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Asymptotic Stability of Gaver’s Parallel System Attended by a Cold Standby Unit and a Repairman with Multiple Vacations

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World Journal of Engineering and Technology 2015年第3期3卷 277-283页

作者： abdukerim haji College of Mathematics and System Sciences Xinjiang University Urumqi 830046 China

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.

关键词： Gaver’s Parallel Pystem C0-Semigroup Irreducibility Asymptotic Stability

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

Asymptotic Stability 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 2017年第1期5卷 185-193页

作者： Tursunjan Keyim abdukerim haji College of Mathematics and System Sciences Xinjiang University Urumqi China

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.

关键词： Series-Parallel Repairable System C0-Semigroup Irreducibility Asymptotic Stability

Well-Posedness of Gaver’s Parallel System Attended by a Cold Standby Unit and a Repairman with Multiple Vacations

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Journal of Applied Mathematics and Physics 2015年第7期3卷 821-827页

作者： abdukerim haji Bilikiz Yunus College of Mathematics and System Sciences Xinjiang University Urumqi 830046 China College of Mechanical Engineering Xinjiang University Urumqi 830008 China

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... 详细信息

关键词： Gaver’s Parallel Pystem C0-Semigroup Well-Posedness

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

Asymptotic Stability of the Dynamic Solution of an N-Unit Series System with Finite Number of Vacations

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Journal of Applied Mathematics and Physics 2018年第11期6卷 2202-2218页

作者： Abdugeni Osman abdukerim haji Askar Ablimit College of Mathematics and System Sciences Xinjiang University Urumqi China School of Mathematics and Physics Xinjiang Education Institute Urumqi China

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.

关键词： N-Unit Series System C0-Semigroup Irreducibility Asymptotic Stability