Chain Definition and 979 Threads

Suppose X is a random walk with probability P(X_k=+1)=p and P(X_k=-1)=q=1-p and S_n=X_1+X_2+...+X_n Can anyone explain why does line 3 equal to line 4? P(S_k-S_0≠0 ,S_k-S_1≠0 ,…,S_k-S_{k-1}≠0) =P(X_k+X_{k-1}+⋯+X_1≠0 ,X_k+X_{k-1}+⋯+X_2≠0 ,…,X_k≠0) =P( X_k≠0 ,X_k+X_{k-1}≠0...

Homework Statement For the van der Waals equation of state, confirm the following property: (∂P/∂T)V (∂T/∂V)P (∂V/∂P)T = -1 Homework Equations The van der Waals equation of state is: P = nRT/(v-nb) - an2/V2 *R, n, a, b are const. The Attempt at a Solution I...

It's been years since I've done maths properly so I'm rusty with it. I'm helping out a colleague at work who is studying maths for an OU course. Homework Statement Part 1: Differentiate function. f(x) = e^(0.5x+cos(x)) Part 2: Use answer from part 1 to show. g(x) =...

Solve the following: d/dt cos(theta) d/dt t sin(theta) d/dt r cos (theta) d/dt r^2 (theta) d/dt e^ (-3x) d/dt (x^2 + y^2) I would assume all by the second one are 0 since your solving for terms dt and not theta, x, y, or r... I don't think its right at all. I know it goes something...

Hi, Say x=position, v=velocity, a=acceleration, t=time. Thanks! EDIT: I just realized that 2/x is not a constant and thus I shouldn't have treated it as a constant (taking the derivative of it as 0). However, I don't understand how to take the derivative with respect to t of it.

I want to find the second order derivative for f(x,y),x(u,v),y(u,v), f depends on x and y, and x and y depends on u and v. I'm trying to find \frac{{\partial^2 f}}{{\partial v \partial u}}This is what I did: \frac{{\partial f}}{{\partial u}}=\frac{{\partial f}}{{\partial x}}\frac{{\partial...

I'm confident in my math ability, but how is it that by using the chain rule... W_{x_1 \rightarrow x_2} = \int^{x_2}_{x_1} m \frac{dv}{dt} dx can be turned into W_{x_1 \rightarrow x_2} = \int^{x_2}_{x_1} m \frac{dv}{dx} \frac{dx}{dt} dx = \int^{v_2}_{v_1}mv dv ? I understand the...

From james stewart calculus Early Transcendentals.Before he states the proof he intoduced a property of differentiable funcion My problem is how we defined \epsilon to be 0 when \Delta x=0 where this is not in the Domain.

Is there an elegant and simple proof of the Chain Rule? Every proof I've found is complex and mind-boggling

Hi, I have been searching the internet for some gentle introductions of Fibonacci chain, but so far I haven't found anything. I wonder if anyone can recommend some good introductions to me, e.g. a book, an article... Thank you.

Let X be a non-empty set, and let S contain all countable subsets of X. Partially order S by inclusion. Let C be a totally ordered subset ("chain") of S, and let U = \cup_{E \in C} E It appears that U is not always countable: if it were, U would be an upper bound of the chain C, and U would...

Homework Statement Use the chain rule, the derivative formula Dxsinu=cosuDxu, together with the identities cosx=sin(\pi/2 -x) and sinx=cos(\pi/2 -x) to obtain the fomula for Dxcosx. Homework Equations Chain rule: dy/dx=dy/du\cdotdu/dx The Attempt at a Solution For my second...

I have a state transition probability matrix and a state probability vector [0.9 0.1; 0.1 0.9] & [0.4 0.6] respectively. Now, I want to generate the states of 1 and 0 according to this. say 100 state sequence. Any sort of help would be appreciated. Thanks.

In a Markov chain, show that a state i is persistent if and only if the mean number of visits to the state i is infinite given the chain started in state i. I thought about looking at the mean recurrence time, but that's all I have so far.

Let X be a Markov chain with a state s that is absorbing, i.e. pss(1) = 1. All other states communicate with s i.e. i → s for all states i ∈ S. Show that all states in S except s are transient. I understand this intuitively, but I'm not really sure how to start the proof.

I have learned that the primers in PCR are added to the DNA in the annealing phase, but what exactly do these primers do to the DNA? Thank you

Homework Statement A flexible chain of mass M and length L lies on a frictionless table, with a very short portion of its length L0 hanging through a hole. Initially the chain is at rest. Find a general equation for y(t), the length of chain through the hole, as a function of time. (Hint...

Can anyone explain the mechanics of a chain hoist and its mechanical advantage, in mathematical terms,? thank you Bashyam

Homework Statement Use implicit differentiation to find dy/dx 2x^3+x^2y-xy^3 = 2 Homework Equations Chain Rule et al. The Attempt at a Solution My questions is this. When deriving something like xy^3, apply the product rule to get 1y^3 + x\frac{d}{dx}y^3 I am confused on...

* I have already posted this in the General Math, but I guess the problem is more like a linear algebra problem. Currently I am using a rather simple way, to solve vector w from (M-I)w=0 (replace one equation by w1+w2+...wn=1). Is there any faster way to do this? Thank you.

From this day , if we take in account . How much population will be my following generation at the end of 2000 years(from this day). My question is , will the population be thousands or millions? Will it likely be fade away in the middle and no trace remains in the end? Any...

Homework Statement If u=f(x,y) where x=escost and y=essint show that d2u/dx2+d2u/dy2 = e-2s[d2u/ds2+d2u/dt2 The Attempt at a Solution i have no idea! question though, do the partial derivitives have to be solved and expanded then just show that one side equals the other or can...

Homework Statement \frac{d}{dx}(x+(x+sin^2(x))^3)^4 Homework Equations Calc up to Chain Rule. The Attempt at a Solution Using product and chain rule I got: \frac{dy}{dx}=4(x+(x+sin^2(x))^3)^3(1+3(x+sin^2(x))^2)(1+\frac{d}{dx}sin^2(x)) Then I calculated the derivative of sin^2(x)...

Homework Statement I have proven in two ways (correctly) that the derivative of ln|x| = 1/x (note absolute value does vanish) Now I open my textbook and see a general rule that \frac{d}{dx} ln (u) = \frac{u'}{u} And the not so general derivative of |x| is \frac{d}{dx} |x| =...

Homework Statement Homework Equations Seems pretty straightforward ... The Attempt at a Solution Here's what I put: P = zeros(10,10); P(1,2) = 1; P(2,1) = 1/2; P(2,3) = 1/2; P(3,1) = 1/2; P(3,4) = 1/2; P(4,1) = 1/3; P(4,2) = 1/3; P(4,5) = 1/3...

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...

Homework Statement I am having some trouble with a bicycle chain drive. I need to find the torque required to have a bicycle travel up an incline. The bicycle is already moving Homework Equations \tau = r*F Torque is equal to the radius of the wheel, multiplied by the force...

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...