A review on some classes of algebraic systems

ABSTRACT

In this paper, we review some algebraic control system. Precisely, linear and bilinear systems on Euclidean spaces and invariant and linear systems on Lie groups. The fourth classes of systems have a common issue: to any class, there exists an associated subgroup. From this object, we survey the controllability property. Especially, from those coming from our contribution to the theory.     

探针馈电圆柱共形微带天线阻抗特性的FDTD法分析

将圆柱坐标系下非分裂式理想匹配层吸收边界条件(UPML)引入到圆柱共形微带天线的全波分析中，并给出了其中的场量迭代方程，明显地减小了计算空间，简化了编程；提出了圆柱坐标系下考虑有限尺寸探针半径的新算法，使得计算结果更加精确；应用GPOF方法预估了时域晚时响应，使计算时间减少了70％～90％。本文给出的模型能够对任意多层圆柱共形结构的微带天线进行计算，因此对此类天线的CAD设计具有实际意义。     

Controllability of One Spin and Two Interacting Spins

Mathematics of Control, Signals, and Systems - ?We consider the problem of steering control for the systems of one spin ½ particle and two interacting spin ½ particles in an...     

Peirce algebras

We present a two-sorted algebra, called aPeirce algebra, of relations and sets interacting with each other. In a Peirce algebra, sets can combine with each other as in a Boolean algebra, relations can combine with each other as in a relation algebra, and in addition we have both a set-forming operator on relations (the Peirce product of Boolean modules) and a relation-forming operator on sets (a cylindrification operation). Two applications of Peirce algebras are given. The first points out that Peirce algebras provide a natural algebraic framework for modelling certain programming constructs. The second shows that the so-calledterminological logics arising in knowledge representation have evolved a semantics best described as a calculus of relations interacting with sets.     

An ideal topology type convergent theorem on scale effect algebras

The famous Antosik-Mikusinski convergent theorem on the Abel topological groups has very extensive applications in measure theory, summation theory and other analysis fields. In this paper, we establish the theorem on a class of effect algebras equipped with the ideal topology. This paper shows also that the ideal topology of effect algebras is a useful topology in studying the quantum logic the- ory.     

Space-time block codes which can be identified as rings

In this paper, we give a general criterion to determine when a complex space-time block code has a ring structure and then we provide a complete list of complex space-time block codes which have ring structures up to size 4.     

Equitone Predicate Algebras and Their Applications

Predicates that preserve their values on a larger (extended) body of data are called equitone. An algebra of such predicates is constructed, a system of its generators is specified, and a complete system of transformations of identities is defined. The results obtained are used for construction and investigation of complete classes of compositions of various types and levels of abstractions that are used in logics of partial predicates.     

Congruences and ideals in pseudoeffect algebras

This paper is devoted to congruences and ideals in pseudoeffect algebras. Let I be a normal ideal in a pseudoeffect algebra E. We show that: (1) the relation ~ _I induced by I is a congruence if and only if for every a∈E, I∩ [0,a] is upper directed; (2) the relation ~ _I induced by I is a strong congruence if and only if I is a normal weak Riesz ideal in a pseudoeffect algebra E. Moreover, we introduce a stronger concept of congruence—namely Riesz strong congruence—and we prove that, if I is a normal weak Riesz ideal in a pseudoeffect algebra E, then ~ _I is a Riesz strong congruence and, conversely, if ~ is a Riesz strong congruence, then I = [0]_~ is a normal weak Riesz ideal, and ~ _I = ~. This work was supported by the National Natural Science Foundation of China (Grant No. 10271069).     

What is a free name in a process algebra?

There are two popular approaches to specifying the semantics of process algebras: labelled transition semantics and reaction semantics. While the notion of free name is rather unproblematic for labelled transition semantics this is not so for reaction semantics in the presence of a structural congruence for unfolding recursive declarations.We show that the standard definition of free name is not preserved under the structural congruence. We then develop a fixed point approach to the set of free names and show that it is invariant under the structural congruence.     

再论变化电磁场中带电超微粒子的精确量子论

利用创新的SU(1 ,1 )Lie代数理论及SO(3)Lie代数理论 ,得到变化电磁场中带电超微粒子的精确量子论 ,由此进一步明确微观领域中的时空概念