An example of new singularities in the semi-linear interaction of a cusp and a plane

We obtain a complete characterization of the Fredholm spectrum of the semigroup generated by hyperbolic initial-boundary value problems. These are accompanied by sharp energy estimates on the norm of the semigroup from above and below (whenever possible).     

On finitely generated subsemigroups of a free semigroup

A finitely generated semigroup S given by generators and the set of relations between these generators is called an F-semigroup if it is isomorphic to a subsemigroup of a free semigroup. In this paper three theorems concerning F-semigroups are proven and some unsolved problems are presented.     

半群环的右Artin性

本文研究了一般半群环的右Artin性的刻划问题，改进了JanOkniski在[3]中的结果，并给出了半群环是右Artin环的刻划．最后进一步指出在一定条件下，R[S1]和R[S1]的链条件是等价的．     

Inverse Subsemigroups of the Monogenic Free Inverse Semigroup

It is shown that every finitely generated inverse subsemigroup (submonoid) of the monogenic free inverse semigroup (monoid) is finitely presented. As a consequence, the homomorphism and the isomorphism problems for the monogenic free inverse semigroup (monoid) are proven to be decidable.     

Undecidability of representability for lattice-ordered semigroups and ordered complemented semigroups

We prove that the problems of representing a finite ordered complemented semigroup or finite lattice-ordered semigroup as an algebra of binary relations over a finite set are undecidable. In the case that complementation is taken with respect to a universal relation, this result can be extended to infinite representations of ordered complemented semigroups.     

On the Structure of the Semigroup of Entire Étale Mappings

The motivation for this paper comes from new ideas for solving the two-dimensional Jacobian Conjecture. The Jacobian Conjecture is one of the most famous open problems in algebraic geometry. This long-standing conjecture is no doubt one of the central problems in this well developed field of mathematics and hence the importance of investigating it. We can consider a semigroup of local diffeomorphisms on the affine space with a composition of mappings as its binary operation. We put a geometric fractal-like structure on this semigroup after equipping it with a natural metric (this is heavily dependent on the fact that our mappings are local diffeomorphisms). This structure is much more general than the structure of the ind-variety suggested by Kambayashi for étale polynomial mappings in the algebraic context. Hence, it applies to other semigroups such as the semigroup of all the entire functions in one complex variable with a nonvanishing first order derivative. This last semigroup is the theme of the current paper. We hope that the corresponding Hausdorff measure and Hausdorff dimension will enable us to relate the structure of the semigroup with arithmetic machinery such as certain Zeta functions.     

关于带跳的反射扩散过程的随机最优控制问题

研究一类半空间上带泊松跳的反射扩散过程的随机最优控制问题。得到关于这一控制问题的非线性Nisio半群,和联系这一半群的带Neumann边界条件的哈密顿。雅可比。贝尔曼方程。讨论这一类方程的粘性解的存在唯一性等问题。证明该控制问题中的价值函数是这一方程的一个粘性解。     

Thickness of Feathers

Briefly, a feather is a semigroup derivation diagram with the labels on the edges removed. In this paper, we are concerned with possible definitions for the thickness of a feather.

A major open problem is whether the word problem is solvable for semigroup presentations with one defining relation. It is known that word problems for semigroup presentations are solvable if the number of regions in minimal derivation diagrams is bounded. For some definitions for thickness, the number of regions in a derivation diagram over a presentation with one relation will be bounded if the thickness of the diagram is bounded.     

Algorithms for solving generalized equilibrium problems and fixed points of nonexpansive semigroups in Hilbert spaces

In this article, strong convergence theorems by the modified viscosity approximation method associated with Meir–Keeler contractions are proved for solving fixed point problems of a nonexpansive semigroup and generalized equilibrium problems in a Hilbert space.     

