Related papers: Statistically p-Upward Quasi-Cauchy Sequences and …

We prove that, for $1\leq p< 2$, if a $W^{1,p}$-quasiconvex integrand $\,f\colon\mathbb{R}^{N\times n}\rightarrow\mathbb{R}$ has linear growth from above on the rank-one cone, then it must satisfy this growth for all matrices in…

A generic uniformly distributed sequence $(x_n)_{n \in \mathbb{N}}$ in $[0,1)$ possesses Poissonian pair correlations (PPC). Vice versa, it has been proven that a sequence with PPC is uniformly distributed. Grepstad and Larcher gave an…

We study the interplay between additivity (as in the Cauchy functional equation), subadditivity and linearity. We obtain automatic continuity results in which additive or subadditive functions, under minimal regularity conditions, are…

We derive sharp upper and lower bounds for the pointwise concentration function of the maximum statistic of $d$ identically distributed real-valued random variables. Our first main result places no restrictions either on the common marginal…

We introduce the post-processing preorder and equivalence relations for general measurements on a possibly infinite-dimensional general probabilistic theory described by an order unit Banach space $E$ with a Banach predual. We define the…

Combining individual p-values to aggregate multiple small effects has a long-standing interest in statistics, dating back to the classic Fisher's combination test. In modern large-scale data analysis, correlation and sparsity are common…

This paper analyzes general spatially-coupled (SC) systems with multi-dimensional coupling. A continuum approximation is used to derive potential functions that characterize the performance of the SC systems. For any dimension of coupling,…

In this paper, we introduce the notion of topologically Banach contraction mapping defined on an arbitrary topological space X with the help of a continuous function $g:X\times X\rightarrow \mathbb{R}$ and investigate the existence of fixed…

Let $\mathcal{T}(x,\eps)$ denote the occupation measure of an interval of length $2\eps$ centered at $x$ by the Cauchy process run until it hits $(-\infty,-1]\cup [1,\infty)$. We prove that $\sup_{|x|\leq…

In this work, we give sufficient conditions for the almost global asymptotic stability of a cascade in which the subsystems are only almost globally asymptotically stable. The result is extended to upper triangular systems of arbitrary…

We consider a sequence of bubble converging minimal hypersurfaces, or H-CMC hypersurfaces, in compact Riemannian manifolds without boundary, of dimension 4, 5, 6 or 7, and prove upper semicontinuity of index plus nullity, for such a bubble…

Let x be a quadratic irrational and let P be the set of prime numbers. We show the existence of an infinite subset S of P such that the statistics of the period of the continued fraction expansions along the sequence {px: p\in S} approach…

This article consists of two connected parts. In the first part, we study the shift invariant subspaces in certain $\mathcal{P}^2(\mu)$-spaces, which are the closures of analytic polynomials in the Lebesgue spaces $\mathcal{L}^2(\mu)$…

We give necessary and sufficient conditions for a real-valued quasiconvex function f on a Baire topological vector space X (in particular, Banach or Frechet space) to be continuous at the points of a residual subset of X. These conditions…

We consider metrics which are preserved under a $p$-Wasserstein transport map, up to a possible contraction. In the case $p=1$ this corresponds to a metric which is uniformly curved in the sense of coarse Ricci curvature. We investigate the…

It is shown that if $C$ is a nonempty convex and weakly compact subset of a Banach space $X$ with $M(X)>1$ and $T:C\rightarrow C$ satisfies condition $(C)$ or is continuous and satisfies condition $(C_{\lambda})$ for some $\lambda \in…

For the Euler equations of isentropic gas dynamics in one space dimension, also knowns as p-system in Lagrangian coordinate, it is known that the density can be arbitrarily close to zero as time goes to infinity, even when initial density…

A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…

We establish a new algebraic characterization of sectional curvature bounds $\sec\geq k$ and $\sec\leq k$ using only curvature terms in the Weitzenb\"ock formulae for symmetric $p$-tensors. By introducing a symmetric analogue of the…

We prove that for any $2<p<\infty$ and for every $n$-dimensional subspace $X$ of $L_p$, represented on $\mathbb R^n$, whose unit ball $B_X$ is in Lewis' position one has the following two-level Gaussian concentration inequality: \[ \mathbb…