一类温贮备可修系统算子的性质
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摘要
研究了一类温贮备可修系统算子的性质.讨论了由两个不同型部件和一个修理工组成的温贮备可修系统模型,在该模型中引入了修理工可延误休假的概念.证明系统算子A+B是空间中稠密的预解正算子,通过求系统算子的共轭算子证明了0是其几何重数为1的特征值,并且证明算子A+B的增长界为0.运用预解正算子中共尾的概念,证明系统算子的谱上界也是0.最后结合预解正算子和C0半群的理论,证明系统动态解存在且唯一.
We investigate the Properties of a Warm Standby Redundant Repairable System.This paper discusses a model for the warm standby repairable system with two different units and one repairman,in which the conception of a repairman to delay vacation is introduced.By choosing state space and defining operators of systems,we transfer model into an abstract Cauchy problem.Studying the nature of the system operator,that is,using C0-semigroup theory,we first prove the system operator A+Bis a densely defined resolvent positive operator.Then we obtain the adjoint operator of the system operator and its domain.Furthermore,we prove that the eigenvalue of the adjoint operator and 0 is the growth bound of the system operator.We show that 0 is also the upper spectral bound of the system operator using the concept of cofinal and relative theory.Finally,the unique existence of the system solution is discussed by using C_0-semigroup theory and resolvent positive operator.
We investigate the Properties of a Warm Standby Redundant Repairable System.This paper discusses a model for the warm standby repairable system with two different units and one repairman,in which the conception of a repairman to delay vacation is introduced.By choosing state space and defining operators of systems,we transfer model into an abstract Cauchy problem.Studying the nature of the system operator,that is,using C0-semigroup theory,we first prove the system operator A+Bis a densely defined resolvent positive operator.Then we obtain the adjoint operator of the system operator and its domain.Furthermore,we prove that the eigenvalue of the adjoint operator and 0 is the growth bound of the system operator.We show that 0 is also the upper spectral bound of the system operator using the concept of cofinal and relative theory.Finally,the unique existence of the system solution is discussed by using C_0-semigroup theory and resolvent positive operator.
引文
[1]张晓丽,徐光甫,李伟源,等.两同型部件温贮备可修系统算子性质[J].数学的实践与认识,2014,44(3):236-244.
[2]吕文静,郑海鹰.修理工可延误休假的温贮备系统[J].温州大学学报(自然科学版),2014,35(4):8-16.
[3]孟娅丽,郑海鹰.修理工可多重休假的温贮备系统[J].浙江大学学报(理学版),2012,39(5):518-523.
[4]刘仁斌,唐应辉.具有多重延误休假的单部件可修系统[J].工程数学学报,2006,23(4):721-724.
[5]ZHANG Xin.Reliability Analysis of a Cold Standby Repairable System with Repairman Extra Work[J].Syst Sci Complex,2015,28:1015-1032.
[6]ARENDT W.Resolvent positive operators[J].Proc London Math Soc,1987,54(3):321-349.
[2]吕文静,郑海鹰.修理工可延误休假的温贮备系统[J].温州大学学报(自然科学版),2014,35(4):8-16.
[3]孟娅丽,郑海鹰.修理工可多重休假的温贮备系统[J].浙江大学学报(理学版),2012,39(5):518-523.
[4]刘仁斌,唐应辉.具有多重延误休假的单部件可修系统[J].工程数学学报,2006,23(4):721-724.
[5]ZHANG Xin.Reliability Analysis of a Cold Standby Repairable System with Repairman Extra Work[J].Syst Sci Complex,2015,28:1015-1032.
[6]ARENDT W.Resolvent positive operators[J].Proc London Math Soc,1987,54(3):321-349.