Chain Definition and 979 Threads

Homework Statement Solve (d^2x)/(dt^2) = 2x(9 + x^2) given that dx/dt = 9 when x = 0 and x = 3 when t = 0 Homework Equations The Attempt at a Solution v = dx/dt ...... dv/dx = d^2x/dt^2 dv/dx = v(dv/dx) v(dv/dx) = 18x +2x^3 integrating and evaluating using...

Homework Statement We are deriving the PDE that models a hanging chain of Length L. The x-axis is placed vertically. Positive direction points upwards. The fixed end of the chain is at x=L. Let u(x,t) denote the deflection of the chain. We assume the deflection is in the x,u plane. Let...

[b]1. Ashcroft and Mermin 22.1 Reexamine the theory of the linear chain without making the assumption that only nearest neighbors interact, using the harmonic potential energy of the form: U^harm=∑_n▒∑_(m>0)▒1/2 K_m [u(na)-u([n+m]a) ]^(1/2) Show that the dispersion relation must be...

could someone show me how \frac{∂}{∂t}(\frac{∂z}{∂u})= \frac{∂^2z}{∂u^2} \frac{∂u}{∂t} where z=z(u) u=x+at

Homework Statement The atoms having in each case, the mass m and are located at positions with x i i ∈ Z. The rest position of the ith atom is i · a where a is the lattice constant of the crystal. The interaction between the atoms can be modeled in a simple approximation, as a spring force of...

It seems to me to follow from the definition of a partial derivative. If f(x,y) = fx + fy, then what else can Δf be other than ∂f/∂x*Δx + ∂f/∂y*Δy? Then in the limiting case, the changes in f, x and y becomes differentials instead. All this seems to be given by the definitions themselves, is...

mechanical design -- cam timing chain versus gear-driven hey all, I am a mech-e student, but I am still in the infancy of my degree, so I haven't really had any courses pertaining to this sort of thing, but having work with cars for a number of years, and having what I consider a strong...

Hi! I do not understand the math used in the beginning of this video: In example 1 (4 minutes in the video), why is it wrong to simply solve the problem like this: \vec{V} = [x,-y] \Rightarrow \frac{d\vec{V}}{dt} = [\frac{dx}{dt},-\frac{dy}{dt}] = \vec{a} = [V_x,-V_y], where V_x and V_y are...

Is \frac{∂y}{∂x}×\frac{∂x}{∂z}=-\frac{∂y}{∂z}?

Homework Statement Consider the following (simple) epidemic model: A population of size N consists of infected and susceptible individuals. During each time period, each of the N choose 2 possible pairs in the population will come in contact with probability p. If a pair is in contact and...

Homework Statement A chain AB of length ##l## is located in a smooth horizontal tube so that its fraction of length ##h## hangs freely and touches the surface of the table with its end B. At a certain moment, the end A of the chain is set free. With what velocity will this end of the chain slip...

1. Homework Statement . Prove that an infinite chain contains an a chain isomorphic (with the order) to N (the natural numbers) or to -N (negative integers). 3. The Attempt at a Solution . I think I know how to solve the problem but I have problems to write a formal proof. I want to...

I am so annoyed with Facebook users who sharing information that is either a hoax (strawberry quick) or outdated information (missing people, abused animals). Why don't they check the source if they are so concerned? The hoax has long been revealed, the missing people were found months ago, the...

is this proof valid? I thought it out myself with some help from textbooks?

Is this proof of the chain rule valid ?

A question in regards to nomenclature. I am curious as to the significance of using the symbol π for a time-independent distribution. Does it have any relation to the number π or circular geometry? Or does it come maybe from the invariance of i in the P Matrix such that Pi,j → πj? I don't like...

Hey could someone explain why this is true? I am trying to understand how to solve such a problem but I don't understand the solution. Problem: Given a Markov chain \left\{X_{n}: n\in\ \mathbb{N}\right\} with four states 1,2,3,4 and transition matrix P = \begin{pmatrix} 0 &...

1. The problem statement Consider the Binomial Distribution in the form P_{N}(m)=\frac{N!}{(\frac{N+m}{2})!(\frac{N-m}{2})!}p^{\frac{N+m}{2}}q^{\frac{N-m}{2}} where p+q=1, m is the independent variable and N is a parameter. Show that it satisfies the marcoff chain...

how do I find the integral of ∫√(t^4+x^3)dt from 0 to x^2?

