Laguerre Polynomials, Restriction Principle, and Holomorphic Representations of SL(2,R)

The restriction principle is used to implement a realization of the holomorphic representations of SL(2,R) on L ² (R ⁺,t dt) by way of the standard upper half plane realization. The resulting unitary equivalence establishes a correspondence between functions that transform according to the character e^–i(2n++1); under rotations and the Laguerre polynomials. The standard recursion relations amongst Laguerre polynomials are derived from the action of the Lie algebra.     

Reinvestigation of mucohalic acids,versatile and useful building blocks for highly functionalized alpha,beta-unsaturated gamma-butyrolactones

[reaction: see text] Mucohalic acids (mucochloric acid (1, 3,4-dichloro-5-hydroxy-5H-furan-2-one) and mucobromic acid (2, 3,4-dibromo-5-hydroxy-5H-furan-2-one)) are inexpensive, commercially available starting materials with multiple functional groups. These compounds have been modified by way of reduction followed by Suzuki cross-coupling reactions involving arylboronic acids to afford highly functionalized alpha,beta-unsaturated gamma-butyrolactones in excellent yield. The synthetic utility of these building blocks was effectively demonstrated through preparation of the antiinflammatory drug Vioxx.     

Canonical hadron gas interpretation ofp-A E802 data

Hadron gas models have proved successful in predicting particle production in relativistic nucleus-nucleus collisions. The extension of these models to the smaller systems formed in proton-nucleus collisions requires that the finite size of the system be considered. We study two features introduced by the finite size: the need to conserve strangeness and baryon number exactly by performing calculations in the canonical ensemble, and the inclusion of a finite size geometrical correction term in the single particle density of states. We find significant differences between the grand canonical and canonical ensembles and a strong dependence on the baryon number of the system.     

Transition moment closure tests for ethylene

The completeness of a basis set for ethylene is examined relative to its ability to describe transition moments. The double zeta (Dunning contraction) plus polarization plus Rydberg Cartesian Gaussian set does much better for length than for velocity moments. An attempt is made to interpret the transition moment sums for the occupied orbitals.     

Some charge transfer reactions of excited aromatic compounds with sulphides

Photo-reductive dehalogenation of aromatic halides to their parent hydrocarbons is stimulated in the presence of electron donors such as di-ethyl sulphide. Evidence is presented for the involvement of radicals ions in these reactions.     

Observation of a superdeformed band in <Superscript>190</Superscript>Pb

A superdeformed band has been observed in the N = 108 isotope ¹⁹⁰Pb. This is the most neutron-deficient Pb isotope in which superdeformed states have been observed. Several theoretical approaches have predicted that N = 108 will mark the limit of observable superdeformation in the Pb isotopes. The band, which consists of five (possibly six) transitions, is observed to feed at least one isomeric level in its decay to the ground state. This decay pattern supports a spin assignment of 10 for the lowest observed level.     

The rate of gasification by CO2 of chars from waste

Three chars and an activated carbon were gasified by reaction with CO₂ in a fluidised bed of sand, at 800–1050 °C. The chars were produced from (i) dried sewage sludge, (ii) car tyres, and (iii) a bituminous coal. For the conditions used, the rate of CO₂ + C → 2CO was largely determined by chemical kinetics; there was a small effect from mass transfer for the most reactive char, derived from sewage sludge. The rate of CO formation, r, differed greatly for these chars, but was well described by:

The reactivity of a char depends on: (i) its pore structure, (ii) catalytic activity of the associated ash, and (iii) the activity of the char’s carbon. The sewage sludge char was the most reactive, on the basis of either BET area or mass by 2 orders of magnitude. The activated carbon had the lowest reactivity per unit BET surface area, indicating that the area in its micropores is comparatively unreactive.     

Excited states in 163,164Ho populated through incomplete-fusion reactions

High-spin states in ^163,164Ho were investigated by means of in-beam -ray spectroscopy techniques using the multidetector array GASP. Excited states in ^163,164Ho were populated predominantly through the incomplete-fusion mechanism in the ¹⁶⁰Gd (¹¹B reaction at a beam energy of 61 MeV. Known rotational bands in ¹⁶³ Ho have been extended to higher spins and a three-quasiparticle band has been observed in this nucleus. Rotational bands have been identified in ¹⁶⁴Ho and their configurations have been discussed. Empirical Gallagher-Moszkowski (GM) splitting energies were extracted from the and GM doublets. Alignments, band crossing frequencies, and electromagnetic properties have been analyzed in the framework of the cranking model.Received: 13 February 2004, Revised: 18 March 2004, Published online: 14 September 2004PACS: 21.10.Re Collective levels - 21.60.Ev Collective models - 23.20.Lv transitions and level energies - 27.70. + q