一类冷贮备可修系统算子的性质  

Properties of Operators for a Class of Cold Standby Repairable Systems

作　　者：原文志[1] 寇玉芳 YUAN Wenzhi;KOU Yufang(Department of Mathematics,Taiyuan Normal University,Jinzhong 030619,China)

机构地区：[1]太原师范学院数学系,山西晋中030619

出　　处：《太原师范学院学报（自然科学版）》2021年第1期37-42,共6页Journal of Taiyuan Normal University:Natural Science Edition

摘　　要：冷贮备系统由一个修理工以及两个不同型部件组成,其中引入了修理工空闲状态.文章讨论了这个系统的算子性质.选取合适的状态空间且定义算子,首先证明系统算子是预解正算子,再证明0是特征值,而且得到算子的增长界和谱上界均是0.最后根据C 0半群理论得到系统的动态解的性质是存在唯一的.The cold standby system consists of a repairman and two different types of components,in which the Repairman idle state is introduced.In this paper,the operator properties of the system are discussed.By choosing a suitable state space and defining the operator,it is proved that the system operator is a resolvent positive operator,then it is proved that 0 is an eigenvalue,moreover,the growth bounds and spectral upper bounds of the operator are both 0.Finally,according to the theory of C 0 semigroups,the existence and uniqueness of the dynamic solution of the system are obtained.

关 键 词：预解正算子 增长界 谱上界 C0半群 动态解 

分 类 号：O177[理学—数学]