Recent content by Manchot

Yeah, I tried diagonalizing both A and the initial condition. No dice.

I tried all sorts of versions of the scalar equation, maajdl. They all run into the same commutation problem. Unfortunately, U is a function of both A and the initial condition, which means that it doesn't commute with A unless the initial condition does.

I'm trying to find a general solution for the logistic ODE \frac{dU}{dx}=A(I-U)U, where A and U are square matrices and x is a scalar parameter. Inspired by the scalar equivalent I guessed that U=(I+e^{-Ax})^{-1} is a valid solution; however, U=(I+e^{-Ax+B})^{-1} is not when U and A don't...

Usually, the answer is "somewhere else." For example, in a Michelson interferometer, light that destructively interferes in one arm will constructively interfere in the other. In a thin film, if a reflection destructively interferes, transmission constructively interferes. Of course, if light is...

If anyone even knew what this class of problem is called, that would be tremendously helpful. (A Google search on various terms related to "eigenvalues" comes up with a lot of useless results.)

Electrical engineering grad student here. I've had a fair amount of Analysis and personally proved the fundamentals of undergraduate calculus starting from ZFC, but I can sympathize with the OP's point-of-view. If you do experimental work, rigor must eventually be sacrificed if you want to get...

I'm trying to do something that requires solving an eigenvalue problem of the form A_{imkl} c_m c_k c^*_l=\lambda c_i where A is a known rank-4 tensor, \lambda is the eigenvalue, and the c_i's are a set of unknown coefficients that I need to determine. I would guess that this type of problem...

When Mathematica spits one out as the answer to some problem.

^ Yeah, talk to your professor. I once got an unexpected B in a class I thought I was doing well in, so I asked and it turned out that my grade had been entered incorrectly.

If you're switching between the two systems, the joint system is no longer time-invariant. It's probably going to be not so simple.

Bonhead, the confusion comes from the fact that in the U.S., "high school" always refers to the schooling that 14-18 year olds do. It's not focused on anyone subject, and is only repeated if you fail. People typically take the SAT in high school when they're 17 or 18, and that test is often used...

Wait, are you implying that your theory is *not* in mathematical form? If so, I can tell you right now that absolutely no one will take it seriously.

For all I know, it could also be related to the federal government's impending shutdown. If that happens, I expect that new proposals will be put on hold.

If the U.S. government shuts down, will federal funding for all research dry up as well?

I'm a grad student who responded to some of those e-mails as of late. I would say that you should feel free to ask them about their own research and group dynamics, but you should refrain from asking about other professors. To me, that sounds like gossip. Having said that, I would probably...