2-Dimension from the Topological Viewpoint

In this paper we study the 2-dimension of a finite poset from the topological point of view. We use homotopy theory of finite topological spaces and the concept of a beat point to improve the classical results on 2-dimension, giving a more complete answer to the problem of all possible 2-dimensions of an n-point poset.      

Discrete storage processes and their Poisson flow and fluid flow approximations

Consider discrete storage processes that are modulated by environmental processes. Environmental processes cause interruptions in the input and/or output processes of the discrete storage processes. Due to the difficulties encountered in the exact analysis of such discrete storage systems, often Poisson flow and/or fluid flow models with the same modulating environmental processes are proposed as approximations for these systems. The analysis of Poisson flow and fluid flow models is much easier than that of the discrete storage processes. In this paper we give sufficient conditions under which the content of the discrete storage processes can be bounded by the Poisson flow and the fluid flow models. For example, we show that Poisson flow models and the fluid flow models developed by Kosten (and by Anick, Mitra and Sondhi) can be used to bound the performance of infinite (finite) source packetized voice/data communication systems. We also show that a Poisson flow model and the fluid flow model developed by Mitra can be used to bound the buffer content of a two stage automatic transfer line. The potential use of the bounding techniques presented in this paper, of course, transcends well beyond these examples.Supported in part by NSF grant DMS-9308149.     

QSAR modeling with the electrotopological state indices: Corticosteroids

A structure-activity analysis of a series of steroids binding to corticosteroid-binding globulin was made using the electrotopological state index for each atom in the molecule. Two indices were found to correlate well with the binding affinity. The indices encode structural characteristics in the A and the D rings of the steroids in the study. One of the indices was formulated as the difference between two indices in the A ring. The two were not intercorrelated, suggesting that the composite index signals the influence of structure changes in or near the A ring that can be monitored by the composite index. This is a new observation using this structure-activity method. It is suggested that this model makes some contributions towards detection of the pharmacophore.     

Stochastic flows on a countable set: Convergence in distribution

Consider a sequenceF ₁,F ₂,... of i.i.d. random transformations from a countable setV toV. Such a sequence describes a discrete-time stochastic flow onV, in which the position at timen of a particle that started at sitex isM _n(x), whereM _n =F _n F _n–1 F ₁. We give conditions on the law ofF ₁ for the sequence (M _n) to be tight, and describe the possible limiting law. an example called the block charge model is introduced. The results can be formulated as a statement about the convergence in distribution of products of infinite-dimensional random stochastic matrices. In practical terms, they describe the possible equilibria for random motions of systems of particles on a countable set, without births or deaths, where each site may be occupied by any number of particles, and all particles at a particular site move together.     

取代脂环烃物理化学性质的拓扑化学研究

为了探讨有机化合物的分子结构与理化性质的关系,作者在以前的工作基础上,基于一阶分子连通性拓扑指数构建了一个信息拓扑指数.将拓扑指数与取代脂环烃系列分子的气态标准生成热、气态标准熵、气态标准生成自由能、沸点、临界温度、临界压力、临界体积、汽化热、密度、热容及表面张力等十一种热力学性质及物理化学性质相关联,用一个通用公式对各类性质进行概括,然后用已有的实验数据与拓扑指数进行回归分析,得到一系列计算各性质的经验公式.回归结果发现,分子的理化性质与拓扑指数有较好的相关性,有5类性质的复相关系数大于0.99.用经验公式对各类性质进行重新计算,其结果与实验值比较符合,用实验值对计算值作图,发现各数据点紧靠对角线,说明误差较小.残差分布呈正态分布.     

胺、醇、醚类化合物电离能的自相关拓扑研究

原子的染色序数 fi 定义为 :fi=gi·xi,式中 gi 为原子i在分子中的序数 ,xi 为其染色系数 .基于fi 建立改进的原子序数自相关拓扑指数mF ,其中的1F对烷烃及其衍生物具有良好的结构选择性 .使用第一电离能 (Ip)与0 F ,1F的数量关系模型对 32种脂肪族胺、醇、醚进行估算、预测 ,结果令人满意     

Structural Analogy Method in Studies of Adamantanes

The potential of the structural analogy method in the topological studies of adamantane derivatives and analogs is demonstrated. The topological and structural characteristics of these compounds are calculated. Chromatographic retention indices were determined experimentally. Correlations between the topological indices and the physicochemical and chromatographic characteristics are investigated.     

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。     

2D层状焦磷酸锰(Ⅱ)[NH4]2[Mn3(P2O7)2(H2O)2]的结构和磁性研究

A two-dimensional layered manganese(Ⅱ) pyrophosphate, [NH₄]₂[Mn₃(P₂O₇)₂(H₂O)₂] (1), has been synthesized hydrothermally. Its structure is determined by single-crystal X-ray diffraction analysis. Its structure is built up by MnO₆ octahedra and P₂O₇ units, with ammonium NH₄⁺ cations residing in the interlayer regions. The manganese pyrophosphate layer consists of infinite chains of cis and trans edge sharing MnO₆ octahedra linked by P₂O₇ units. Magnetic susceptibility measurements show that this compound exhibits ferrimagnetic-like ordering below 3.2 K. Further study shows that there are two possible superexchange pathways via the oxygen anions in Mn²⁺ ions. Owing to the different bridging modes of O^2-, the competition between ferromagnetic interactions and antiferromagnetic interactions in Mn²⁺ ions results in the ferrimagnetic behavior of 1.