Hi everybody I'm trying to solve this equation the text in shown picture basically asks to find meaning of Xo By doing this But it says my answer is wrong, can anyone tell me why, Thank you?(Also what is this equation called in English?)

Homework Statement Take a constant p ≥ 1 and f(x, y) a function of two variables with continuous first order partial derivatives. If, f(λx, λy) = (γ^p)f(x,y) for λ ε ℝ, prove that x(∂f/∂x) + y(∂f/∂y) = pf Homework Equations x(∂f/∂x) + y(∂f/∂y) = pf f(λx, λy) = (λ^p)f(x,y)The Attempt at a...

Hi all! In questions having implicit functions, this expression -> "d/dx y^2" often appears in the calculation process. I use the chain rule to convert it to 2y x dy/dx But why can the chain rule be used here? I actually don't understand at all.. Any help is appreciated. Thanks guys!

Hi, I was trying to understand why the chain rule is needed to differentiate expressions implicitly. I began by analyzing the equation used by most websites I visited: e.g. x2+y2 = 10 After a lot of thinking, I got to a reasoning that satisfied me... Here it goes: From my...

Hello everybody! First of all,I would like to apologize for my English because I'm not a native speaker. I'm 16 and I have a pretty good knowledge on physics but I need help with solving certain type of problems. In my country we now have a summer vacation so I decided to look for a forum where...

Homework Statement question from early transcendentals (Edwards, penny) . chapter 12 partial differentiation problem 38 1/R = 1/R1 + 1/R2 + 1/R3 R is resistance measured in Ω R1 and R2 are 100Ω and increasing with 1Ω/s R3 are 200Ω and decreasing with 2Ω/s Is R increasing or...

For the decay chain N1 -> N2 -> N3 -> ... -> Ni -> ... -> Nd, how can I find the amount of particles of Ni, n(Ni), at any point in time t, with a single equation where i can vary from 1 to d? I have already seen WIkipedia's suggestion on the Bateman equations but that method seems to collapse...

1. -Find a regular transition matrix that is not time reversible, i.e., doesn't satisfy the balance equations? 2.Pi,j=0≠Pj,ifor some i and j My understanding from Markov Chain Monte Carlo is that for the transition matrix to be regular the matrix has to have all positives entries and each row...

I was wondering if anyone could help me with this problem dealing with Markov Chain Monte Carlo -Find a regular transition matrix that is not time reversible, i.e., doesn't satisfy the balance equations? My understanding from Markov Chain Monte Carlo is that for the transition matrix to be...

I have a composite function f(g(x,y)). When is it true that ∂f/∂g = (∂f/∂x)(∂x/∂g) + (∂f/∂y)(∂y/∂g)? Does g have to be invertible with respect to x and y for this to be true?

This is slightly applied stuff. Please look at the PDF attached. How do we express the function f(n)ij, found at the bottom of page 4, in closed form, in terms of the values of n, i and j? If we can figure this out, then, as noted half-way down page 5, fij is simply the sum of f(n)ij from n=1...

Hi, I was reading about Markov chains and came across the following statement: "The conditional distribution p(x_n|x_{n-1}) will be specified by a set of K-1 parameters for each of the K states of x_{n-1} giving a total of K(K-1) parameters." In the above we have assumed that the...

Homework Statement Consider a circle with radius r diagrammed as the unit circle, but take only the second quadrant. On this quarter of the circle lies a chain with mass per unit length \rho (the length of the chain is \pi r/2). If \theta is the angle made with the vertical axis at any point on...

Homework Statement If f(x) = e^{3x^2+x} , find f'(2)Homework Equations f'(x) = a^{g(x)}ln a g'(x)The Attempt at a Solution f'(x) = (e^{3x^2+x})(ln e)(6x+1) f'(2) = (e^{3(2)^2+2})(ln e)(6(2)+1) = 2115812.288 I was checking online and I'm seeing a different answer, but this is EXACTLY how...

Hi PF, I would like to simulate N th order markov chain (not by means of hidden markov models, but ordinary markov chain) using Matlab. If n-th order is a heavy thing atleast 2nd or 3rd order will do. TIA

Hello, Given is the function f = f(a,b,t), where a=a(b) and b = b(t). Need to express first and second order derivatives. \frac{\partial f}{\partial a} and \frac{\partial f}{\partial b} should be just that, nothing more to it here, correct? But \frac{df}{dt} = \frac{\partial...

