Recent content by Mindscrape

My wife is working on problems to study for the GMAT, and asks her fellow math nerd (me) to help on some of them. Originally I had an error and wanted to see if any of you could help me find it, but as I was typing I found it myself! Can I still put this up in case someone stumbles on it and it...

I'm pretty sure there have to be some theorems out there, but I am probably not putting in the right search terms to be able to find them. Here's the problem: I have a signal uniquely composed of a finite summation of standing wave sinusoids (well there's some DC and other background, but let's...

Does anyone know of an article that has a good in-depth, side by side comparison of DFB edge emitting lasers and VCSEL lasers? From my research it seems to me that the VCSEL papers are all trying to justify why laser production should shift towards VCSEL, and mostly list the advantages over an...

That's right, and you know the squares certainly won't be negative so it comes down to the cross term (which I think you mislabeled) to cause a negative number.

Homework Statement This is a subset of a larger problem I'm working on, but once I get over this hang up I should be good to go. I have a set of measurements x_n that are exponentially distributed p(x_n|t)=e^{-(x_n-t)} I_{[x_n \ge t]} and I know that t is exponentially distributed as...

I'm not going to answer myself, since that will not be helpful, but maybe I can ask questions of you that can guide you in the right direction. 33) You need a better reason than the others do not seem right. What is the equation for orders of diffracted light? 34) What happens in the convex...

Congrats, man. It's funny, I had your opposite problem: all As in physics and all Bs in math (didn't help that math used std dev for grading). Don't know what your job is, but you could always switch over to engineering for grad school. Engineering is much less competitive for grad school...

See, the problem with people simply dismissing paranormal claims and telling someone, "you experienced something in which you were deceived but there's a scientific method that will say how you were deceived," is that the scientific method hasn't done anything itself. As scientists, we tend to...

Not quite, what is the potential term of a dipole? Is there a B_l that will match that term? Hmm, I honestly kind of forget how these problems work with dielectrics.

Yes, ground state is the lowest energy. The energies are determined as solutions (observables) to the hamiltonian operator. So actually, the ground state is the first eigenvalue (the first energy), and I'm pretty sure anything that would not have the first eigenvalue be the lowest energy would...

A good start is to look at the potential inside and outside the sphere. On the outside, for example, you can look at r>>R, and on the inside you know that the only thing allowed to blow up is the dipole.

If you can show g=constant then the solution is unique, within a constant (for dirichlet conditions it's obviously unique). Your first equation doesn't make sense, I think you mean to put g*laplacian(g). Also, if you managed to get rid of this term, your logic should probably also apply to the...

As you said, it really only works in the approximation that the cylinder looks infinite at a particular field point, i.e. the distance from the end of the cylinder to the field point is much greater than the perpendicular distance. Still, I invite you to calculate the field on a symmetric axis...

There's a bunch of math that just has loads of tabulated values. e, for example, can be generated by plugging in high enough values of n. sin and cos along with tons of other functions need look up tables, or fast computing algorithms. Younger generations, such as mine, are so used to...

That looks good to me at least, and you do see that in the limit m<<M the stick goes back to L/2 CM.