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Problem:Evaluate the following integral.$$ int_{-1}^{-1} frac{dx}{x^frac{2}{3}} $$ Answer: This integral includes the point $x = 0$ which results in a division by $0$. To get...
Asked on 11/29/2021
1 answerLet $f(t)$ be a progressively measurable process wrt Brownian motion $B(t)$ so that $$Pleft(int_0^Tf^2(s)ds<inftyright)=1$$Is it true then that the exponential $$expleft(int_0^T f(s)dB(s)-frac12int_0^Tf^2(s)dsright)$$ defines a density...
Asked on 11/29/2021 by user658409
1 answerConsider a two-dimensional random walk, but this time the probabilities are not $1/4$, but some values $p_1, p_2, p_3, p_4$ with $sum p_i=1$. For example, from $(0,0)$, it goes to...
Asked on 11/29/2021
3 answerLet $R$ be a commutative Noetherian ring, and let $ain R$ be a non-unit and a non-zerodivisor. Let $P$ be a prime ideal of $R$ such...
Asked on 11/29/2021
1 answerNow I am new to the subject so, having some rotational problems. My issues are -What is the meaning of $P(text{good bus tomorrow}|x) $ and $P(text{good bus...
Asked on 11/29/2021
1 answerI know the area and the lengths of two sides (a and b) of a non-right triangle. I also know P1 (vertex between a and c) and P2 (vertex between...
Asked on 11/29/2021
3 answer(After 3 bounties I've also posted on mathoverflow). While discussing theta functions, I thought: $zeta(s)=sum n^{-s}=1+2^{-s}+3^{-s}+ cdotcdotcdot$ and $Phi(s)=sum e^{-n^s}=e^{-1}+e^{-2^s}+e^{-3^s}+cdotcdotcdot $What is the analytic continuation...
Asked on 11/29/2021 by geocalc33
1 answerConsider a commutative, cancellative, torsion-free monoid $M$ and a commutative ring $R.$ If the monoid algebra $R[M]$ is finitely generated as an $R$-algebra, then $M$...
Asked on 11/29/2021 by Dylan C. Beck
2 answerIf $L$ is a finite-dimensional simple Lie algebra (over $mathbb{C}$), then it is apparently the case that $H^2(Lotimesmathbb{C}[t,t^{-1}],mathbb{C})$ ($Lotimesmathbb{C}[t,t^{-1}]$ being the loop algebra of $L$,...
Asked on 11/29/2021 by B. Pasternak
0 answerLet $A$ be a positive self-adjoint linear operator (not necessarily bounded) in the Hilbert space $mathcal{H}$. Then $a=(1+A)^{-1}inmathcal{B}(mathcal{H})$. For a given $n$, let us consider the...
Asked on 11/29/2021 by Surajit
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