On the approximate solution of time-optimal control problems

In this paper we are concerned with the approximate solution of time-optimal control problems in a nonreflexive Banach SpaceE by sequences of similar problems in Banach spacesE _n which are assumed to approximateE in a fairly general sense. The problems under consideration are such that the solution operator of the associated evolution equation is a strongly continuous holomorphic contraction semigroup and the class of controls is taken from the dual of the Phillips adjoint space with respect to the infinitesimal generator of that semigroup. The main object is to establish convergence of optimal controls, transition times and corresponding trajectories of the approximating control problems which can be done by means of some results from the theory of approximation of semigroups of operators. Finally, these abstract convergence results will be applied to time-optimal control problems arising from heat transfer and diffusion processes.Research supported in part by the Deutsche Forschungsgemeinschaft (DFG)     

The loop problem for Rees matrix semigroups

We study the relationship between the loop problem of a semigroup, and that of a Rees matrix construction (with or without zero) over the semigroup. This allows us to characterize exactly those completely zero-simple semigroups for which the loop problem is context-free. We also establish some results concerning loop problems for subsemigroups and Rees quotients.     

Distances on the Commuting Graph of the Ring of Real Martices

The vertices of the commuting graph of a semigroup S are the noncentral elements of this semigroup, and its edges join all pairs of elements g, h that satisfy the relation gh = hg. The paper presents a proof of the fact that the diameter of the commuting graph of the semigroup of real matrices of order n ≥ 3 is equal to 4. A survey of results in that subject matter is presented, and several open problems are formulated.     

Semi-linear problems in infinite dimensions

We prove existence, smoothness and ergodicity results for semilinear parabolic problems on infinite dimensional spaces assuming the Logarithmic Sobolev inequality is satisfied. As a consequence we construct a class of nonlinear Markov semigroup which are hypercontractive.     

半群环的右Noether性

研究了一般半群的右Noetber性，得到了几个刻划定理．     

Local semigroups of contractions and some applications to Fourier representation theorems

It is proved that every local semigroup of contraction operators can be dilated to a group of unitary operators. Applications to some problems related with results of M. G. Krein, Bochner and Koosis are given.     

保特征2的域上幂等矩阵的线性算子

设Ｆ是特征２的域．本文确定Ｆ上ｎ×ｎ矩阵保幂等性的可逆的线性算子的半群Ｈ（Ｆ）的结构，同时回答了文献［１］提出的两个未解决的问题．     

Isomorphisms of Endomorphism Semigroups of Mixed Abelian Groups

We study abelian groups whose endomorphism rings are rings with unique addition. This means that there exists a unique binary operation of addition on the endomorphism semigroup which turns it into a ring. We also solve some close problems.     

Normed Groups and Their Applications in Noncommutative Differential Geometry

A normed semigroup is a semigroup having both rich topological and rich algebraic structure. This work is devoted to an abstract study of normed semigroups that arise in some problems of noncommutative geometry. The most interesting example, namely, the Abel semigroup , where A is a von Neumann algebra, is considered in detail. The definition of the latter semigroup is based on the notion of stable equivalence of normal elements of W^*-algebras, which generalizes the notion of stable equivalence of projectors. Bibliography: 8 titles.     

On a pull-back diagram for orthodox semigroups

In the present paper we deal with two problems concerning orthodox semigroups. M. Yamada raised the questions in [6] whether there exists an orthodox semigroup T with band of idempotents E and greatest inverse semigroup homomorphic image S for every band E and inverse semigroup S which have the property that is isomorphic to the semilattice of idempotents of S, and if T exists then whether it is always unique up to isomorphism. T. E. Hall [1] has published counter-examples in connection with both questions and, moreover, he has given a necessary and sufficient condition for existence. Now we prove a more effective necessary and sufficient condition for existence and deal with uniqueness, too. On the other hand, D. B. McAlister's theorem in [4] saying that every inverse semigroup is an idempotent separating homomorphic image of a proper inverse semigroup is generalized for orthodox semigroups. The proofs of these results are based on a theorem concerning a special type of pullback diagrams. In verifying this theorem we make use of the results in [5] which we draw up in Section 1. The main theorems are stated in Section 2. For the undefined notions and notations the reader is referred to [2].