Mark Eichenlaub
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 Nov 21 comment Fourier transform for dummies I'm not sure I understand the question, sorry. What do you mean by having it "work"? I'm not familiar with Mathematica, but in general you will need an infinite number of circles, not just two. Dec 9 comment Solution to $\frac{\partial G}{\partial t}=(1-s)\left(-k_1G+k_2\frac{\partial G}{\partial s}\right)$ Yes, $s\in \mathbb{R}$ and $t \ge 0$. I'll look up the method of characteristics. Oct 10 comment Why can I exchange the order of integration in a multiple Ito stochastic integral? In the portion where I set W=s^2, I am not talking about stochastic integrals, but instead just a regular integral, so your criticisms do not make sense. Oct 10 comment Why can I exchange the order of integration in a multiple Ito stochastic integral? $(s+ds)^2 - s^2 = 2s ds + ds^2 = 2s ds$ Sep 19 comment Demystify integration of $\int \frac{1}{x} \mathrm dx$ I wrote this blog post about it a while ago. arcsecond.wordpress.com/2011/12/17/… My blog says people followed a link from here to there, but I can't find that link on this page, so here it is. It takes a picture-based approach to the problem. Jan 31 comment Find five positive integers whose reciprocals sum to $1$ @gmline This wasn't supposed to be a method for enumerating all the answers or anything like that; just a way to approach it visually that might help for some kids. Nov 29 comment What's the expected value of a lottery ticket? @cardinal I hadn't thought of it that way, but it's a good point and looks right to me, thanks. Nov 29 comment What's the expected value of a lottery ticket? @FlybyNight $n$ is a random variable whose distribution is determined from $p$ and $t$. I believe you do have enough information. Feb 13 comment Singing Bird Problem @BrianM.Scott Yes, you're right, thanks. Tried a new answer. Jan 22 comment Can there be a cubical bubble? @Rahul Ah, now I see. What I meant is that the performer made a roughly cubical compartment, but it is not perfect. I wanted to know if a perfect cube was mathematically possible, or whether, for example, the corners would always be a little rounded off. Jan 21 comment Can there be a cubical bubble? Great answer! Thanks for all the references. Jan 21 comment Can there be a cubical bubble? @Rahul Yup, that's what I wanted to know. I just don't really understand how your comment addressed the question. I think there is something about it I'm missing. (I'm not a mathematician.) Will Jagy's answer was pretty much what I wanted. Jan 21 comment Can there be a cubical bubble? @Rahul I don't understand, sorry. How does this address whether or not there can be a cubical bubble? Jan 12 comment How many ways can $b$ balls be distributed in $c$ containers with no more than $n$ balls in any given container? Thank you. Yes, that was how I got that identity. Dec 17 comment Fourier transform for dummies Thanks! I will check it out. Nov 25 comment Point me the primordial and intuitive concepts about this operations on physics For an intro to EM, "Electricity and Magnetism" by Purcell is what I used. It was great. Nov 25 comment Point me the primordial and intuitive concepts about this operations on physics Well, I'm a physicist and I think I understand electric charge pretty well, but that page still doesn't make sense to me. I suggest finding a better resource. Nov 25 comment Point me the primordial and intuitive concepts about this operations on physics what are a, b, and c? It doesn't look like you ever defined them. Nov 18 comment Fourier-like expansion of a closed curve in 2D demonstration: youtube.com/watch?v=QVuU2YCwHjw Nov 18 comment Fourier-like expansion of a closed curve in 2D We can also think of it as just a usual complex-valued Fourier transform, since complex numbers can represent two dimensions. (I now see that Greg P pointed this out in the comments to the main question.)