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These are replies submitted by Zeineb


tank you for your answer, I tried but it does not work

solve(f>0, assuming  1<=x, x<=4, 0<y,y<1)


Thanks in advance for  your remarks

I want to verify the convolution product theorem using an example


many thanks


Thanks for your remarks.

I study the function f(y), I proved that this function is always positive by hand and it has a minimum at y_star= 1/4*log(5/15*4))

so according to your idea, 1/f(y) will be always positive and bounded above by 1/f(y_star).


x-0=int(1/f(y), y=y0 .. y(x)) <= y(x)-y(0)/f(y_star)

so, for any y(0) the solution will always diverge to +infty
maybe this can be the answer why the solution diverges. Hope this idea conclude my question

many thanks


Thanks .. very nice computation


Thanks for your answer.
All quantities are obtained by hand. How can I get the coefficient of  1/z in the quantity H defined in maple code 




I appreciate all answer proposed for this question. thanks


in this case : y=0 and 3<=x<=4, we get g =0<=0  ( this case is true)

I  want to show that max{g(x,y)} <=0 less or equal zero.


Thank you

this can be proved by hand, its enough to use that 1-y/1+y always less than one. after that we obtain a function which depends only on x and simple derivative give us the critical point. 



Thank you for your time to see my question.

The solution proposed by maple satify all conditions maybe its the unique solution


My vector is [u[1, 0], u[2, 0], u[3, 0], u[1, 1], u[2, 1], u[3, 1], u[1, 2], u[2, 2], u[3, 2], u[1, 3], u[2, 3], u[3, 3]]
the quanties



u[0, 0]=  u[0, 1]= u[0, 2]= u[0, 3]=100

so all these parameters are fixed.



the quantities f[1, 0], f[1, 1], f[1, 2], f[1, 3], f[2, 0], f[2, 1], f[2, 2], f[2, 3], f[3, 0], f[3, 1], f[3, 2], f[3, 3]   are constant , we can drop them from the sytem if you want, my goal is obtain the matrix whose entries are coefficient of u[i,j]



Thank your for your remarks

maybe empty solution because f is discontinous function


Please find the modified version of the code but how can we deduce the general form of u[n]


@Preben Alsholm 

Thank you for your remark. We can fix N=10 for example

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