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Integral with some symmetries

  1. Apr 26, 2009 #1
    1. The problem statement, all variables and given/known data

    Hi, i need to integrate a function which has a very nice structure. however, in case i cannot do the same, i would need a bound on the value of the integral. The problem is basically a minmization problem with n parameters. Please follow the link to acquaint your self with the problem.
    http://img522.imageshack.us/img522/7894/equations640x480.gif [Broken]

    2. Relevant equations

    http://img522.imageshack.us/img522/7894/equations640x480.gif [Broken]
    here, d_i and theta_i are the distances and angles of point (x,y) from (xi,yi)

    3. The attempt at a solution
    My attempt is as follows:
    First of al, i could not directly integrate the function, so i tried to find a bound on it. I used the mod of the function (extension of triangle inequality) on the denominator to eliminate the sine squared in the denominator.
    Upon doing that i tried to split the denominator through chebyshev sum inequality but didnt get anywhere.

    I hope you can give me some insights into either solving the integral or getting a bound on its value.

    thanks and regards
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 30, 2009 #2

    benorin

    User Avatar
    Homework Helper

    Would you elaborate on the geometry of the sum, specifically, where does the [tex]d_{i}^{-2}d_{j}^{-2}\sin^2 (\theta_{i}-\theta_{j})[/tex] term come from?
     
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