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In the Elephant, Peter Johnston remarks that internal categories may be regarded as simplicial objects that “preserve all limits that happen to exist in $Delta^{op}$“ (I guess you might...
Asked on 01/09/2021 by Ben MacAdam
1 answerLet $Fto M$ be a holomorphic vector bundle over a complex manifold $M$ and let $s:Mto F$ be a no-zero section. Let $E$ be the complexification...
Asked on 01/08/2021 by user158773
0 answerLet $A$ be a self-adjoint (unbounded) operator on a separable Hilbert space $H$.From the following form of spectral theorem, we may define a functional calculus by ...
Asked on 01/08/2021 by Ma Joad
0 answerI am trying to get compute at least the directional component of the following expectation, where $M$ is a symmetric, invertible, PD matrix:$$mathbb{E}_{v sim N(0, I)}left[frac{vv^T}{||Mv||_2}right]$$ (Note...
Asked on 01/07/2021 by B Merlot
1 answerLet $(Omega,mathcal A,operatorname P)$ be a probability space, $(E,mathcal E)$ be a measurable space, $(W_n)_{ninmathbb N_0}$ be a time-homogeneosu Markov chain on $(Omega,mathcal A,operatorname P)$ with...
Asked on 01/07/2021
0 answerI read Oxley's book on matroid theory and found the theory fascinating. At the end, Oxley stated some open problems and conjectures in matroid theory.Are there any modern lists about...
Asked on 01/06/2021 by LogicTheorist
2 answerFor a hermitian symmetric space $M$ one has its group of biholomorphic maps $operatorname{Hol}(M)$ and its group of Riemannian isometries $operatorname{Isom}(M)$. According to Prop. 1.6 of ...
Asked on 01/05/2021 by ThiKu
1 answerSuppose a function $G:mathbb{R}^drightarrowmathbb{R}$ is given. What are some necessary or sufficient conditions on $G$ for there to exist a probability space $(Omega,mathcal{F},mathbb{P})$ and a jointly-measurable function...
Asked on 01/05/2021 by Cabbage
1 answerI've been reading the Xena Project blog, which has been loads of fun. In the linked post Kevin gives the natural isomorphism $V to V^{ast ast}$ from...
Asked on 01/04/2021 by Qiaochu Yuan
0 answerLet $p$ be a fixed small prime (I'm particularly interested in $p = 2$), and let $Q, R in mathbb{F}_p[X]$ be polynomials. Consider the problem of determining...
Asked on 01/04/2021 by Adam P. Goucher
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