In this paper, the existence, uniqueness, and asymptotic behavior of the solution of the density evolution equation for M/M/∞ model was studied by the semigroup theory of linear operators.
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
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
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
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
This paper deals with the problem of approximate controllability of infinite dimensional linear systems in nonreflexive state spaces. A necessary and sufficient condition for approximate controllability via L^p（[0, T...This paper deals with the problem of approximate controllability of infinite dimensional linear systems in nonreflexive state spaces. A necessary and sufficient condition for approximate controllability via L^p（[0, T], U）, 1≤p〈∞ is obtained,where L^p（ [0, T], U） is the control function space.展开更多
We establish the exponential stability of global solutions and C0-semigroup for the compressible Navier.Stokes equations of a viscous polytropic ideal gas in both bounded domain in R^1 and bounded annular domains in R...We establish the exponential stability of global solutions and C0-semigroup for the compressible Navier.Stokes equations of a viscous polytropic ideal gas in both bounded domain in R^1 and bounded annular domains in R^n （n=2,3）.展开更多
In this paper,we study the well-posedness for the thermoelastic Timoshenko system with a constant delay and mass diffusion effects.Heat and mass exchange with the environment during thermodiffusion in Timoshenko beam....In this paper,we study the well-posedness for the thermoelastic Timoshenko system with a constant delay and mass diffusion effects.Heat and mass exchange with the environment during thermodiffusion in Timoshenko beam.The C_(0)-semigroup theory will be used to prove the well-posedness of the considered problem.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
We investigate Gaver’s parallel system attended by a cold standby unit and a repairman with multiple vacations. By using C0-semigroup theory of linear operators in the functional analysis, we prove well-posedness and...We investigate Gaver’s parallel system attended by a cold standby unit and a repairman with multiple vacations. By using C0-semigroup theory of linear operators in the functional analysis, we prove well-posedness and the existence of the unique positive dynamic solution of the system.展开更多
This paper presents a conception of an exponential observer for a class of linear distributed-parameter systems (DPSs), in which the dynamics are partially unknown. The given distributed-parameter observer ensures asy...This paper presents a conception of an exponential observer for a class of linear distributed-parameter systems (DPSs), in which the dynamics are partially unknown. The given distributed-parameter observer ensures asymptotic state estimator with exponentially decay error, based on the theory of C0-semigroups in a Hilbert space. The theoretical observer developed is applied to a chemical tubular reactor, namely the isothermal Plug-Flow reactor basic dynamical model for which measurements are available at the reactor output only. The process is described by Partial differential equations with unknown initial states. For this application, performance issues are illustrated in a simulation study.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
Starting from 2016,the raw Global Navigation Satellite System(GNSS)measurements can be extracted from the Android Nougat(or later)operating systems.Since then,GNSS smartphone positioning has been given much attention....Starting from 2016,the raw Global Navigation Satellite System(GNSS)measurements can be extracted from the Android Nougat(or later)operating systems.Since then,GNSS smartphone positioning has been given much attention.A high number of related publications indicates the importance of the research in this field,as it has been doing in recent years.Due to the cost-effectiveness of the GNSS smartphones,they can be employed in a wide variety of applications such as cadastral surveys,mapping surveying applications,vehicle and pedestrian navigation and etc.However,there are still some challenges regarding the noisy smartphone GNSS observations,the environment effect and smartphone holding modes and the algorithm development part which restrict the users to achieve high-precision smartphone positioning.In this review paper,we overview the research works carried out in this field with a focus on the following aspects:first,to provide a review of fundamental work on raw smartphone observations and quality assessment of GNSS observations from major smart devices including Google Pixel 4,Google Pixel 5,Xiaomi Mi 8 and Samsung Ultra S20 in terms of their signal strengths and carrier-phase continuities,second,to describe the current state of smartphone positioning research field until most recently in 2021 and,last,to summarize major challenges and opportunities in this filed.Finally,the paper is concluded with some remarks as well as future research perspectives.展开更多
In this paper,the boundary stabilization of the Timoshenko equation of a nonuniform beam,with clamped boundary condition at one end and with bending moment and shear force controls at the other end, is considered.It i...In this paper,the boundary stabilization of the Timoshenko equation of a nonuniform beam,with clamped boundary condition at one end and with bending moment and shear force controls at the other end, is considered.It is proved that the system is exponentially stabilizable when the bending moment and shear force controls are simultaneously applied.The frequency domain method and the multiplier technique are used.展开更多
文摘In this paper, the existence, uniqueness, and asymptotic behavior of the solution of the density evolution equation for M/M/∞ model was studied by the semigroup theory of linear operators.
