Recent content by 3029298

While studying the derivation of the normal modes of oscillation of a liquid sphere in the paper "Nonradial oscillations of stars" by Pekeris (1938), which can be found here, on page 193 and 194 two coupled second order differential equations in two variables are merged into one fourth order...

Homework Statement Prove that the transformation law \Gamma^{\sigma '}_{\lambda '\rho '}=\frac{\partial x^\nu}{\partial x^{\lambda '}}\frac{\partial x^\rho}{\partial x^{\rho '}}\frac{\partial x^{\sigma '}}{\partial x^{\mu}}\Gamma^{\mu}_{\nu\rho}+\frac{\partial x^{\sigma '}}{\partial...

So if I understand it correctly, this problem is resolved as follows: - If we do not allow time dilation to account for the compensation in the train/clock experiment to keep the light speed constant in both frames, the distance w between the mirrors of the moving frame must shrink for the...

Dear All, In the http://galileoandeinstein.physics.virginia.edu/lectures/srelwhat.html" , there is one assumption I don't understand. Why do we assume that the distance w between the mirrors is constant for both the observer in the train and the observer outside the train? We could also let...

http://math.nyu.edu/student_resources/wwiki/index.php/Complex_Variables:_2006_January:_Problem_5" using Taylor's theorem.

The furthest I could come was by working out the parentheses: CBx = (2CAC-1+2CA2+I+A)b I hope someone else can get some answer...

I really do not understand... what is the use of the fact that the factors of the direct products commute with each other?

I do not know any general property of this kind... the subgroups H x 1 and 1 x K only have the identity in common and (H x 1)(1 x K)=H x K, but I do not see how this helps...

Homework Statement If G contains a normal subgroup H which is isomorphic to \mathbb{Z}_2, and if the corresponding quotient group is infinite cyclic, prove that G is isomorphic to \mathbb{Z}\times\mathbb{Z}_2 The Attempt at a Solution G/H is infinite cyclic, this means that any g\{h1,h2\} is...

I get it now! If x+Q=Q, x must be rational. Therefore, a nonidentity element of R/Q has the form Q+r where r is irrational. Now if n*(Q+r)=Q, n*r+Q=Q and n*r is rational. But this cannot be the case since r is irrational, and we have a contradiction, and a nonidentity element of R/Q does not...

The only thing confusing me a little from the beginning is that if we have a nonidentity element of R/Q it has to have the form Q+r where r is irrational. Does r have to be irrational because Q is the identity of R/Q?

If x is not Q, then this can never be true, since the sum of a non-rational and a rational number is non-rational. If x is in Q then x+Q = Q since for each element q in Q there exists an element q-x in Q which gives x+q-x=q, and each element in x+Q is in Q. x must be a rational.

oh no... 1/7=1/14+1/14

n*(Q+r)=n*r+Q since Q is normal. has it got something to do with the fact that for p=prime 1/p cannot be written as the sum of two rationals?

Homework Statement Show that every element of the quotient group \mathbb{Q}/\mathbb{Z} has finite order but that only the identity element of \mathbb{R}/\mathbb{Q} has finite order. The Attempt at a Solution The first part of the question I solved. Since each element of...