Rational approximation schemes for bi-continuous semigroups

This paper extends the Hille-Phillips functional calculus and rational approximations results due to R. Hersh, T. Kato, P. Brenner, and V. Thomée to generators of bi-continuous semigroups. The method yields error estimates for rational time-discretization schemes for such semigroups, in particular for dual semigroups, Feller semigroups such as the Ornstein-Uhlenbeck semigroup, the heat semigroup, semigroups induced by nonlinear flows, implemented semigroups, and evolution semigroups. Furthermore, the results provide error estimates for a new class of inversion formulas for the Laplace transform.     

非汉字符号~*-覆盖正则半群的构造(Ⅰ)

本文刻画了■*-覆盖正则半群的结构,得到了弱覆盖正则半群和覆盖正则半 群的分类.作为其主要结论的应用, 我们还得到了(？)-覆盖完全正则半群, 弱覆盖完 全正则半群和覆盖完全正则半群的结构刻画.     

非汉字符号~*-覆盖正则半群的构造(Ⅰ)

本文刻画了■*-覆盖正则半群的结构,得到了弱覆盖正则半群和覆盖正则半 群的分类.作为其主要结论的应用, 我们还得到了(？)-覆盖完全正则半群, 弱覆盖完 全正则半群和覆盖完全正则半群的结构刻画.     

Rees matrix covers for a class of locally U-commutative semigroups

Given the importance of Morita theory of semigroups, we continue the study on the local structure of semigroups. Here we consider a class of nonregular semigroups, called locally U-commutative semigroups having U-local units, containing the classes of locally inverse semigroups, locally adequate semigroups, locally Ehresmann semigroups, and semigroups with local units having locally commuting idempotents. Our aim is to give a Rees matrix covering theorem for such semigroups with a partial McAlister sandwich bundle, and hence to put all the existing results into one context.     

The structure of superabundant semigroups

A structure theorem for superabundant semigroups in terms of semilattices of normalized Rees matrix semigroups over some cancellative monoids is obtained. This result not only provides a construction method for superabundant semigroups but also generalizes the well-known result of Petrich on completely regular semigroups. Some results obtained by Fountain on abundant semigroups are also extended and strengthened.     

Computing finite commutative semigroups: Part II

New precedence results are obtained for semigroups with zero, which describe the first non-zero row in detail and provide effective comparisons with subsequent rows. These results are used to further sharpen existing algorithms for the computation of finite commutative semigroups, confirm the number of distinct commutative semigroups of order 9, and determine the number of distinct commutative semigroups of order 10.     

The dynamics of semigroups of transcendental entire functions II

We introduce the concept of escaping set for semigroups of transcendental entire functions using Fatou-Julia theory. Several results of the escaping set associated with the iteration of one transcendental entire function have been extended to transcendental semigroups. We also investigate the properties of escaping sets for conjugate semigroups and abelian transcendental semigroups. Several classes of transcendental semigroups for which Eremenko’s conjecture holds have been provided.     

Semigroups of transcendental entire functions and their dynamics

We investigate the dynamics of semigroups of transcendental entire functions using Fatou–Julia theory. Several results of the dynamics associated with iteration of a transcendental entire function have been extended to transcendental semigroups. We provide some condition for connectivity of the Julia set of the transcendental semigroups. We also study finitely generated transcendental semigroups, abelian transcendental semigroups and limit functions of transcendental semigroups on its invariant Fatou components.     

Semigroups of mappings on graphs

At present, there are quite a few investigations in the theory of semigroups devoted to semigroups of mappings on graphs. Up to now, endomorphism semigroups of graphs, extensive transformation semigroups of graphs, coloring semigroups of graphs and other semigroups of special mappings on graphs have been studied. The results obtained show the way graphs are determined by the above-mentioned semigroups. They also show the structure of semigroups of mappings and interrelations between properties of graphs and corresponding properties of semigroups associated with the graphs. This paper gives a survey of the main results in this field.     

Self-automaton semigroups

After reviewing automaton semigroups, we introduce Cayley automata and the corresponding Cayley automaton semigroups. We investigate which semigroups are isomorphic to their Cayley automaton semigroup and give some results for special classes of semigroups. We answer a question posed by Cain relating to the dual construction.     

