Pawlak, Ryszard J.
Published in
Tatra Mountains Mathematical Publications

In this paper we consider the issues of local entropy for a finite family of generators (that generates the semigroup). Our main aim is to show that any continuous function can be approximated by s-chaotic family of generators.

IWABUCHI, Tsukasa

This is a survey of recent results on function spaces associated with the Dirichlet Laplacian. We study the well-definedness of the Besov spaces, properties of semigroup generated by the fractional Laplacian, and bilinear estimates.

Laurençot, Philippe Walker, Christoph

Local and global well-posedness of the coagulation-fragmentation equation with size diffusion are investigated. Owing to the semilinear structure of the equation, a semigroup approach is used, building upon generation results previously derived for the linear fragmentation-diffusion operator in suitable weighted $L^1$-spaces.

Al’pin, Yu. A. Tregubov, V. G.
Published in
Russian Mathematics

The Frobenius form of an irreducible bistochastic matrix is clarified. A generalization of the Frobenius form for irreducible semigroups of bistochastic matrices is described.

Laurençot, Philippe Walker, Christoph

The dynamics of the fragmentation equation with size diffusion is investigated when the size ranges in (0, ∞). The associated linear operator involves three terms and can be seen as a nonlocal perturbation of a Schrödinger operator. A Miyadera perturbation argument is used to prove that it is the generator of a positive, analytic semigroup on a wei...

Kavian, O Mischler, S

We consider the Fokker-Planck equation with subcritical confinement force field which may not derive from a potential function. We prove the existence of an equilibrium (in the case of a general force) and we establish some (polynomial and stretch exponential) rate of convergence to the equilibrium (depending on the space to which belongs the initi...

Gervais, Pierre

The aim of this paper is to extend to the spaces L^2(R^d , (1+|v|)^2k dv) the spectral study led in L^2(R^d , exp(|v|^2/2)dv) by R. Ellis and M. Pinsky on the space inhomogeneous linearized Boltzmann operator for hard spheres. More precisely, we look at the Fourier transform in the space variable of the inhomogeneous operator and consider the dual ...

Zhuchok, A. V.
Published in
Lobachevskii Journal of Mathematics

AbstractLoday and Ronco introduced the notion of a trioid. We construct a trioid which is isomorphic to the free \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end...

Bertram, Wolfgang

We prove an identity for five arguments, valid in the lattice of natural numbers with gcd and lcm as lattice operations. More generally, this identity characterizes arbitrary distributive lattices. Fixing three of the five arguments, we always get associative products, and thus every distributive lattice carries many semigroup structures. In the ar...

Devillet, Jimmy

This thesis, which consists of two parts, focuses on characterizations and descriptions of classes of idempotent n-ary semigroups where n >= 2 is an integer. Part I is devoted to the study of various classes of idempotent semigroups and their link with certain concepts stemming from social choice theory. In Part II, we provide constructive descript...