关于拓扑BCI-代数

目的 为研究拓扑BCI 代数的拓扑子代数、拓扑理想和拓扑同态的概念。试图在代数结构中嵌入拓扑结构。方法 将拓扑方法和代数方法结合起来,在代数结构中引入了拓扑连续概念。结果 得到了拓扑BCI 代数的拓扑子代数、拓扑理想和拓扑同态的一些相关性质。结论 通过理论分析表明在BCI 代数中嵌入拓扑结构是可行的也是有意义的。

Inductive Topologies of L-fuzzy Topological Vector Spaces

In this paper, using the theory of L _fuzzy topological vector spaces [1]-[6] , we study some properties of L _fuzzy inductive topologies determined by a family of L _fuzzy linerar order_homomorphisms [2] of L _ftvs, and give a characterization of inductive topologies determined by a single FLOH. As an application of this results, we prove that the quotient space of L _ftvs is also L _ftvs.

Lattice Im plication Homom orphism inIm plication Filter Spaces

In this paper,we investigate some special properties of lattice implication homomorphism in implication filter spaces. We show that lattice implication homomorphism is a continuous function with respect to implication filter topology. Moreover,we give a structural characterstic of left translation topology and right translation topology,which finally leads to the structural characteristics of product topology.

Effects of Scale-Free Topological Properties on Dynamical Synchronization and Control in Coupled Map Lattices

In the paper, we study effects of scale-free （SF） topology on dynamical synchronization and control in coupled map lattices （CIVIL）. Our strategy is to apply three feedback control methods, including constant feedback and two types of time-delayed feedback, to a small fraction of network nodes to reach desired synchronous state. Two controlled bifurcation diagrams verses feedback strength are obtained respectively. It is found that the value of critical feedback strength γc for the first time-delayed feedback control is increased linearly as e is increased linearly. The GML with SF loses synchronization and intermittency occurs if γ 〉 γc. Numerical examples are presented to demonstrate all results.

柔拓扑空间的连通性

研究了柔拓扑空间的连通性,在柔拓扑空间中定义了隔离柔集,利用隔离柔集给出了连通柔拓扑空间和连通柔集的概念,并为连通柔拓扑空间提供了等价的定义。通过引入了柔拓扑空间之间的连续序同态,证明了柔拓扑空间的连通性在连续序同态下具有不变性,最后得出了柔拓扑空间连通的几个充分条件。

MULTI-AGENT TRACKING OF A HIGH-DIMENSIONAL ACTIVE LEADER WITH SWITCHING TOPOLOGY

This paper considers a multi-agent tracking problem for a high-dimensional active leaderand variable interconnection topology. The state of the leader not only keeps changing but also maynot be measured. To estimate the state such a leader individually, a neighbor-based local controllertogether with a neighbor-based state-estimation rule is given for each autonomous agent. Then, theauthors prove that, with the help of a constructed common Lyapunov function (CLF), each agent cantrack the active leader with unmeasurable states. Finally, the authors explicitly construct a CLF foran active leader with unknown periodic input for illustration.

Topology of unitary groups and the prime orders of binomial coefficients

Let c : SU(n) → PSU(n) = SU(n)/Zn be the quotient map of the special unitary group SU(n) by its center subgroup Z_n. We determine the induced homomorphism c*: H*(PSU(n)) → H*(SU(n)) on cohomologies by computing with the prime orders of binomial coefficients.