Chain Definition and 939 Threads

Homework Statement Homework Equations The Attempt at a Solution A few things. First of all, the homework problem notes that "all the columns should sum to 1," whereas Wikipedia says ∑Pij = 1 when we sum all along the the row i. Second of all, I don't know where to...

Anyone on this forum know what the highest-probability fission chain reaction of plutonium-239 is? Mike Fontenot

Is anyone thoroughly familiar what von Neumann was trying to say in his von Neumann Chain concept where one can locate anywhere the observer and the observed? I've been reading the original and analyzing it for hours and can't seem to completely get the context in light of present day concept...

i want to know how to calcuate Starting and running for motor in 2 post lift for lifting 3.0T. Actually i have 2 columns having trapezoidal screw rod and nut in each side. One column is getting drive by motor through pulley belt mechanism. Another shaft is getting driven by chain at the...

Homework Statement The background: We performed an experiment testing the fatty acid binding difference of caproic (hexanoic) acid and lauric (dodecanoic) acid to bovine serum albumin. The experiment was performed using a fluorescent marking called ANS(which fluoresces when bound to bovine...

Hello! I'm currently taking Mth 251 and have been working on this chain rule for a bit. It's kind of straight forward, there's just a lot of chains inside of chains and so forth. I think I have a solution, but I'm not entirely sure its correct. Homework Statement Find the derivative of...

So I have a chain driven system on a tricycle that I am kind of stuck with. the center distance of the two sprockets is 65 inches, and the chain is a 530 series, which has a pitch of 5/8. Now I have seen some sources reference or mention a 60 to 80 maximum of center distance to pitch ratio...

1. Derive arcsin(1 - 2 e ^-t) 2. The derivative of arcsin is 1/√(1-x^2) 3. I tried using the chain rule for 1 - 2 e ^-t, but that didn't work out. What should I take the chain rule of?

hi does anyone know why the 2nd derivative chain rule is as such? i roughly know that if u = f(x,y) and x=rcos(T) , y = rsin(T) then du/dr = df/dx * dx/dr + df/dy * dy/dr but if i am going to have a second d/dr, then how does it work out?

Homework Statement A flexible chain weighing 41.0 N hangs between two hooks located at the same height. At each hook, the tangent to the chain makes an angle θ = 41.5° with the horizontal. (a) Find the magnitude of the force each hook exerts on the chain. (b) Find the tension in the chain at...

Homework Statement Let \textbf{F}: \textbf{R}^m \rightarrow \textbf{R}^n and \textbf{G}: \textbf{R}^p \rightarrow \textbf{R}^m Prove that ({\textbf{F} \circ \textbf{G}})'(x) = {\textbf{F}}'(\textbf{G}(\textbf{x})) {\textbf{G}}'(\textbf{x}) Homework Equations Assume the single...

Homework Statement The movement of an object with a mass of 1500kg is given by v(x)=(4.0 [1/ms]) * x^2 Determine the net force acting on the object as a function of x. Homework Equations F=ma The Attempt at a Solution I know I'm supposed to use the chain rule to solve this but...

Homework Statement http://www.math.wvu.edu/~hjlai/Teaching/Tip-Pdf/Tip3-27.pdf Example 7. Not this question in particular, but it shows what I'm talking about. I understand how they get the first partial derivative, but I'm completely lost as how to take a second one. I have tried...

Homework Statement Consider phonons propagating on a one-dimensional chain of N identical atoms of mass M interacting by nearest-neighbour spring constants of magnitude C. Show that the Debye frequency can be written as w_{D}=\pi \left(\frac{C}{M}\right)^{1/2}. Homework Equations The...

r' = 4r - rf f' = -3f + rf In this question, there was three parts: a) find all the critical points of this system. b) Derive the linearised system about each critcal point... c) Use the chain rule to derive the path equation of the trajectories in the phase plane. I managed to get a...

Homework Statement Find the derivative of: f(x)=\sqrt{2x} Homework Equations So using the chain rule: \frac{dy}{dx}=\frac{dy}{du}.\frac{du}{dx} The Attempt at a Solution Isn't it just a simple matter of setting u=2x, therefore du/dx=2, and y=\sqrt{u}=u^1/2, therefore dy/du=1/2 *...

I just learned about chain rule in calculus, but I was wondering why exactly chain rule works. I understand how to use it, just not exactly why it works. Thanks in advance

Homework Statement Let z = z (x,y) be a function with x = x(s), y = y(t) satisfying the partial differential equation (Ill write ddz/ddt for the partial derivative of z wrt t and dz/dt for the total derivative of z wrt t, as I have no idea how to use Latex.) ddz/ddt +...

Homework Statement Say that f(x) is some function whose second derivative exists and say u(x, t)=f(x + ct) for c > 0. Determine \frac{\partial u}{\partial x} In terms of f and its derivatives. Homework Equations PD Chain rule. The Attempt at a Solution Say that x and y are...

What is the difference between martingale and markov chain. As it seems apparently, if a process is a martingale, then the future expected value is dependent on the current value of the process while in markov chain the probability of future value (not the expected value) is dependent on the...

I have a question about the variable changes in the proofs of Proposition 1.3.4 and Proposition 1.3.6. In the first one, it seems like the author does the variable change but once he applies the chain rule he doesn't do it completely. While in the second it seems like it does the variable...

Homework Statement A chain hangs b'n two points in the vertical plane, find its centre of mass. I have no idea where to start. Homework Equations The Attempt at a Solution

A chain of length 'l' and mass 'm' lies on the surface of a smooth sphere of radius 'R' > 'l', with one end tied to the top of the sphere. (a) Find the gravitational potential energy of the chain with reference level at the center of the sphere. (b) Find the tangential acceleration dv/dt...

Homework Statement A uniform chain of total mass m is laid out straight on a frictionless table and held stationary so that one-quarter of its length, L = 2.87 m, is hanging vertically over the edge of the table. The chain is then released. Determine the speed of the chain at the instant when...

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.

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...

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.

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...