Chain Definition and 939 Threads

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I am so annoyed with Facebook users who sharing information that is either a hoax (strawberry quick) or outdated information (missing people, abused animals).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...

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...

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 $r(r^2+1)^{-0.5}$

Homework Statement Consider the transformation \mathbf{x}=G(\mathbf{u}), \text{ where } \mathbf{x}=(x_1,x_2,x_3),\:\mathbf{u}=(u_1,u_2,u_3) given byx_1=u_1+u_3^2x_2=u_3-u_1^2x_3=u_1+u_2+u_3 I need to compute the derivative of this transformation, and then show that the transformation is...

Homework Statement Find the derivative of the following cos(e^-θ^2) Homework Equations cos=-sin e^x=e^x power rule The Attempt at a Solution So I have gotten this far: -sin(e^-θ^2) * ... but then i don't know where to go. Would I treat the -θ^2 as the next step inwards? My...

Homework Statement Use chain rule to find the derivative of f(x)= sin(x)/(1+x^2) Homework Equations Chain Rule (f(g(x)))'*g'(x) The Attempt at a Solution y'(x)= cos (x)/(1+x^2)* (1-x^2)/((1+x^2)^2) I just want to make sure I am doing it correctly and this would be acceptable as a final answer.

Homework Statement A chain of mass 4Kg and length 2m is lying on a table, such that 60 cm of one end is hanging from one edge off the table. Find the work done to pull the entire chain on the table. Homework Equations (anything that'll work i suppose) The Attempt at a Solution I...

If f is a differntiable function, find the expression for derivatives of the following functions. a) g(x)= x/ f(x) b) h(x) [f(x^3)]^2 c) k(x)= sqrt (1 + [f(x)]^2) First off, I am not even sure what they are asking. I am assuming that they want the derivative for each component of the...

How is the double derivative equal to that in the equation 2 in the attachment? =|

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: Use...

Let $G$ be a group, and $\left \{ H_{i} \right \}_{i\in \mathbb{Z}}$ be an ascending chain of subgroups of $G$; that is, $H_{i}\subseteq H_{j}$ for $i\leqslant j$. Prove that $\bigcup _{i\in \mathbb{Z}}H_{i}$ is a subgroup of $G$. I don't need the proof now. But can you show an example for me...

Homework Statement g:ℝ^{ 2 }\rightarrow ℝ is everywhere differentiable. For all (x,y) and for all t: g\left( tx,ty \right) =tg\left( x,y \right) . Prove g is linear (that there exist constants A, B such that for all (x,y): g\left( x,y \right) =Ax+By . I think my solution is correct, but the...

Homework Statement The end of a chain of length L and mass per unit length ρ, which is piled up on a horizontal platform is lifted vertically with a constant velocity u by a variable force F. Find F as a function of height x of the end above platform. A)ρ(gx+2u^2) B)ρ(gx+u^2) C)ρ(2gx+ρu^2)...

I've been poking around, learning a little about homology theory. I had a question about the boundary operator. Namely, how it's defined. There's two definitions I've seen floating around. The first is at: http://en.wikipedia.org/wiki/Simplicial_homology The second, at...