In this paper,the author study the spectrum of high rank differential operators T (n) (t) of C 0 Semigroup T(t) ,given an approach to construct the spectral set opetator T (n) (t) ,and discussed the relat...In this paper,the author study the spectrum of high rank differential operators T (n) (t) of C 0 Semigroup T(t) ,given an approach to construct the spectral set opetator T (n) (t) ,and discussed the relation between the spectral points of both T (n) (t) and infinitesimal generator A of T(t) .展开更多
In this paper,we consider a multi-state device redundant systems with common-cause failures and one standby unit. We proved C0-semigroup generated by the system operator is quasi-compact by analyzing its spectrum and ...In this paper,we consider a multi-state device redundant systems with common-cause failures and one standby unit. We proved C0-semigroup generated by the system operator is quasi-compact by analyzing its spectrum and estimating essential growth bound semi-group generated by this system, 0 is an isolated eigenvalue with algebra multiply one. Moreover, we prove it is also irreducible. So we obtain the time-dependent solution exponentially converges to the steady-state solution.展开更多
The exponential stability of a reparable system with two types of repair facilities is discussed in this paper. We present that the c0-semigroup generated by the system operator is quasi-compact and irreducible. It is...The exponential stability of a reparable system with two types of repair facilities is discussed in this paper. We present that the c0-semigroup generated by the system operator is quasi-compact and irreducible. It is known that 0 is a simple eigenvalue of the system operator. In combination with this, we obtain that the time-dependent solution exponentially converges to the steady-state solution, which is the positive eigenfuction corresponding to the simple eigenvalue 0.展开更多
文摘In this paper,the author study the spectrum of high rank differential operators T (n) (t) of C 0 Semigroup T(t) ,given an approach to construct the spectral set opetator T (n) (t) ,and discussed the relation between the spectral points of both T (n) (t) and infinitesimal generator A of T(t) .
文摘In this paper,we consider a multi-state device redundant systems with common-cause failures and one standby unit. We proved C0-semigroup generated by the system operator is quasi-compact by analyzing its spectrum and estimating essential growth bound semi-group generated by this system, 0 is an isolated eigenvalue with algebra multiply one. Moreover, we prove it is also irreducible. So we obtain the time-dependent solution exponentially converges to the steady-state solution.
文摘The exponential stability of a reparable system with two types of repair facilities is discussed in this paper. We present that the c0-semigroup generated by the system operator is quasi-compact and irreducible. It is known that 0 is a simple eigenvalue of the system operator. In combination with this, we obtain that the time-dependent solution exponentially converges to the steady-state solution, which is the positive eigenfuction corresponding to the simple eigenvalue 0.