Weakly Strict Regular Semigroups

Weakly strict regular semigroups WS represent a generalization of strict regular semigroups. For the intersection of WS with some usual e-varieties of regular semigroups, such as left regular orthodox semigroups and similar e-varieties V, we provide WS ⋂ V with a basis of identities and forbidden semigroups. The latter, by exclusion, characterize the given e-variety. We do this also for WS. Coupled with some results of Hall, Churchill and Trotter, we characterize in this way also the e-varieties of completely regular semigroups as well as regular semigroups which are locally completely regular. The e-varieties studied are depicted in a diagram.     

Minimal isometric dilations of operator cocycles

We obtain existence, uniqueness results for minimal isometric dilations of contractive cocycles of semigroups of unital *-endomorphisms ofB(H. This generalizes the result of Sz. Nagy on minimal isometric dilations of semigroups of contractive operators on a Hilbert space. In a similar fashion we explore results analogus to Sarason's characterization that subspaces to which compressions of semigroups are again semigroups are semi-invariant subspaces, in the context of cocycles and quantum dynamical semigroups.This research is supported by the Indian National Science Academy under Young Scientist Project.     

Proper two-sided restriction semigroups and partial actions

Two-sided restriction semigroups and their handed versions arise from a number of sources. Attracting a deal of recent interest, they appear under a plethora of names in the literature. The class of left restriction semigroups essentially provides an axiomatisation of semigroups of partial mappings. It is known that this class admits proper covers, and that proper left restriction semigroups can be described by monoids acting on the left of semilattices. Any proper left restriction semigroup embeds into a semidirect product of a semilattice by a monoid, and moreover, this result is known in the wider context of left restriction categories. The dual results hold for right restriction semigroups.What can we say about two-sided restriction semigroups, hereafter referred to simply as restriction semigroups? Certainly, proper covers are known to exist. Here we consider whether proper restriction semigroups can be described in a natural way by monoids acting on both sides of a semilattice.It transpires that to obtain the full class of proper restriction semigroups, we must use partial actions of monoids, thus recovering results of Petrich and Reilly and of Lawson for inverse semigroups and ample semigroups, respectively. We also describe the class of proper restriction semigroups such that the partial actions can be mutually extendable to actions. Proper inverse and free restriction semigroups (which are proper) have this form, but we give examples of proper restriction semigroups which do not.     

Semilattices of bisimple orthodox semigroups

A structure theorem for bisimple orthodox semigroups was given by Clifford [2]. In this paper we determine all homomorphisms of a certain type from one bisimple orthodox semigroup into another, and apply the results to give a structure theorem for any semilattice of bisimple orthodox semigroups with identity in which the set of identity elements forms a subsemigroup. A special case of these results is indicated for bisimple left unipotent semigroups.     

A Hille-Yosida theorem for weakly continuous semigroups

We introduce a new class of weakly continuous semigroups and give a characterization of their infinitesimal generators, generalizing the classical Hille-Yosida Theorem for strongly continuous semigroups. The results are illustrated by the example of transition semigroups corresponding to the solutions of certain stochastic differential equations.     

右Clifford左商半群

本文讨论了右Ｃｌｉｆｆｏｒｄ左商半群．利用所谓的可适对刻划了右Ｃｌｉｆｆｏｒｄ半群中的左次半群,因此扩展了商半群的研究范围．     

关于Wrpp半群上的Lawson偏序(英文)

In this paper,we introduce Lawson partial order ≤ w on wrpp semigroups.After obtaining some properties of ≤ w,we determine when ≤ w is(left;right) compatible with the multiplication.These results extend and enrich the related results of Lawson and GuoLuo on abundant semigroups,of Guo-Shum on rpp semigroups and of Liu-Guo on wrpp semigroups.     

Automatic Rees Matrix Semigroups over Categories

We consider the preservation of the properties of automaticity and prefix-automaticity in Rees matrix semigroups over semigroupoids and small categories. Some of our results are new or improve upon existing results in the single-object case of Rees matrix semigroups over semigroups.