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If $f:U_1tomathcal L^p(mu;E_2)$ is Fréchet differentiable, can we say anything about the Fréchet differentiability of $umapsto f(u)(omega)$?

Let $(Omega,mathcal A,mu)$ be a $sigma$-finite measure space, $pge1$, $E_i$ be a $mathbb R$-Banach space, $U_1subseteq E_1$ be open and $f:U_1to L$ be...

Asked on 12/27/2021

0 answer

Convergence properties of related series

Let $u_m = ln ^2 m$.Does there exist a non-increasing sequence of positive numbers ${g_n}_{n in mathbb{N}}$, $g_n to 0$, such that $$sumlimits_{n in mathbb{N}...

Asked on 12/27/2021

1 answer

If $A$ is a cofibrant commutative dg-algebra over a commutative ring of characteristic $0$, then its underlying chain complex is cofibrant

Let $R$ be a commutative ring with characteristic $0$, namely it contains the field of rational numbers. Higher Algebra Proposition 7.1.4.10 tells that the category...

Asked on 12/27/2021 by Francesco Genovese

2 answer

Rowmotion for general lattices

Let $L$ be a finite lattice and $x in L$ with covers $r_1,...,r_l$ in $L$. One can define $row(x):= min { y | y leq...

Asked on 12/27/2021

0 answer

Is $mathrm{End}-{0}=mathrm{Aut}$ for derivation Lie algebra?

Is it true that every nonzero endomorphism of Lie $mathbb{C}$-algebra $mathbb{C}[x_1,ldots, x_n]partial_{x_1}oplusldotsoplusmathbb{C}[x_1,ldots, x_n]partial_{x_n}$ is an automorphism?As I know a positive answer to question implies the Jacobian conjecture for...

Asked on 12/25/2021

0 answer

Explicit transitive flow on disc

$D_ntriangleq left{x in mathbb{R}^n:, |x|leq 1right}$ with its subspace topology. By a transitive flow on $D_n$ I mean a continuous function$$phi: [0,1]times D_nrightarrow D_n,...

Asked on 12/25/2021

1 answer

Multiplicative and additive groups of the field $(prod_{ninomega}mathbb{Z}/p_nmathbb{Z})/simeq_{cal U}$

Let ${cal U}$ 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 12/25/2021

2 answer

Which mathematical definitions should be formalised in Lean?

The question. Which mathematical objects would you like to see formally defined in the Lean Theorem Prover? Examples. In the current stable version of the Lean Theorem...

Asked on 12/21/2021 by Kevin Buzzard

28 answer

Does the Riemann Xi function possess the universality property?

Here is the question.   Does the Riemann Xi function possess the universality property,  or something similar to Voronin's universality property?  Here is why the answer to this question is...

Asked on 12/21/2021

1 answer

Convex hull of prefix sum of $n$ ordered random points

Suppose we have $n$ ordered realizations of a random variable uniformly distributed over the unit cube $P = (p_1, p_2, cdots, p_n), p_i in [0,1]^d $. And we...

Asked on 12/21/2021 by yupbank

0 answer

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