Recent content by LineIntegral

Homework Statement Compare the probabilities for the following processes to happen: 1. e^+ + e^- \to \nu_\mu + \bar{\nu}_\mu 2. e^+ + e^- \to \nu_\mu + \bar{\nu}_e 3. e^+ + e^- \to \nu_e + \bar{\nu}_e Homework Equations N/A The Attempt at a Solution I really have no idea...

Solved it, thanks :)

Solved it, thanks :)

Homework Statement Let G=A U B be a bipartite graph. For each a in A and for each b in B we have d(a)≥d(b)≥1 where d(v) is the degree of vertex v. Show that there exists a matching which saturates A. Homework Equations The Attempt at a Solution I guess I need to use Hall's...

Homework Statement Let A be a 100x100 matrix such that each number from the set {1,2,...,100} appears exactly 100 times. Prove that there exists a row or column with at least 10 different numbers. Homework Equations The Attempt at a Solution I suspect that I should use the...

Thanks! Now it finally makes sense... :)

Homework Statement The problem is conveniently located here: http://www.dur.ac.uk/resources/cpt/graduate/lectures/mscps.pdf Problem no. 31. There's even a solution, here: http://www.dur.ac.uk/resources/cpt/graduate/lectures/grsolns.pdf However, I don't understand the solution...

Ok, I got it now... Thanks! :)

Homework Statement I need to calculate the integral: \int_{0}^{\frac{\pi}{2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}\mathrm{d}x Homework Equations The Attempt at a Solution There is a tip: "try substituting y=\frac{\pi}{2}-x. I tried it and didn't get anywhere. I also tried several...