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    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...
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    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.
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    Curious problem with resistors

    If it so easy for you, please, write me your answer :) We will check.
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    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]
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    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 ;)
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    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)?
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    Myuon decay

    Thank you all.
  8. T

    Saturability by smoothness

    Any references coresponding to this theme? Any books, links and so on?
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    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...
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    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...
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    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...
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    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. T

    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!
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    Myuon decay

    Please, arivero, tell me about your minimum answer. What did you get?
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    Myuon decay

    Thanks!!! I'm reading, translating and trying to understand....
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    Myuon decay

    Thank you, arivero. The second book of the Landau series laying on my table (in Russian of course) :) But the only thing I found in this book is collision of two particles, when after boom we have the same two particles (and also I found decay of the particle when we have two particles in the...
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    Myuon decay

    Please, give me advice about the textbook, where I can find the answer or, at least, some ideas about this.
  18. T

    Myuon decay

    arivero, thank you for almost complete answer. You showed my mistake very clearly. But it still bother me, how can I prove, that your solution is right, when we say nothing about momentum of the neutrinos and/or the electron along y or z? When we simplify our equations, don't we make a mistake?
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    Myuon decay

    I'm sorry, what do you mean backward or forward??? Please, read my calculations. Emax is when impulses of neutrino and antineutrino have opposite directions and equals in absolute! Isn't it?
  20. T

    Disintegration of a particle

    Please, delete this theme. I posted this problem in "Advenced Physics".
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    Myuon decay

    [SOLVED] myuon decay First, sorry for my English. I'm not very well in it... Please, try to understand. I wrote this problem in "Introductory Physics", but some man sayed its not "introductory", so I decided to post it in "Advenced Physcis". The problem. We have reaction: \mu \rightarrow e...
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    Disintegration of a particle

    I'm very sorry, what forum corresponds to this theme?
  23. T

    Disintegration of a particle

    First, sorry for my English. I'm not very well in it... Please, try to understand :) The problem. We have reaction: \mu \rightarrow e + \nu + \tilde{\nu} We know energy of myuon - E. Question: Find the maximum and the minimum energy of electron. My attept: Conservation of energy: E =...
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