粗糙有限状态机的分解

利用代数的方法研究了粗糙有限状态机的可恢复性、连通性与可分离性等代数性质,得到了一个粗糙有限状态机是可恢复的当且仅当它的每一个准素粗糙子有限状态机都是强连通的当且仅当其每一个单生成粗糙子有限状态机都是准素的当且仅当其每一个非空连通粗糙子有限状态机都是准素的,给出了粗糙有限状态机不是连通的的充分必要条件,讨论了粗糙有限状态机的一些分解性质。     

模糊有限状态机的商与同态北大核心

文章利用模糊有限状态机的容许划分讨论了模糊有限状态机的商与同态问题,得到了在强满同态或强同构意义下模糊有限状态机之间的关系,以及它们的商模糊有限状态机的相互关系,获得了模糊有限状态机的同态分解定理,给出了可识别集的一些性质。     

双极模糊有限状态机的半群

利用双极模糊集的定义,引入了双极模糊有限状态机的两种同余关系,刻画了这两种同余关系的性质,讨论了由这两种同余关系产生的双极模糊有限状态机的半群的一些性质,给出了两种半群之间的关系。     

模糊有限状态机的一些性质

讨论模糊有限状态机的一些代数性质,得到模糊有限状态机在同态作用下子系统(强子系统)的前像仍是子系统(强子系统),证明若两个模糊有限状态机之间存在满足一定条件的同态映射时,前一个模糊有限状态机是强连通的(循环的),则后一个模糊有限状态机也是强连通的(循环的),且若这个同态是强满同态,则其中一个模糊有限状态机是完全的当且仅当另一个模糊有限状态机是完全的。对模糊有限状态机的积与原来的模糊有限状态机的完全性、强连通性、循环性、交换性等关系也进行讨论,得到一些结果。     

双极模糊有限状态机的代数刻画

利用双极模糊集的定义,提出了完全的,循环的,强连通的,可恢复的双极模糊有限状态机,双极模糊有限状态机的子机的概念。讨论了双极模糊有限状态机在同态作用下的一些性质,刻画了强连通的与可恢复的双极模糊有限状态机的性质。     

模糊有限状态机笛卡尔合成的一些结果

讨论了模糊有限状态机的笛卡尔合成的一些性质,得到了模糊有限状态机的笛卡尔合成在强同构意义下满足交换律,结合律,讨论了模糊有限状态机的笛卡尔合成与其因子在子系统(强子系统),自由子集,基等方面的相似的结构性质,给出了模糊有限状态机的笛卡尔合成的准素子机分解,证明了模糊有限状态机的笛卡尔合成的容许关系的投影是其因子的容许关系.     

有限型流形上的粗糙奇异积分

探讨了沿有限型曲面的粗糙奇异积分算子在Triebel-Lizorkin空间和Besov空间上的有界性,建立了该算子的l~q值不等式.     

循环模糊有限状态机的半群和同态

定义了循环模糊有限状态机M=(Q,X,μ)输入字集X*上的右同余关系,讨论了其等价类做成的半群E(M)的性质,及以该半群的子集为状态集的循环模糊有限状态机(M)与原循环模糊有限状态机M的同态关系,得出了在某些条件下,(M)与M是强同构的.     

粗糙不变子群的若干性质与粗糙商群

讨论粗糙集理论在代数系统——群上的应用。基于有关粗糙群、粗糙子群和粗糙不变子群的基本概念以及粗糙子群的一些性质和有关粗糙不变子群的定理，讨论了粗糙不变子群的若干性质和粗糙商群的概念，并给出了这些性质的严格证明。     

Fuzzy粗糙半群的Fuzzy粗糙同态与同构

给出Fuzzy粗糙半群与Fuzzy粗糙同态的定义,并讨论Fuzzy粗糙半群的Fuzzy粗糙同态与Fuzzy粗糙商半群的Fuzzy粗糙同构。     

A Finite Field Framework for Modeling,Analysis and Control of Finite State Automata

