On two finite covering problems of Bambah,Rogers, Woods and Zassenhaus

Bambah, Rogers, Woods, and Zassenhaus considered the general problem of covering planar convex bodiesC byk translates of a centrally-symmetric convex bodyK ofE ² with the ramification that these translates cover the convex hullC _k of their centres. They proved interesting inequalities for the volume ofC andC _k . In the present paper some analogous results in euclideand-spaceE ^d are given. It turns out that on one hand extremal configurations ford5 are of quite different type than in the planar case. On the other hand inequalities similar to the planar ones seem to exist in general. Inequalities in both directions for the volume and other quermass-integrals are given.     

Ruthenium(II) complexes of monodonor ligands: efficient reagents for asymmetric ketone hydrogenation

[Chemical reaction: See text] A series of BINOL-derived ligands have been prepared and incorporated into ruthenium(II) complexes containing a diamine ligand. The complexes have proven to be excellent catalysts for the asymmetric hydrogenation of ketones, giving reduction products with enantiomeric excesses of up to 99%.     

A Titration Microcalorimetric Study of the Effects of Halide Counterions on Vesicle-Forming Aggregation in Aqueous Solution of Branched-Chain Alkylpyridinium Surfactants

Titration microcalorimetry is used to study the influences of iodide, bromide, and chloride counterions on the aggregation of vesicle-forming 1-methyl-4-(2-pentylheptyl)pyridinium halide surfactants. Formation of vesicles by these surfactants was characterised using transmission electron microscopy. When the counterion is changed at 303 K through the series iodide, bromide, to chloride, the critical vesicular concentration (cvc) increases and the enthalpy of vesicle formation changes from exo- to endothermic. With increase in temperature to 333 K, vesicle formation becomes strongly exothermic. Increasing the temperature leads to a decrease in enthalpy and entropy of vesicle formation for all three surfactants. However the standard Gibbs energy for vesicle formation is, perhaps surprisingly, largely unaffected by an increase in temperature, as a consequence of a compensating change in both standard entropy and standard enthalpy of vesicle formation. Interestingly, standard isobaric heat capacities of vesicle formation are negative, large in magnitude but not strikingly dependent on the counterion. We conclude that the driving force for vesicle formation can be understood in terms of overlap of the thermally labile hydrophobic hydration shells of the alkyl chains. Copyright 2000 Academic Press.