Recent content by albertshx

Thank you for your patience. To be more specific, I want to start the branching process below: the distribution of the progency number of an object in generation d is P(d,0) = 1- \sum_{i>0} P(d,i) P(d,r) = βP(d-1,r) , for r>0. r has a limited range of values. P(0,r) is known. β < 1is a...

Dear Chiro, I know Markovian processes well. But I really can't catch your idea of random walking with Wiener process. To be more specific, I want to describe a branching process whose distibution of number of progeny is determined by time or the generation the parent object is in. Simple...

I understand that in the simple branching process, each object gives birth to its children according to the same distribution. However, I now need to handle a special branching process in which objects generate decedents according to different distributions. For example, objects generate...

Dear all, I have a question on the basic concept of branching process. Say, in such a process, different objects of a generation don't interfere with each other. Consider an email forwarding analogy where one node forwards an email to some other users. And...

Thanks and I get your idea. For I need to do integral with y, I'm concerned that whether computing y in many data points would slow down the computation.

Hello, I think it might be the problem of the online plotter... I plot the figure of this function with Matlab together with its contour. They look fine... The contour line for z = 0 are two axes... Your can show that the value of the function converges to 0 around (0,0).

Hello every one! I'm trying to solve a differential equation y' = f(t,y) with MATLAB ode45. Besides the original y, y' is also very useful to me. But I simply don't know how to get it. Is there any convenient method to do this? Or what I can do is just to compute y in many point and use diff...

Many, many thanks! You are much more careful than me. I just tried with MATLAB and dsolve reports explicit solution not found. So I look for some approximation.

I'm working on this differential equation this few days... Could you give some guidance on approximate solutions to it? i(t) is the only function while all others are parameters. \frac{di(t)}{dt} = -\lambda(\sigma\phi\sqrt{i(t)(1-i(t))} + N\mu i(t)(1-i(t)) Thank you a lot!

Thank you all! I get the idea!

Please see my reply. At least, I want an approximation f(s,t) when a = 1.

Sorry, even I myself was confused. Let me clarify a bit. I want to find a function f(a, s,t) which is differentiable to s and t to approximate the infinite sum of this series, \sum_{k=a}^{inf}k^{-s}e^{-kt} in case s>=2, t > 0. Surely the RHS < inf. I have tried integration, but the effect is...

Hello every one, now I'm dealing with a series a(k) = k^(-s)e^(-tk), s,t > 0 I want to find a continuous function to approximate the partial sum, S(n)of it. I hope there can be a good approximation. Please help me find it, thanks!