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.     

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.     

The vacuum ultraviolet absorption spectrum of ClO

The flash photolysis of ClO₂ has yielded a new absorption spectrum of ClO in the vacuum ultraviolet. Six electronic transitions have been assigned and vibrational constants for the upper states are given. All of the transitions are Rydberg in nature. The first four of these transitions are thought to be ²Σ ← X²Π_i from which a spin-orbit coupling constant A = ?318 ± 5 cm^?1 is obtained for the ground state.Hot bands in three of the above systems of ClO have been observed in absorption. This has enabled the direct measurement of the ground state vibrational constant ($\text{Δ}\text{G}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{″ = 845 ± 4}\text{cm}{}^{\mathrm{?1}}$; ω_e″ = 859 cm^?1) for the first time.Extinction coefficients for a number of the ClO transitions have been measured.     

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.     

Coordination chemistry of bidentate diflourophospines IV. Complexes of 1,2-bis(diflourophosphino)ethane with Ni(O) and Mo(O).

The ligand, 1,2-bis(difluorophosphino)ethane, (PF₂C₂H₄PF₂), reacts with Ni(CO)₄ in the gas phase and in solution to produce carbon monoxide and a polymer, [Ni(PF₂C₂H₄PF₂)₂]_x. PF₂C₂H₄PF₂ displaces norbornadiene from (C₇H₈)Mo(CO)₄ to yield the relatively air-stable complex, Mo(CO)₄-(PF₂C₂H₄PF₂). Analysis of the infrared spectrum of the monomeric complex indicates that the ligand exhibits π-acceptor strength equal to PF₂C₆H₁₀PF₂.     

Modulation of amyloid-β aggregation by metal complexes with a dual binding mode and their delivery across the blood–brain barrier using focused ultrasound

One of the key hallmarks of Alzheimer''s disease is the aggregation of the amyloid-β peptide to form fibrils. Consequently, there has been great interest in studying molecules that can disrupt amyloid-β aggregation. While a handful of molecules have been shown to inhibit amyloid-β aggregation in vitro, there remains a lack of in vivo data reported due to their inability to cross the blood–brain barrier. Here, we investigate a series of new metal complexes for their ability to inhibit amyloid-β aggregation in vitro. We demonstrate that octahedral cobalt complexes with polyaromatic ligands have high inhibitory activity thanks to their dual binding mode involving π–π stacking and metal coordination to amyloid-β (confirmed via a range of spectroscopic and biophysical techniques). In addition to their high activity, these complexes are not cytotoxic to human neuroblastoma cells. Finally, we report for the first time that these metal complexes can be safely delivered across the blood–brain barrier to specific locations in the brains of mice using focused ultrasound.

We report a series of non-toxic cobalt(iii) complexes which inhibit Aβ peptide aggregation in vitro; these complexes can be safely delivered across the blood–brain barrier in mice using focused ultrasound.     

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.