Two new direct product-type constructions for resolvable group-divisible designs

We present two direct product-type constructions which will prove useful in the construction of resolvable designs. We use our constructions to complete the spectrum for resolvable group-divisible designs with block size three, as well as to give a short proof of the existence of decompositions of K_6n into a one-factors and b triangle-factors for any a, b, n with a + 2b = 6n ? 1 and a > 1. © 1993 John Wiley & Sons, Inc.     

Surface defects in semiconductor lasers studied with cross-sectional scanning tunneling microscopy

Cross-sectional scanning tunneling microscopy is used to study defects on the surface of semiconductor laser devices. Step defects across the active region caused by the cleave process are identified. Curved blocking layers used in buried heterostructure lasers are shown to induce strain in the layers above them. Devices are also studied whilst powered to look at how the devices change during operation, with a numerical model that confirms the observed behavior. Whilst powered, low-doped blocking layers adjacent to the active region are found to change in real time, with dopant diffusion and the formation of surface states. A tunneling model which allows the inclusion of surface states and tip-induced band bending is applied to analyze the effects on the tunneling current, confirming that the doping concentration is reducing and defect surface states are being formed.     

Space hybrids

The theory of defining localized functions as simultaneous eigenfunctions of commuting matrices representing the variables x, y, and z is developed further to include r, the radial variable. The appropriate complete basis set for use when the weight function in the scalar product is an exponential is described. Hybrid functions that are each strongly localized around a center are defined as eigenfunctions and can be used to describe the electron density of an atom. The hybrid centers lie at the vertices of regular polyhedra centered on the nucleus. The hybrids have the important property of vanishing at the centers of all the other hybrids. Two simple examples are given to illustrate the theory and the methods of calculation. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Determination of the sulphur content of a lunar sample by neutron capture gamma-ray spectrometry

The technique of prompt neutron capture gamma-ray spectroscopy has been used to determine sulphur concentrations in extraterrestrial materials. In particular an effort was made to resolve reported discrepancies in the sulphur assays for the lunar rock sample 70215. While the validity of chemical analysis techniques are often influenced by the chemical form of the sulphur, particularly when in low concentration, the method used here is independent of such effects. The lunar and a bulk Allende meteorite sample were analyzed for sulphur, iron and silicon. The latter material, being well documented, was analyzed in order to verify the techniques of measurement and the subsequent methods of data reduction. Based upon our measurements and the acceptance of the silicon and iron content of the lunar sample the sulphur content was found to be 1741±112 ppm by weight.     

A theorem on tits geometries of type Cn

In this paper we extend a result of [2] to cover a more general situation. In [2] it was shown that a finite C_n geometry (n 4) in which all lines are thick and all C₃ residues are either buildings or flat has to be a building. Here we observe that the finiteness assumption of [2] was unnecessary in order to achieve the major part of the result. If we drop the finiteness assumption we can still prove that such a geometry is either a quotient of a building or flat. Flat C_n geometries for n 4 are seen to be degenerate in a certain sense. In the finite case with thick lines such degenerate geometries are easily shown not to exist, while finite buildings of type C_n with thick lines do not admit non-trivial quotients (Brouwer and Cohen, [1]). Thus the result of [2] follows as an immediate corollary of this more general case. The result does not hold when we drop the assumption that all lines are thick. In Section 3 we produce some examples of geometries of this type.     

Thermal rhythms in composite ladle walls

Conclusions Analytical and numerical solutions have been obtained for the propagation of thermal rhythms in a composite ladle wall. In particular an analytical model simulating switch on-off thermal conditions at the inner ladle wall with Newton Cooling at the outer ladle wall is found to be in exact agreement with the full numerical solution for the composite wall. This analytical solution is seen to possess novel mathematical features.From a practical viewpoint, to obtain minimum heat loss from the ladle of molten steel it is clear that in early operations the insulating region is most effective if it were located close to the inner wall. As the thermal rhythms approach periodicity it is seen that minimum heat loss would be achieved if the insulating region were placed close to the outer ladle wall. Moreover in the later operational stages it was shown that the minimum heat loss is actually obtained if the insulating layer was omitted altogether. Since it is also shown that the time taken to achieve a periodic thermal rhythm is always least when the insulating region is located centrally in the composite ladle wall it can be argued that the evolution of the thermal rhythm is controlled by its inclusion. Inclusion of the insulating layer yields a marked reduction in the outside wall temperature and this could have considerable bearing on the life of the ladle in an integrated steel works.Preheating the ladle walls was found to reduce the ladle heat loss by more than 50 percent during the initial cycle.Finally it is hoped that the above theoretical results will be of considerable value in the understanding of thermal stratification in ladles of molten steel during standing and pouring.     

Atomic and molecular cubature grids

This article presents cubature grids of the Gaussian type that are adapted for the purpose of wave function calculation on atoms and molecules. The problems of the singularity at the nucleus, the derivatives in the kinetic energy, and the presence of two‐electron integrals are shown to be resolved. Each grid has a definite degree of accuracy so that it reproduces the exact values of all the integrals in a defined class. Seventh‐degree accuracy can be obtained from a grid of 143 nodes. The grids are applied, as simple illustrations, to well‐known self‐consistent field (SCF) calculations on helium. Grids for homonuclear diatomics are also discussed and an illustrative application given to a homonuclear diatomic molecule. A comparison between a molecular grid and the union of two unmodified atomic grids shows that overlaps and distortions in weights can occur to the extent that this is not practical. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Regiospecific Suzuki coupling of 3,5-dichloroisothiazole-4-carbonitrile

3,5-Dichloroisothiazole-4-carbonitrile 1 react with aryl- and methylboronic acids to give in high yields the 3-chloro-5-(aryl and methyl)-isothiazole-4-carbonitrile 2 regiospecifically. The reaction was optimized with respect to base, phase transfer agent and palladium catalyst. Suzuki coupling at C-5 was also achieved in high yield using potassium phenyltrifluoroborate. The regiospecificity of either coupling method is maintained with 3,5-dibromoisothiazole-4-carbonitrile 4 to give exclusively 3-bromo-5-phenylisothiazole-4-carbonitrile 5. Suzuki cross-coupling conditions applied to 3-chloro-5-phenylisothiazole-4-carbonitrile 2a gave 3-phenoxy-5-phenylisothiazole-4-carbonitrile 6, which was prepared independently, and not the 3-phenyl derivative. All isothiazole products were fully characterized.