二元关系的传递性和传递闭包探讨

探讨了二元关系传递性的判定和传递闭包的计算及其教学的有关问题 ,提出了中途点的概念 ,得到传递性在乘幂运算下的不变性 ,以及简化了计算传递闭包的算法 .     

On a conjecture of Brualdi and Shen on block transitive tournaments

The following conjecture of Brualdi and Shen is proven in this paper: let n be partitioned into natural numbers no one of which is greater than (n + 1) / 2. Then, given any sequence of wins for the players of some tournament among n players, there is a partition of the players into blocks with cardinalities given by those numbers, and a tournament with the given sequence of wins, that is transitive on the players within each block. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 215–230, 2003     

Kaplansky Density and Kadison Transitivity Theorems for Irreducible Representations of Real C＊-Algebras

We prove analogs of the Kaplansky Density Theorem and the Kadison Transitivity Theorem for irreducible representations of a real C＊-algebra on a real Hilbert space. Specifically, if a C＊-algebra is acting irreducibly on a real Hilbert space, then the Hilbert space has either a real, complex, or quaternionic structure with respect to which the density and transitivity theorems hold.     

λ型传递矩阵与多因素模糊决策

基于已知常用的模糊矩阵传递性概念定义了λ型传递。给出了它的几个等价条件。研究它的图论特征，指出λ型传递矩阵的圈都过强对边二元圈。随后证明了与全传递模糊矩阵的等价性。进一步研究与截矩阵的性质一致问题，证明了λ型传递满足一致性。最后给出λ型传递在模糊排充中的应用，表明它是一种新的实用的多因素模糊决策的数学模型。     

Robustly transitive actions of ℝ<Superscript>2</Superscript> on compact three manifolds

In this paper, we define robust transitivity for actions of ℝ² on closed connected orientable manifolds. We prove that if the ambient manifold is three dimensional and the dense orbit of a robustly transitive action is not planar, then the action is defined by an Anosov flow, i.e. its orbits coincide with the orbits of an Anosov flow.     

UNIFORM CONVERGENCE AND SEQUENCE OF MAPS ON A COMPACT METRIC SPACE WITH SOME CHAOTIC PROPERTIES

Recently, C. Tain and G. Chen introduced a new concept of sequence of time invariant function. In this paper we try to investigate the chaotic behavior of the uniform limit function f ： X →X of a sequence of continuous topologically transitive （in strongly successive way） functions fn ： X →X, where X is a compact interval. Surprisingly, we find that the uniform limit function is chaotic in the sense of Devaney. Lastly, we give an example to show that the denseness property of Devaney＇s definition is lost on the limit function.     

Generalized ergodicity

This paper introduces generalized ergodicity which contains ergodicity and Lipschitz ergodicity, proves the equivalence relation between generalized ergodicity and chain transitivity and gives its geometrical structure     

Uniform convergence and sequence of maps on a compact metric space with some chaotic properties

Recently, C. Tain and G. Chen introduced a new concept of sequence of time invariant function. In this paper we try to investigate the chaotic behavior of the uniform limit function f : X → X of a sequence of continuous topologically transitive (in strongly successive way) functions fn : X → X, where X is a compact interval. Surprisingly, we find that the uniform limit function is chaotic in the sense of Devaney. Lastly, we give an example to show that the denseness property of Devaney’s definition is lost on the limit function.     

有限群在某个极小子群共轭类上的传递性

有限群在某个极小子群共轭类上的某种传递性影响或决定群的构造.运用抽象群和置换群的理论得到:(1)如果有限群G共轭作用在它的所有极小子群上传递,G一定是循环P-群或广义四元数群;(2)如果有限群G在它的某个极小子群共轭类上二重传递,G是某些特殊的群的扩张;(3)如果有限群G是一个几乎单群,G在某个极小子群共轭类上二重传递,G的Socle一定是以下子群之一:PSL(2,P),PSU(3,P2),PSL(2,8).