Billiards and Teichmüller curves on Hilbert modular surfaces

This paper exhibits an infinite collection of algebraic curves isometrically embedded in the moduli space of Riemann surfaces of genus two. These Teichmüller curves lie on Hilbert modular surfaces parameterizing Abelian varieties with real multiplication. Explicit examples, constructed from L-shaped polygons, give billiard tables with optimal dynamical properties.

     

‘Doing the right problem’ <Emphasis Type="Italic">versus</Emphasis> ‘doing the problem right’: problem structuring within a Land Force environment

The essential first step of any OR investigation is to ensure that the ‘right problem’ is studied. Our approach is to propose a set of six ‘rights’ or questions whereby achievement against particular aspects of a problem space is made and these provide the basis for scoping the context, understanding the system, and proposing sound options to the decision-maker. This style of problem structuring is an essential element of the Defence problem domain, and especially so for the Land Force, where there exist multiple degrees of freedom for poorly defined problems in an environment of uncertainty and ambiguity. Central to this is performing conceptual rather than analytical modelling, as perturbations then provide a basis for exploring a space, rather than solving a problem.     

Large area bolometers for millimeter-wave power calibration

An accurate monolithic power meter has been developed for millimeter-wave applications. The detector is a large-area Bismuth bolometer, integrated on a fused-Quartz substrate. It simply measures the temperature change caused by the absorption of millimeter-wave radiation. The power meter is simple to fabricate, inexpensive, and can be easily calibrated using a low-frequency network. The measured responsivity for a 50 bolometer, with an area of 1×1cm, at a bias of 1V. and a video modulation of 100Hz, is 1mV/W. The noise spectrum exhibits a 1/f rolloff till 1KHz, and is limited by the Johnson noise for higher frequencies. The NEP of the detector is 3WHz^–1/2 at a video modulation of 1KHz. It is possible to decrease the current NEP by fabricating bolometers with higher responsivities. Possible application areas are absolute power calibration and localized power density measurements at millimeter and submillimeter wavelengths.     

Synthesis of some benzimidazole- and benzothiazole-derived ligand systems and their precursory diacids

Procedures are described for the preparation of various bidentate and linear tetradentate benzimidazoles and benzothiazoles incorporating units such as pyridyl and thioether, and for the preparation of certain thioether dicarboxylic acids precursory to them. Condensations of ortho-functinal anilines with carboxylic acids were carried out in polyphosphoric acid or refluxing HCl solution. Syntheses are reported for: [HO₂C(CH₂)2S(CH₂)₂]₂X (X = O, S), 1,9-bis(benzimidazol-2-yl)-2,5,8-trithianonane, 1,11-bis(N-methylbenzimidazol-2-yl)-3,6,9-trithiaundecane, 1,11-bis(2-benzimidazol-2-yl)-6-oxo-3,9-dithiaundecane, 2-(2-pyridyl)benzothiazole, 2,6-bis(benzothiazol-2-yl)pyridine, 2-(2-pyridyl)-N-methylbenzimidazole, 2-(2-pyridylmethyl)benzimidazole and 2-(N-methyl-2-piperidyl)benzimidazole. The compounds were characterized, where appropriate, by their mass, uv and ¹H-nmr spectra.     

Crystal field in rare-earth fluorides—I. Molecular orbital calculation of PrF3 parameters

Crystal field parameters have been calculated, using ab initio LCAO-MO theory, for the ion pair Pr³⁺—F⁻ at five metal ligand distances appropriate to Pr³⁺:LaF₃. The parameters are found to be twice as large as in PrCl₃, but with only half the distance dependence. In the absence of precise Pr³⁺:LaF₃ experimental parameters only qualitative agreement with experiment can be recorded. However, very good numerical agreement is obtained with the experimental covalency parameters for Yb³⁺:CaF₂, which provides a check on the methods adopted for calculating energy denominators.     

Pseudo goldstones at future colliders from the extended BESS model

Decays and branching ratios of light neutralino production in $Z_R^0 \to \tilde \chi _i^0 \tilde \chi _j^0 $ in the left-right super-symmetric model are considered. We study in detail the signatures of one and two sided events in $Z_R^0 \to \tilde \chi _1^0 \tilde \chi _2^0 $ and $Z_R^0 \to \tilde \chi _2^0 \tilde \chi _2^0 $ respectively, and their dependence on the parameters of the light neutralino mixing matrix.     

Primeness of the enveloping algebra of a Cartan type Lie superalgebra

We show that a primeness criterion for enveloping algebras of Lie superalgebras discovered by Bell is applicable to the Cartan type Lie superalgebras , even. Other algebras are considered but there are no definitive answers in these cases.