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 well-posedness for the time-dependent neutron transport equationwith integral boundary conditions is established in L^1 space. Some spectral propertiesof the transport operator are discussed, the dominant eigenval...The well-posedness for the time-dependent neutron transport equationwith integral boundary conditions is established in L^1 space. Some spectral propertiesof the transport operator are discussed, the dominant eigenvalue is proved existing,and furthermore, the conservative law of migrating particle numbers is established.展开更多
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...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.展开更多
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.
文摘The well-posedness for the time-dependent neutron transport equationwith integral boundary conditions is established in L^1 space. Some spectral propertiesof the transport operator are discussed, the dominant eigenvalue is proved existing,and furthermore, the conservative law of migrating particle numbers is established.
基金Premium Funding Project for Academic Human Resources Development in Beijing Union University(BPHR2020CZ06)。
文摘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.
