Matrix multiplication operators on Banach function spaces

In this paper, we study the matrix multiplication operators on Banach function spaces and discuss their applications in semigroups for solving the abstract Cauchy problem.     

On disjunctions of algebraic sets in completely simple semigroups

A semigroup S is called an equational domain if any finite union of algebraic sets over S is algebraic. We give some necessary and su?cient conditions for a completely simple semigroup to be an equational domain.     

Sharp regularity theory for thermo-elastlc mixed problems

We give a sharp (optimal) regularity theory of thermo-elastic mixed problems. Our approach is by P.D.E. methods and applies to any space dimension and, in principle, to any set of boundary conditions- We consider two sets of boundary conditions: hinged and clamped B.C. In one approach, the original coupled P.D.E. system is split into two suitable uncoupled P.D.E. equations: A Kirchoff mixed problem and a heat equation, whose delicate, optimal regularity is either available in, or can be deduced by duality from, the literature. Ultimately, the original problem with boundary non-homogeneous term is reduced to the same problem, however, with homogeneous B.C. and a known 'right-hand term' in the equation, which is easier to analyze. A direct proof is also given in the seriously more demanding clamped case.     

On a mathematical model of age–cycle length structured cell population with non‐compact boundary conditions (II)

This work is a natural continuation of an earlier one in which a mathematical model has been studied. This model is based on an age–cycle length structured cell population. The cellular mitosis is mathematically described by a non‐compact boundary condition. We investigate the spectral properties of the generated semigroup, and we give an explicit estimation of its type. Copyright © 2015 John Wiley & Sons, Ltd.     

The subvariety lattice of the join of two semigroup varieties

The join A ∨ B of two semigroup varieties A and B is investigated. The latrine of subvarieties of A ∨ B is completely described, It is shown that this lattice is finite and non-modular and that all varieties in it are finitely based and finitely generated.     

关于置换因子循环布尔矩阵半群（英文）

PMn（B）表示布尔代数B={0,1}上的所有n×n置换因子循环矩阵组成的集合.PMn（B）对于矩阵乘法成为一个半群.刻画了PMn（B）中的幂等元,并给出了半群PMn（B）中的Euler-Fermat定理.     

Invariance of asymptotic stability of perturbed linear systems on Hilbert space

The questions of stabilizability of structurally perturbed or uncertain linear systems in Hilbert space of the form are considered. The operatorA is assumed to be the infinitesimal generator of aC ₀-semigroup of contractionsT(t),t0, in a Hilbert spaceX;B is a bounded linear operator from another Hilbert spaceU toX; and {P(r),r } is a family of bounded or unbounded perturbations ofA inX, where is an arbitrary set, not necessarily carrying any topology. Sufficient conditions are presented that guarantee controllability and stabilizability of the perturbed system, given that the unperturbed system has similar properties. In particular, it is shown that, for certain classes of perturbations, weak and strong stabilizability properties are preserved for the same state feedback operator.This work was supported in part by the Natural Science and Engineering Research Council of Canada under Grant No. A7109.     

Observability of coupled systems

By applying the theory of semigroups, we generalize an earlier result of Komornik and Loreti [5] on the observability of compactly perturbed systems. As an application, we answer a question of the same authors concerning the observability of weakly coupled linear distributed systems. This revised version was published online in June 2006 with corrections to the Cover Date.