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I am trying to understand the computation of $[T^t]^{beta *}_{gamma *}$ from Friedberg linear algebra. $T:P_1(R)→ R^2$ and $T(p(x))=(p(0),p(2))$$beta$ and $gamma$ are the...
Asked on 11/19/2021 by Ruochan Liu
2 answerDefinition:- A right ideal $I$ of a ring $R$ is called small right ideal if $I+J=Rimplies J=R$ for any right ideal $I$ of $R$. My...
Asked on 11/19/2021 by Nirbhay Kumar
1 answer$$int_{0}^{infty} x^{nu} frac{e^{-sqrt{x^2+a^2}}}{sqrt{x^2+a^2}} , dx$$ Is it possible to calculate this for $a>0$ and $nu=0, 2$ ? I think the result seems to include exponential integral function,...
Asked on 11/19/2021 by Ui-Jin Kwon
1 answerI’ve come across an interesting problem where a square is constructed within a circle , we then construct the circle inscribed within the previous square and so on. The idea...
Asked on 11/19/2021
1 answerSuppose an entire function $f$ satisfies $|f(z)| leq pi|z|$ for all $z in mathbb{C}$. (a) Evaluate $f^{prime prime}(z)$ for each $z in mathbb{C}$ using Cauchy's...
Asked on 11/19/2021
2 answerShouldn't $left(frac{1}{cos^2x}right)^{frac{1}{2}} = |sec(x)|$?Why does Symbolab as well as my professor (page one, also below) claim that $left(frac{1}{cos^2x}right)^{frac{1}{2}} = sec(x)$, which...
Asked on 11/19/2021 by underdisplayname
1 answerProblem: A random non-zero positive even integer, $E$ is picked. We can call the bracketed section in the statement $E = {Acdot2^n}$ the factored form of this number...
Asked on 11/19/2021 by Dddb
2 answerLet $a_1,a_2,...$ be an infinite sequence of positive real numbers such that for each positive integer $n$ we have $$frac{a_1+a_2+..+a_n}ngesqrt{frac{a^2_1+a^2_2+...+a^2_{n+1}}{n+1}}.$$ Prove that the sequence ...
Asked on 11/19/2021
1 answerLet ${cal U}$ be a non-principal ultrafilter on $omega$, and for each $ninomega$, let $p_n$ denote the $n$th prime, that is $p_0 = 2,...
Asked on 11/19/2021
3 answerThis is part of a proof from René Schilling's Brownian Motion. Here, $f$ is a function in $mathscr{L}_T^2$, which is closure of the simple processes $mathscr{S}_T$ in...
Asked on 11/19/2021
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