Note on the application of the reduced graph model in conjunction with search trees to the enumeration ofKekulé structures

The reduced graph model, when used in conjunction with the search trees method, provides a novel combinatorial procedure for the enumeration and generation ofKekulé structures. The procedure is suited for large benzenoid hydrocarbons consisting of cata- and thin peri-condensed parts.

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Zur Anwendung des Reduced Graph Model im Zusammenhang mit Search Trees zur Ermittlung der Anzahl möglicherKekulé-Strukturen

Zusammenfassung Das Modell erlaubt mit der im Titel genannten Kombination eine neuartige Methode zur Ermittlung und Generierung vonKekulé-Strukturen. Das Verfahren ist für große benzoide Kohlenwasserstoffe geeignet, die aus cata- und (dünnen) peri-kondensierten Teilstrukturen bestehen.

     

A novel nomenclature of polycyclic aromatic hydrocarbons without using graph centre

In this paper, we develop a novel adjacency matrix, He-matrix, corresponding to the dualist graph. Without using the graph center concept, we advance a novel nomenclature of polycyclic aromatic hydrocarbons. Further, we derive some distinguishing theorems about PAH molecules and present some results of our automatic derivatization and automatic classification counting of fused PAH molecules.     

Cyclic Conjugation Energy Effects in Polycyclic π-Electron Systems

Summary. The fact that cyclic arrangements of double bonds have a dramatic effect on the behavior of conjugated organic molecules is known since the 19th century. The fact that in monocyclic conjugated systems the size of the cycle and the number of -electrons involved is decisive for their stability (aromaticity) or lack of stability (antiaromaticity) is known since the 1930s. In polycyclic -electron systems several cyclic effects are present simultaneously and their separation became possible only recently. A molecular orbital method has been elaborated, by means of which the energy effects of individual cycles in polycyclic -electron systems can be estimated. This method is briefly outlined and illustrated by pertinent examples. An exhaustive bibliography of the topic considered is given.     

阿斯美胶囊中四种组分的高效液相色谱分析

建立了反相高效液相色谱法测定阿斯美胶囊中氨茶碱、盐酸甲氧非那明、马来酸氯苯那敏及那可汀四种组分的含量。色谱柱为ＳｐｈｅｒｉｓｏｒｂＣ８，５μｍ，２００ｃｍ×４０ｍｍＩＤ，流动相为体积分数０５％的三乙胺溶液（磷酸调节ｐＨ５５）＋乙腈＋甲醇（５５０＋３６８＋８２），检测波长为２６４ｎｍ，线性范围分别为：氨茶碱３１２５～２５０ｍｇ／Ｌ，γ＝０９９９６，盐酸甲氧非那明１５６２５～１２５０ｍｇ／Ｌ，γ＝１００００，马来酸氯苯那敏２５～２００ｍｇ／Ｌ，γ＝０９９９９，那可汀８７５～７００ｍｇ／Ｌ，γ＝０９９９９；回收率（ｎ＝３）分别为１０１２％，１００８％，９９９％，９９５％；精密度：日内平均ＲＳＤ（ｎ＝６）分别为０７％，０４％，０４％，０６％；日间平均ＲＳＤ（ｎ＝３）分别为１０％，１０％，１１％，１２％。     

On Schreier graphs of gyrogroup actions

The notion of a group action can be extended to the case of gyrogroups. In this article, we examine a digraph and graph associated with a gyrogroup action on a finite nonempty set, called a Schreier digraph and graph. We show that algebraic properties of gyrogroups and gyrogroup actions such as being gyrocommutative, being transitive, and being fixed-point-free are reflected in their Schreier digraphs and graphs. We also prove graph-theoretic versions of the three fundamental theorems involving actions: the Cauchy–Frobenius lemma (also known as the Burnside lemma), the orbit-stabilizer theorem, and the orbit decomposition theorem. Finally, we make a connection between gyrogroup actions and actions of symmetric groups by evaluation via Schreier digraphs and graphs.     

非全局Lipschitz条件下跳适应向后Euler方法的强收敛性分析

本文研究跳适应向后Euler方法求解跳扩散随机微分方程在非全局Lipschitz条件下的强收敛性.通过克服方程非全局Lipschitz系数给收敛性分析带来的主要困难,我们成功地建立了跳适应后向Euler方法的强收敛性结果并得到相应的收敛率.最后,我们通过数值试验对前文所得理论结果做进一步的验证.     

Large cycles in random generalized Johnson graphs

This paper studies thresholds in random generalized Johnson graphs for containing large cycles, i.e. cycles of variable length growing with the size of the graph. Thresholds are obtained for different growth rates.     

On Tutte polynomial expansion formulas in perspectives of matroids and oriented matroids

We introduce the active partition of the ground set of an oriented matroid perspective (or morphism, or quotient, or strong map) on a linearly ordered ground set. The reorientations obtained by arbitrarily reorienting parts of the active partition share the same active partition. This yields an equivalence relation for the set of reorientations of an oriented matroid perspective, whose classes are enumerated by coefficients of the Tutte polynomial, and a remarkable partition of the set of reorientations into Boolean lattices, from which we get a short direct proof of a 4-variable expansion formula for the Tutte polynomial in terms of orientation activities. This formula was given in the last unpublished preprint by Michel Las Vergnas; the above equivalence relation and notion of active partition generalize a former construction in oriented matroids by Michel Las Vergnas and the author; and the possibility of such a proof technique in perspectives was announced in the aforementioned preprint. We also briefly highlight how the 5-variable expansion of the Tutte polynomial in terms of subset activities in matroid perspectives comes in a similar way from the known partition of the power set of the ground set into Boolean lattices related to subset activities (and we complete the proof with a property which was missing in the literature). In particular, the paper applies to matroids and oriented matroids on a linearly ordered ground set, and applies to graph and directed graph homomorphisms on a linearly ordered edge-set.     

Two Hamiltonian cycles

If the line graph of a graph G decomposes into Hamiltonian cycles, what is G? We answer this question for decomposition into two cycles.     

The spum and sum-diameter of graphs: Labelings of sum graphs

A sum graph is a finite simple graph whose vertex set is labeled with distinct positive integers such that two vertices are adjacent if and only if the sum of their labels is itself another label. The spum of a graph G is the minimum difference between the largest and smallest labels in a sum graph consisting of G and the minimum number of additional isolated vertices necessary so that a sum graph labeling exists. We investigate the spum of various families of graphs, namely cycles, paths, and matchings. We introduce the sum-diameter, a modification of the definition of spum that omits the requirement that the number of additional isolated vertices in the sum graph is minimal, which we believe is a more natural quantity to study. We then provide asymptotically tight general bounds on both sides for the sum-diameter, and study its behavior under numerous binary graph operations as well as vertex and edge operations. Finally, we generalize the sum-diameter to hypergraphs.