有扭仿射李代数赋值模的某些性质

设g为有限维复单李代数,g^^[σ]为对应的有扭仿射李代数,U1,…,U,为不可约g-模,z1,…,zr为互不相同的非零复数．利用生成函数的方法证明赋值模U1（z1）×…Ur（zr）为g^^[σ]-模范畴E中不可约模并证明其同构定理．     

度量空间的大尺度几何与高指标问题(特约稿)

粗几何上的指标理论是＂非交换几何＂领域近年来非常活跃的研究分支,与几何、拓扑、算子代数、几何群论、Banach空间几何理论等都有密切联系。对该领域的若干思想、主要问题和部分最新研究进展进行综述性介绍。     

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.     

Formal Performance Modelling and Evaluation of an Adaptive Mechanism for Packetised Audio over the Internet

A case study is presented which concerns the design of an adaptive mechanism for packetised audio for use over the Internet. During the design process, the audio mechanism was modelled with the stochastically timed process algebra EMPA and analysed via simulation by the EMPA based software tool TwoTowers in order to predict the percentage of packets that are received in time for being played out. The predicted performance figures obtained from the algebraic model illustrated in advance the adequacy of the approach adopted in the design of the audio playout delay control mechanism. Based on these performance figures, it was possible to implement and develop the complete mechanism without incurring additional costs due to the late discovery of unexpected errors or inefficiency. Performance results obtained from experiments conducted on the field confirmed the predictive simulative results. Received March 1997 / Accepted in revised form July 1998     

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.     

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.     

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.     

ON TEMPORAL DEDUCTIVE DATABASES

This article introduces a temporal deductive database system featuring a logic programming language and an algebraic front-end. The language, called Temporal DATALOG, is an extension of DATALOG based on a linear-time temporal logic in which the flow of time is modeled by the set of natural numbers. Programs of Temporal DATALOG are considered as temporal deductive databases, specifying temporal relationships among data and providing base relations to the algebraic front-end. The minimum model of a given Temporal DATALOG program is regarded as the temporal database the program models intensionally. The algebraic front-end, called TRA, is a point-wise extension of the relational algebra upon the set of natural numbers. When needed during the evaluation of TRA expressions, slices of temporal relations over intervals can be retrieved from a given temporal deductive database by bottom-up evaluation strategies.
A modular extension of Temporal DATALOG is also proposed, through which temporal relations created during the evaluation of TRA expressions may be fed back to the deductive part for further manipulation. Modules therefore enable the algebra to have full access to the deductive capabilities of Temporal DATALOG and to extend it with nonstandard algebraic operators. This article also shows that the temporal operators of TRA can be simulated in Temporal DATALOG by program clauses.     

An object-oriented approach to Computer Integrated Systems

In recent years computers have been incorporated into large scale systems such as nuclear plant, flight control, and manufacturing systems. Such Computer Integrated Systems (CIS) normally consist of heterogeneous subsystems. The integration of heterogeneous subsystems requires that the subsystems be portable, inter-operable, and integrable at both software and hardware levels so that the integrated system should function properly. Objects and nets are proposed as the atomic elements of CIS's. An object is defined as a computational model of an arbitrary entity. Then three representation schemes of an object are introduced: algebraic, modular, and graphical. Two operations on objects,Composition andUnion, are introduced as means of combining two objects into a larger one. As an application of this approach, a Computer Integrated Manufacturing (CIM) system is represented as a network of objects.     

Huffman algebras for independent random variables

Based on a rearrangement inequality by Hardy, Littlewood, and Polya, we define two-operator algebras for independent random variables. These algebras are called Huffman algebras since the Huffman algorithm on these algebras produces an optimal binary tree that minimizes the weighted lengths of leaves. Many examples of such algebras are given. For the case with random weights of the leaves, we prove the optimality of the tree constructed by the power-of-2 rule, i.e., the Huffman algorithm assuming identical weights, when the weights of the leaves are independent and identically distributed.