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《Acta Analysis Functionalis Applicata》 2013-01
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Properties of the Operator of the Gnedenko System with Simple Vacations of a Repairman

SUN Wenyuan,ZHANG Xiaomin~*,LI Weiyuan,YIN Zhe,ZHANG Yufeng College of Science,Yanbian University,Yanji 133002,China  
We investigate the Gnedenko system which is an iV-unit series system supported by a warm standby unit and a simple-vacation repairman.Using Co-semigroup theory,we first prove the system operator is a densely defined resolvent positive operator.Then,we obtain the adjoint operator of the system operator and its domain.Furthermore,we prove that 0 is the growth bound of the system operator.Finally,we show that 0 is also the upper spectral bound of the system operator using the concept of cofinal and relative theory.
【CateGory Index】: O213.2
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