Boundary Stabilization of a Cosserat Elastic Body

Boundary stabilization of vibrating three‐dimensional Cosserat elastic solids are studied using mathematical tools, such as operator theory and semigroup techniques. The advantages of the boundary control laws for both boundary stabilization problems are investigated. The boundary stabilization problems are studied using a Lyapunov stability method and LaSalle's invariant set theorem. Numerical simulations are provided to illustrate the effectiveness and performance of the designed control scheme.     

Asymptotic stability for the Lamé system with fractional boundary damping

We consider a Lamé system damped by fractional boundary damping of Neumann type. We prove well-posedness by semigroup theory. Moreover, we prove stabilization by using multipliers method and Rellich type relation combined with the frequency domain method.     

半群上的一类陷门单向映射

本文首次给出半群Ｓ上的一类陷门单向映射，基于这类陷门单向映射，选择适当的半群Ｓ，可以建立公钥密码体制。     

Sufficient conditions for controllability of a class of distributed parameter systems

In the paper we present certain results on the question of controllability for (i) linear evolution equations (parabolic and hyperbolic) with distributed controls and (ii) a class of linear parabolic equations with boundary controls.     

基于分布参数模型的柔性臂变结构力控制

提出一种基于受约束柔性臂分布参数模型的麦结构力控稍方法,避免了集中参数模型的缺陷,解决了系统存在模型不确定性和外部干扰影响下的力控制问题.通过Lyapunov函数设计了系统的变结构控制器,其中滑模面设计为系统转动角、转动角速度和柔性臂根部应变的线性组合.利用线性算子半群理论和LaSalle不变集原理,证明了闭环系统的渐近稳定性.仿真结果验证了该方法的有效性.     

TL-Fuzzy半群

给出了TL－fuzzy半群,TL－fuzzy左（右）理想,TL－fuzzy双理想,TL－正则半群及TL－fuzzy正则半群的定义,讨论了他们的性质,这里L是任一给定的完备Brouwerian格,T是L上的任一分配的t－模。     

Compositions of maximal codes

The proposition “For composable thin codes Y and Z, the composition Y°Z is maximal if and only if Y and Z are maximal” put forward by J. Berstel and D. Perrin in their book “Theory of Codes” is well known. Is the proposition also true without the assumption that Y and Z are thin? We give an example showing that the answer is negative. Furthermore, several generalizations of the above proposition are also given.     

Automatic semigroups

The area of automatic groups has been one in which significant advances have been made in recent years. While it is clear that the definition of an automatic group can easily be extended to that of an automatic semigroup, there does not seem to have been a systematic investigation of such structures. It is the purpose of this paper to make such a study.We show that certain results from the group-theoretic situation hold in this wider context, such as the solvability of the word problem in quadratic time, although others do not, such as finite presentability. There are also situations which arise in the general theory of semigroups which do not occur when considering groups; for example, we show that a semigroup S is automatic if and only if S with a zero adjoined is automatic, and also that S is automatic if and only if S with an identity adjoined is automatic. We use this last result to show that any finitely generated subsemigroup of a free semigroup is automatic.     

Free poset algebras and combinatorics of cones

In Free poset Boolean algebra F(P ), uniqueness of normal form of non-zero elements is proved and the notion of support of a non-zero element is, therefore, well defined. An Inclusion–Exclusion-like formula is given by defining, for each non-zero element x, using support of x ∈F(P ) in a very natural way.      

The structure of pan-addition operator with pre-determined pan-multiplication

Based on the structure of general pan-multiplication operators and the theory of first order linear partial differential equations, we study the structure of pan-addition operators with pre-determined pan-multiplication operators. At first, we describe the structure of pan-addition operators under the ordinary multiplication. Then, with this structure in place, we derive the general representation for the structure of pan-addition operators.