = e^x solving this type of diff. eq. says to use y=y_1(x)V(x) which gives me y=Ve^x differentiating y gives me y'=V'e^x & y''=V''e^x...

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Homework Statement My book talks about the "reduction formulas" for evaluating trigonometric integrals by parts. However, is this the same thing as "recursive" formulas for integration by parts, a term which is not mentioned in my calculus book? Homework Equations The Attempt at...

Homework Statement Are there any sample problems worked out for trig functions of higher powers which are integrated by reduction formula? Like cos^8 or cos^10 or even just cos^6 or maybe?

Homework Statement Homework Equations The Attempt at a Solution I thought the answer should be this: But in the answer key, its something else. In the answer key, it is: I don't understand why the left ring doesn't react.

Homework Statement (x2+2y')y''+2xy'=0 with initial conditions of y(0)=1 and y'(0)=0 Homework Equations reduction of order, and exact equations.. The Attempt at a Solution let y'=p and y''=p' Giving: (x2+2p)p'+2xp Let M=2xp and N=(x2+2p) So, Mp=2x and Nx=2x Therefore, they are...

Hey all, I was going through a few video lectures on youtube. To be specific, this is the video I watched. Now, the professor in the video talks about Dynamic reduction techniques and puts Guyan reduction in that category. For a fact, Guyan reduction is also called Static condensation and...

Homework Statement reduce the fraction \frac{943578}{1978935} to its lowest terms using Euclid's algorithm The Attempt at a Solution I start with finding the gcd of these two numbers using E.algorithm 1978935=943578*2+91779 942578=91779*10+25788 91779=25788*3+14415 25788=14415*1+11373...

Hi, I and my team-mate have proposed an idea to develop a CO2 emission reduction device to be installed in automobiles. We have mentioned that it will operate on the principle of 'active adsorption of CO2 on charcoal'. However, although the basic scientific principle is pretty simple...

Homework Statement Given ∫xn2xdx= 2/ln(2) -n/ln(2)∫xn-12xdx, for n≥1 find ∫x32xdx all integrals have limits 1and 0. Homework Equations The Attempt at a Solution doing this I get... 2/ln2 -3/ln2(2/ln2-2ln2)(2/ln2 -1/ln2)(2/ln2-1/ln2) but this just gives me 0 I...

Hello guys, I just registered on this forum, so I hope you can help me with some differential entropy stuff. So I have made the attached pdf file (it's a bit messy, sorry) that demonstrates a toy version of the problem I'm trying to solve. Thing is I'm quite new to information theory, so...

I have a big pipe with known diameter, length and velcity at big pipe. There are two pipes dividing form the big pipe with varing diameter and length. 1) How to calculate velocity of water in these two pipes? 2) If I add one more pipe of known length and diameter, what would be the velocity...

I love Physics! I've been thinking about if... you were in a room with a window, bouncing a ball... and you were looking at another building where you could see a room with a person bouncing a ball, but ... their time was moving at half speed (Caused by gravitational time dilation only ( not...

Homework Statement \ddot{y} = - \dot{y} - y -sin(y) Homework Equations The Attempt at a Solution to reduce the order I need to find a solution y1. it seems to me the only obvious solution is y1 = 0 but i can't use this to do a reduction can i

Homework Statement Solve the following using the method of reduction of order. 4x^2y''+y=0 y_1=\sqrt{x}lnx Homework Equations y_2=v(x)y_1 v(x) = ∫ (e^(-∫P(x)dx / y_1) Sorry if that's tough to read, couldn't figure out the latex for it, but it's supposed to be a forumla for...

Homework Statement finding the overall transfer equation Homework Equations not sure which equation to use The Attempt at a Solution unsure how to solve this, don't know where to start off from

Homework Statement If In denotes \int_0^∞ \! \frac{1}{(1+x^2)^n} \, \mathrm{d} x Prove that 2nI_{n+1} = (2n-1)I_n, and state the values of n for which this reduction formula is valid. Homework Equations The Attempt at a Solution I_n=\int_0^∞ \! \frac{1}{(1+x^2)^n} \, \mathrm{d} x =\int_0^∞...

