Variation Definition and 575 Threads

I can't get the variation of formula http://img813.imageshack.us/img813/3754/38919739.png in the form of [PLAIN][PLAIN]http://img839.imageshack.us/img839/536/96608635.png. Can anyone help me. Sorry, I am not good at math :)

Hello, in the paper from sean carroll "the cosmological constant" we can read this: Does this variation of the cosmological constant after symetry breaking is considered as real and accepted in standard cosmology? I find very few talks about a varying cosmological constant, and it is about...

Homework Statement \mathbb{x'}= \begin{bmatrix} 1 & 1 \\ 4 & 1 \end{bmatrix} \mathbf{x} \ + \ \begin{bmatrix} 2e^{t} \\ -e^{t} \end{bmatrix} Find the general solution. Homework Equations The Attempt at a Solution Well i found the eigenvalues of the matrix That i'll call...

Homework Statement A single pair of rabbits (male and female) is born at the beginning of a year. Assume the following conditions: (1) Rabbit pairs are not fertile during their first two months of life, but thereafter give birth to three new male/female pairs at the end of every month...

Hi everyone! Here's my problem: Let's suppose that we have a functional I[f,g]=\int{L(f,\dot{f},g,\dot{g},x)\,dx}. Is it right to say that the variation of I whit respect to g (thus taking g\;\rightarrow\;g+\delta g) is \delta I=\int{[L(f,\dot{f},g+\delta g,\dot{g}+\delta \dot...

Homework Statement An enclosed vertical tube rotates about its vertical axis at w=3000rpm. At the axis, r=0, P=1.5bar and T=293K. What is the pressure distribution as a function of r? And hence calculate the pressure at r=2m. The Attempt at a Solution I have seen this type of questions...

ty''-(t+1)y'+y=t^2 I know I have to use variation of parameters to solve this. But I am stuck and cannot figure out how to get the homologous equation! y''-(1+\frac{1}{t})y'+\frac{1}{t}*y=t I don't know how to solve this homologous equation in this format. Is it R^2+(1+1/t)R+1/t = 0 ? How...

Greetings everyone: I am trying to create a software for estimating temperature for a liquid in a group of tanks lying side by side touching each other in a span of 24 hours. The initial data with me is: X THE FINAL TEMPERATURE OF THE TWO TANKS WHEN THEY COME INTO EQUILIBRIUM T1 and T2 -...

Homework Statement If a function f is of bounded variation on [a,b], show it is Riemann integrable Homework Equations Have proven f to be bounded S(P) is the suprenum of the set of Riemann integrals of a partition (Let's say J) s(P) is the infinum of J S(P) - s(P) < e implies f...

I am working on a problem requiring variation of parameters. When I calculated the wronskian, I got an answer, which differed from the book only by a "-" (mine was -, the book's was +). So I switched my functions for y1 and y2 and got the answer the book had. Is there a standard for which...

I have already read one thread on Lagrange's method of variation of parameters and it was very useful, but I am still confused about the use of the constraint. If the solution to the homogeneous second order equation contains two functions, with arbitrary constants: y= Ay1 + By2...

Homework Statement A gambler has 2$ and wants to have 10$. To get the money he enters a game where a fair coin is tossed. If he bets on the right side he wins doubles his stake and if he bets wrong he loses his stake. The strategy is to bet everythig if he has 5$ or less and just enough to walk...

I am trying to solve a problem along the lines of y'' + 2y' + y = e^(-x) (2 + 1/x^2).. The actual one I am trying to solve differs slightly. I was trying to solve it using the method of variation of parameters.. However it is new to me and was too confusing. So first I get: y comlpiment...

Homework Statement Find a particular solution by method of variation of parameters: t2y'' - 2y = 3t2 - 1 given: y1 = t2 y2 = t-1 Homework Equations The Attempt at a Solution I get Y(t) = t^2ln(t) - \frac{1}{3}t^2 + \frac{1}{2} The book gives Y(t) = t^2ln(t) +...

I was looking through my DE book and a problem intrigued me. I eventually figured it out but I do not understand the logic. I was wondering if anyone here could help me out. The question says: Use the method of variation of parameters to show that...

in varying an action like Polyakov's action with respect to the metric on the world sheet we have to consider the variation of the square root of the determinant. I have not found how to express the variation of the determinant of the metric. From reverse engineering I found that \delta(h)=2...

