若干图类的邻强边染色

研究了若干图类的邻强边染色 .利用在图中添加辅助点和边的方法 ,构造性的证明了对于完全图 Kn和路 Lm 的笛卡尔积图 Kn× Lm,有χ′as(Kn× Lm) =△ (Kn× Lm) +1 ,其中△ (Kn× Lm)和χ′as(Kn× Lm)分别表示图 Kn× Lm的最大度和邻强边色数 .同理验证了 n阶完全图 Kn的广义图 K(n,m)满足邻强边染色猜想 .     

关于Ramsey数下界的部分结果

本文得到 Ramsey数下界的一个计算公式 :R( l,s+ t-2 )≥ R( l,s) + R( l,t) -1 ,(式中 l、s、t≥ 3) .用此公式算得的 Ramsey数的下界比用其它公式算得的下界好 .     

Electrode “edge effects” analyzed by the Green function method

An exact method based on Green's equation is used to find the diffusion-controlled faradaic current for certain electrode geometries that incorporate edges and vertices. Thereby the magnitudes of the time-independent current density associated with angled electrode/electrode and electrode/insulator junctions are calculated. As well, the square-root-of-time-dependent currents associated with vertices, receive attention. These terms extend to longer times, the Cottrell formulation appropriate for short times. Though most of the problems solved here have been tackled previously, the novel Green function approach is shown to be straightforward and intuitive.     

A linear time algorithm for balance vertices on trees

The concept of balance vertices was first investigated by Reid (1999). For the main result “the balance vertices of a tree consist of a single vertex or two adjacent vertices”, Shan and Kang (2004) and Reid and DePalma (2005) improved the length and technique of the proof. In this paper we further discuss the balance vertices on trees in a generalization context. We do not only provide a simple efficient proof for the relevant result but also develop a linear time algorithm to find the set of balance vertices on the underlying tree.     

On dynamics of vertices of locally connected polynomial Julia sets

Let be a polynomial whose Julia set is locally connected. Then a non-preperiodic non-precritical vertex of must have the limit set which coincides with the limit set of an appropriately chosen recurrent critical point of . In particular, if all critical points of are non-recurrent then all vertices of are preperiodic or precritical.

     

The structure of matrices with a maximum multiplicity eigenvalue

There is remarkable and distinctive structure among Hermitian matrices, whose graph is a given tree T and that have an eigenvalue of multiplicity that is a maximum for T. Among such structure, we give several new results: (1) no vertex of T may be “neutral”; (2) neutral vertices may occur if the largest multiplicity is less than the maximum; (3) every Parter vertex has at least two downer branches; (4) removal of a Parter vertex changes the status of no other vertex; and (5) every set of Parter vertices forms a Parter set. Statements (3), (4) and (5) are also not generally true when the multiplicity is less than the maximum. Some of our results are used to give further insights into prior results, and both the review of necessary background and the development of new structural lemmas may be of independent interest.     

Z[6~(1/2)]上的正定么模格的分类

本文利用推广的邻格方法，完成了Ｚ[ ］上秩 ４判别式 １的所有正定么模格的分类．     

分子拓扑学方法估算多环芳香烃类化合物的电离能

在构建多环芳烃类化合物分子的邻接矩阵主对角元时,结合烷基极化效应指数考虑分子图顶点的性质,以分子碎片C、CH、CH2、CH3等的相对能量作主元,用分子拓扑学方法构建了多环芳香烃类化合物新的邻接矩阵.研究结果发现,新的邻接矩阵特征根与多环芳香烃类化合物的电离能有良好的相关性Ipi=4.756+2.870OMOi,R=0.9853,s=0.1765,n=446.用这种新方法估算多环芳香烃类化合物的电离能,所用参数少且为分子结构性参数,稳定可靠,计算简便,结果较满意.     

Cubical d-Polytopes with Few Vertices for d>4

A cubical polytope is a convex polytope all of whose facets are combinatorial cubes. A d-polytope P is called almost simple if, in the graph of P, each vertex of P is d-valent or (d+1)-valent. We show that, for d>4, all but one cubicald -polytopes with up to 2 ^d+1 vertices are almost simple. This provides a complete enumeration of all the cubical d-polytopes with up to 2 ^d+1 vertices, for d>4.