Alex Nelson
Reputation
959
Top tag
Next privilege 1,000 Rep.
Create new tags
 Feb 14 comment Meaning of $\simeq$ symbol. And for linear algebra...? Feb 14 comment Meaning of $\simeq$ symbol. In the context of linear algebra, it probably refers to matrix similarity. Aug 29 comment What are super-translations? Sabine Hoffsteder has some references to the literature on her blogpost about Hawking's recent work, which probably will lead you to the right direction. (Try searching for "BMS Supertranslations"; also see chapter 11 of Wald's General Relativity.) Aug 7 comment How do you calculate $\lim_{z\to0} \frac{\bar{z}^2}{z}$? More explicitly $|\bar{z}^{2}/z|=|\bar{z}|^{2}/|z|=|z|^{2}/|z|=|z|$. Jun 14 comment which branch of computer science is most math intensive? Automated theorem proving will involve a lot of logic and foundations of math, but I don't know if it's what you're after... Jan 25 comment For what values is my integral diverging or converging? You ought to simplify $\alpha_{1}/2$ as 1 everywhere...it cleans things up a bit... Jan 25 comment Simplify the sum $\sum_{k=1}^{\infty} (\frac{1}{2})^kk$ What's $\sum_{n=0}x^{n}$ converge to? What's its derivative? Dec 8 comment Is it possible to create division via Set Theory? You can formally construct the integers with an equivalence relationship atop the natural numbers, then construct the rationals using the integers you've just constructed. Sep 29 comment Geometric Interpretation of QFT Scattering Integrals @Dave, the "generalization to $n$ dimensions" section discusses $\int_{\mathbf{R}^n} \delta(g(\mathbf{x}))\, f(g(\mathbf{x}))\, |\det g'(\mathbf{x})|\, d\mathbf{x} = \int_{g(\mathbf{R}^n)} \delta(\mathbf{u}) f(\mathbf{u})\,d\mathbf{u}$ and $\int_{\mathbf{R}^n} f(\mathbf{x}) \, \delta(g(\mathbf{x})) \, d\mathbf{x} = \int_{g^{-1}(0)}\frac{f(\mathbf{x})}{|\mathbf{\nabla}g|}\,d\sigma(\mathbf{x})$ Sep 26 comment Riemann Zeta of 1/2 $\zeta(\frac{1}{2})$ For your first equation, why is it true for $x>1$, but you conclude a result for $x>0$? [I can't immediately see it, so even if you say something like "Equation x justifies it" would be appreciated :)] Aug 14 comment Is Category Theory geometric? This book review claims "in this book his principal objective is to establish the claim that category theory is a generalization of Felix Klein's Erlangen program." So, what the author means by "geometrical" should probably be understood in that light... Jul 27 comment How to I write $\frac{7^{2n}}{4^{3n}}$ as a geometric series? Wait, you are trying to consider $\sum(7/4)^{2n}$? That would diverge badly... Jul 20 comment An English question for a logical term Well, be fair, the three google results are: this thread, the other thread you linked to, and a paper which has the exact phrase "...depend only on the presence, in the tuple, of implications...". It looks like no one uses the term "tuple of implications", per se. Jun 17 comment How to compute this integral involving sech? I think you might want to consider the stationary phase approximation...or method of steepest descent, whichever (I always get them confused!). Jun 17 comment How to compute this integral involving sech? What have you tried? (And is $\epsilon$ "small and positive"?) Jun 17 comment Question on $\mathfrak{sl}(2,\mathbb R)$ @PeterFranek, could you remind me why it's not a group? I thought it was a subgroup (since it has the identity element and the Baker-Campbell-Hausdorff formula suggests it is closed under multiplication, right?) but rarely is it the full group...am I mistaken? Jun 8 comment Intuition behind the definition of a derivative by Lang Maybe it's because I'm drunk, but isn't the $\lambda y$ term merely the linear term (i.e., derivative) and $\varphi(y)$ the "bonus parts which vanish in the appropriate limit"? Just as if for a usual function in calculus 101 we would Taylor expand $f(x+h)=f(x)+f'(x)h+g(h)$ where $g(h)\sim o(h^{2})$. The derivative would naturally be the linear (first) term...well, the coefficient to $h$... May 11 comment What's the term for a “physical vector space”? @RobertIsrael perhaps use the "accountant's trick" and let negative fruit be a deficit owed to someone, and fractional fruit be a fraction of a fruit? (It works in Sraffian economics!) May 3 comment How would you evaluate $I:=\int_ {0}^{\infty} \frac {\cos(ax)} {(x^2 + b^2)^n} \ \mathrm{d}x$? Consider the real part of the integral $\int(x^2+b^2)^{-n}\exp(iax)\,\mathrm{d}x$ might help... Apr 22 comment What's the name of this category Isn't it isomorphic to the category $C_{A\times B}$?