一类树问题的快速并行算法

本文给出了一类树问题的快速并行算法.这些问题包括:求树中任意两顶点之间的路径和路径长度、求所有顶点的深度等.以这些基本算法为基础,给出了求树中任意两个顶点的最小公共祖先问题、边修改动态最小生成树问题和树同构问题的并行算法.本文使用的模型是单指令流多数据流共享存贮器并行计算机,允许多个处理机同时读存贮器的一个单元的内容但不允许同时写,称这种模型为CREW PRAM.对n个顶点的树,以上算法均使用O(n)个处理机,时间复杂度为O(logn).按Cook的定义,证明了以上问题都属于NC类.     

On the core of the minimum cost steiner tree game in networks

A cost allocation problem arising from the Steiner Tree (ST) problem in networks is analyzed. This cost allocation problem is formulated as a cost cooperative game in characteristic function form, referred to as theST-game. The class ofST games generalizes the class of minimum cost spanning tree games which were used in the literature to analyze a variety of cost allocation problems. In general, the core of anST-game may be empty. We construct an efficient Core Heuristic to compute a good lower bound on the maximum fraction of the total cost that can be distributed among users while satisfying the core constraints. Based on the Core Heuristic, we also provide a sufficient condition for a givenST not to be optimal for the linear programming relaxation of an integer programming formulation of theST problem. The Core Heuristic was implemented and tested on 76 data sets from the literature (Wong's, Aneja's and Beasley's Steiner tree problems). Core points were found for 69 of these cases, and points close to the core were computed in the others.     

Capillary gas chromatography of plant tissues and soil phenolic acids

Summary A method for the separation of phenolic acids along with shikimic and quinic acids by means of capillary gas chromatography is described and discussed. The method involves the previous derivatization of the acids to trimethylsilyl derivatives and it has been applied to the separation of acids extracted from olive leaves and roots, elm leaves and a soil A horizon. Quite good results were achieved both from qualitative and quantitative points of view. Qualitative differences have been pointed out in the phenolic acid composition of two olive cultivars and between leaves and roots of the same cultivar; also two elm species can be discriminated on the basis of the phenolic acid content.     

Interacting walkers on the Cayley tree,and polymer statistics

We obtain the generating function for an ensemble of random walkers on the Cayley tree of coordination numberz. The pair interaction between walkers is taken into account. This forbids two walkers to occupy the same lattice point after an equal number of steps. Interacting polymer statistics results from this model if one associates time (or the number of steps) with an additional space coordinate. The limiting free energy appears in a form that corresponds to the phase transition of 3/2 order.     

Quantitative HPTLC separation of flavonoid glycosides in the taxonomy of elm (Ulmus spp.)

Summary The flavonoid glycosides of elm (Ulmus spp.) leaves have been separated by means of HPTLC on silica gel and quantitative analysis carried out by densitometry. The results obtained were used for discriminant analysis in order to investigate whether the flavonoid pattern could be used for the classification of elms. The results readily showed the different provenance of four species and the attribution of an unknown sample to a species can be carried out. This result is important as it offers a chemical tool in the taxonomy of the elm. The classification method is compared with one based on qualitative data from two-dimensional chromatography of the flavonoid aglycones. It was found to exhibit much better results than those obtained from the cluster analysis of these qualitative data.     

On mean field equations for spin glasses

In this paper we study rigorously the random Ising model on a Cayley tree in the limit of infinite coordination numberz 8. An iterative scheme is developed relating mean magnetizations and mean square magnetizations of successive shells far removed from the surface of the lattice. In this way we obtain local properties of the model in the (thermodynamic) limit of an infinite number of shells. When the coupling constants are independent Gaussian random variables the SK expressions emerge as stable fixed points of our scheme and provide a valid local mean-field theory of spin glasses in which negative local entropy (at low temperatures) while perfectly possible mathematically may still perhaps be physically undesirable. Finally we examine the TAP equations and show that if the average over bond disorder and the limitz 8 are actually performed, one recovers our iterative scheme and hence the SK equations also in the thermodynamic limit.On leave from Mathematics Department, University of Melbourne, Parkville, Victoria 3052, Australia.     

自组织神经树用于3－甲基芬太尼衍生物构效关系的研究

用自组织神经树方法研究３－甲基芬太尼衍生物的镇痛活性与其结构特征参数间的非线性关系，结果表明：该网络性能良好、识别成功率高，可望成为药物构效关系研究的有效辅助手段。     

A_α型缩聚物的分子量分布函数及对凝胶的分子解释

非线型缩聚物的分子量分布,最早由Flory和Stockmayer应用组合理论得到。不少实际的非线型缩聚体系,分布函数相当复杂。江元生用解动力学方程的方法得到了和组合法相同的结果。Gordon用无规支化理论处理了A_a型缩聚物的分布问题。近年来,唐敖庆等又提出了通过溶胶凝胶分配理论推导分布函数的方法。本文给出一种分子树模型,能更     

图的ABC指标与直径

为了更好地研究拓扑指标在物理化学领域的良好性质,考虑基于度和基于距离的指标之间的关系问题,在直径这一作为距离的不变量的基础上,研究了图的ABC指标和直径的关系。根据相关引理,推导出了树和单圈图的ABC指标与直径的关系,得出了ABC指标和直径差值的紧的下界。