The system which consists of a reliable machine, an unreliable machine and a storage buffer with infinite many workpieces has been studied. The existence of a unique positive time-dependent solution of the model corre...The system which consists of a reliable machine, an unreliable machine and a storage buffer with infinite many workpieces has been studied. The existence of a unique positive time-dependent solution of the model corresponding to the system has been obtained by using C 0-semigroup theory of linear operators in functional analysis.展开更多
This paper deals with a cold standby repairman who can do extra work in idle time. The repairable system with two identical units and one authors are devoted to studying the unique existence and exponential stability ...This paper deals with a cold standby repairman who can do extra work in idle time. The repairable system with two identical units and one 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.展开更多
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 eigenval...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.展开更多
讨论了具有热储备和两个独立相同部件的平行系统在由常规错误引起失效下的渐进稳定性.首先,利用B anach空间的V o lttera算子方程得到了非负动态解的存在唯一性;然后,利用强连续线性算子半群理论证明了系统正的动态解的存在唯一性,而由...讨论了具有热储备和两个独立相同部件的平行系统在由常规错误引起失效下的渐进稳定性.首先,利用B anach空间的V o lttera算子方程得到了非负动态解的存在唯一性;然后,利用强连续线性算子半群理论证明了系统正的动态解的存在唯一性,而由于初始值不在定义域内,故得到的是m ild解.但在t>0时系统古典解存在唯一,所以此时m ild解即为古典解.最后,利用线性算子半群稳定性的结果,证明了该动态解在范数意义下收敛到稳态解,进而得到了系统的渐进稳定性.展开更多
In this paper,we consider a new differential variational inequality（DVI,for short）which is composed of an evolution equation and a variational inequality in infinite Banach spaces.This kind of problems may be regard...In this paper,we consider a new differential variational inequality（DVI,for short）which is composed of an evolution equation and a variational inequality in infinite Banach spaces.This kind of problems may be regarded as a special feedback control problem.Based on the Browder＇s theorem and the optimal control theory,we show the existence of solutions to the mentioned problem.展开更多
This paper considers a multi-state repairable system that is composed of two classes of components,one of which has a priority for repair.First,we investigate the well-posedenss of the system by applying the operator ...This paper considers a multi-state repairable system that is composed of two classes of components,one of which has a priority for repair.First,we investigate the well-posedenss of the system by applying the operator semigroup theory.Then,using Greiner’s idea and the spectral properties of the corresponding operator,we obtain that the time-dependent solution of the system converges strongly to its steady-state solution.展开更多
基金Natural Science Foundation of Henan Province( 994 0 51 2 0 0 )
文摘The system which consists of a reliable machine, an unreliable machine and a storage buffer with infinite many workpieces has been studied. The existence of a unique positive time-dependent solution of the model corresponding to the system has been obtained by using C 0-semigroup theory of linear operators in functional analysis.
基金supported by the National Natural Science Foundation of China under Grant No.11201007
文摘This paper deals with a cold standby repairman who can do extra work in idle time. The repairable system with two identical units and one 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.
基金The research is supported by Beijing Institute of Technology Foundation under Grant No.20060742011.
文摘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.
基金supported by NNSF of China(11671101)the National Science Center of Poland Under Maestro Advanced Project(UMO-2012/06/A/ST1/00262)Special Funds of Guangxi Distinguished Experts Construction Engineering
文摘In this paper,we consider a new differential variational inequality（DVI,for short）which is composed of an evolution equation and a variational inequality in infinite Banach spaces.This kind of problems may be regarded as a special feedback control problem.Based on the Browder＇s theorem and the optimal control theory,we show the existence of solutions to the mentioned problem.
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region(No.2022D01C46)National Natural Science Foundation of China(No.11801485)。
文摘This paper considers a multi-state repairable system that is composed of two classes of components,one of which has a priority for repair.First,we investigate the well-posedenss of the system by applying the operator semigroup theory.Then,using Greiner’s idea and the spectral properties of the corresponding operator,we obtain that the time-dependent solution of the system converges strongly to its steady-state solution.
