This is a survey on recent developments of the theory of one-parameter semigroups and evolution equations with special emphasis on functional calculus and kernel estimates. Also other topics as asymptotic behavior for large time and holomorphic semigroups are discussed. As main application we consider elliptic operators with various boundary conditions. Semigroups and evolution equations: Funct...

1. J. F. Berglund and K. H. Hofmann, Compact semitopological semigroups and weakly almost periodic functions, Lecture Notes in Math., vol. 42, Springer-Verlag, Berlin and New York, 1967. MR 36 #6531. 2. Mary Katherine Bennett, Review of "Distributive Lattices by R. Balbes and P. Dwinger," Bull. Amer. Math. Soc. 82 (1976), 246-249. 3. R. Burckel, Weakly almost periodic functions on semigroups, G...

We study quantum dynamical semigroups generated by noncommutative unbounded elliptic operators which can be written as Lindblad type unbounded generators. Under appropriate conditions, we first construct the minimal quantum dynamical semigroups for the generators and then use Chebotarev and Fagnola’s sufficient conditions for conservativity to show that the semigroups are conservative.

r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.

In this paper, the study of vague structures of Γ-semigroups is initiated by introducing the concepts of vague subsemigroup, vague bi-ideal and vague (1, 2)-ideal in a Γ-semigroup and some fundamental results are obtained. Then the concept of vague weakly completely prime ideals in Γ-semigroups has been introduced and studied directly and via operator semigroups

Xiaomin Zhang Department of Mathematics, Linyi Normal University, Shandong 276005, China E-mail: [email protected] Abatract The aim of this paper is to study eventually strong wrpp semigroups whose idempotents satisfy permutation identities, that is, so-called PI-strong wrpp semigroups. After some properties are obtained, the structure of such semigroups are investigated. In particular, the struct...

The setting of this research is Bishop’s constructive mathematics. Following ideas of Chan and Shum, exposed in their famous paper “Homomorphisms of implicative semigroups”, we discuss the structure of implicative semigroups on sets with tight apartness. Moreover, we use anti-orders instead of partial orders. We study concomitant issues induced by existence of apartness and anti-orders giving s...

In this paper we have studied   q   , -fuzzy semiprime ideals in semigroups. We have characterized completely regular semigroups by the properties of their   q   , -fuzzy quasi ideals. Moreover we have characterized semigroups that are semilattices of groups by   q   , -fuzzy quasi ideals.

In this paper it is shown how the graphical methods developed by Stephen for analyzing inverse semigroup presentations may be used to study varieties of inverse semigroups. In particular, these methods may be used to solve the word problem for the free objects in the variety of inverse semigroups generated by the five-element combinatorial Brandt semigroup and in the variety of inverse semigrou...

A new topological representation for free profinite R-trivial semigroups in terms of spaces of vertex-labeled complete binary trees is obtained. Such a tree may be naturally folded into a finite automaton if and only if the element it represents is an ω-term. The variety of ω-semigroups generated by all finite R-trivial semigroups, with the usual interpretation of the ω-power, is then studied. ...