I have a question about calculus of variation. does anybody here know a proof for the chain rule: \delta S= \frac{dS}{dx} \delta x and for the formulation: \delta S= p \delta x => \frac{dS}{dx}= p it would be totally sufficient, if anyone here knows(e.g. a weblink) where one could see this...

Homework Statement Alright, so I just want some clarification on direct variation, since it seems that every internet source I can find is (seemingly to me) wrong. To me, direct variation means that the ratio of y to x is fixed with y=kx where k is the constant of proportionality...

hey I do not understand a step here! The integral is: \delta S(x,t)=-mc \int_a^b u_i d \delta x^i =0 and now they say one should do integration by parts, but I do not know how this should work here? Where are my two functions?As far as I see there is only the four-velocity and I do not how...

Homework Statement No specific problem to solve, just looking for a better explanation of the implications of the quadratic variation not being zero in Brownian motion. Why is this so important in the study of stochastic calculus and Brownian motion? I understand that quadratic variation in...

1. Homework Statement [/b] If f has a continuous derivative on [a,b], and if P is any partition of [a,b], show that V(f,P)\leq \intablf'(t)l dt. Hence, Vba\leq\intablf'(t)ldt. Homework Equations Monotone function \subset BV[a,b] \sumf(ti+1)-f(ti) = lf(b) - f(a)l The Attempt at a...

Homework Statement Given a sequence of scalars (cn) and a sequence of distinct points (xn) in (a, b), define f(x) = cn if x = xn for some n, and f(x) = 0 otherwise. Under what condition(s) is f of bounded variation on [a,b]? Homework Equations Vbaf = supp(\Sigmalf(ti) - f(ti-1)l< +inf...

I am reading about a branch of mathematics which does not allow separable spaces. The author of the text gives the space of functions of bounded variation as an example of a non-separable space, which is fine - except for the fact that he goes on to claim that "this space is relevant to both...

Homework Statement 4y'' + y = cosx Solve using variation of parameters Homework Equations The Attempt at a Solution from a) -> yc(x) = c1cos(x/2) + c2sin(x/2) let y1 = cos(x/2) , y2 = sin(x/2) y1y2' - y2y1' = 1/2cosx/2 + 1/2sinx/2 = 1/2 u1' = ? How do I find this?

1.Homework Statement We know the derivation of the method of variation of parameters for second order scalar differential. The task is to derive the method of variation of parameters for scalar equations using this approach: first convert the scalar equation into the first order system and...

Homework Statement Let {fn} be a sequence of real-valued functions on [a, b] that converges pointwise on [a, b] to the real-valued function f. Show that TV (f) <= lim inf TV (fn). Homework Equations The Attempt at a Solution I prove it in the follwoing way: |fn(xi) - f(xi) |...

The equation of motion of a rocket with mass depletion during ascent and subject to drag forces can be written as M(t) dV/dt = A - M(t)g - BV^2 (Eq. 1) with initial condition V(t=0) = 0 (V is velocity and t is time) Let us assume a linear mass depletion according to...

Homework Statement Hello, i have a small problem regarding this questions, If the function vs(t) is a function for t>=0, i can solve thus no problem (we are required to solve using variation of parameters). now i have a small problem, its not about how to solve it ,but how to approach...

Here is a brain teaser I came across recently. Ten prisoners are arranged single file in a line. They are sorted so that the shortest prisoner (prisoner #1) is in the front, and the tallest prisoner (prisoner #10) is in the back. The are all looking forward (in the direction of #1). They...

I've fabricated a simple half-wave microstrip resonator with gap-coupled microstrip feed lines. It's designed to operate around 10GHz, but due to slight over etching, the half-wave portion is 5-10um shorter than I intended. What might be more significant is that the gap, which was originally...

So, I've been trying to solve a variation of the famous birthday problem. The problem is a more generalized version and goes like this: given n people, what is the probability at least k people share a birthday? You could also describe the problem as such: given m items randomly distributed into...

Homework Statement Find a particular solution using variation of parameters. y'' + 3y' + 2y = 4e^x Homework Equations yp = -y1 * INT (y2f(x)/W[y1,y2]) dx + y2 * INT (y1f(x)/W[y1,y2]) dx The Attempt at a Solution So, first I find the homogeneous solution, correct? r2 + 3r + 2 = 0, so...

suppose I have a number of permutations of a vector of bits and i want to have some measure of how varied the sequence is. e.g. i want a single measure that can express the difference between this: 1010101010 and this: 1111100000 the measure would ideally place vectors on a spectrum so...

