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...
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...
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...
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...