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Let ${a_n }_{n geq 1}$ and ${b_n }_{n geq 1}$ be two sequences of real numbers such that the infinite series $sumlimits_{n=1}^{infty} a_n$ and $sumlimits_{n=1}^{infty} b_n$...
Asked on 11/09/2021 by Antonio Claire
1 answerI am reading the Wikipedia article on the SIR model with vital dynamics.I am wondering about the birth and death rate. The birth rate seems to...
Asked on 11/09/2021
0 answerSuppose $f(x)=int_{0}^x e^{-t}t^{-1/2}dt$. If $x to infty$, this is the gamma function. But how to compute this integral if $t$ is not $infty$? Is there any...
Asked on 11/09/2021
1 answerI encountered the result below in a paper of Claude Viterbo (Intersection de sous-variétés lagrangiennes, fonctionnelles d’action et indice des systèmeshamiltoniens, p. 379) that I was...
Asked on 11/09/2021
0 answer(i) Construct a conformal map $T$ such that $T(mathbb{C}-[0,1])subset B(0,1).$ (ii) If $f$ is entire such that $f(mathbb{C})subset mathbb{C}-[0,1]$, show that $f$ is constant....
Asked on 11/09/2021
2 answerI've been struggling with this answer for hours and now I just don't get at all only a detail on it (maybe there are something miss typed (?) )....
Asked on 11/09/2021 by Robson
1 answerDefine $K:mathbb{R}^{2}timesmathbb{R}^{2} to mathbb{R}$ by $$K(a,b)=Kleft((a_{1},a_{2}),(b_{1},b_{2})right)=a^{T}b+cosleft(frac{(a_{2}-b_{2})pi}{3}right)=a_{1}b_{1}+a_{2}b_{2}+cosleft(frac{(a_{2}-b_{2})pi}{3}right).$$ Let $a_{1},a_{2},cdots a_{n}inmathbb{R}^{2}$ are arbitrary vectors. And $A$ is $ntimes n$ matrix with $A_{ij}=K(a_{i},a_{j}).$ I want to prove...
Asked on 11/09/2021 by Tree23
1 answerI am an analyst who is new to algebraic number theory. I am learning on Cyclotomic polynomials and came across this problem, which I am having hard time solving. Let...
Asked on 11/09/2021
0 answerLet $f:Asubset mathbb{R}^nrightarrow mathbb{R}^n$ an submersion of class $C^1$. Show that $f$ is a local diffeomorphism at each point in open A. I thought so, if...
Asked on 11/09/2021 by user810255
0 answerLet $mathcal A$ be an abelian category. Denote by $Inj-mathcal A$ the former’s full subcategory consisting of injective objects. Is there any known literature as to when the...
Asked on 11/06/2021 by Sampah
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