Homework Statement A particle is moving in a simple harmonic oscillator potential V(x)=1/2*K*x^2 for x\geq0, but with an infinite potential barrier at x=0 (the paddle ball potential). Calculate the allowed wave functions and corresponding energies.Homework Equations I am thinking that the...

Homework Statement What do you do if one of the roots to the characteristic equation of a differential equation is zero when using variation of parameters? Homework Equations The Attempt at a Solution The problem I encountered this in is y" - y' = 4t Characteristic equation r2 - r = 0 so...

We know, in optics Fermat's principle is written in analogy with principle of Maupertuis in Classical mechanics (given by \delta S=\delta\int\vec{p}\cdot d\vec{l}=0). In terms of the wave vector it is written as \delta\psi=\delta\int\vec{k}\cdot d\vec{l}=0. Here \psi is known as eikonal (or...

Hi all, I'm going to ask a naive question - hope that's ok. There's been a lot of recent discussion of the results from Webb et al. which indicate that the fine structure constant varies spatially. I realize the results are very controversial - I'm wondering, hypothetically, if these...

Homework Statement Solve xy' - y = x3 (1) by using variation of parameters. The Attempt at a Solution Solving the homogeneous version of (1) gives yh = c1x Now we are to seek yp = A(x)*x (2) from (2) y'2 = A'*x +A plugging into (1) we have: x[A'*x + A] - Ax = x3...

Homework Statement s varies directly as r and inversely as t. s=10 when r=5 and t=3. What value of t will s=3 and r-4? Homework Equations Direct variation: y=kx; Indirect variation: y=k/x The Attempt at a Solution I tired s=kr=k/x and plugging in the given, but I could not get t in the end. My...

Hi, I was solving the following second order ODE: http://www.texify.com/img/%5CLARGE%5C%21x%5E2%20y%5E%27%27-5xy%5E%27%2B5y%3Dx%5E6%20sinx.gif I used variation of parameters and found this solution...

Do know anybody explicit form of variation action quadratic in Riemann tensors (for general dimension)? Link to internet sources? Or computer program for symbolic and tensors algebra, which the variation tell me (preferably open-source)? Thx

Homework Statement If y varies inversely as the square of x, and y = 1/8 when x = 1, find y when x = 5. y = 8/25 y = 1/200The Attempt at a Solution The equation to find this is y=k/x, I know that. I've tried to plug in both given answers to see which ones matched but neither of them did...

Background: Math: An affine parameter provides a metric along a geodesic but not a metric of the space, for example between geodesics. A connection provides an affine parameter, and a non-trivial connection gives rise to Riemann curvature. Given the existence of a connection with Riemann...

Imagine the setup of the original Schrodinger's Cat; The cat is behind the wall, locked. I am adding another element to it, a person that will enter the room without the knowledge of the experimenter, and exit through another door and seal the place again. So for the Observer unaware of this...

I conducted an experiment involving a 555IC timer circuit and the hypothesis investigated the frequency and period of the LED connected. Using the formula for frequency; 1.44/(Ra + 2Rb)C where R1= 1000R R2= 10000R C = 10uF the frequency equals 6.857 (rounded value) now using data...

Hi all, this will be my first physics qns:D more to come... I just learned that value of g at the equator is not exactly equal to the gravitational field strength. Can anyone explain with workings? i don't really understand my teacher workings. Also can i clarify if -We're assuming Earth...

hey, i am trying to find what is the process going on in the conductor while conducting ac. what is happening to electrons? what is the physical meaning of negative voltage in sin curve?

http://www.cdeep.iitb.ac.in/nptel/Mechanical/Heat%20and%20Mass%20Transfer/Conduction/Module%202/main/2.6.3.html" Kindly see the above link I will be placing a temperature sensor in the hollow area and insulate the outer surface(with let's say Plaster of paris)...I will place a fire...

Hey, I'm doing some examples in QFT and I don't want to go too far with this one: Doing gauge symmetries, we first introduce the Unitary spacetime-dependent gauge transformation that gives us a gauge potential. With the new gauge added Lagrangian, I want to take its variation to confirm the...

So I'm planning a senior honors thesis that'll start next summer. In my last post, I talked about testing magnetoreception, which is kind of risky. Another idea of mine is to take human subjects into a dark room, use filtered light to produce light at increments one 1 nm, and note the longest...