In this paper, we address the modeling, analysis and control of finite state automata, which represent a standard class of discrete event systems. As opposed to graph theoretical methods, we consider an algebraic framework that resides on the finite field <formula form="inline">${\Op F}_2$</formula> which is defined on a set of two elements with the operations addition and multiplication, both carried out modulo 2. The key characteristic of the model is its functional completeness in the sense that it is capable of describing most of the finite state automata in use, including non-deterministic and partially defined automata. Starting from a graphical representation of an automaton and applying techniques from Boolean algebra, we derive the transition relation of our finite field model. For cases in which the transition relation is linear, we develop means for treating the main issues in the analysis of the cyclic behavior of automata. This involves the computation of the elementary divisor polynomials of the system dynamics, and the periods of these polynomials, which are shown to completely determine the cyclic structure of the state space of the underlying linear system. Dealing with non-autonomous linear systems with inputs, we use the notion of feedback in order to specify a desired cyclic behavior of the automaton in the closed loop. The computation of an appropriate state feedback is achieved by introducing an image domain and adopting the well-established polynomial matrix method to linear discrete systems over the finite field <formula form="inline">${\Op F}_2$</formula>. Examples illustrate the main steps of our method.     

Computing the throughput of Concatenation State Machines

Concatenation State Machine (CSM) is a labeled directed And–Or graph representing a deterministic push-down transducer. In the high-performance version of CSM, labels associated to edges are words (rather than letters) over the input alphabet. The throughput of a path p is defined as the sum of the lengths of the labels of the path, divided by the number of edges of p. The throughput of a CSM M is defined as the infimum of the throughput of all accepting paths of M. In this paper we give an $\mathrm{O}(nm\log (\frac{\mathit{max}-\mathit{min}}{\epsilon }))$ algorithm, computing an ε-approximation of the throughput of a CSM M, where n is the number of nodes, m is the number of edges, and max (min) is the maximum (respectively, minimum) of the lengths of the edge labels of M. While we have been interested in a particular case of an And–Or graph representing a transducer, we have actually solved the following problem: if a real weight function is defined on the edges of an And–Or graph G, we compute an ε-approximation of the infimum of the complete hyper-path mean weights of G. This problem, if restricted to digraphs, is strongly connected to the problem of finding the minimum cycle mean.     

Quantah的连通性

The concepts of connectedness and locally connectedness is introduced for right-side idempotent quantales. Some properties of connected quantale are studied, and then the equivalent characterization of connected quantale is also given.     

Connectedness of curve complex of surface

For a closed orientable surface Sg of genus not smaller than 2,C(Sg) is the curve complex on S g whose vertices consist of the isotopy classes of nontrivial circles on Sg. It has been showed that any two vertices in C(Sg) can be connected by an edge path,and C(Sg) has an infinite diameter. We show that for 0 ≤i≤3g-5,two i-simplices can be connected by an(i +1)-path in C(Sg),and the diameter of C(Sg) under such a distance is infinite.     

Interior Operators and Topological Connectedness

Abstract

A categorical notion of interior operator is used in topology to define connectedness and disconnectedness with respect to an interior operator. A commutative diagram of Galois connections is used to show a relationship between these notions and Arhangelskii and Wiegandt's notions of connectedness and disconnectedness with respect to a subclass of topological spaces. Examples are included.     

Contractibility and Connectedness of Efficient Point Sets

Using the technique of space theory and set-valued analysis, we establish contractibility results for efficient point sets in a locally convex space and a path connectedness result for a positive proper efficient point set in a reflexive space. We also prove a connectedness result for a positive proper efficient point set in a locally convex space; as an application, we give a connectedness result for an efficient solution set in a locally convex space.     

直觉模糊有限状态机的积

利用代数方法给出直觉模糊有限状态机的直觉笛卡尔积、直觉直积、直觉限制直积、直觉圈积、直觉级联积构造方法,并且讨论了它们的代数性质,同时探讨了直觉模糊有限状态机的直觉限制直积的覆盖,级联积的可分离的,以及利用直觉模糊变换半群探索了直觉圈积的结合性.     

超空间2^X的连通性及其相关性质

研究了赋予Vietoris拓扑的超空间2X的连通性及其相关性质.这改进了Micheal[1]的一个定理的结论.