On pseudo-BL algebras and BCC-algebras

We further study the filter theory of pseudo-BL algebras. We give some equivalent conditions of filter, normal filter and Boolean filter. We introduce the notion of pseudo MV-filter, pseudo-G filter and characterize Boolean algebras, pseudo-MV algebras and pseudo Gödel algebras (i.e. Gödel algebras) in pseudo-BL algebras. We establish the connections between BCC-algebras, pseudo-BCK algebras, pseudo-BL algebras and weak pseudo-BL algebras (pseudo-MTL algebras).     

Semirings and pseudo MV algebras

In this paper, we describe the relationships between pseudo MV algebras and semirings. We also give definitions of automata on lattice ordered semirings, prove that the family of K-Languages is closed under union, and discuss the conditions for the closedness of families of K-languages under intersection, generalized intersection and reversal operations.     

State space reduction by non-standard semantics for deadlock analysis

In recent years many techniques have been developed for automatically verifying concurrent systems and most of them are based on the representation of the concurrent system by means of a transition system. State explosion is one of the most serious problems of this approach: often the prohibitive number of states renders the verification inefficient and, in some cases, impossible.

We propose a method for reducing the state space of the transition system corresponding to a CCS process that suites deadlock analysis. The reduced transition system is generated by means of a non-standard operational semantics containing a set of rules which are, in some sense, an abstraction, preserving deadlock freeness, of the inference rules of the standard semantics. Our method does not build the standard transition system, but directly generates an abstract system with a fewer number of states, so saving memory space. We characterize a class of processes whose abstract transition system is not exponential in the number of parallel components.     

Finite dimensional filters with non-linear drift IX Construction of finite dimensional estimation algebras of non-maximal rank

The idea of using estimation algebra to construct finite-dimensional nonlinear filters was first proposed by Brockett and Mitter independently. It has proven to be an invaluable tool in the study of nonlinear filtering problem. In 1983, Brockett proposed to classify all finite-dimensional estimation algebras. In this paper, we give the construction of finite-dimensional estimation algebras of non-maximal rank. These non-maximal rank finite-dimensional estimation algebras play an important role in Brockett's classification problem.     

Semiring induced valuation algebras: Exact and approximate local computation algorithms

Local computation in join trees or acyclic hypertrees has been shown to be linked to a particular algebraic structure, called valuation algebra. There are many models of this algebraic structure ranging from probability theory to numerical analysis, relational databases and various classical and non-classical logics. It turns out that many interesting models of valuation algebras may be derived from semiring valued mappings. In this paper we study how valuation algebras are induced by semirings and how the structure of the valuation algebra is related to the algebraic structure of the semiring. In particular, c-semirings with idempotent multiplication induce idempotent valuation algebras and therefore permit particularly efficient architectures for local computation. Also important are semirings whose multiplicative semigroup is embedded in a union of groups. They induce valuation algebras with a partially defined division. For these valuation algebras, the well-known architectures for Bayesian networks apply. We also extend the general computational framework to allow derivation of bounds and approximations, for when exact computation is not feasible.     

R_0代数的可证等价类

讨论了R0代数的滤子以及相应的可证等价类.在R0代数里给出了一些滤子的具体例子,得到:F是R0代数M的超滤当且仅当F是M的固执滤子;当F是R0代数的蕴涵滤子时,M/F是布尔代数;当F是R0代数的极大布尔滤子时,M/F是只有两个元的布尔代数.     

三角代数上中心化子的刻画

设[T]是一个三角代数,[φ:T→T]是一个可加映射。证明了如果存在正整数[m,n,r],使得[(m+n)φ(ar+1)-(mφ(a)ar+][narφ(a))∈Z(T)]对任意的[a∈T]成立,那么存在[λ∈Z(T)],使得对任意的[a∈T,]有[φ(a)=λa]。     

空间弹性变形构件的李群和李代数分析方法

重点研究了具有三维空间弹性变形的杆件,即杆件同时受弯曲、拉伸和扭转等力作用而发生空间变形的李群和李代数理论描述问题。将杆件任意一点处的弹性变形与力的关系进行分析得到系统的空间变形柔度矩阵,并通过对弹性势能的分析,进一步得到了弹性杆件系统的空间变形的柔性密度。结合Rayleigh-Ritz法计算了系统的特征频率。阐明了所用理论方法解决空间弹性变形杆件问题的方便和有效性,并以空间变形简化处理为简单变形的传统方法进行了仿真结果的分析对比。