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.
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.
文摘This paper deals with the problem of approximate controllability of infinite dimensional linear systems in nonreflexive state spaces. A necessary and sufficient condition for approximate controllability via L^p（[0, T], U）, 1≤p〈∞ is obtained,where L^p（ [0, T], U） is the control function space.
基金Foundation item: Supported by the NSF of ChinaSupported by the Prominent Youth from Henan Province(0412000100)
文摘We establish the exponential stability of global solutions and C0-semigroup for the compressible Navier.Stokes equations of a viscous polytropic ideal gas in both bounded domain in R^1 and bounded annular domains in R^n （n=2,3）.
基金Supported by the NNSF of China(Grant No.12171082)Fundamental Funds for the Central Universities(Grant No.2232021G-13).
文摘In this paper,we study the well-posedness for the thermoelastic Timoshenko system with a constant delay and mass diffusion effects.Heat and mass exchange with the environment during thermodiffusion in Timoshenko beam.The C_(0)-semigroup theory will be used to prove the well-posedness of the considered problem.
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.
文摘We investigate Gaver’s parallel system attended by a cold standby unit and a repairman with multiple vacations. By using C0-semigroup theory of linear operators in the functional analysis, we prove well-posedness and the existence of the unique positive dynamic solution of the system.
文摘This paper presents a conception of an exponential observer for a class of linear distributed-parameter systems (DPSs), in which the dynamics are partially unknown. The given distributed-parameter observer ensures asymptotic state estimator with exponentially decay error, based on the theory of C0-semigroups in a Hilbert space. The theoretical observer developed is applied to a chemical tubular reactor, namely the isothermal Plug-Flow reactor basic dynamical model for which measurements are available at the reactor output only. The process is described by Partial differential equations with unknown initial states. For this application, performance issues are illustrated in a simulation study.
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 Sciences and Engineering Research Council of Canada(NSERC).
文摘Starting from 2016,the raw Global Navigation Satellite System(GNSS)measurements can be extracted from the Android Nougat(or later)operating systems.Since then,GNSS smartphone positioning has been given much attention.A high number of related publications indicates the importance of the research in this field,as it has been doing in recent years.Due to the cost-effectiveness of the GNSS smartphones,they can be employed in a wide variety of applications such as cadastral surveys,mapping surveying applications,vehicle and pedestrian navigation and etc.However,there are still some challenges regarding the noisy smartphone GNSS observations,the environment effect and smartphone holding modes and the algorithm development part which restrict the users to achieve high-precision smartphone positioning.In this review paper,we overview the research works carried out in this field with a focus on the following aspects:first,to provide a review of fundamental work on raw smartphone observations and quality assessment of GNSS observations from major smart devices including Google Pixel 4,Google Pixel 5,Xiaomi Mi 8 and Samsung Ultra S20 in terms of their signal strengths and carrier-phase continuities,second,to describe the current state of smartphone positioning research field until most recently in 2021 and,last,to summarize major challenges and opportunities in this filed.Finally,the paper is concluded with some remarks as well as future research perspectives.
文摘In this paper,the boundary stabilization of the Timoshenko equation of a nonuniform beam,with clamped boundary condition at one end and with bending moment and shear force controls at the other end, is considered.It is proved that the system is exponentially stabilizable when the bending moment and shear force controls are simultaneously applied.The frequency domain method and the multiplier technique are used.
