Chain Definition and 979 Threads

Today we encountered a problem with markov chains and are wondering if this can be solved analytically. Suppose we have a banded transition probability matrix M of the following form: M= [ P P 0 0 0 ... Q 0 P 0 0 ... 0 Q 0 P 0 ... 0 0 Q 0 P ... 0 0 0 Q 0 ... . . . . . . . . . . ]...

If I have two functions, f(x,y,z) and g(x,y,z), do I use the chain rule to calculate df/dg? e.g. df/dg=df/dx df/dy df/dz Cheers! Romeo

Without introducing any other atoms or double bonds into the chain? (just replace the halogen with a hydrogen atom). Assume for now that the halogen was introduced in the middle of the carbon chain.

Homework Statement Hi I'm currently trying to revise for a Calculus exam, and have very little idea of how to do the following: Let f be defined by f(x,y) = (y+e^x, sin(x+y)) Let g be of class C2 (twice differentiable with continuous second derivatives) with grad(g)(1,0) = (1,-1) and Hg(1,0)...

I'm looking at the proof of the multivariable chain rule & just a little bit curious about something. In the single variable chain rule proof the way I know it is that you take the derivative: f'(x) \ = \ \lim_{ \Delta x \to \infty} \frac{ \Delta y}{ \Delta x} and manipulate it as follows...

A chain of length L,mass M kept vertical so it just touches ground.A height x of it from bottom falls down.Find the total force exerted by it on ground. My attempt: Force due to its weight=Mg Force due to falling and change in momentum: consider small element dy at height y Change in...

Homework Statement A uniform chain of total length 'a' has a portion 0<b<a hanging over the edge of a smooth table AB. Prove that the time taken for the chain to slide off the table if it starts from rest is (a/g)1/2*ln(a+((a2-b2)/b)1/2)

Homework Statement The function F is defined by F (r, θ) = f (x(r, θ), y(r, θ)), where f is twice continuously differentiable and x(r, θ) = r cos θ, y(r, θ) = r sin θ. Use the chain rule to find d2F/dθ2Homework Equations The Attempt at a Solution I know that dF/dθ = (df/dx)(dx/dθ) +...

Ive studied how chain reaction of proton-proton powers the stars, I also know that proton-proton fusion will convert firstly one proton to neutron then fuse it with the other proton...my question is... Is the main reason for them not being fused is that they both have +ve charge?

I've written a scifi short story for a contest on the theme of environmental disaster, and I want to check the plausibility of the chain of events that occurs in the story. 1. It opens with a spill of massive quantities of methyl and phenyl isocyanate into a bay area on a planet in the...

Homework Statement A chain consisting of five links, each of mass 0.10 kg, is lifted vertically with a constant acceleration of 2.5m/s^2. a.) Find the forces acting between adjacent links. b.) Find the force F exerted in the top link. Homework Equations F=ma W=mg The Attempt at...

Greetings, As someone who is interested in the history of the nuclear age, I have been unable to find an answer for this: Once the fuel rods are loaded into the fuel assembly and the assembly is loaded into the core, how does the chain reaction start which creates the heat? Do they...

Homework Statement Two carts can slide along a horizontal rail without friction. The carts are connected: (a) by an elastic spring of spring constant k and unstretched length l; (b) by a chain of length l and linear density p. The spring is going along the rail, the chain hangs in the...

Hello, in relation to Markov chains, could you please clarify the following equations: In particular, could you please expand on why the first line is equal. Surely from , along with the first equation, this implies that: I just don't see why they are all equal. Please could you...

Homework Statement Two carts can slide along a horizontal rail without friction. The carts are connected: (a) by an elastic spring of spring constant k and unstretched length l; (b) by a chain of length l and linear density p. The spring is going along the rail, the chain hangs in the...

Homework Statement I'm looking for a proof for the chain rule that is relatively easy to understand. Can someone show / link me one? Thanks. Homework Equations The Attempt at a Solution

Homework Statement Find dy/dx at x = 2. y = (1 + s)/(1 - s); s = t - 1/t; t = sqrt(x) Homework Equations I know if f = f(g(x)), then f1(x) = f1(g(x)) * g1(x) The Attempt at a Solution I think I may need to combine the chain rule and quotient rule, but all of the separate...

Homework Statement Apply the two cases of th change rule. For example: The voltage V in an electrical circuit is slowly decreasing as a battery wears out and the resistance R is slowly increasing as the resistor heats up Use Ohm's law V=IR to find how the current is changing (with respect to...

Problem with proof of Chain rule for f:R-->R Hi, Analysts: I am going over problems in Rosenlicht's Intro. Analysis book. In this problem , he asks one to find the flaw in this argument to the effect that (f(g(x))'=f'(g(x))g'(x). Unfortunately, author does not clearly state the...

