阿贝尔半群图

本文引入了阿贝尔半群图与幂等阿贝尔半群图的概念 ,并给出了树及圈是阿贝尔半群图与幂等阿贝尔半群图的充要条件。     

关于交换半环上一类矩阵的研究

对半环上可逆矩阵的概念进行推广,给出了[e]-可逆矩阵的定义。通过探讨可逆矩阵与[e]-可逆矩阵之间的内在联系,给出了交换半环上[e]-可逆矩阵的等价刻画。同时,对交换半环上[e]-可逆矩阵的全体关于矩阵乘法构成的半群进行研究,给出了此类矩阵半群的分解定理,并证明了此类矩阵半群均存在极大子群,且所有极大子群的并是Clifford半群。     

关于矩形带和周期群的半格

运用Clifford半群的结构研究矩形带和周期群的半格的性质和结构,给出矩形带和周期群的半格的等价刻画.所得结果推广了关于矩形带和满足附加恒等式x2+1≈x的群的半格的刻画.     

一类有限半格的自同态半环

研究两条有限链直积上自同态半环的性质。利用有限链直积上的两种二元运算，给出了两条有限链直积的子集构成自同态像集的充要条件，证明了自同态半环的乘法半群是正则半群。通过对有限链直积上的自同态进行分解，得到了自同态半环可由其乘法半群的幂等元集生成；推广了有限链上自同态半群的一些结果。     

On a doubly dynamically controlled supermarket model with impatient customers

In this paper, we provide a key generalization of the supermarket model both from the impatient customers and from a doubly dynamic control, which may also be related to the size-based scheduling through the centered management of the customer resource as well as the total service ability. We first use an infinite-dimensional Markov process to express the states of this supermarket model, and set up an infinite-dimensional system of differential equations satisfied by the expected fraction vector. Then we use the operator semigroup to provide a mean-field limit for the sequence of infinite-dimensional Markov processes, which asymptotically approaches a single trajectory identified by the unique and global solution to the infinite-dimensional system of limiting differential equations. Finally, we provide an effective and efficient algorithm for computing the fixed point of the infinite-dimensional system of limiting differential equations, and use the fixed point to give performance analysis of this supermarket model. Also, some numerical examples are given to demonstrate how the performance measures depend on some crucial parameters of this supermarket model. We believe that the mean-field method developed in this paper will be useful and effective for analyzing more complicated supermarket models in many practical areas.     

On the existence of global attractors in principal bundles

This article discusses necessary and sufficient conditions for the existence of global attractors for transformation semigroups on principal bundles. Since the global attractor is a compact set, the discussion involves the compactness of the fibres. A compact structure group is a necessary condition for the existence of the global attractor. In specific situations, the global attractor exists if the structure group is compact.     

带有记忆的粘弹方程解的整体存在性

研究了带有记忆的高维线性齐次粘弹方程,利用半群方法,证明了弱解和经典解的整体存在唯一性结果。     

Clifford半群的逆半群扩张

借助已知半群作扩张半群,是构造半群的主要方法之一.本文讨论Clifford半群的逆半群扩张.首先引入完整逆半群的概念并给出完整逆半群的Green关系的重要性质,其次引入Clifford半群的逆半群可扩张成逆半群的定义并作了初步的讨论.     

基于分布参数模型的柔性臂变结构控制

提出了一种针对柔性臂分布参数模型的变结构控制方法,解决了系统存在参数不确定性和在外部干扰下的镇定问题。通过Lyapunov函数方法设计了系统的变结构控制器,其中滑模面设计为关节角、关节角速度和柔性臂根部应变的线性组合。由线性算子半群理论和LaSalle不变集原理证明了闭环系统是渐近稳定的。仿真结果验证了该方法的有效性。