We study many-body localization (MBL) in a one-dimensional system of spinless fermions with deterministic aperiodic potential the presence random interactions ${V}_{ij}$ decaying as power-law ${V}_{ij}/{({r}_{ij})}^{\ensuremath{\alpha}}$ distance ${r}_{ij}$. demonstrate that MBL survives even for $\ensuremath{\alpha}<1$ and is preceded by broad nonergodic subdiffusive phase. Starting from pa...

We define the fractional powers Ls=(−aij(x)∂ij)s, 0<s<1, of nondivergence form elliptic operators L=−aij(x)∂ij in bounded domains Ω⊂Rn, under minimal regularity assumptions on coefficients aij(x) and boundary ∂Ω. show that these appear several applications such as Monge–Ampère equations, elasticity, finance. The solution u to nonlocal Poisson problem{(−aij(x)∂ij)su=finΩu=0on∂Ω is characterized ...

We obtain an asymptotically sharp error bound in the classical Sudakov-Fernique comparison inequality for finite collections of gaussian random variables. Our proof is short and selfcontained, and gives an easy alternative argument for the classical inequality, extended to the case of non-centered processes. 1 Statement of the result Gaussian comparison inequalities are among the most important...

Flavour-violating interactions of the stop-quarks are expected to provide an additional few GeV contributions Higgs-Boson mass, particularly when mix with scharm-quarks, thereby allowing reduced supersymmetry (SUSY) breaking scale compared flavour-conserving constrained minimal supersymmetric Standard Model (CMSSM). Inspired by this, we analyse mentioned above in context CMSSM using information...

In this article we describe the use of the new font selection scheme in the standard IJ.'lEX environment. The main characteristics are: 297 . The possibility to change family, series, shape and sizes independently of one another. . The existence of a style file to process older documents without any changes to their layout and their input files. . A macro setup which is consistent with existing...

In this paper we prove the weak and strong convergence of the implicit iterative process with errors to a common fixed point of a finite family {Tj}i=1 of asymptotically quasi Ij−nonexpansive mappings as well as a family of {Ij}j=1 of asymptotically quasi nonexpansive mappings in the framework of Banach spaces. The obtained results improve and generalize the corresponding results in the existin...

We investigate a set of stochastic models of biodiversity, population genetics, language evolution, and opinion dynamics on a network within a common framework. Each node has a state 0<x(i)<1 with interactions specified by strengths m(ij). For any set of m(ij), we derive an approximate expression for the mean time to reach fixation or consensus (all x(i)=0 or 1). Remarkably, in a case relevant ...

The accurate prediction of physicochemical properties chemical compounds in mixtures (such as the activity coefficient at infinite dilution $\gamma_{ij}^\infty$) is essential for developing novel and more sustainable processes. In this work, we analyze performance previously-proposed GNN-based models $\gamma_{ij}^\infty$, compare them with several mechanistic a series 9 isothermal studies. More...