Recent content by penguin007

For p(jx), you mean?: P(jx)=(jx)p-1*(jx-1)p...(jx-n)p I wanted to find an inequality for each abs((jx-q)), but my problem is that since jx is between 0 and n, I don't know the sign of jx-q... I also tried: * abs(jx-q)<=q, but this inequality is obviously wrong(for q=5, x=1 and j=11)...

Hi everyone, Homework Statement P(X)=Xp-1*(X-1)p*...*(X-n)p j is an integer between 1 and n; x a real beatween 0 and 1. Prove that abs(P(jx))<=(n!)p Homework Equations The Attempt at a Solution I tried to find an inequality for each abs(jx-q) but the problem is that I...

No, it's not a probability question actually. E is the integer part of a number.

Hi everyone, I'm studying an exercise and I got stuck. Indeed, I was asked to prove that: E((1+sqrt(3))(2n+1))=(1+sqrt(3))(2n+1)-(sqrt(3)-1)(2n+1) and I admit I haven't got a clue how to do it. Any indication is welcome!

I think you forgot an overline in the end, but I can't understand why we have: <x,ux>=conjugate(<ux,x>) ?

Hi, We know that if u is a real symetric endomorphism, then u has a real eigenvalue and that u is diagonalizable. But can we say that u is diagonalizable with only real eigenvalues?

I can see if k>2, thank you, but why is it wrong if k=2 ?

That's right indeed. But what if k is prime??

Thanks for all your answers! I also read a lot of stuff on the internet (amid them Liouville's theorem: even if I didn't understand everything it helped me a lot). I retained that the coordinates of a phase space are constituted by INDEPENDENT parameters of the system (is that right?). Thanks...

Homework Statement Hi everyone. I'm studying a problem and I need to prove that I have a basis. I tryed a proof and to achieve it I need to show that : if k divides a*b and also divides a2 +2*b2 Then k divides both a and b. Homework Equations I'm not sure what I'm asserting is...

Could anyone explain me what a phase space is and how we can build it?? Thanks in advance.

thank you for your proof estro.

Thanks estro, I would be very interested in your proof, if you don't mind then...

I got it. thank you very much!

Hi, I must be mistaken, but I don't know where. Could you please correct me?: * int(f(x), x=1..infinity) converges is equivalent to int(abs(f(x)),x=1..infinity) coonverges; *for x>=1, f(x)/x<=f(x). *then, int(f(x)) converges implies int(f(x)/x) converges. ??