Applications of B‐bounded nonlinear semigroups to particle transport problems

In this paper we study an application of nonlinear B‐bounded semigroups introduced in a previous paper. The application is similar to the particle transport problem which led to B‐bounded linear semigroups. We deal with a nonlinear particle transport problem, which can be solved by using B‐bounded nonlinear semigroups. Copyright © 2010 John Wiley & Sons, Ltd.     

完备 wrpp 半群

研究一类 wrpp 半群,即完备 wrpp 半群,并给出完备 wrpp 半群的若干性质定理.特别地,得到完备 wrpp 半群的织积结构.作为织积的应用,我们证明完备 wrpp 半群是(R)-左消板的强半格.因此,唐向东关于 C-wrpp 半群的结果得到进一步发展.     

PERFECT rpp SEMIGROUPS

The aim of this paper is to study a class of rpp semigroups, namely the perfect rpp semigroups. We obtain some characterization theorems for such semigroups. In particular, the spined product structure of perfect rpp semigroups is established. As an application of spined product structure, we prove that a perfect rpp semigroup is a strong semilattice of left cancellative planks. By a left cancellative plank, we mean a product of a left cancellative monoid and a rectangular band. Thus, the work of J.B. Fountain on C-rpp semigroups is further developed.

     

On Perfect Semigroups

It is shown that in order to characterize perfect semigroups in general, it suffices to characterize perfect semigroups among semigroups S such that S is a subsemigroup of a rational vector space, carries the identical involution, and has an archimedean component H such that S = H {0}.     

Constructing 2 × 2 Bricks from Unitary Numerical Semigroups

This paper investigates numerical semigroups that yield 2 × 2 bricks. We demonstrate the existence of an infinite family of 2 × 2 bricks that includes all of the perfect 2 × 2 bricks. We provide a formula for the Frobenius numbers of these semigroups as well as a necessary and sufficient condition for the semigroups to be symmetric.     

Finite aperiodic semigroups with commuting idempotents and generalizations

It is proved that any pseudovariety of finite semigroups generated by inverse semigroups, the subgroups of which lie in some proper pseudovariety of groups, does not contain all aperiodic semigroups with commuting idempotents. In contrast we show that every finite semigroup with commuting idempotents divides a semigroup of partial bijections that shares the same subgroups. Finally, we answer in the negative a question of Almeida as to whether a result of Stiffler characterizing the semidirect product of the pseudovarieties ofR-trivial semigroups and groups applies to any proper pseudovariety of groups.     

A product formula for semigroups of Lipschitz operators associated with abstract quasilinear evolution equations

The notion of semigroups of Lipschitz operators associated with abstract quasilinear evolution equations is introduced and a product formula for such semigroups is established. The product formula obtained in the paper is applied to the solvability of the Cauchy problem for a first order quasilinear system through a finite difference scheme of the Lax‐Friedrichs type.     

Domains of attraction of stable semigroups on simply connected nilpotent Lie groups

The classical Doeblin-Gnedenko conditions characterizing the domain of attraction of a non-Gaussian stable law, which have been proved to be sufficient for stable semigroups on simply connected nilpotent Lie groups by Carnal, are shown to be also necessary in that case. We also mention some consequences for the domain of normal attraction. Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part I, Eger, Hungary, 1994.     

An analogue of Hunt's representation theorem in quantum probability

In quantum mechanics certain operator-valued measures are introduced, called instruments, which are an analogue of the probability measures of classical probability theory. As in the classical case, it is interesting to study convolution semigroups of, instruments on groups and the associated semigroups of probability operators, which now are defined on spaces of functions with values in a von Neumann algebra. We consider a semigroup of probability operators with a continuity property weaker than uniform continuity, and we succeed in characterizing its infinitesimal generator under the additional hypothesis that twice differentiable functions belong to the domain of the generator. Such hypothesis can be proved in some particular cases. In this way a partial quantum analogue of Hunt's representation theorem for the generator of convolution semigroups on Lie groups is obtained. Our result provides also a closed characterization of generators of a new class of not norm continuous quantum dynamical semigroups.     

Duality results for the joint spectral radius and transient behavior

For linear inclusions in discrete or continuous time several quantities characterizing the growth behavior of the corresponding semigroup are analyzed. These quantities are the joint spectral radius, the initial growth rate and (for bounded semigroups) the transient bound. It is discussed how these constants relate to one another and how they are characterized by various norms. A complete duality theory is developed in this framework, relating semigroups and dual semigroups and extremal or transient norms with their respective dual norms.     

Some Results Concerning Convergence of Convolution Products of Probability Measures on Discrete Semigroups

Two types of conditions have been significant when considering the convergence of convolution products of nonidentical probability measures on groups and semigroups. The essential points of a sequence of measures have been useful in characterizing the supports of the limit measures. Also, enough mass eventually on an idempotent has proven sufficient for convergence in a number of structures. In this paper, both of these types of conditions are analyzed in the context of discrete non-abelian semigroups. In addition, an application to the convergence of nonhomogeneous Markov chains is given.     

