The Choquet-Deny convolution equation μ=μ*σ for probability measures on Abelian semigroups

In this note, we characterize the regular probability measures satisfying the Choquet-Deny convolution equation =* on Abelian topological semigroups for a given probability measure .     

Diagrams,orientations, and varieties

One of the central problems in the theory of ordered sets is to describe the orientations of the covering graph of an ordered set. We show that the particular operation called inversion, together with the classical constructions of retraction and product, provide a context for the classification of all such orientations. AMS subject classifications (1980). 06A10, 05C75, 05C20.     

酶分子在试管内的定向进化及其在手性有机物合成中的应用

本文扼要介绍了当今改进酶分子性能的有效手段———分子定向进化技术的基本方法如易错PCR和DNA洗牌,以及派生的一些新技术的原理与进展,并列举了在手性有机物合成中一些成功的实例,为该领域的研究与应用提供了一些新的信息。     

Global Forcing Number of Benzenoid Graphs

A global forcing set in a simple connected graph G with a perfect matching is any subset S of E(G) such that the restriction of the characteristic function of perfect matchings of G on S is an injection. The number of edges in a global forcing set of the smallest cardinality is called the global forcing number of G. In this paper we prove several results concerning global forcing sets and numbers of benzenoid graphs. In particular, we prove that all catacondensed benzenoids and catafused coronoids with n hexagons have the global forcing number equal to n, and that for pericondensed benzenoids the global forcing number is always strictly smaller than the number of hexagons.     

Unicyclic Graphs with Minimal Energy

If G is a graph and ₁,₂,..., _n are its eigenvalues, then the energy of G is defined as E(G)=|₁|+|₂|++| _n |. Let S _n ³ be the graph obtained from the star graph with n vertices by adding an edge. In this paper we prove that S _n ³ is the unique minimal energy graph among all unicyclic graphs with n vertices (n6).     

Electrode processes in the oxidation of tetrahydroisoquinoline derivatives

The electrochemical oxidation of the alkaloid laudanosine (Ia) to O-methylflavinantine (II) has been studied in acetonitrile solvent. Using cyclic voltammetry, rotating disc voltammetry and preparative electrolyses on several alkaloids, simple aliphatic amines and aromatic compounds, some aspects of the mechanism of this coupling reaction are elucidated. The first anodic wave for laudanosine at platinum has E_p=0.55 V vs. Ag/Ag⁺. The electrode rapidly becomes partially passivated at potentials above 0.5 V. This is due to a film which “dissolves” below 0.5 V, at a rate independent of the potential. It is shown that the reaction (Ia)→(II) proceeds at 0.5 V by initial oxidation of the amine moiety. If acids such as sodium bicarbonate are added to the anolyte the amine is protonated causing the first wave to disappear. Oxidation at 1.1 V under these acidic conditions produces the same product, but more rapidly and in significantly higher yield because electrode filming and side reactions resulting from the amine oxidation are abrogated.     

Electrochemical behaviour of mono- and oligonucleotides I. Effects of charge and configuration of adenine mononucleotides on their adsorption at the mercury—solution interface

A systematic study of the adsorption and interfacial behaviour of the adenine mono-nucleotides (5′-AMP, 3′-AMP, cyclic 3′,5′-AMP, 5′-ADP and 5′-ATP) and adenosine for comparison at the HMDE has been carried out at pH 3.4 to 3.5. Thus, the N(1) of the adenine moiety is protonated to a major extent.The adsorption was followed by single sweep voltammetry (measurement of the time integral of the reduction peak of the adsorbed adenine moiety) and by a.c. voltammetry (out-of-phase component of the a.c. response being proportional to the differential double layer capacity). In this paper the situation corresponding to a “dilute” adsorption layer existing at low bulk concentrations is studied for various degrees of coverage. The potential dependence of the coverage is of bell shaped type with an extended maximum region around the potential of electrocapillary maximum (E_ecm) of the blank. For the same bulk concentration the coverage decreases in the series AMP, ADP, ATP, i.e. with increasing negative charge of the nucleotide, and at the same time the potential range of adsorption narrows. Among the monophosphates the coverage decreases in the series 3′-AMP, 5′-AMP, cyclic 3′,5′-AMP. The variations are connected with the varying charge of the mononucleotides and with the possibilities for interactions with adjacent molecules in the adsorption layer.At elevated bulk concentrations above a threshold value a substantial increase in coverage occurs around E_ecm as due to strong interactions between the adsorbed base moieties a rather compact film is formed.     

Pattern of separatrices and intrinsic reaction coordinates for degenerate thermal rearrangements

A structurally stable model of the standard adiabatic gradient field of the potential energy surface for certain pericyclic reactions is derived.These reactions are not subjected to the principles of orbital isomerism or to the Woodward-Hoffmann rules.Use is made of a principle established by Ariel Fernández and Oktay Sinanolu which precludes direct meta-IRC connections between transition states.It is shown that Jahn-Teller isomers of the singlet biradicals involved in the process are not interconvertible since the biradical configuration is not a transition state but a critical point with Hessian matrix with two negative eigenvalues.The topological features of the PES obtained by combinatorial methods are in full agreement with earlier results obtained from MINDO calculations.     

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.