This is a very basic problem which you all must have seen somewhere. But recently an itching doubt has come up to me regarding this problem. Problem: A chain lies on a table with some part of it hanging over the edge. Now if the coefficient of friction is μ, then find out the maximum part...

Homework Statement Differentiate f(x) = (x^2 - 3x)^2 Homework Equations f'(x) = nf'(x)f(x)^(n-1) The Attempt at a Solution f’(x) = 2(x2-3x)’(x2-3x)2-1 = 2(2x-3)(x2-3x)1 = 2(2x3 – 6x2 – 3x2 + 9x) = 2(2x3 – 9x2 + 9x) = 4x3 – 18x2+ 18x Is this correct?

Homework Statement h(x) = f[g(x)] h'(x) = f'[g(x)] * g'(x) Homework Equations h(x) = sin(-x) The Attempt at a Solution So, this one is pretty simple, except I just want to confirm something. When I do it it, it looks like this: The derivative of sin = cos, so you have...

A teacher leaves out a box of N stickers for children to take home as treats. Children form a queue and look at the box one by one. When a child finds k⩾1 stickers in the box, he or she takes a random number of stickers that is uniformly distributed on {1,2,…,k}. 1- What is the expectation of...

Homework Statement Use \frac{\partial z}{\partial r}=\cos\theta\frac{\partial z}{\partial x}+\sin\theta\frac{\partial z}{\partial y} and \frac{\partial z}{\partial\theta}=-r\sin\theta\frac{\partial z}{\partial x}+r\cos\theta\frac{\partial z}{\partial y} to show that...

Homework Statement Write out a tree (this will be a big tree) of dependencies and hence write down an expression for ∂z/∂rHomework Equations z=k(x, y)=xy2, x=(w1)(w2)+w3, y=w4; w1=t, w2=t2, w3=2t+1, w4=sin(t); t=r2+2s2The Attempt at a Solution This is the tree I drew and followed the...

It's probably a stupid question but is it possible to attach a long proline chain - 8 or more residues - at the C terminal of a protein and have it connect to another protein and not affect folding? It's for a project and it's not actually necessary but I have to make a protein that binds to an...

Homework Statement Subpart of the question requires me to find the steady state of the transition matrix: P=\begin{bmatrix} 0.1 & 0.7 & 0.2 \\ 0.1 & 0.8 & 0.1\\ 0.3 & 0.1 & 0.6 \end{bmatrix} Homework Equations We thus need to find vector \boldsymbol{v} in the equation...

Hello MHB, I got one exempel that I don't get same result as my book. Exempel: If z=f(x,y) has continuos second-order partial derivates and x=r^2+s^2 and y=2rs find \frac{d^2z}{dr^2} So what I did before checking soulotion: \frac{d^2z}{dr^2}=\frac{dz}{dr} \frac{d}{dr} So I start with solving...

Exempel 6: If g(s, t) = f(s^2-t^2, t^2-s^2) and f is differentiable, show that g satisfies the equation t\frac{dg}{ds}+s\frac{dg}{dt}=0 I always try solve it before I look 'soloution' so this is how we both did it. (remember this is a exempel in my book so they show how to solve it but they...

Hi there, I'm having some problems trying to write down the Lagrangian of the following system: A uniform flexible chain of mass M and length L is hung under gravity on a frictional pulley of radius a and moment of inertia I whose axle is fixed at a point above the ground. Write down the...

Homework Statement 32) A stone dropped into a pond at time t=0 seconds causes a circular ripple that ravels out from the point of impact at 5 metres per second. At what rate (in square metres per second) is the area within the circle increasing when t=10? Homework Equations I need to use...

Homework Statement Let (u,v)=\mathbf{f}(x,y,x)=(2x+y^3,xe^{5y-7z}) Compute D\mathbf{f}(x,y,z),\;\partial (u,v)/\partial(x,y),\;\partial (u,v)/\partial(y,z)\text{ and }\partial (u,v)/\partial(x,z) Homework Equations -chain rule The Attempt at a Solution well I can get...

Homework Statement this is kinda funny I've been strugglnig with the proof for 3 hours straight today long story short(<--sorry couldn't find the best way t o say this ) i made it to this statement lim(x->a) g(x) if this is equal to g(x) then my proof is done lim(x->a) f(a) if this is equal...

Hello, I got problem again with chain rule and would like to have advice for this problem, $\frac{\displaystyle r} {\displaystyle \sqrt{r^2+1}}$ is it product rule I shall also use because I have rewrite it as $r(r^2+1)^{-0.5}$