弹性弦Dirichlet边界反馈控制的镇定与Riesz基生成

本文通过一端固定 ,一端 Dirichlet边界控制的一维波动方程说明系统是 Salamon- W eiss意义下适定和正则的 .由此说明 ,由 J.L.Lions引入的用于研究双曲方程精确可控性的 H ilbert唯一性方法是控制论中著名的对偶原理 .我们讨论了系统的指数镇定及闭环系统的广义本征函数生成 Riesz基和谱确定增长条件 .我们希望通过本文使读者对目前线性偏微分控制理论的一个新动向有一基本的了解 .     

P-反演半群上的正则P-同余

令S(P)为P-反演半群，本文借助于P-核正规系来刻画S(P)上的强P-同余，证明了S(P)上的任一正则P-同余可以决定S(P)的一个P-核正规系；反之，S(P)的任一P-核正规系可以决定S(P)上的一个正则P-同余．     

Controllability of Nonlinear Systems in Banach Spaces: A Survey

This paper presents a survey on research using fixed-point theorems and semigroup theory to study the controllability of nonlinear systems and functional integrodifferential systems in Banach spaces. Also discussed is the use of this technique in K-controllability and boundary controllability problems for nonlinear systems and integrodifferential systems in abstract spaces.     

Capture and escape from resonance in the dynamics of the rigid body in viscous medium

Summary The problem of capture and escape from resonance generally arises when certain nonlinear integrable Hamiltonian systems are subjected to non-Hamiltonian perturbation. The essential features of this problem are independent of the nature of the system under consideration. As an example we examine in detail the abovementioned resonance phenomena in rotational motions of a rigid body in a viscous medium. Our analysis is based on the averaging method. Conditions for the existence of the motions captured into resonance are derived. Scattering of the phase trajectories is estimated in the case of passage through resonance without capture.     

Les triplets de la variété de Grassmann G2(R6)

It is shown that a triple of two-dimensional planes in R⁶ is determined up to isometry by nine angular invariants – the six critical angles and the three angles between the critical bases in each plane – and four signs. Conditions of existence of these triples are then analyzed. These results are used to study some noteworthy triples.     

扭环粘正n棱柱外侧面数的确定

本文给出了一个确定扭环粘正 n棱柱外侧面数的简洁且具有一般性的结论 ,它可以看成是麦比乌斯带在一定意义下的推广 .对该棱柱的其它性质也进行了讨论 .     

关于拟内正则序半群

对拟内正则序半群给出了在理想和格林关系理论方面的若干刻划。这些刻划推广和扩充了由N．Kehayopulu给出的对内正则序半群的刻划．     

On Complexity of the Word Problem for Finitely Presented Commutative Semigroups

The word problem is tractable on a real-time Turing machine for every finitely presented commutative semigroup.     

积分半群与几个排队模型的适定性

应用积分半群理论证明M／G^k,B/1排隐模型的时间依赖解的存在惟一性。由此推出M／G^B/1和M／G／1排队模型的时间依赖解的存在惟一性     

群的正则带的拟强半格分解

推广了半群的强半格分解的定义,得到了半群的拟强半格分解,并证明了完全正则半群为群 的正则(或右拟正规)带当且仅当它是完全单半群的拟强半格(且 )).