Duality in graph families

The concepts of complete and free families are studied by Catlin. It has been noted by Catlin that these concepts are, in some sense, dual to each other. In this paper, we investigate the duality between edge-contractions and edge-deletions, and establish some results dual to several Catlin's theorems.     

Echo-wave scattering characteristics of the diffuse target in the slant atmospheric turbulence

The extended Huygens–Fresnel principle is utilized to make analysis of the received intensity for laser beam propagation through the atmospheric turbulence in the slant path. For a diffuse target, the effects of the turbulence on the statistical parameters such as the mutual coherence function and the mean intensity are studied in detail. The influence of the incident wave radius and the distance of the incident beam on these parameters are discussed.     

Supereulerian complementary graphs

Nebeský in [12] show that for any simple graph with n ≥ 5 vertices, either G or G^c contains an eulerian subgraph with order at least n - 1, with an explicitly described class of exceptional graphs. In this note, we show that if G is a simple graph with n ≥ 61 vertices, then either G or G^c is supereulerian, with some exceptions. We also characterize all these exceptional cases. These results are applied to show that if G is a simple graph with n ≥ 61 vertices such that both G and G^c are connected, then either G or G^c has a 4-flow, or both G and G^c have cut-edges. © 1993 John Wiley & Sons, Inc.     

The size of strength-maximal graphs

Let G be a graph and let k′(G) be the edge-connectivity of G. The strength of G, denoted by k?′(G), is the maximum value of k′(H), where H runs over all subgraphs of G. A simple graph G is called k-maximal if k?′(G) ≤ k but for any edge e ∈ E(G^c), k?′(G + e) ≥ k + 1. Let G be a k-maximal graph of order n. In [3], Mader proved |E(G)| ≤ (n - k)k + (). In this note, we shall show (n - 1)k - () In?n/k + 2)? ≤ |E(G|, and characterize the extremal graphs. We shall also give a characterization of all k-maximal graphs.     

利用^1H CIDNP效应对芳基重氮盐还原反应的研究

芳基重氮盐在有机合成反应中是一类十分重要的中间体,通过重氮盐的取代或消除,可以得到预期的衍生物,因而深入研究其反应性质是非常必要的。利用CIDNP效应研究Lewis碱,如氢氧化钠、胺、硼氢化钠等对芳基重氮盐的还原过程已有不少报道,证实了重氮盐的还原过程,具有自由基反应的特点。为     

关于超欧拉图的一个注记

设G是无向无环的有限图 ,若G有一个生成子图是欧拉图 (Euler) ,则称G是超欧拉图 (Supereulerian) .本文不利用收缩方法 ,直接证明了 :当图G至多差一边有两棵边不相交的生成树时 ,G是超欧拉图或者G有割边 .     

共轭聚合物薄膜中光生载流子的产生及输运机制

对共轭聚合物光生载流子的产生机制进行了初步探讨,分析了由最初产生的电子 空穴对经过晶格驰豫之后形成极化子 激子的热离化过程,认为同一链上的激子会迅速复合,只有链间激子对光电流作出贡献.研究了共轭聚合物中载流子的输运机制,导出了共聚物的电导率公式,其计算值与实验结果符合,我们认为是极化子的链间跃迁实现了整个共聚物的电导和光致发光,较好地解释了实验事实.