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Tensor product of unit and co-unit in a closed compact category

Consider a compact closed category, i.e., a symmetric monoidal category with a unit $eta$ and co-unit $epsilon$. It seems natural to demand that the tensor product of two...

Asked on 12/13/2021 by Andi Bauer

1 answer

Finite subgroups of $SL_2(mathbb{C})$ arising as a semi-direct product

I am trying to find all finite subgroups of $SL_2(mathbb{C})$ that arise as a semi-direct product of two finite (non-trivial) subgroups of $SL_2(mathbb{C})$. Is there any such characterization?...

Asked on 12/13/2021 by user45397

1 answer

Uniqueness of solutions of Young differential equations

Consider the following one dimensional Young differential equation:$$Y_t=int_0^t Y_s dX_s,quad tin[0,1].$$ Here the driving process $X$ is a bounded functions $[0,1]tomathbb{R}$, which is ...

Asked on 12/13/2021

0 answer

Differentiation under the integral sign for a $L^1$-valued function (shape derivative)

Let$dinmathbb N$;$Usubseteqmathbb R^d$ be open and $$mathcal A:={Omegasubseteq U:Omegatext{ is bounded and open and }partialOmegatext{ is of class }C^{0,:1}};$$$E:=bigcup_{Omegainmathcal A}L^1(Omega)$;$y:mathcal Ato E$ with $$y(Omega)in...

Asked on 12/13/2021

0 answer

Digraphs with exactly one Eulerian tour

I’ve been thinking about the following problem from Richard Stanley’s list of bijective proof problems (2009). There, this problem is said to lack a combinatorial solution. The problem is the...

Asked on 12/13/2021

2 answer

Exactness of completed tensor product of nuclear spaces

Let $0 to V to W to L to 0$ be a strict short exact sequenceof (complete) nuclear spaces, i.e. it is a short exact sequence of(complete)...

Asked on 12/11/2021

1 answer

An integral with respect to the Haar measure on a unitary group

Let $A,Din mathbb{C}^{n times n}$ be diagonal matrices. I need to calculate$$int_{U(n)}det{(A-HDH^dagger)},mathrm{d}H$$where $dH$ is the unit invariant Haar measure on the group of unitary matrices and $H^dagger$ is...

Asked on 12/11/2021

1 answer

Best known upper bound for Dedekind zeta function on line $sigma=1$ in the $t$ aspect

What's the best known upper bound for the Dedekind zeta function $zeta_K(s)$ of a number field $K$ for $s=1+it$ as $trightarrow infty$. For example, is something...

Asked on 12/11/2021

0 answer

Regularity with respect to the Lebesgue measure through dimensions

Let us consider two probability measures $mu in mathcal{P}(mathbb{R}^{p})$ and $nu in mathcal{P}(mathbb{R}^{q})$ with $p,q in mathbb{N}^{*}$. We note $#$ the push forward operator i.e for...

Asked on 12/11/2021 by Titouan Vayer

0 answer

Reference request on Gentzen's proof of the consistency of PA

I've always been interested in having a good understanding of Gentzen's proof of the consistency of arithmetic. Being more precise, he showed that $PRA + WF(epsilon_0) vdash Con(PA)$. I...

Asked on 12/11/2021

1 answer

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