We describe the point spectrum of the operator which corresponds to the M/M/1 queueing model with vacations and multiple phases of operation.Then by using this result we prove that the essential growth bound of the C0...We describe the point spectrum of the operator which corresponds to the M/M/1 queueing model with vacations and multiple phases of operation.Then by using this result we prove that the essential growth bound of the C0-semigroup generated by the operator is 0,the C0-semigroup is not compact,not eventually compact,even not quasi-compact.Moreover,we verify that it is impossible that the time-dependent solution of the M/M/1 queueing model with vacations and multiple phases of operation exponentially converges to its steady-state solution.In addition,we obtain the spectral radius and essential spectral radius of the C0-semigroup.Lastly,we discuss other spectrum of the operator and obtain a set which belongs to the union of its continuous spectrum and residual spectrum.展开更多
In this paper,we introduce and study the diskcyclicity and disk transitivity of a set of operators.We establish a diskcyclicity criterion and give the relationship between this criterion and the diskcyclicity.As appli...In this paper,we introduce and study the diskcyclicity and disk transitivity of a set of operators.We establish a diskcyclicity criterion and give the relationship between this criterion and the diskcyclicity.As applications,we study the diskcyclicty of Co-semigroups and C-regularized groups.We show that a diskcyclic Co-semigroup exists on a complex topological vector space X if and only if dim(X)=1 or dim(X)=∞and we prove that diskcyclicity and disk transitivity of C0-semigroups(resp C-regularized groups)are equivalent.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
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
In this paper,we study complex symmetric C0-semigroups on the Bergman space A^2(C+) of the right half-plane C+.In contrast to the classical case,we prove that the only involutive composition operator on A^2(C+) is the...In this paper,we study complex symmetric C0-semigroups on the Bergman space A^2(C+) of the right half-plane C+.In contrast to the classical case,we prove that the only involutive composition operator on A^2(C+) is the identity operator,and the class of J-symmetric composition operators does not coincide with the class of normal composition operators.In addition,we divide semigroups{φt}of linear fractional self-maps of C+into two classes.We show that the associated composition operator semigroup{Tt}is strongly continuous and identify its infinitesimal generator.As an application,we characterize Jσ-symmetric C0-semigroups of composition operators on A^2(C+).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
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
By using the strong continuous semigroup theory of linear operators we prove the existence of a unique positive time-dependent solution of the model describing a re-pairable, standby, human & machine system.
This paper deals with the existence and uniqueness of mild solutions to neutral stochastic delay functional integro-differential equations perturbed by a fractional Brownian motion BH, with Hurst parameter H E （1/2, ...This paper deals with the existence and uniqueness of mild solutions to neutral stochastic delay functional integro-differential equations perturbed by a fractional Brownian motion BH, with Hurst parameter H E （1/2, 1）. We use the theory of resolvent operators developed by R. Grimmer to show the existence of mild solutions. An example is provided to illustrate the results of this work.展开更多
基金the National Natural Science Foundation of China (Grant No. 11961062)。
文摘We describe the point spectrum of the operator which corresponds to the M/M/1 queueing model with vacations and multiple phases of operation.Then by using this result we prove that the essential growth bound of the C0-semigroup generated by the operator is 0,the C0-semigroup is not compact,not eventually compact,even not quasi-compact.Moreover,we verify that it is impossible that the time-dependent solution of the M/M/1 queueing model with vacations and multiple phases of operation exponentially converges to its steady-state solution.In addition,we obtain the spectral radius and essential spectral radius of the C0-semigroup.Lastly,we discuss other spectrum of the operator and obtain a set which belongs to the union of its continuous spectrum and residual spectrum.
文摘In this paper,we introduce and study the diskcyclicity and disk transitivity of a set of operators.We establish a diskcyclicity criterion and give the relationship between this criterion and the diskcyclicity.As applications,we study the diskcyclicty of Co-semigroups and C-regularized groups.We show that a diskcyclic Co-semigroup exists on a complex topological vector space X if and only if dim(X)=1 or dim(X)=∞and we prove that diskcyclicity and disk transitivity of C0-semigroups(resp C-regularized groups)are equivalent.
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.
文摘In this paper,we study complex symmetric C0-semigroups on the Bergman space A^2(C+) of the right half-plane C+.In contrast to the classical case,we prove that the only involutive composition operator on A^2(C+) is the identity operator,and the class of J-symmetric composition operators does not coincide with the class of normal composition operators.In addition,we divide semigroups{φt}of linear fractional self-maps of C+into two classes.We show that the associated composition operator semigroup{Tt}is strongly continuous and identify its infinitesimal generator.As an application,we characterize Jσ-symmetric C0-semigroups of composition operators on A^2(C+).
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.
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This research is supported by the Tianyuan Mathematics Foundation (No. 10226007) and the Science Foundation of Xinjiang University
文摘By using the strong continuous semigroup theory of linear operators we prove the existence of a unique positive time-dependent solution of the model describing a re-pairable, standby, human & machine system.
文摘This paper deals with the existence and uniqueness of mild solutions to neutral stochastic delay functional integro-differential equations perturbed by a fractional Brownian motion BH, with Hurst parameter H E （1/2, 1）. We use the theory of resolvent operators developed by R. Grimmer to show the existence of mild solutions. An example is provided to illustrate the results of this work.
