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ASYMPTOTIc PROPERTY OF THE TIME-DEPENDENT SOLUTION OF A RELIABILITY MODEL

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Journal of Systems Science & complexity 2005年第3期18卷 319-339页

作者： GeniGupur GUOBaozhu AcademyofMathematicsandSystemsScience ChineseAcademyofSciencesBeijing100080China collegeofMathematicsandSystemsScience Xi'njiangUniversityUrumqi830046China

We discuss a transfer line consisting of a reliable machine, an unreliable machine and a storage buffer. This transfer line can be described by a group of partial differential equations with integral boundary conditions. First we show that the operator corresponding to these equations generates a positive contraction c0-semigroup T(t), and prove that T(t) is a quasi-compact operator. Next we verify that 0 is an eigenvalue of this operator and its adjoint operator with geometric multiplicity one. Last, by using the above results we obtain that the time-dependent solution of these equations converges strongly to their steady-state solution.

关键词： c_0-semigroup quasi-compact operator adjoint operator eigenvalue

WELL-POSEDNESS OF THE MODEL DEScRIBING A REPAIRABLE,STANDBY,HUMAN & MAcHINE SYSTEM

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Journal of Systems Science & complexity 2003年第4期16卷 483-493页

作者： Geni Gupur college of Mathematics and Systems Sciences Xinjiang University Urumqi 830046 China

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.

关键词： c_0-semigroup dispersive operator conservative operator

Differentiability of the Pritchard-Salamon systems with admissible state-feedback

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2005年第4期6卷 311-314页

作者：于欣 Laboratory of Information and Optimization Technology Ningbo Institute of Technology Zhejiang University

Many papers on a wide range of control problems for Pritchard-Salamon systems have appeared and many of its important mathematical and system theoretical properties have been revealed. This paper deals with the differentiability of the Pritchard-Salamon system with admissible state-feedback. Spectrum analysis showed that under definite condition, the unbounded perturbation semigroup of the Pritchard-Salamon system is eventually differentiable.

关键词： c_0-semigroup Differentiability Admissible operator Pritchard-Salamon systems Perturbation

Existence and Uniqueness of the Dynamic Solution of a Series-Parallel Repairable System consisting of Three-Unit with Multiple Vacations of a Repairman

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Journal of Applied Mathematics and Physics 2016年第8期4卷 1585-1591页

作者： Abdukerim Haji Tursunjan Keyim Bilikiz Yunus college of Mathematics and System Sciences Xinjiang University Urumqi China college of Mechanical Engineering Xinjiang University Urumqi China

We investigate a series-parallel repairable system consisting of three-unit with multiple vacations of a repairman. By using c0-semigroup theory of linear operators in the functional analysis, we prove that the system... 详细信息

关键词： Series-Parallel Repairable System c_0-semigroup Dynamic Solution

Well-Posedness of an N-Unit Series System with Finite Number of Vacations

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Journal of Applied Mathematics and Physics 2016年第8期4卷 1592-1599页

作者： Abdugeni Osman Abdukerim Haji college of Mathematics and Systems Science Xinjiang University Urumqi China

We investigate the solution of an N-unit series system with finite number of vacations. By using c0-semigroup theory of linear operators, we prove well-posedness and the existence of the unique positive dynamic soluti... 详细信息

关键词： N-Unit Series System c_0-semigroup Dynamic Solution Well-Posedness