Galaxy groups : Proceedings from a Swinburne University workshop

We present the proceedings from a two-day workshop held at Swinburne University on 2005 May 24-25. The workshop participants highlighted current Australian research on both theoretical and observational aspects of galaxy groups. These proceedings include short one-page summaries of a number of the talks presented at the workshop. The talks presented ranged from reconciling N-body simulations with observations, to the Hi content of galaxies in groups and the existence of 'dark galaxies'. The formation and existence of ultra-compact dwarfs in groups, and a new supergroup in Eridanus were also discussed.

Oxoketene-oxoketene, imidoylketene-imidoylketene and oxoketenimine-imidoylketene rearrangements. 1,3-shifts of phenyl groups

Dibenzoylketene 5 undergoes degenerate 1,3-shifts of the phenyl group between acyl and ketene carbon atoms, thus interconverting it with 6 and 7. This 1,3-shift takes place in the gas phase under flash vacuum thermolysis (FVT) conditions, but not in solution at 110-145 degrees C. Imidoyl(benzoyl)ketene 13 undergoes degenerate 1,3-shift of the phenyl group on FVT, thus interconverting it with 14, but the ketenimine isomer 15 is not formed, and none of these shifts take place in the solid state at 250 degrees C. Imidoyl(p-toluoyl)ketene 21 undergoes a 1,3-p-tolyl shift, interconverting it with ketene 22 but not with ketenimine 23. The imidoyl(p-toluoyl)ketene rotamer 25 cyclizes to 4-toluoyloxyquinoline 28 and 4-quinolone 29. The cyclization of imidoyl(benzoyl)ketene 13 to 4-benzoyloxyquinoline 18, and of 25 to 28 involves 1,3-C-to-O shifts of benzoyl (toluoyl) groups. Calculations of the transition states for the transformations at the B3LYP/6-31G** level of theory are in agreement with the observed reaction preferences.

A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PE-symmetric wavefunctions defined on a contour in the complex plane. (c) 2006 Elsevier B.V. All rights reserved.