Homework Statement Homework Equations The Attempt at a Solution a) (∂z/∂x)=-(∂f/∂x)*(∂z/∂f) i used that (AxB)=-(BxA) so i get (∂z/∂x)=-[-(∂z/∂f)(∂f/∂x)] =(∂z/∂x) is this correct if not can someone give me hints pls thanks

I have a function for velocity, V in terms of position, x. The equation is of the form V(x) = a*x2+b*x+c. Initial conditions are x=0, t=0. How do I change from V(x) to V(t)? It seems this would be an application of the chain rule, dy/dx = dy/du * du/dx, but I'm struggling to adapt it to...

Homework Statement A chain of metal links with total mass m = 7 kg is coiled up in a tight ball on a low-friction table. You pull on a link at one end of the chain with a constant force F = 52 N. Eventually the chain straightens out to its full length L = 0.8 m, and you keep pulling until you...

Homework Statement Find: ∂f/∂x f(r,θ)=rsin^2(θ), x=rcosθ, y=rsinθ The Attempt at a Solution ∂f/∂r=sin^2θ ∂r/∂x=-cosθ/x ∂f/∂θ=2*r*cosθ*sinθ ∂θ/∂x=-1/sqrt(1-(x^2)/(r^2) ∂f/∂x = -sin^2θcosθ/x^2 + -2*r*cosθ*sinθ/sqrt(1-(x^2)/(r^2) ∂f/∂x = -y-sqrt(x^2+y^2) /...

I'm kind of confused about how to approach a function with the chain rule. For example in the equation ƒ(x) = sqrt(1-sin(x)) I know i simplify it to ƒ(x) = 1-sin(x)^(1/2) but I'm lost from there.

Homework Statement Image you have one of the old fashion chain shots from the 1800’s where they had two cannon balls connected by a chain. Now let’s say you wish to try to fire the chain shot from two cannons. The synchronized cannon firing nearly works, but one cannon ball receives a...

Problem Use the chain rule to proof \dot{A}=\partial_t A+v_j\partial_jA_i Attempt at Solution \dot{A}=\frac{dA_i}{dt} = \partial_t A_i+\frac{dr_i}{dt}\frac{\partial A_i}{\partial r_i} Obviously v_j = \frac{dr_j}{dt} I'm puzzled where the v_j and partial d_j come in

Homework Statement Reduce the order of a Cauchy-Euler Equation Homework Equations x = e^t \mbox{ and } \ln x = t The Attempt at a Solution \displaystyle \frac{d y}{d x} = \displaystyle \frac{d y}{d t} \displaystyle \frac{d t}{d x} = \displaystyle \frac{d y}{d t} \cdot...

How do I find the stationary distribution of the Markov chain with the countable state space {0, 1, 2, ..., n, ...}, where each point, including 0, can either a. return to 0 with probability 1/2, or b. move to the right n -> n+1 with probability 1/2? Thanks.

Homework Statement A cubical block of ice is melting in such a way that each edge decreases steadily by 9.8 cm every hour. At what rate is its volume decreasing when each edge is 10 meters long? Homework Equations V(t) = (l(t))^3 m^3 l'(t) = 0.098 m/h The Attempt at a Solution...

Homework Statement One side of a triangle is increasing at a rate of 3cm/s and a second side is decreasing at a rate of 2cm/s. If the area of the triangle remain constant, at what rate does the angle between the sides change when the first side is 20cm long and the second side is 30cm, and...

Homework Statement uploaded Homework Equations rocket equation The Attempt at a Solution i can calculate the force acting on the chain by the ground using rocket equation but i cannot show that the velocity is that.

Homework Statement Prove that (\frac{\partial u}{\partial x})^{2} + (\frac{\partial u}{\partial t})^{2} = e^{-2s}[(\frac{\partial u}{\partial s})^{2} + (\frac{\partial u}{\partial t})^{2}].Homework Equations u = f(x,y) x = e^{s}cost y = e^{s}sint The Attempt at a Solution I started out by...

Homework Statement Let \left( X_n \right)_{n \geq 0} be a Markov chain on {0,1,...} with transition probabilities given by: p_{01} = 1, p_{i,i+1} + p_{i,i-1} = 1, p_{i,i+1} = \left(\frac{i+1}{i} \right)^2 p_{i,i-1} Show that if X_0 = 0 then the probability that X_n \geq 1 for all n \geq 1 is...

This is strictly a math question but I figured that since it is something which would show up in QM, the quantum folks might be already familiar with it. Suppose we have an operator valued function A(x) of a real parameter x and another function f, both of which have well defined derivatives...

