It is proved that a system under compact perturbation cannot be uniformly exponentially stable for an isometric C0-semigroup or a C0-group with polynomial growth for negative time in a Banach space. The results extend...It is proved that a system under compact perturbation cannot be uniformly exponentially stable for an isometric C0-semigroup or a C0-group with polynomial growth for negative time in a Banach space. The results extend and improve the corresponding results of previous literature.展开更多
We investigate an N-unit series system with finite number of vacations. By analyzing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system...We investigate an N-unit series system with finite number of vacations. By analyzing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system operator we prove that the dynamic solution converges strongly to the steady state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.展开更多
We study a series-parallel repairable system consisting of three units with multiple vacations of a repairman. We first show that all points on the imaginary axis except zero belong to the resolvent set of the operato...We study a series-parallel repairable system consisting of three units with multiple vacations of a repairman. We first show that all points on the imaginary axis except zero belong to the resolvent set of the operator and zero is an eigenvalue of the operator, and then we prove that the semigroup generated by the operator is irreducible. By combining these results with our previous result we deduce that the dynamic solution of the system converges strongly to its steady-state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.展开更多
We investigate Gaver’s parallel system attended by a cold standby unit and a repairman with multiple vacations. By analysing the spectral distribution of the system operator and taking into account the irreducibility...We investigate Gaver’s parallel system attended by a cold standby unit and a repairman with multiple vacations. By analysing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system operator we prove that the dynamic solution converges strongly to the steady state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.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
基金Project of Sichuan Provincial Science and Technology Department (No.2007J13-006)
文摘It is proved that a system under compact perturbation cannot be uniformly exponentially stable for an isometric C0-semigroup or a C0-group with polynomial growth for negative time in a Banach space. The results extend and improve the corresponding results of previous literature.
文摘We investigate an N-unit series system with finite number of vacations. By analyzing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system operator we prove that the dynamic solution converges strongly to the steady state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.
文摘We study a series-parallel repairable system consisting of three units with multiple vacations of a repairman. We first show that all points on the imaginary axis except zero belong to the resolvent set of the operator and zero is an eigenvalue of the operator, and then we prove that the semigroup generated by the operator is irreducible. By combining these results with our previous result we deduce that the dynamic solution of the system converges strongly to its steady-state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.
文摘We investigate Gaver’s parallel system attended by a cold standby unit and a repairman with multiple vacations. By analysing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system operator we prove that the dynamic solution converges strongly to the steady state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.
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.
