Properties Of The Main Operator Of The Coldstorage Of Two Same Unit Repairable System

Cold-maintain system is a very important system which is discussed in reliability theory, it is one of the main objects of the reliability of mathmatics.Following most of the applications,many literature are just related to the conversion of a Banach space with Cauchy problem for the processing. But for Banach space, we can not cite some inner product calculation similar to Euclidean space, which makes the processing model itself too thin, also the relationship between the variables is too pure.Therefore, this paper is existing models on Banach spaces to the Hilbert space, and proved that the two corresponding parallel conclusions:equality of the spectrum of and the growth of the space. Two kinds of space actually get consistent results. But the conclusion of Hilbert space has more value than the conclusion of Banach space. This is a try to improve space model and conclusions unchanged, its meaning is obvious.In the first chapter, we briefly review the status of research repairable systems at home and abroad as well as a brief introduction to the establishment of the Banach space model and The main research content and methods.The second chapter introduces the knowledge corresponding linear space and Hilbert space. In the third chapter, we use Co semigroup theory, proved that the system operator is densely defined resolvent positive operator, obtained conjugated system operator.The fourth chapter is about the existing of model on Banach space, to the new model of the abstract Cauchy problem on Hilbert space. Using spectral theory of regular operators, then the complex integrating was transformed into real integration, and get the same conclusion as the system on the model of Banach space. When we give the model changed from the Banach space to the Hilbert space, but the conclusion has not changed!...