Recent content by Esran

It wasn't me, but thanks for the link!

Let f:G --> H be a surjective homomorphism. |C_G(g)| >= |C_H(f(g)| Homework Statement Suppose G is a finite group and H is a group, where θ:G→H is a surjective homomorphism. Let g be in G. Show that |CG(g)| ≥ |CH(θ(g))|. Homework Equations This problem has been bugging me for a day now. I'm...

Actually no, I think you're right. Assuming the neutron is scattered elastically by the electron in the well, the neutron will lose energy equal to that of the electron. So, this is correct.

I'm not sure. The mass of the neutron is obviously different from that of the electron, and what you've found is the different energies the electron could take on inside the well. I don't see how this would relate to energy decrements of a neutron scattered by the same system. Maybe someone else...

My definition of basis is as follows: The base elements cover X. Let B1, B2 be base elements and let I be their intersection. Then for each x in I, there is a base element B3 containing x and contained in I.

The difficulty though is first proving that with the given definition of local path connectedness, x has such a neighborhood. After that, I know exactly what to do. Going from the class definition to the more standard one is my problem.

Homework Statement The definition for local path connectedness is the following: let x be in X. Then for each open subset U of X such that x is in U, there exists an open V contained in U such that x is in V and the map induced by inclusion from the path components of V to the path components...

Haha! Thanks for clearing that up.

Let X and Y be topological spaces; let p:X -> Y be a surjective map. The map p is said to be a quotient map provided a subset U of Y is open in Y if and only if p^-1(U) is open in X. Let X be the subspace [0,1] U [2,3] of R, and let Y be the subspace [0,2] of R. The map p:X -> Y defined by...

Homework Statement Find the curve y(x) that passes through the endpoints (0,0) and (1,1) and minimizes the functional I[y] = integral(y'2 - y2,x,0,1). Homework Equations Principally Euler's equation. The Attempt at a Solution We choose f{y,y';x} = y'2 - y2. Our partial...

Ah, never mind. I got it.

Homework Statement Show that the shortest distance between two points in three dimensional space is a straight line. Homework Equations Principally, the Euler Lagrange equation. The Attempt at a Solution I understand how to do this for a plane, but when we move into three...

Homework Statement Newton's model of the tidal height, using two wells dug to the center of Earth (one from the North pole, one from the equator on the side of Earth facing away from the Moon), used the fact that the pressure at the bottom of the two wells should be the same. Assume water is...

Thanks!

Homework Statement Show that the Fourier series formula F(t)=\frac{1}{2}a_{0}+\sum^{\infty}_{n=1}(a_{n}cos(nwt)+b_{n}sin(nwt)) can be expressed as F(t)=\frac{1}{2}a_{0}+\sum^{\infty}_{n=1}c_{n}cos(nwt-\phi_{n}). Relate the coefficients c_{n} to a_{n} and b_{n}. Homework Equations We...