Note on exclusive semigroups

In the SEMIGROUP FORUM, Vol. 1, No. 1, B. M. Schein proposed the following problem: Describe the structure of semigroups S such that for every a,b,c∈S, abc=ab, bc or ac. At present, we shall call such a semigroup S anexclusive semigroup. Recently, the author heard that the structure of commutative exclusive semigroups was completely determined by T. Tamura [3]. In this paper, we deal with exclusive semigroups which are not necessarily commutative. The paper is divided into three sections. At first, the structure of exclusive semigroups whose idempotents form a rectangular band will be clarified. Next, we shall investigate a certain class of exclusive semigroups called “exclusive homobands”. Especially, in the final section we shall deal with medial exclusive homobands and show how to construct them. The proofs are omitted and will be given in detail elsewhere.     

Unitary Numerical Semigroups and Perfect Bricks

This article completes a previous investigation of balanced and unitary numerical semigroups. The main result establishes the equivalence of unitary numerical semigroups and perfect 2 × 2 bricks.     

Completely Hyperexpansive Operator Tuples

The notion of a completely hyperexpansive operator on a Hilbert space is generalized to that of a completely hyperexpansive operator tuple, which in some sense turns out to be antithetical to the notion of a subnormal operator tuple with contractive coordinates. The countably many negativity conditions characterizing a completely hyperexpansive operator tuple are closely related to the Levy–Khinchin representation in the theory of harmonic analysis on semigroups. The interplay between the theories of positive and negative definite functions on semigroups forces interesting connections between the classes of subnormal and completely hyperexpansive operator tuples. Further, the several–variable generalization allows for a stimulating interaction with the multiparameter spectral theory.     

On Some Monogenic Semigroups with an Associate Subgroup

Let S be any semigroup and a, s ∈ S. If a = asa, then s is an associate of a. A subgroup G of S is an associate subgroup of S if every a ∈ S has a unique associate a* in G. It turns out that G = H _z for some idempotent z, the zenith of S. The mapping a → a* is a unary operation on S. We say that S is monogenic if S is generated, as a unary semigroup, by a single element.

We embark upon the problem of the structure of monogenic semigroups in this sense by characterizing monogenic ones belonging to completely simple semigroups, normal cryptogroups, orthogroups, combinatorial semigroups, cryptic medial semigroups, cryptic orthodox semigroups, and orthodox monoids. In each of these cases, except one, we construct a free object. The general problem remains open.     

Normal forms for semigroup amalgams

We define a class of inverse semigroup amalgams and derive normal forms for the amalgamated free products in the variety of semigroups. The class includes all amalgams of finite inverse semigroups, recently studied by Cherubini, Jajcayova, Meakin, Nuccio, Piochi and Rodaro (2005–2014), and lower bounded amalgams, that were introduced by the author (1997). We provide sufficient conditions for decidable word problem. We show that the word problem is decidable for an amalgamated free product of finite inverse semigroups. The normal forms can be used to study amalgams in subvarieties of inverse semigroups. In a forthcoming paper by the author, the results are used for varieties of semilattices of groups.     

Perfect semigroups and aliens

A topologized semigroup is called perfect if its multiplication is a perfect map (= a closed continuous mapping such that the inverse image of every point is compact). Thus a locally compact topological semigroup is perfect if and only if its multiplication is closed and each of its elements is compactly divided, that is, its divisors form a compact set. In the present paper we study compactly and non-compactly divided elements in the contexts of general locally compact semigroups, subsemigroups of groups, Lie semigroups and subsemigroups of Sl(2, ?).     

Perfect Semigroups and Aliens

Abstract. A topologized semigroup is called perfect if its multiplication is a perfect map (= a closed continuous mapping such that the inverse image of every point is compact). Thus a locally compact topological semigroup is perfect if and only if its multiplication is closed and each of its elements is compactly divided , that is, its divisors form a compact set. In the present paper we study compactly and non-compactly divided elements in the contexts of general locally compact semigroups, subsemigroups of groups, Lie semigroups and subsemigroups of Sl(2,R).     

On Weierstrass semigroups of double covering of genus two curves

In this work we prove that are Weierstrass semigroups all numerical semigroups whose three first positive non-gaps are 6, 8 and 10, resolving the problem of the numerical semigroups that appear as Weierstrass semigroups in double coverings of genus two curves.     

Flows in networks with delay in the vertices

Our goal is to show asynchronous exponential growth (AEG) for a flow in a network with delay in the vertices. For this purpose we show first that its wellposedness can be characterized via an appropriate operator being the generator of a strongly continuous semigroup. We investigate the long term behavior of the system via the spectrum of this generator using techniques from operator matrices, Hille‐Yosida operators and positive semigroups. Finally, we apply our results to deduce that our problem has (AEG).