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Asymptotic Stability of the Solution of a Cold Standby Repairable System

Author: FanWeiFeng
Tutor: ShenZiFei
School: Zhejiang Normal University
Course: Basic mathematics
Keywords: Cold Standby Compactness in Asymptotically stable Availability
CLC: O175.13
Type: Master's thesis
Year: 2007
Downloads: 54
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Abstract


This master's thesis, we study the asymptotic stability of two identical unit cold standby repairable system solution . In the first chapter , we briefly review the Repairable system research status and a brief introduction to the main research content and methods . In the second chapter , we introduce the use of supplementary variables and probability theory to establish two identical parts Cold Standby repairable differential - integral form of the mathematical model of the system , combined with the Volterra integral equation theory , the system is proved the existence and uniqueness of solutions . In the third chapter , we define the physical background of the research questions Banach space , Banach space defined , the appropriate definition of the system operator , to prove the generated C 0 semigroup is intended tight ; system operator spectrum points are located in the plane of the left half of the complex plane , and then obtained the imaginary smoke on the important conclusions addition to 0 outside without spectrum , to arrive at the asymptotic stability of the system solution . In the fourth chapter , we discuss as the reliability of the system one of the important indicators of the system steady state availability can be obtained directly by the steady-state solution of the standardized system .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Ordinary Differential Equations > Stability theory
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