Recent content by jarvisyang

OK.Thank you for your suggestion, jackmell. I've got it. I will post my question together with my efforts or scripts next time.

Actually, I have made a lot efforts. The first identity has been proved by myself. But as for the second identities, I have been thinking for a long time and I still can not figure it out.

Prove two integral identities? 1. The following integral identity holds \dfrac{d}{dx}\intop_{x}^{a}\dfrac{F(\rho)d\rho}{\sqrt{\rho^{2}-x^{2}}}=-\dfrac{F(a)x}{a\sqrt{a^{2}-x^{2}}}+x\intop_{x}^{a}\dfrac{d\rho}{\sqrt{\rho^{2}-x^{2}}}\dfrac{d}{d\rho}\left[\dfrac{F(\rho)}{\rho}\right] Hints: this...

The matrix \mathbf{B}satifies the following Lyapunov equation \begin{gathered}\mathbf{A}^{T}\mathbf{B}\end{gathered}+\mathbf{BA}=-\mathbf{I} prove that necessary and sufficient condition generating a symmetric and positive determined \mathbf{B}is that all of the eigen values of...