A census of semisymmetric cubic graphs on up to 768 vertices

A list is given of all semisymmetric (edge- but not vertex-transitive) connected finite cubic graphs of order up to 768. This list was determined by the authors using Goldschmidt's classification of finite primitive amalgams of index (3,3), and a computer algorithm for finding all normal subgroups of up to a given index in a finitely-presented group. The list includes several previously undiscovered graphs. For each graph in the list, a significant amount of information is provided, including its girth and diameter, the order of its automorphism group, the order and structure of a minimal edge-transitive group of automorphisms, its Goldschmidt type, stabiliser partitions, and other details about its quotients and covers. A summary of all known infinite families of semisymmetric cubic graphs is also given, together with explicit rules for their construction, and members of the list are identified with these. The special case of those graphs having K_1,3 as a normal quotient is investigated in detail. Supported in part by N.Z. Marsden Fund (grant no. UOA 124) and N.Z. Centres of Research Excellence Fund (grant no. UOA 201) Supported in part by “Ministrstvo za šolstvo, znanost in šport Slovenije”, research program no. 101-506. Supported in part by research projects no. Z1-4186-0101 and no. Z1-3124-0101. The fourth author would like to thank the University of Auckland for hospitality during his visit there in 2003.     

A Note on Groups Associated with 4-Arc-Transitive Cubic Graphs

A cubic (trivalent) graph is said to be 4-arc-transitive ifits automorphism group acts transitively on the 4-arcs of (wherea 4-arc is a sequence v₀, v₁, ... v₄ of vertices of such thatv_i–1 is adjacent to v_i for 1 i 4, and v_i–1 v_i+1for 1 i < 4). In his investigations into graphs of thissort, Biggs defined a family of groups 4⁺(a^m), for m = 3,4,5...,each presented in terms of generators and relations under theadditional assumption that the vertices of a circuit of lengthm are cyclically permuted by some automorphism. In this paperit is shown that whenever m is a proper multiple of 6, the group4⁺(a^m) is infinite. The proof is obtained by constructing transitivepermutation representations of arbitrarily large degree.     

Hurwitz Groups with Arbitrarily Large Centres

In this paper a new family of quotients of the triangle group is obtained. Each group in this family is constructed as centralproduct of the groups SL(2, q) for various prime-powers q, andin this way it is shown that for every positive integer s thereare infinitely many Hurwitz groups with a centre of size 2⁸.     

On-line identification of tropane alkaloids from Erythroxylum vacciniifolium by liquid chromatography-UV detection-multiple mass spectrometry and liquid chromatography-nuclear magnetic resonance spectrometry

The bark of catuaba (Erythroxylum vacciniifolium Martius, Erythroxylaceae), a tree native to the northern part of Brazil, was investigated for its alkaloid content. With the aim of obtaining preliminary structure information on-line, the alkaloid extract was analysed by high-performance liquid chromatography coupled to diode array UV detection, to mass spectrometry and to nuclear magnetic resonance. Interpretation of on-line spectroscopic data obtained from this extract led to structural elucidation of six new alkaloids and partial identification of 18 potentially original alkaloids bearing the same tropane skeleton esterified in positions 3 and 6 by 1-methyl-1H-pyrrol-2-carboxylic acid and/or 4-hydroxy-3,5-dimethoxybenzoic acid.     

Leaky helical flexural wave backscattering contributions from tilted cylindrical shells in water: observations and modeling

For tilt angles smaller than the meridional ray coupling condition previously investigated [S. F. Morse et al., J. Acoust. Soc. Am. 103, 785-794 (1998)], flexural helical waves on cylindrical shells can significantly enhance the backscattering. These contributions are compared and modeled here for an empty cylinder. Experiments using tone bursts were performed on a tilted stainless steel shell to investigate the contributions caused by flexural leaky Lamb waves above the coincidence frequency of the shell. In some of the measurements the tone bursts were of sufficient duration to superpose helical wave contributions of successive circumnavigations, along with the meridional contribution near the critical tilt, to arrive at a quasi-steady-state backscattering amplitude for the cylinder. These measurements are compared with an approximate numerical partial-wave series solution and a ray theory as a function of the tilt angle. The data for ka = 20 follow the basic shape of the ray theory and the relevant features of the partial-wave model. They illustrate the importance of the interference of successive helical wave contributions. Measurements (also as a function of the tilt angle) using tone bursts that were sufficiently short to separate the earliest helical wave contribution from later contributions also support the ray theory.     

Thermally enhanced neutralization in hyperthermal energy ion scattering

Neutralization probabilities are presented for hyperthermal energy Na+ ions scattered from a Cu(001) crystal as a function of surface temperature and scattered velocity. A large enhancement in neutralization is observed as the temperature is increased. Velocity-dependent charge transfer regimes are probed by varying the incident energy, with the most prominent surface temperature effects occurring at the lowest energies. The data agree well with results obtained from a model based on the Newns-Anderson Hamiltonian, where the effects of both temperature and velocity are incorporated.     

Backscattering enhancements associated with subsonic Rayleigh waves on polymer spheres in water: observation and modeling for acrylic spheres

Unlike most common solids, "plastic" polymer solids typically have shear and Rayleigh wave phase velocities less than the speed of sound in water. Subsonic Rayleigh waves on smooth objects in water are not classified as leakey waves and it is necessary to reexamine backscattering mechanisms. Also the intrinsic material dissipation of the Rayleigh wave can be significant. Backscattering by acrylic or polymethlmethacrylate (PMMA) spheres in water is analyzed and measured in the region ka = 1.5-7 and it is found that prominent low-lying resonance peaks of the form function f exist. The peaks can be modeled with quantitative ray theory as the result of coupling of subsonic Rayleigh waves with sound through acoustic tunneling. The most prominent maximum of f=5.63 occurs at ka = 1.73 and is associated with the quadrupole (or n=2) partial wave. In addition to explaining the scattering, the target strength is found to be sufficiently large that such spheres may be useful for passive low frequency targets.     

Quasi-Gaussian Bessel-beam superposition: application to the scattering of focused waves by spheres

A superposition of zero-order Bessel beams is examined that closely resembles an idealized paraxial Gaussian beam, provided the superposition is not tightly focused. Plots compare wavefield properties in the focal region and in the far field for different values of kw(0), the product of the wavenumber k, and the focal-spot-radius w(0). The superposition (which is an exact solution of the Helmholtz equation) has the important property that the scattering by an isotropic sphere can be calculated without any approximations for the commonly considered case of linear waves propagating in an inviscid fluid. The nth partial wave amplitude is similar to the case of plane-wave illumination except for a weighting factor that depends on incomplete gamma functions. An approximation for the weighting factor is also discussed based on a generalization of the Van de Hulst localization principle for a sphere of radius a at the focus of a Gaussian beam. Examples display differences between the directionality of the scattering with the plane wave case even though for the cases displayed, ka does not exceed 2 and w(0)∕a is not less than 2. Properties of tightly focused wavefields and the partial wave weighting factors are discussed.