Abundant semigroups with a multiplicative quasi-adequate transversal

The concept of quasi-adequate transversals is introduced. Some properties and characterizations for abundant semigroups with a multiplicative quasi-adequate transversal are obtained. In particular, a structure theorem for such abundant semigroups is given. Finally, some special cases are considered. This research was partially supported by the National Natural Science Foundation of China (No. 10571077) and the Natural Science Foundation of Gansu Province (No. 3ZS052-A25-017).     

Numerical semigroups: Apéry sets and Hilbert series

Let a ₁,…,a _n be relatively prime positive integers, and let S be the semigroup consisting of all non-negative integer linear combinations of a ₁,…,a _n . In this paper, we focus our attention on AA-semigroups, that is semigroups being generated by almost arithmetic progressions. After some general considerations, we give a characterization of the symmetric AA-semigroups. We also present an efficient method to determine an Apéry set and the Hilbert series of an AA-semigroup. Dedicated to the memory of Ernst S. Selmer (1920–2006), whose calculations revealed the “Selmer group”.     

A supplement to ‘A note on invariant measure semigroups’

A unified definition of measure semigroup is given and it is shown how the types of invariance for the measure are formulated and what effect they have on the embeddability of an Abelian semigroup in a group. The online version of the original article can be found under doi:.     

Semilinear fractional integro-differential equations with compact semigroup

In this paper, we study the local and global existence of mild solutions to a class of fractional integro-differential equations in an arbitrary Banach space associated with operators generating compact semigroup on the Banach space.     

半环上的三角矩阵乘法半群的自同构

设R是含有恒等元1的半环,C是R上的中心子半环.Tn(R)是R上的n阶上三角矩阵C-代数.证明了当R是一个幂等元都是中心元的半环时,映射Φ:Tn(R)→Tn(R)是乘法半群自同构当且仅当存在Tn(R)中的可逆矩阵G和R中的半环自同构τ使得A=(aij)n×n∈Tn(R),均有Φ(A)=G-1τ(A)G.这里τ(A)=(τ(aij))n×n,n2.     

Generalized Bessel and Riesz Potentials on Metric Measure Spaces

We introduce generalized Bessel and Riesz potentials on metric measure spaces and the corresponding potential spaces. Estimates of the Bessel and Riesz kernels are given which reflect the intrinsic structure of the spaces. Finally, we state the relationship between Bessel (or Riesz) operators and subordinate semigroups.      

Pseudo almost periodic in distribution solutions to impulsive partial stochastic functional differential equations

In this paper, we study the piecewise pseudo almost periodicity in distribution for a stochastic process. Using the analytic semigroup theory and fixed point strategy with stochastic analysis theory, we obtain the existence and the exponential stability of piecewise pseudo almost periodic in distribution mild solutions for impulsive partial neutral stochastic functional differential equations under non-Lipschitz conditions. Moreover, an example is given to illustrate the general theorems.     

The existence of global attractors for 2D Navier-Stokes equations in <Emphasis Type="Italic">H</Emphasis><Superscript><Emphasis Type="Italic">k</Emphasis></Superscript> spaces

In this paper, we prove that the 2D Navier-Stokes equations possess a global attractor in Hk（Ω,R2） for any k ≥ 1, which attracts any bounded set of Hk（Ω,R2） in the H^k-norm. The result is established by means of an iteration technique and regularity estimates for the linear semigroup of operator, together with a classical existence theorem of global attractor. This extends Ma, Wang and Zhong＇s conclusion.     

A construction of weakly inverse semigroups

Let S° be an inverse semigroup with semilattice biordered set E° of idempotents and E a weakly inverse biordered set with a subsemilattice Ep = { e ∈ E ｜ arbieary f ∈ E, S（f , e） loheain in w（e）} isomorphic to E° by θ：Ep→E°. In this paper, it is proved that if arbieary f, g ∈E, f ←→ g→→ f°θD^s° g°θand there exists a mapping φ from Ep into the symmetric weakly inverse semigroup P J（E∪ S°） satisfying six appropriate conditions, then a weakly inverse semigroup ∑ can be constructed in P J（S°）, called the weakly inverse hull of a weakly inverse system （S°, E, θ, φ） with I（∑） ≌ S°, E（∑） ∽- E. Conversely, every weakly inverse semigroup can be constructed in this way. Furthermore, a sufficient and necessary condition for two weakly inverse hulls to be isomorphic is also given.