Recent content by dsfranca

Hi, I didn't understand what I should do exactly in this problem and I would really appreciate it if you guys could give me some directions! Homework Statement Given the "bump function" B(x)=exp(-1/x²) for x>0 and 0 if x<=0, modify it to construct a C$^{\infty}$ function which...

Thanks for the answer lanedance. First of all, the answer I am looking for is only k, and I don't see how this problem would make sense with only one deck, as the most important aspect of it are two cards in the same position... I am still stuck...

Homework Statement Suppose we have two decks with n distinct cards each. After we shuffle the decks, what is the probability that k cards are in the same position in the two decks? Homework Equations The Attempt at a Solution I have worked out that when n tends to infinity, the...

I understand what you mean. I think we can compare this situation with a limit, given an arbitrary n ball, we can find an even bigger n so that the ball will back in the box. But what really bothers me is the fact that this solution points to every ball being in the box, although the number of...

I was confonoted with the following problem today, and thought it was interesting enough to discuss it here: Homework Statement You have a box with balls numbered 1,2,3...n. Suppose you began, by taking out balls numbered 1–100 and then put ball 1 back. Suppose you then removed balls...

The most advanced things I know in calculus are integration by parts and partial derivatives, I know the basics of group theory and have a good knowledge of linear algebra, actually the whole content of Poole's Linear Algebra book, besides the usual high-school math. Ebolapox, thank you for your...

Books for self-study in "pure areas" of mathematics Hi, I am starting an applied mathematics course this year at university. Unfortunately I don't have the option to study "pure" areas of mathematics, but I would like to learn more about them to become a more complete mathematician at the end...

The issue is clear to me now. This also explains why the rho quickly decays to pions, as the in the rho is repulsive. But once again I can't understand the numbers exactly, I wonder when and how I will be able to make more solid mathematical discussions on this subject! Thank you all

Thanks for the answer Norman, but why would a different spin result in a different mass? Is it becuase as they have a greater spin they will also have more energy and thus greater rest mass? Is there a way I can infere the mass of the rho knowing the masss of the pion?

The pion \pi+ has the same quark content as the rho\rho+, but different rest mass. Why is that? And does the same apply to the \pi- and \rho-. Will they have the same mass difference? Thanks for your help!

Hum! Everything makes sense now, how could I not have considered optics when talking about reflection! Thank you for the explanation tiny-tim!

Yes, I see what you mean, but wouldn't 2$2\pi r^{2}$ be a better approximation in this case? Afterall, I am trying to determine the area of the earth's surface that is reflecting light, and by common knowledge, one would say that half of the Earth is always illuminated (half of the earth is...

Thanks for the answer, but I still did not understand why the effective surface is only one quarter of the Earth's surface. Could you go into more detail please? Thanks

Hi! I was reading about the relationship between the surface area of Earth that reflects light and the one that radiates. As the whole Earth emits radiation, the area that would radiate is A=4\Pir2, where r is the radius of earth. But the weird part is that the textbook says that only one...

Just got a solution. It needs two energy sources, one hot and one cold. Should have thought more before posting it here... Sorry