Hi and thanks for taking the time to read this post. I am trying to decide component values for 2 parallel capacitors, in an effort to reduce esr, which will be for use as power supply smoothing capacitors to be placed after the bridge rectifier. After examination i noticed that consumer...

I'm going to be giving a 1st year student chemistry tutoring so I'm going over some of his past exam papers to make sure I know all the stuff but I'm already at a question I can't do: http://img571.imageshack.us/img571/5716/26705030.png So from the formula, I can see that the degree of...

Homework Statement Find y_2(x) given that y_1(x) = e^x for (x – 1)y'' – xy' + y = sin x. Homework Equations Reduction of order method. The Attempt at a Solution My attempt is attached as MyWork.jpg. Is what I did so far 100% correct? Assuming it is, what do I do now? Any help in...

Use integration by parts to prove the reduction formula: int(sec^n)x dx = (tan(x)*sec^(n-2)*x)/(n-1) + [(n-2)/(n-1)]int(sec^(n-2)*x dx n /= 1 (n does not equal 1) I used "int" in place of the integral sign. This was a problem on the corresponding test from the cal A class I am from...

If I n =integral sin (nx) dx/sinx,prove that In =2sin((n-1)x)/n-1 +In-2 for all integers n>(egual) . I don't know how to start...

Hi all, Before posting here I've read couple of articles, some books and through google search for this topic. I've basic perception of what's the reduction, what's the main goal and how we achieve it. But still got a dangling questions in my mind. For sake of simplicity let's assume...

hey guys i've been trying to work out this ode reduction question, http://img204.imageshack.us/img204/8198/asdawt.jpg after i use the hint and end up with a seperable equation then integrate to get \begin{align} & p=\pm \frac{1}{\sqrt{{{y}^{2}}-2c}} \\ &...

I semi understand the reduction of order method, and i understand the general solution for a 2nd order with repeated roots. however, i can't seem to form up the correct thing to solve this question, and research again proves futile. Any assistance will be appreciated. Use the method of...

Homework Statement Find the specified particular solution: (x^2+2y')y'' + 2xy' = 0, y(0)=1, y'(0)=0 Homework Equations The Attempt at a Solution The equation seems amenable to the substitution p=y', so it can be transformed into (x^2 + 2p)p' + 2xp=0, or (x^2 + 2p)dp + 2xpdp=0. Since...

This is dealing with computer vision, but the only part I'm having trouble understanding is a step in the matrix math. So it seems appropriate it should go here. The paper/chapter I'm reading takes one of those steps saying "from this we can easily derive this" and I'm not quite sure what...

hi everyone! i was wondering how gear reduction is done besides connecting a small gear to a larger gear (radius speaking)? In my problem i have a gear - radius:5cm, angular velocity: 1000rpm I have a second gear - radius:5 cm, anguler velocity required: 1 rpm How do i make this...

Hi everyone! I'm in need for some help with Matrix Reduction! I have two questions: Question 1 Find the inverse of Matrix A by reducing the array (A|I), where A= 2 4 6 4 5 5 3 1 -3 Question 2 Find all solutions of the following system: 2x1 + 4x2 + x3 - 3x4 - 3x5 = -5 x1 + 2x2 - x3 + 3x4 -...

Homework Statement Find the general solution for the equation (x - 1)y'' - xy' + y = sin(x), x > 1 Given that y_1(x) = e^x satisfies the associated homogeneous equation. Homework Equations y_2 = v_2(x) * y_1 The Attempt at a Solution I read...

Homework Statement Hello, I'm searching for the formula for the 2 pictures in attachment. The first is de reduction factor day and the other is the reduction factor night. As example for the factor day: on X I put the distance 10 Km, then I choose the value off L = 3 then I have as...