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Studying for qualifying exams, I came across the following problem: using complex analysis, compute$$int_{-infty}^{infty}frac{x^2sin(pi x)}{x^3-1}dx$$I decided to use the integrand $f(z)=frac{z^2e^{ipi z}}{z^3-1}$ (the goal is...
Asked on 12/05/2021 by Anubhav Nanavaty
1 answerI am reading Betancourt's introduction on HMC. In the first chapter, I see the following statement I am not quite sure what...
Asked on 12/05/2021 by Slangevar
1 answerI am studying ordinary differential equations. There are some solved examples in my book to learn the material from. For this one below however, I do not know how this...
Asked on 12/05/2021 by Mathica
1 answerLet $M$ be an $ntimes n$ real matrix with strictly positive elements, i.e. $M_{ij}>0, forall 1leq i,jleq n$, and let $lambda_1$ be its ...
Asked on 12/05/2021
1 answerAre there some easy ways to verify conditions on a nonnegative matrix with $0$ diagonal which ensure that it is conditionally negative definite (i.e., $x^TAx le 0$ for...
Asked on 12/05/2021 by Hrushikesh Mhaskar
0 answerLet $frac{a}{b}$ and $frac{e}{f}$ be two rationals where all parameters are positive integers and are in their lowest terms. Let $gcd(b,f) = g$ so that $b...
Asked on 12/05/2021 by Nilotpal Sinha
1 answerI need help understanding and finding MMSE for these two, I researched on my own but i found many solutions that dealt with matrices(from what I understand those dealt with...
Asked on 12/05/2021 by Saad Salman
1 answerI am a graduating high school senior, and I will be starting college this September. During my middle and high school years, I have done introductory math competitions like Mathcounts,...
Asked on 12/05/2021 by whjjp
1 answerLet $A$ be $3 times 3$ real matrix (which is not necessarily symmetric or diagonalizable) such that $v^T A v>0$ for every $v in mathbb R^3...
Asked on 12/05/2021
3 answerMy friend and I are interested in playing the lottery. We plan to enter multiple number combinations (a.k.a. "lines") per drawing to increase our chances of winning. Specifically, we would...
Asked on 12/05/2021
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