分子结构的数学表示式

本文叙述一种用图论方法得出的分子结构的编码方法,我们把这种编码称为分子结构的数学表示式,它具有计算简单、几何意义明显等特点。文中给出了从分子结构图计算出它的数学表示式的两个算法,论证了表示式的唯一性,并编出了分子结构图与它的数学表示式之间互相转换的计算机程序。最后给出若干分子结构的数学表示式的示例。     

浮点遗传算法的收敛性及其在模型参数提取问题中的应用

浮点遗传算法是一种模拟生物进化的最化搜索法,由于其运算简单、稳定性好、不需要计算目标函数的导数、高精度和能处理多维数值问题,浮点遗传算法在科学研究和工程技术中得到了广泛应用.通过对浮点遗传算法收敛性的分析,本文证明了"简单浮点遗传算法不收敛于全局最优解,而每代保留最优个体的浮点遗传算法才收敛于全局最优解".在此基础上,本文设计了一种采用连续突变和每代保留最优个体的改进浮点遗传算法,它克服了精确度与计算量之间的矛盾.本文利用该算法较好地解决了半导体器件模型参数提取问题,使计算量降低了约27%.     

Laplacian spectrum analysis and spanning tree algorithm for circuit partitioning problems

The spectrum of a graph is the set of all eigenvalues of the Laplacian matrix of the graph. There is a closed relationship between the Laplacian spectrum of graphs and some properties of graphs such as connectivity. In the recent years Laplacian spectrum of graphs has been widely applied in many fields. The application of Laplacian spectrum of graphs to circuit partitioning problems is reviewed in this paper. A new criterion of circuit partitioning is proposed and the bounds of the partition ratio for weighted graphs are also presented. Moreover, the deficiency of graph-partitioning algorithms by Laplacian eigenvectors is addressed and an algorithm by means of the minimal spanning tree of a graph is proposed. By virtue of taking the graph structure into consideration this algorithm can fulfill general requirements of circuit partitioning.     

Hamiltonian和它的充分条件

美国专家Faudree等最先创立NC条件,其后他们在文[1]中得到条件NC≥n－δ下熟知的Hamiltonian结果。文中我们进一步研究更好条件NC≥n－δ－1下的情况,其结论仅比Faudree等在文[1]中的结论多两个熟悉的例外图。可见NC≥n－δ－1条件是有用的。且它也直接推出Faudree等在文[1]中的结果。