Regular Cayley maps for finite abelian groups

A regular Cayley map for a finite group A is an orientable map whose orientation-preserving automorphism group G acts regularly on the directed edge set and has a subgroup isomorphic to A that acts regularly on the vertex set. This paper considers the problem of determining which abelian groups have regular Cayley maps. The analysis is purely algebraic, involving the structure of the canonical form for A. The case when A is normal in G involves the relationship between the rank of A and the exponent of the automorphism group of A, and the general case uses Ito's theorem to analyze the factorization G = AY, where Y is the (cyclic) stabilizer of a vertex. Supported in part by the N.Z. Marsden Fund (grant no. UOA0124).     

Properties of C60 polymerized under high pressure and temperature

60 polymers. Pure and mixed phase polymeric samples were synthesized by simultaneously subjecting microcrystalline C₆₀ powder or pellets to various pressures () and temperatures (). The optical spectra of the orthorhombic, tetragonal, and rhombohedral C₆₀ polymer phases are observed to be quite distinct and rich. These spectra exhibit numerous lines and an overall downshift in frequency relative to C₆₀ is observed, consistent with a loss of double bonds from the fullerene cage. The LDMS spectra of a sample synthesized at under hydrostatic conditions and , exhibited a succession of clear peaks at mass numbers corresponding to , similar to the LDMS data on the C₆₀ photopolymer. This is taken as further evidence for interfullerene bonds in these high-pressure polymers. The XRD pattern of this sample indicates the presence of a strong texture in the sample. Received: 14 November 1996/Accepted: 8 January 1997     

Electrochemical reduction of pyrethroid insecticides based on esters of α-cyano-3-phenoxybenzyl alcohol at glassy carbon and mercury electrodes in acetonitrile

The electrochemical reduction of eight commercially important pyrethroid insecticides which are esters of either α-cyano-3-phenoxybenzyl alcohol (cycloprothrin, cyphenothrin, cyhalothrin, deltamethrin, esfenvalerate and cypermethrin) or 4-fluro-α-cyano-3-phenoxybenzyl alcohol (cyfluthrin and flumethrin) has been studied under conditions of voltammetry and bulk electrolysis at both glassy carbon and mercury electrodes in acetonitrile. In general, the peak potential of the initial reduction process observed at very negative potentials at both electrode surfaces shifts to a more positive value under conditions of consecutive potential cycling. At the hanging mercury drop electrode the reduction occurs at even more negative potentials than at a glassy carbon electrode because a blocking mechanism appears to be operative. Despite this major difference in the primary reduction step, common voltammetric features are observed at less negative potentials on second and subsequent cycles of the electrode potential at either electrode surface. For example, the initial reduction process always results in the formation of a species which is reversibly reduced at less negative applied potentials. Furthermore, despite the definition of the voltammetric response being highly sensitive to the individual pyrethroid structure, long time-scale bulk electrolysis experiments at glassy carbon or mercury pool electrodes led to the formation of analogous final products. The fact that pyrethroids with a widely varying range of acid moieties exhibit similar voltammetric behaviour suggests that the acid moiety is not directly involved in the initial electron transfer process. Controlled potential electrolysis studies at both electrode surfaces coupled with HPLC and mass spectral identification of products obtained after ethylation with ethyl iodide showed that the reduction mechanism on the longer time-scale involves cleavage of the ester with liberation of free cyanide ion. The major reduction product identified was the anion of either 3-phenoxybenzoic acid or 4-fluoro-3-phenoxybenzoic acid in yields ranging from 31 to 66%.     

The memory function approach to the relaxation shape function for the spin 12, X-Y model

The relaxation shape function obtained by making a Gaussian assumption at the second step in a continued fraction expansion is compared with the exact result and that based on the three-pole approximation of Lovesey and Meserve.     

Closed currents,vector fields,and phenomena

A pedagogical discussion is given of the role played by certain vector fields and closed currents in the formulation and interpretation of quantum mechanics and quantum field theory.     

Uniquely colorable perfect graphs

This paper defines the concept of sequential coloring. If G or its complement is one of four major types of perfect graphs, G is shown to be uniquely k-colorable it and only if it is sequentially k-colorable. It is conjectured that this equivalence is true for all perfect graphs. A potential role for sequential coloring in verifying the Strong Perfect Graph Conjecture is discussed. This conjecture is shown to be true for strongly sequentially colorable graphs.     

A bivariate strong law of large numbers

Probability Theory and Related Fields -