Recent content by emob2p

=> Counterexample very easy

Hi, I'm trying to prove that b^{r+s}=b^r*b^s for any real r,s where b^r = sup{b^t:t \leq r} and t is rational. (This is prob 1.6f in Rudin) My question. Can one show that for two sets X and Y: sup(XY)=(supX)(supY) where XY = {x*y: x\in X, y\in Y} Thanks, E

Why does this follow? And if so, how does one use the covariance matrix to obtain a probability density that can be integrated to find expectation values?

Hi, I have encountered the following problem in my research. As I do not have a strong background in probability theory, I was wondering if anyone here could help me through the following. I would like to know how one makes rigorous the problem of randomly choosing a unit n-dimensional...

Hi, I am a graduate student at the University of Michigan and I have been tutoring a high school student in math and physics for about a year now. As he will be taking Calc AB next fall, he asked me to teach him calculus this summer. I am excited to do this, but am not sure the best way to...

Hi, Does anyone know the general form of a 3x3 Unitary Matrix? I know for 2x2 it can be parametrized by 2 complex numbers. I remember once seeing a general form for the 3x3 in terms of 6, I think, complex numbers. Anyway, I'm having trouble finding that now...so if anyone could help me it...

Homework Statement If L is a straight line in the plane, describe the topology L inherits as a subspace of RlxR and as a subspace of RlxRl in each case it is a familiar topology.(Rl= lower limit topology) The Attempt at a Solution RlxR topology is the union of intervals...

Not quite, the "Cartesian product topology" is generated from the set of Cartesian products of two open sets. If we took your definition for open sets in R^2, then it would be possible for the union of two open sets to not be open. See the difference?

Homework Statement I am asked to show that T=[particular point topology on R^2 ((0,0) being the particular point)] is equal to T'=[topology on R^2 from taking the product of R in the particular point topology (0 being particular point) with itself]. The Attempt at a Solution I'm...

Hi, I'm taking a course in Stat Mach using Kerson and Huang's Statistical Mechanics book. I am quite confused with their treatment of a Gibbsian Ensemble. They say imagine an infinite copies of the same system whose state can be represented by a point in phase space. Then \rho (p,q,t) =...

I guess it's more appropriate to say F=dp/dt.

why no F=ma in SR?

So if the transformation were not linear, then an object would appear to be accelerating in one inertial frame but moving at a constant velocity in another. This would mean F=ma doesn't hold in both frames, a violation of a relativity assumption. Does that argument sound good to you guys?

All derivations of the Lorentz Transformations I've seen assume a linear transformation between coordinates. Why must this be the case? Thanks.

Suppose I have a total population with x/y percent having a certain property q. If I take an n-number sample of this population, what is the most likely number of elements in this sample that will have property q? I want to say the fraction z/n will be as close to x/y as possible where z is...