COMPLEX SYMMETRIC C_(0)-SEMIGROUPS ON THE WEIGHTED HARDY SPACES H_(γ)(D)

In this paper,we study the complex symmetric C_(0)-semigroups of weighted composition operators W_(ψ,φ)on the weighted Hardy spaces H_(γ) of the unit disk D.It is well-known that there are only two classes of weighted composition conjugations A_(u,v) on H_(γ)(D):either C_(1) or C_(2).We completely characterize C_(1)-symmetric(C_(2)-symmetric)C_(0)-semigroups of weighted composition operators W_(ψ,φ) on H_(γ)(D).

On U-ample ω-semigroups

The investigation of U-ample ω-semigroups is initiated. After obtaining some properties of such semigroups, a structure of U-ample ω-semigroups is established. It is proved that a semigroup is a U-ample ω-semigroup if and only if it can be expressed by WBR（T, 0）, namely, the weakly Bruck-Reilly extensions of a monoid T. This result not only extends and amplifies the structure theorem of bisimple inverse ω-semigroups given by N. R. Reilly, but also generalizes the structure theorem of ,-bisimple type A ω-semigroups given by U. Asibong-Ibe in 1985.

A Class of Regular Simple ω2-semigroups-Ⅱ

In this paper, we study regular simple ω2-semigroups in which D｜Es = Wd by the generalized Bruck-Reilly extension and obtain its structure theorem.

A Class of ＊-simple Type A ω~2 -semigroups （Ⅰ）

In this paper, we study ＊-simple type A ω2 -semigroups in which D＊= D and D＊｜ES = Md by the generalized Bruck-Reilly extension and obtain its structure theorem. We also obtain a criterion for isomorphisms of two such semigroups.

On Commutative Δ-Semigroups

In this paper entitled on commutative Delta-Semigroups, we have obtained important results on commutative Δ-semigroups.

The Isomorphism Theorem of Regular Bisimple ω2-semigroups

In this paper we study the isomorphisms of two regular bisimple ω2- semigroups and obtain a criterion for two such semigroups to be isomorphic.

Exponential Stabilization for C_0-Semigroups Under Compact Perturbation

It is proved that a system under compact perturbation cannot be uniformly exponentially stable for an isometric C0-semigroup or a C0-group with polynomial growth for negative time in a Banach space. The results extend and improve the corresponding results of previous literature.

C_0-Semigroup Method of the Density Evolution Equation for M/M/∞ Model

In this paper, the existence, uniqueness, and asymptotic behavior of the solution of the density evolution equation for M/M/∞ model was studied by the semigroup theory of linear operators.

Structural Theorem for Completely Simple Г-Semigroups and Г-Semigroups with a Completely Simple Г-Kernel

We prove structural theorem for completely simple Г-semigroups and semi- groups with a completely simple Г-kernel.

Reliability Analysis of a Cold Standby Repairable System with Repairman Extra Work

This paper deals with a cold standby repairman who can do extra work in idle time. The repairable system with two identical units and one authors are devoted to studying the unique existence and exponential stability of the system solution. C0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by using the theory of resolvent positive operator, the authors derive that dynamic solution of the system exponentially converges to its steady-state one which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Some reliability indices of the system are discussed with a different method from traditional one. The authors also make a profit analysis to determine the optimal service time outside the system to maximize the system profit.

DIFFERENTIAL VARIATIONAL INEQUALITIES IN INFINITE BANACH SPACES

In this paper,we consider a new differential variational inequality（DVI,for short）which is composed of an evolution equation and a variational inequality in infinite Banach spaces.This kind of problems may be regarded as a special feedback control problem.Based on the Browder＇s theorem and the optimal control theory,we show the existence of solutions to the mentioned problem.

MIXED VARIATIONAL INEQUALITIES DRIVEN BY FRACTIONAL EVOLUTIONARY EQUATIONS

The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation in the framework of Banach spaces. Using discrete approximation approach, an existence theorem of solutions for the inequality is established under some suitable assumptions.

Complex Symmetric C0-semigroups on A^2(C+)

In this paper,we study complex symmetric C0-semigroups on the Bergman space A^2(C+) of the right half-plane C+.In contrast to the classical case,we prove that the only involutive composition operator on A^2(C+) is the identity operator,and the class of J-symmetric composition operators does not coincide with the class of normal composition operators.In addition,we divide semigroups{φt}of linear fractional self-maps of C+into two classes.We show that the associated composition operator semigroup{Tt}is strongly continuous and identify its infinitesimal generator.As an application,we characterize Jσ-symmetric C0-semigroups of composition operators on A^2(C+).

On Some Subsemigroups of the 4-cyclic Semigroup-Ⅱ

In this paper, we study subsemigroups Bd,o of the 4-cyclic semigroup Bω2 and characterize the Green＇s relations of Bd,o. We show that, up to isomorphism, the only fundamental simple inverse w2-semigroups such that D│E（s） =Md are the semigroupsBd,o（d = 1, 2, 3,... ）.

Asymptotic Stability of the Dynamic Solution of an N-Unit Series System with Finite Number of Vacations

We investigate an N-unit series system with finite number of vacations. By analyzing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system operator we prove that the dynamic solution converges strongly to the steady state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.

Existence and Uniqueness of the Dynamic Solution of a Series-Parallel Repairable System Consisting of Three-Unit with Multiple Vacations of a Repairman

We investigate a series-parallel repairable system consisting of three-unit with multiple vacations of a repairman. By using C0-semigroup theory of linear operators in the functional analysis, we prove that the system is well-posed and has a unique positive dynamic solution.

Well-Posedness of an N-Unit Series System with Finite Number of Vacations

We investigate the solution of an N-unit series system with finite number of vacations. By using C0-semigroup theory of linear operators, we prove well-posedness and the existence of the unique positive dynamic solution of the system.

BOUNDARY STABILIZATION OF NONUNIFORM TIMOSHENKO BEAM

In this paper,the boundary stabilization of the Timoshenko equation of a nonuniform beam,with clamped boundary condition at one end and with bending moment and shear force controls at the other end, is considered.It is proved that the system is exponentially stabilizable when the bending moment and shear force controls are simultaneously applied.The frequency domain method and the multiplier technique are used.

Differentiability of the Pritchard-Salamon systems with admissible state-feedback

Many papers on a wide range of control problems for Pritchard-Salamon systems have appeared and many of its important mathematical and system theoretical properties have been revealed. This paper deals with the differentiability of the Pritchard-Salamon system with admissible state-feedback. Spectrum analysis showed that under definite condition, the unbounded perturbation semigroup of the Pritchard-Salamon system is eventually differentiable.

ON THE TRANSPORT EQUATION WITH INTEGRAL BOUNDARY CONDITIONS AND ITS CONSERVAIVE LAW

The well-posedness for the time-dependent neutron transport equationwith integral boundary conditions is established in L^1 space. Some spectral propertiesof the transport operator are discussed, the dominant eigenvalue is proved existing,and furthermore, the conservative law of migrating particle numbers is established.