Related papers: On the $m$th-order Affine P\'olya-Szeg\"o Principl…

In mathematical logic there are two seemingly distinct kinds of principles called "reflection principles." Semantic reflection principles assert that if a formula holds in the whole universe, then it holds in a set-sized model. Syntactic…

In this work, along with the companion work Oh (2012), we propose a novel approach to the problem of gauge choice for the \emph{Yang-Mills equations} on the Minkowski space $\mathbb{R}^{1+3}$. A crucial ingredient is the associated…

Estimates for eigenvalues of Schr\"{o}dinger operators on the half-line with complex-valued potentials are established. Schr\"{o}dinger operators with potentials belonging to weak Lebesque's classes are also considered. The results cover…

This study formulates the ideal efficiency of light-powered systems in the most general form, based on the first principle of energy-entropy flow analysis under the condition of zero entropy generation within the system. A unified formula…

Affine flows on vector bundles with chain transitive base flow are lifted to linear flows and the decomposition into exponentially separated subbundles provided by Selgrade's theorem is determined. The results are illustrated by an…

In this paper we study the relation between the weighted energy class $\mathcal{E}_{\chi}$ introduced by S. Benelkouchi, V. Guedj and A. Zeriahi recently with the classes $\mathcal{E}$ and $\mathcal{N}$ studied by Cegrell. Moreover, we…

We establish new results on sets of recurrence and van der Corput sets in Z^k which refine and unify some of the previous results obtained by Sarkozy, Furstenberg, Kamae and Mendes France, and Bergelson and Lesigne. The proofs utilize a…

First, we establish the theory of fractional powers of first order differential operators with zero order terms, obtaining PDE properties and analyzing the corresponding fractional Sobolev spaces. In particular, our study shows that…

We establish versions of Szeg\H{o}'s distance formula and Widom's theorem on invertibility of (a family of) Toeplitz operators in a class of finite codimension subalgebras of uniform algebras, obtained by imposing a finite number of linear…

We extend the existence theorems in [Barchiesi, Henao \& Mora-Corral; ARMA 224], for models of nematic elastomers and magnetoelasticity, to a larger class in the scale of Orlicz spaces. These models consider both an elastic term where a…

This work introduces the families of generalized energy operators $([[.]^p]_k^+)_{k\in\mathbb{Z}}$ and $([[.]^p]_k^-)_{k\in\mathbb{Z}}$ ($p$ in $\mathbb{Z}^+$). One shows that with Lemma 1, the successive derivatives of $\big…

The motivation and research design for repeating the EPF experiments are described in the paper.

The classical Szeg\"o theorem can be stated in terms of the sequence of model spaces. In this article, we are interested in the generalization of the Szeg\"o theorem in the case of the sequence of powers of finite Blaschke products.

We prove $L^p$-mass concentration properties of Laplace eigenfunctions away from their nodal sets, extending a recent result in \cite{GM3} to all dimensions, and giving a slight refinement of a result in \cite{JN}. As a consequence, we are…

Lusztig proved the compatibility of induction functors and restriction functors for Lusztig's perverse sheaves. Fang-Lan-Xiao established a categorification of Green's formula and gave a sheaf-level proof of this compatibility for all…

We prove a new uncertainty principle for square-integrable irreducible unitary representations of connected Lie groups. The concentration of the matrix coefficients is measured in terms of weighted $L^p$ norms, with weights in the local…

We generalize the notion of Erd\H{o}s-Ginzburg-Ziv constants -- along the same lines we generalized in earlier work the notion of Davenport constants -- to a ``higher degree" and obtain various lower and upper bounds. These bounds are…

Given a complex, elliptic coefficient function we investigate for which values of $p$ the corresponding second-order divergence form operator, complemented with Dirichlet, Neumann or mixed boundary conditions, generates a strongly…

We prove estimates for the sharp constants in fractional Poincar\'e-Sobolev inequalities associated to an open set, in terms of a nonlocal capacitary extension of its inradius. This work builds upon previous results obtained in the local…

Motivated by the recent characterization of Sobolev spaces due to Brezis-Van Schaftingen-Yung we prove new weak-type inequalities for one parameter families of operators connected with mixed norm inequalities. The novelty here comes from…