非均质Timoshenko梁的边界镇定

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.     

工作休假和休假中止的M/G/1排队模型的适定性

主要研究工作休假和休假中止的M/G/1排队系统,首先将对应于此系统的数学模型转化为抽象Cauchy问题,其次证明对应于此排队模型的主算子生成正压缩C0半群T(t),然后证明T(t)是局部等距的,最后证明此模型存在唯一的非负时间依赖解。     

具有热储备的并行可修复系统指数稳定性分析

应用泛函分析的方法讨论了有两个相同部件和一个热储备的并行可修复系统的指数稳定性.我们通过分析系统算子生成C0半群的本质谱增长阶,证明了该半群是拟紧的.此外,该半群还是不可约的.于是作为半群拟紧性和不可约性的直接结果,得到了系统的时间依赖解指数收敛到其静态解,并且该静态解即为系统算子简单特征值0对应的正的特征向量.     

C_0-半群的谱特征

本文利用(C,1)求和法得到了Banach空间中的C_0-半群e~(At)的谱特征性质和增长阶W_0(A)=的计算公式,我们的主要结果为定理2.2和定理2.3。     

线性控制系统对小时滞的鲁棒能控性

对于在Banach空间中线性控制系统对时滞的鲁棒能控性．给出一个充分条件,在这个条件下,证明对一个能控的线性系统施加某个小的时滞扰动之后,其能控性保持不变．     

积分半群的表示及其在抽象积微分方程中的应用

讨论了积分半群与C0半群的关系,给出了用一组C0半群的积分序列的极限表示积分半群的表示公式.利用该公式证明了积分半群的其它表示式.最后用该公式给出了求解一类抽象积微分方程的新方法.     

修理工可单重休假的带有一个冷贮备部件的Gaver并联系统的时间依赖解的渐进行为

研究修理工可单重休假的带有一个冷贮备部件的Gaver并联系统的时间依赖解.运用C₀-半群理论与算子理论研究该模型相应算子的谱的特征,获得了该系统的时间依赖解强收敛于该系统的稳态解.     

由一个可靠机器,一个不可靠机器与一个具有有限容量的缓冲库构成的生产线的进一步研究

研究了由一个可靠机器，一个不可靠机器与一个具有有限容量的缓冲库构成的生产线．该生产线由具有积分边界条件的一组偏微分方程组描述．首先证明此系统的主算子生成的G0-半群是拟紧算子，然后证明0是该主算子及其共轭算子的几何重数为1的特征值，最后推出此C0-半群指数收敛于一个投影算子．作为特殊情况，推出该模型的时间依赖解强收敛于它的稳态解．     

Spectrum of the Operator Corresponding to the M/M/1 Queueing Model with Vacations and Multiple Phases of Operation and Application

We describe the point spectrum of the operator which corresponds to the M/M/1 queueing model with vacations and multiple phases of operation. Then by using this result we prove that the essential growth bound of the C₀-semigroup generated by the operator is 0, the C₀-semigroup is not compact, not eventually compact, even not quasi-compact. Moreover, we verify that it is impossible that the time-dependent solution of the M/M/1 queueing model with vacations and multiple phases of operation exponentially converges to its steady-state solution. In addition, we obtain the spectral radius and essential spectral radius of the C₀-semigroup. Lastly, we discuss other spectrum of the operator and obtain a set which belongs to the union of its continuous spectrum and residual spectrum.     

Uniform Compact Attractors for a Nonlinear Non-Autonomous Equation of Viscoelasticity

In this paper we prove the regularity, exponential stability of global solutions and existence of uniform compact attractors of semiprocesses, generated by the global solutions, of a two-parameter family of operators for a nonlinear onedimensional non-autonomous equation of viscoelasticity. We employ the properties of the analytic semigroup to show the compactness for the semiprocess generated by the global solutions.