Recent content by nworm

Dear Experts! Do you know any mathematical measurement of roughness of surface? Thank in advance.

You can use this ideas: (i+1)^2=i^2+2i+1 . i^2\times\frac{n!}{i!(n-i)!}=i\times\frac{i\times n!}{i!(n-i)!}= . i\times\frac{n\times (n-1)!}{(i-1)!(n-i)!}= i\times\frac{n\times (n-1)!}{(i-1)!(n-i)!}= . n\times\frac{(i-1+1)\times (n-1)!}{(i-1)!(n-i)!}= ...

Dear experts! I have a small Hermitian matrix (6*6). I need to inverse this matrix. The program memory is bounded. What method is optimal in this case? Can you give any e-links? Thanks In Advance.

Thank you very mach. Eispack is a very good package.

Dear experts! I have a small Hermitian matrix (7*7 or smaller). I need to find all eigenvalues and eigenvectors of this matrix. The program memory is bounded. What method is optimal in this case? Can you give any e-links? Thanks In Advance.

Dear experts. What do you know about applications of linear polynomials with integer coefficients? (For example, I know that these polynomials are applied in the field of integer programming and pattern recognition (clustering). Thanks in Advance.

For example you want to divide n-dimensional "parallelepiped" in s parts. part 1: 0<x<\frac{1000}{s},0<y<1000,0<z<1000,...,0<t<1000 part 2: \frac{1000}{s}<x<\frac{2000}{s},0<y<1000,0<z<1000,...,0<t<1000 ... part s: 1000-\frac{1000}{s}<x<1000,0<y<1000,0<z<1000,...,0<t<1000 If you want...

shrap's link isn't working.

May be it will help. Let we have n-dimensional "parallelepiped". part 1: 0< x_1< 1, 0< x_2< 1,... 0< x_{n-1}< 1, 0< x_n< 1, part 2: 0< x_1< 1, 0< x_2< 1,... 0< x_{n-1}< 1, 1< x_n< 2, part 3: 0< x_1< 1, 0< x_2< 1,... 1< x_{n-1}< 2, 0< x_n< 1, part 4: 0< x_1< 1, 0< x_2< 1,... 1<...

arildno I don't think that ACLerock solve very difficult problems. It is possible to apply more easy methods when solving home and exam tasks. (for example the method from my post).

You can try to find (adjust) one solution (x=0.5). After that you can divide x^3 + 0.5x^2 - 0.25x - 0.125 by x-0.5. The result is x^2+x+0.25. So x^3 + 0.5x^2 - 0.25x - 0.125=(x-0.5)(x^2+x+0.25)=0 You already can solve it.

Do you know any books in the field of neuromathematics? I am interesting in mathematical models that are applying for constructing of artificial neural networks. TIA.

Change this: do while (n>1) i=2 I think that you need write: i=2 do while (n>1)

May be you know any good programs that can test randomness of _short_ integer sequences (the library of test programs).

Thank you. If I understand rightly then you mean "the uniform cost criterion" and "the logarithmic cost criterion" from http://www.cse.ohio-state.edu/~gurari/theory-bk/theory-bk-fivese1.html" I deal with big numbers. So I think to use the logarithmic cost criterion, i.e. O(log N) units...