具有唯一4度最大度点的图的全色数

一个图Ｇ的全色数χ_T（Ｇ）是使得Ｖ（Ｇ）∪Ｅ（Ｇ）中相邻或相关联元素均染不同颜色的最少颜色数．文中证明了，若图Ｇ只有唯一的一个４度最大度点，则χ_T（Ｇ）＝Δ（Ｇ）＋１．     

From dilute to dense self-avoiding walks on hypercubic lattices

A field-theoretic representation is presented to count the number of configurations of a single self-avoiding walk on a hypercubic lattice ind dimensions with periodic boundary conditions. We evaluate the connectivity constant as a function of the fractionf of sites occupied by the polymer chain. The meanfield approximation is exact in the limit of infinite dimensions, and corrections to it in powers ofd ^–1 can be systematically evaluated. The connectivity constant and the site entropy calculated throughout second order compare well with known results in two and three dimensions. We also find that the entropy per site develops a maximum atf1–(2d)^–1. Ford=2 (d=3), this maximum occurs atf~0.80 (f~0.86) and its value is about 50% (30%) higher than the entropy per site of a Hamiltonian walk (f=1).     

Topological investigations of molar excess volumes of quinoline with alkanols

Excess volumes V ^E of binary liquid mixtures of quinoline with alkanols have been determined from densities at 30°C as a function of composition. The excess volumes are negative over the whole mole fraction range for all the mixtures and decrease with increasing length of alkanol (C₁–C₁₀). The V^E data have been analyzed in terms of an approach which uses graph theoretical connectivity parameters of the third degrees for two components. The analysis gives information regarding associated species in the pure state and in the mixture. It is suggested that, in the mixture state, no change occurs in the association of alkanols.     

键连接性指数的建构及其在有机体系中的应用研究

以化学键为基础建构了键连接性指数及分子键连接性指数，该指数同时考虑顶 点原子的化学特征及键的性质．对于任意化学键，键连接性指数Si＝1+△I/R·[（ Z1-h1)m2/n1+(Z2-h2)m1/n2]，分子键连接性指数S为∑i=1^m√Si或∑i=1^m1/√ Si，其中，Z1，Z2为化学键键连原子的价电子数；n1，n2成键原子的价层最高主量 子数；m1，m2为成键原子的氧化数；h1，h2为与成键原子相连的氢原子个数；△I 为成键原子的电负性差(△I≥0)；R为化学键的相对键长．与以顶点为基础的价连 接性指数不同，该指数不仅能方便而有效地应用于饱和碳氢体系亦能有效地应用于 含多重键的不饱和体系及含杂原子的有机体系．研究了饱和碳氢体系标准生成焓， 不饱和碳氢体系和酮、醚、酯体系在水中的溶解度和辛醇/水分配系数，卤代甲烷 体系的标准生成焓，卤代苯体系辛醇/水分配系数，均取得比较满意的结果。     

硫醇的分子连接性指数与气相色谱保留值

硫醇的分子连接性指数与气相色谱保留值赵邦屯王利亚（洛阳师专化学系洛阳４７１０２２）关键词硫醇分子连接性指数气相色谱保留值中图分类号Ｏ６５７．７１有机化合物的色谱保留行为与其结构之间的定量关系研究一直是物理化学、分析化学和生物化学的研究对象之一。长期以...     

不饱和链烃沸点的拓扑研究

基于邻接矩阵与边价 (fi)定义边价连接性指数 ( mF) ,其中的0 F ,1 F与 2 94种不饱和链烃 (包括烯烃、炔烃及烯炔烃 )的沸点 (Tb)关联 ,得到良好的数学模型 :ln( 70 0 -Tb) =6 5 2 3 3 1-0 0 0 4880 F2 -0 3 46771 F0 5(n =2 94,R =0 9979,R2 =0 995 8,F =3 490 4,S =5 12 ) ,该回归模型经Jackknife法检验具有总体稳健性 .可以预示 ,该指数将在定量构效关系研究中成为重要参数 .     

Pattern-specific neural network design

We present evidence that the performance of the traditional fully connected Hopfield model can be dramatically improved by carefully selecting an information-specific connectivity structure, while the synaptic weights of the selected connections are the same as in the Hopfield model. Starting from a completely disconnected network we let genuine Hebbian synaptic connections grow, one by one, until a desired degree of stability is achieved. Neural pathways are thus fixed notbefore, butduring the learning phase.     

q-Hypergeometric Series and Macdonald Functions

We derive a duality formula for two-row Macdonald functions by studying their relation with basic hypergeometric functions. We introduce two parameter vertex operators to construct a family of symmetric functions generalizing Hall-Littlewood functions. Their relation with Macdonald functions is governed by a very well-poised q-hypergeometric functions of type ₄₃, for which we obtain linear transformation formulas in terms of the Jacobi theta function and the q-Gamma function. The transformation formulas are then used to give the duality formula and a new formula for two-row Macdonald functions in terms of the vertex operators. The Jack polynomials are also treated accordingly.     

组合合成阵的不可约性

本文讨论了布尔矩阵的组合合成的基本性质,用图论方法找出了２级组合合成阵为不可约的一些充分条件。