带有缓冲库的串联CIMS渐近稳定性分析

讨论了一个可靠机器,一个不可靠机器和一个缓冲库构成的计算机集成系统(CIMS),利用由该系统所决定的算子A+E生成的Banach空间中的正压缩C0半群,证明了此系统的非负稳定解恰是算子A+E的0本征值所对应的规范化后的本征向量;同时通过对算子A+E的谱点分布的分析,证明了算子A+E的谱点均位于左半平面且在虚轴上除0点外无谱,作为线性算子半群稳定性的一个直接结果,得出了该系统解的渐近稳定性.     

两部件并联维修系统解的渐近稳定性

研究了两部件并联维修系统,在系统非负解存在惟一的基础上,利用系统算子生成的Banach空间中的正压缩C0半群,证明了系统的非负稳定解恰是系统算子0本征值对应的非负本征向量.同时通过研究系统算子的谱特征,证明了系统算子的谱点均位于复平面的左半平面且虚轴上除0外无谱,进而得到系统的渐近稳定性.     

分布参数切换系统的建模及仿真方法

讨论分布参数切换系统的建模与仿真问题.运用算子半群理论建立了分布参数切换系统的发展方程模型,并设计了系统仿真的方法.对于切换律与系统状态相关时切换律难以得出数值解的情况,运用广义正交多项式求出系统的逼近切换律,进而完成系统的仿真.最后,通过两个仿真实例,验证文中提出方法的可行性和有效性.     

一类可修的人机系统解的渐近稳定性

研究了两相同部件温储备可修的人机系统,利用由该系统所决定的算子A+B生成的Banach空间中的正压缩C0半群,证明了此系统的非负稳定解恰是算子A+B的.本征值对应的本征向量,同时通过研究算子A+B的谱特征,得到了算子A+B的谱点均位于复平面的左半平面且在虚轴上除0点外无谱的结论,进而得到了该系统的渐近稳定性.     

一个可靠机器,一个不可靠机器和一个缓冲库构成的系统分析

应用强连续算子半群理论证明一个可靠机器 ,一个不可靠机器和一个缓冲库构成的系统存在唯一的非负时间依赖解.     

拟线性椭圆系统的H—半变分不等式

本文利用伪单调算子理论研究拟线性椭圆系统的Ｈ－半变分不等式，证明了该系统解的存在性。     

具有有限等待空间的成批服务系统

应用有界线性算子半群理论证明一类成批服务系统的解的存在唯一性和非负性.     

非平衡和平衡统计系综的一个统一框架

提出通过子动力学方程(简称SKE)来建立一个非平衡统计系综体系。利用所构建的理论框架来研究在弱相互作用和强相互作用的情况下的自旋玻色子模型,从而很容易的得到正则系统的约简密度算子。也讨论了一种建立在安德森模型上的强关联量子网络。     

发汗烧蚀控制问题

本文讨论了一个发汗烧蚀控制问题。给出了系统的温度对发汗剂流量的单调性。通过应用算子半群理论和Ｈｉｌｂｅｒｔ空间的几何方法，得到了系统的最小范数控制的存在性、唯一性和可逼近性的结果。     

非线性抛物系统H—半变分不等式的周期解

本文研究非线性抛物系统Ｈ－半变分不等式的周期解。我们利用Ｃｌａｒｋｄ广义梯度的伪单调算子理论，证明了这类问题解的存在性。     

Reliability Analysis of Supply Chain System with the Multi-Suppliers and Single Demander

The time-dependent solution of a kind of supply chain system with the multi-suppliers and single demander is investigated in this paper. By choosing state space and defining operator of system, we transfer model into an abstract Cauchy problem. We are devoted to studying the unique existence of the system solution and its exponential stability by using the theory of C_0-semigroup. We prove that the system operator generates C_0-semigroup by the theory of cofinal operator and resolvent positive operator. We derive that the system has a unique nonnegative dynamic solution exponentially converging to its steady-state one which is the eigenfunction corresponding eigenvalue 0 of the system operator.     

Reliability Analysis of a Cold Standby Repairable System with Repairman Extra Work

This paper deals with a cold standby repairable system with two identical units and one repairman who can do extra work in idle time. The authors are devoted to studying the unique existence and exponential stability of the system solution. C0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by using the theory of resolvent positive operator, the authors derive that dynamic solution of the system exponentially converges to its steady-state one which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Some reliability indices of the system are discussed with a different method from traditional one. The authors also make a profit analysis to determine the optimal service time outside the system to maximize the system profit.     

Further research of a new kind of series repairable system

This paper is devoted to studying the uniqueness and existence of the system dynamic solution by using Co-semigroup theory and discussing its exponential stability by analyzing the spectral distribution of system operator and its quasi-compactness.Some primary reliability indices are discussed with the eigenfunction of system operator and the optimal vacation time to get the maximum system profit is analyzed at the end of paper.     

Impulse observability and impulse controllability of regular degenerate evolution systems

Impulse observability and impulse controllability of regular degenerate evolution systems are discussed by using functional analysis and operator theory in Banach space. Necessary and sufficient conditions for the impulse observability and impulse controllability of the system are obtained. This research is theoretically important for studying the design of the degenerate evolution system.     

EXPONENTIAL STABILITY OF A REPARABLE MULTI-STATE DEVICE

The exponential stability of a multi-state device is discussed in this paper. We present that the Co-semigroup generated by the system operator is quasi-compact and irreducible. It is known that 0 is a simple eigenvalue of the system operator. In combination with this, we obtain that the time-dependent solution exponentially converges to the steady-state solution, which is the positive eigenfuction corresponding to the simple eigenvalue O.     

Perturbation and robust controllability of singular distributed parameter control systems in Hilbert space

Perturbation and robust controllability of the singular distributed parameter control system are discussed via functional analysis and the theory of GE-semigroup in Hilbert space.The perturbation principle of GE-semigroup and the sufficient condition concerning the robust controllability of the singular distributed parameter control system are obtained,in which the controllability for singular distributed parameter control system is not destroyed,if we perturb the equation by small bounded linear operator.