Homework Statement F(s) = ( s - \frac{1}{s^2})3 I have to calculate the derivative of this using chain rule everytime i try i get something way different than in the back of the book... my first move is 3( s - \frac{1}{s^2})2 X ( 1 + \frac{2}{s^3}) is this correct? then expand...

I studied physics a long time ago and somebody just asked me this question. After trying for a while I couldn't work it out. The situation is this: there's a chain of length $l$ on a table, of which a portion, of length $x_0$, is hanging out (enough so that when you stop holding it down, the...

Homework Statement A chain of mass M and length L is suspended vertically with its lower end touching a scale. The chain is released and falls onto the scale. What is the reading of the scale when a length of the chain x has fallen? You may neglect the size of the individual links. [10]...

Homework Statement Let x=x^2ysin(u)tan(v), where x(u,v) and y(u,v) are smooth functions that, when evaluated at u=1 and v=-3 satisfy x=2.112, y=4.797, \partialx/\partialu = -3.491, \partialx/\partialv = -2.230 , \partialy/\partialu = 1.787 , \partialy/\partialv = 1.554. Then the...

\hbox { Let }\; u(x,y)=v(x^2-y^2,2xy) \;\hbox { and let }\; t=x^2-y^2,\;s=2xy u_x = 2xv_t \;+\; 2yv_s u_{xx} = 2v_t + 4x^2 v_{tt} + 8xyv_{ts} + 4y^2 v_{ss} The u_{yy} can be done the same way and is not shown here. According to Chain Rule: u_x = \frac{\partial v}{\partial x}...

I am currently learning calculus and just had my lecture on the chain rule. I noticed that we haven't learned how to take the derivative of a function like 2^2+x or 3^4+x. Any example works.. Is this something I will learn later as I progress through calculus or what?

Homework Statement I have a problem with the next exercise: Given de function f(x,y)=\begin{Bmatrix} \displaystyle\frac{xy^2}{x^2+y^2} & \mbox{ if }& (x,y)\neq{(0,0)}\\0 & \mbox{if}& (x,y)=(0,0)\end{matrix} with \vec{g}(t)=\begin{Bmatrix} x=at \\y=bt \end{matrix},t\in{\mathbb{R}} a) Find...

Homework Statement This is from Serway's book Prob 9.71...(busying preparing for GRE) A chain of length L and total mass M is released from rest with its lower end just touching the top of a table, as in figure (a). Find the force exerted by the table on the chain after the chain has...

I need some help with the chain rule...Thank you for helping me:) Question: G(y)=((x-1)^4)/(((x^2)+2*x))^7 I have no idea where to start.

I'm looking for some input on the design of a lifting device. The design is required to accurately lower lower a load of 400 metric tonnes through a height of 50m, return to the top of it's travel and lower the next load and so on. I'm currently thinking along the lines of a two-pronged tower...

Hi I am trying to model the behaviour of 2 independent ON-OFF sources. My state diagram is as follows state 0 = both sources are OFF state 1 = 1 of the sources are ON state 2 = both sources are ON The transition rates are given as BIRTH RATE = lamda(i) = (N-I)*lamda DEATH RATE =...

Homework Statement I trying to find the second derivative of xe^x Homework Equations chain rule The Attempt at a Solution Two find the first derivative I use the chain rule. f'(y)g(y)+f(y)g'(y) so I get e^x+xe^x is the second derivative e^x+f'(y)g(y)+f(y)g'(y)...

1. A particle of mass m is tied on one end of a very long chain which has a linear density μ (kg/m) and lies on a surface with the chain wound next to it. The particle is thrown upwards with an initial velocity V. Find the maximum height the particle is going to reach. My question is not what...

[PLAIN]http://img245.imageshack.us/img245/7903/staticsproblem.jpg I don't know where to start with this because I'm unsure as to how the force is distributed in the chain.

I'm afraid I'm suffering from a bit of brain block in try to get from the simple statement of change in the number of daughter nuclei arising from the decay of parent nuclei. The basic statement is straight forward... \frac {dN_d}{dt} = \lambda_pN_p - \lambda_dN_d Subscripts d and p denote...

Homework Statement If y=f((x2+9)0.5) and f'(5)=-2, find dy/dx when x=4 Homework Equations chain rule: dy/dx=(dy/du)(du/dx) The Attempt at a Solution In my opinion giving f'(5)=-2 is unnecessary as: y=f(u)=u, u=(x2+9)0.5 dy/dx= (dy/du)(du/dx) (dy/du)= 1 (du/dx)= x/((x2+9))0.5 dy/dx =...