# Recent content by Tolya

1. ### Uniform approximation

Function f(t) specified on [t_0;t_1] has a necessary number of derivatives. Find algorithm which can build uniform approximations of this function with help of partial sums: \sum_{i=1}^{N}\alpha_i e^{-\beta_i t}. That is, find such \alpha_i, Re(\beta_i)\geq 0 satisfying the expression...
2. ### Curious problem with resistors

Excuse me, I didn't catch what you wrote when I read your post first time... You are right, the symmetry breakes down! The problem is not easy.

4. ### Curious problem with resistors

We must find the resistance between opposite vertices, not adjacent. The second problem is too easy rather than the first :) Here is the picture of the problem discussed: http://rghost.ru/3908/download/22312f648e26dabce002e347898f5242c521aa58/Hexagons.pdf" [Broken]
5. ### Curious problem with resistors

This is a misunderstanding. :) I have already solved this problem. I was only trying to represent it to the people, who are interested in it. But I suppose I wrote this problem in the wrong forum section... Dick, please, if you have the answer, write me a private message. We'll check the result ;)
6. ### Curious problem with resistors

We have an infinite net of regular hexagons. Each side of hexagons has a resistance R. What is the resistance between two opposite vertexes of hexagon(s)?
7. ### Myuon decay

Thank you all.
8. ### Saturability by smoothness

Any references coresponding to this theme? Any books, links and so on?
9. ### Saturability by smoothness

Sorry for my English. :) Let function f(x) defined on [a,b] and its table f(x_k) determined in equidistant interpolation nodes x_k k=0,1,..,n with step h=\frac{b-a}{n}. Inaccuracy of piecewise-polynomial interpolation of power s (with the help of interpolation polynoms P_s(x,f_{kj}) on the x_k...
10. ### Integral of tanhx.

I=\int \sqrt{tanhx}dx u=tanhx dx=cosh^2xdu I=\int \sqrt{u}cosh^2xdu=\int \frac{\sqrt{u}du}{1-u^2} Notice, that cosh^2x=\frac{1}{1-tanh^2x} Then, let t=\sqrt{u} \frac{dt}{du}=\frac{1}{2\sqrt{u}}=\frac{1}{2t}. I=2\int \frac{t^2dt}{1-t^4}=\int \frac{dt}{1-t^2} + \int...
11. ### Help to find limit

But actually, I didn't use differential equation :) \frac{1}{a_{n+1}}=\frac{1+\left|sin(a_n)\right|}{a_n} It's easy to show that a_n is going to zero at large n, but remains postive. So: \frac{1}{a_{n+1}}=\frac{1+a_n-\frac{1}{6}a_n^3+o(a_n^3)}{a_n} =\frac{1}{a_n}+1+b_n, where b_n \rightarrow...
12. ### Help to find limit

Thanks. With the help of your post, Avodyne, I found that limit equals 1. Is it correct? Sorry, but I'm not sure.
13. ### Help to find limit

Please, help to find limit: \lim_{n \rightarrow \infty} na(n), where a(1)=1; a(n+1)=\frac{a(n)}{1+\left|sin(a(n))\right|} Thanks for any ideas!