平均跟踪与伪轨跟踪

证明了紧致度量空间中有伪轨跟踪的distal同胚不具有平均跟踪性,并给出了有平均跟踪性的同胚是极小的一个充分条件。     

kpm阶2-弧传递图

2-弧传递图是对称图类的一个重要的子类,而拟本原和双拟本原的2-弧传递图在2-弧传递图的研究中具有最基本的意义．文中对阶为kp^m（k,p是素数,k≠p,m≥2是整数)的基本2-孤传递图进行了研究。获得了下列结果：(1)kp^m阶G-拟本原的2-弧传递图是几乎单的．(2)对2p^m阶和2^mk阶双拟本原的2-弧传递图的分类进行了刻划,确定了其自同构群的基柱．     

On transitive Cayley graphs of strong semilattices of right (left) groups

We investigate Cayley graphs of strong semilattices of right (left) groups, of right (left) zero semigroups, and of groups. We show under which conditions they enjoy the property of automorphism vertex transitivity in analogy to Cayley graphs of groups.     

CHAOS AND TOPOLOGICAL MIXING OF TREE MAPS

In the present paper we show that a tree map is totally transitive iff it is topologically mixing. Using this result, we prove that the tree maps having a chaotic (or scrambled) subset with full Lebesgue measure is dense in the space consisting of all topologically mixing (transitive, respectively) maps.     

Practical Method for Determining All the Minimum Solutions of Fuzzy Matrix Equation and Transitive Closure of Fuzzy Relation

In this paper,the new theory frame and practical methhod for determining all the minimumsolutions of Fuzzy matrix equation and transitive closure of Fuzzy relation is described,and it has beencarried out on the miero-computer quickly and accurately.     

3‐Factor‐Criticality of Vertex‐Transitive Graphs

A graph of order n is p ‐factor‐critical, where p is an integer of the same parity as n, if the removal of any set of p vertices results in a graph with a perfect matching. 1‐factor‐critical graphs and 2‐factor‐critical graphs are factor‐critical graphs and bicritical graphs, respectively. It is well known that every connected vertex‐transitive graph of odd order is factor‐critical and every connected nonbipartite vertex‐transitive graph of even order is bicritical. In this article, we show that a simple connected vertex‐transitive graph of odd order at least five is 3‐factor‐critical if and only if it is not a cycle.     

On 5‐Cycles and 6‐Cycles in Regular n‐Tournaments

Let T be a tournament of order n and be the number of cycles of length m in T. For and odd n, the maximum of is achieved for any regular tournament of order n (M. G. Kendall and B. Babington Smith, 1940), and in the case it is attained only for the unique regular locally transitive tournament RLT_n of order n (U. Colombo, 1964). A lower bound was also obtained for in the class of regular tournaments of order n (A. Kotzig, 1968). This bound is attained if and only if T is doubly regular (when ) or nearly doubly regular (when ) (B. Alspach and C. Tabib, 1982). In the present article, we show that for any regular tournament T of order n, the equality holds. This allows us to reduce the case to the case In turn, the pure spectral expression for obtained in the class implies that for a regular tournament T of order the inequality holds, with equality if and only if T is doubly regular or T is the unique regular tournament of order 7 that is neither doubly regular nor locally transitive. We also determine the value of c₆(RLT_n) and conjecture that this value coincides with the minimum number of 6‐cycles in the class for each odd      

Transitive families of projections in factors of type

We introduce a notion of transitive family of subspaces relative to a type factor, and hence a notion of transitive family of projections in such a factor. We show that whenever is a factor of type and is generated by two self-adjoint elements, then contains a transitive family of projections. Finally, we exhibit a free transitive family of projections that generate a factor of type .

     

ON F-SENSITIVE PAIRS

In the present paper, we define sensitive pairs via Furstenberg families and discuss the relation of three definitions: sensitivity, F -sensitivity and F -sensitive pairs, see Theorem 1. For transitive systems, we give some sufficient conditions to ensure the existence of F -sensitive pairs. In particular, each non-minimal E system (M system, P system) has positive lower density ( Fs , Fr resp.)-sensitive pairs almost everywhere. Moreover, each non-minimal M system is Fts -sensitive. Finally, by some examples we show that: (1) F -sensitivity can not imply the existence of F -sensitive pairs. That means there exists an F -sensitive system, which has no F -sensitive pairs. (2) There is no immediate relation between the existence of sensitive pairs and Li-Yorke chaos, i.e., there exists a system (X, f ) without Li-Yorke scrambled pairs, which has κ B -sensitive pairs almost everywhere. (3) If the system (G, f ) is sensitive, where G is a finite graph, then it has κ B -sensitive pairs almost everywhere.     

On the automorphisms of Paley's type II Hadamard matrix

In this paper we determine the automorphism group of Paley's type II Hadamard matrix.