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Dynamic Analysis of the Multi-state Reliability System with Priority Repair Discipline

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 665-694页

作者： Aihemaitijiang YUMAIER Ehmet KASIM college of Mathematics and Systems Science Xinjiang UniversityUrumqi 830046China

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.

关键词： multi-state system C0-semigroup Dirichlet operator well-posedness asymptotic behavior

Asymptotic Behaviors of a Size-structured Population Model

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Acta Mathematicae Applicatae Sinica 2017年第4期33卷 1025-1042页

作者： Xian-long FU Qiong WU Department of Mathematics Shanghai Key Laboratory of PMMP East China Normal University Shanghai 200241 China

In this paper we devote ourselves to the study of the asymptotic behavior of a size-structured pop- ulation dynamics with random diffusion and delayed birth process. Within a semigroup framework, we discuss the local stability and asynchrony respectively for the considered population system under some conditions. We use for our discussion the techniques of operator matrices, Hille-Yosida operators, positivity, spectral analysis as well as Perron-Frobenius theory.

关键词： Population dynamics C0-semigroup stability asynchrony.

DIFFERENTIAL VARIATIONAL INEQUALITIES IN INFINITE BANAcH SPAcES

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Acta Mathematica Scientia 2017年第1期37卷 26-32页

作者：刘振海曾生达 Guangxi Key Laboratory of Universities Optimization control and Engineering calculation and College of SciencesGuangxi University for Nationalities Institute of computer Science Faculty of Mathematics and Computer Science Jagiellonian University

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.

关键词： differential variational inequality C0-semigroup monotone operator existcnceof solutions

Measure of Noncompactness and Semilinear Nonlocal Functional Differential Equations in Banach Spaces

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Acta Mathematica Sinica,English Series 2015年第1期31卷 140-150页

作者： Qi Xiang DONG Gang LI School of Mathematical Sciences Yangzhou University

This paper is concerned with the measure of noncompactness in the spaces of continuous functions and semilinear functional differential equations with nonloeal conditions in Banach spaces. The relationship between the Hausdorff measure of noncompactness of intersections and the modulus of equicontinuity is studied for some subsets related to the semigroup of linear operators in Banach spaces. The existence of mild solutions is obtained for a class of nonlocal semilinear functional differential equations without the assumption of compactness or equicontinuity on the associated semigroups Of linear operators.

关键词： Measure of noncompactness equicontinuity differential equation nonlocal condition C0-semigroup mild solution

Reliability Analysis of a cold Standby Repairable System with Repairman Extra Work

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Journal of Systems Science & complexity 2015年第5期28卷 1015-1032页

作者： ZHANG Xin Department of Basic courses Beijing Union University Academy of Mathematics and Systems Science Chinese Academy of Sciences

This paper deals with a cold standby repairable system with two identical units and one repairman who can do extra work in idle time. The 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.

关键词： C0-semigroup exponential stability repairable system resolvent positive operator

Neutral stochastic delay partial functional integro-differential equations driven by a fractional Brownian motion

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Frontiers of Mathematics in china 2013年第4期8卷 745-760页

作者： Tomas cARABALLO Mamadou Abdoul DIOP Dpto. Ecuaciones Diferenciales y Analisis Numerico Universidad de Sevilla Apdo. de Correos 1160 41080-Sevilla Spain Universite Gaston Berger de Saint-Louis UFR SAT Departement de Mathematiques 234 Saint-Louis Senegal

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.

关键词： Resolvent operator C0-semigroup Wiener process mild solution fractional Brownian motion

Point Spectra of the Operator corresponding to the M/M/1 Queueing Model with Working Vacation and Vacation Interruption

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Journal of Mathematical Research with Applications 2019年第1期39卷 75-88页

作者： Ehmet KASIM Geni GUPUR college of Mathematics and Systems Science Xinjiang University

In this paper, we consider point spectra of the operator corresponding to the M/M/1 queueing model with working vacation and vacation interruption. We prove that the underlying operator has uncountable eigenvalues on the left real line and these results describe the point spectra of the operator. Then, we show that the essential growth bound of the c;-semigroup generated by the operator is 0 and therefore it is not quasi compact, the essential spectral bound of the c;-semigroup is equal to 1. Moreover, our results imply it is impossible that the time-dependent solution of the model exponentially converges to its steady-state solution.

关键词： M/M/1 queueing model working vacation and vacation interruption C0-semigroup eigenvalue essential spectral bound

Reliability Analysis of a cold Standby Repairable System with Repairman Extra Work

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Journal of Systems Engineering and Electronics 2015年第5期26卷 1015-1032页

作者： ZHANG Xin Department of Basic courses Beijing Union University Academy of Mathematics and Systems Science Chinese Academy of Sciences

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.

关键词： C0-semigroup exponential stability repairable system resolvent positive operator.

Spectrum of the Operator corresponding to the M/M/1 Queueing Model with Vacations and Multiple Phases of Operation and Application

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Acta Mathematica Sinica,English Series 2020年第10期36卷 1183-1202页

作者： Nurehemaiti YIMING Geni GUPUR college of Mathematics and Systems Science Xinjiang UniversityUrumqi 830046P.R.China

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.

关键词： M/M/1 queueing model with vacations and multiple phases of operation time-dependent solution C0-semigroup point spectrum spectrum