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%.     

Synthesis of a polymer-supported oxazolidine aldehyde for asymmetric chemistry

An expedient synthesis of the polymer-supported aldehyde 3, as a Garner aldehyde equivalent, is described. Oxazolidine 3 may be obtained through preformation of aldehyde linker 4 in solution and loaded onto amine-terminating resin under peptide-coupling conditions, or alternatively via oxidation of polymer-bound alcohol 14. The integrity of the serine-derived stereocenter is maintained through all steps of the synthesis.     

Electronic structure of platinum at ultrahigh pressure

Abstract

Platinum is studied, theoretically, under very high compression. The calculated equation of state is found to agree well with the recent experimental data. At V/V₀ = 0.4, where V₀ is the experimental equilibrium volume, we find a transition from the face centered cubic structure (fcc), found at ambient pressure, to the body centered cubic structure (bcc). The calculated transition pressure is 26 Mbar. The stabilization of the bcc structure is explained by the eigen value sum.     

Homomorphic Feller Cocycles on a C*-Algebra

When a Fock-adapted Feller cocycle on a C*-algebra is regular,completely positive and contractive, it possesses a stochasticgenerator that is necessarily completely bounded. Necessaryand sufficient conditions are given, in the form of a sequenceof identities, for a completely bounded map to generate a weaklymultiplicative cocycle. These are derived from a product formulafor iterated quantum stochastic integrals. Under two alternativeassumptions, one of which covers all previously considered cases,the first identity in the sequence is shown to imply the rest.     

On regular polyhedra with hidden symmetries

We consider polyhedral realizations of oriented regular maps with or without self-intersections in E³ whose symmetry group is a subsgroup of small index in their. automorphism group. The four classical kepler-poinsot polyhedra are the only ones of index 1. There are exactly five of Index 2, all with icosahedral symmetry group [W2] as the Kepler-poinsot polyhedra. In this paper we show that there are no such polyhedral realizations with octahedral (tetrahedral) symmetry group and index 2 or 3 (2,3,4,5), which is best possible in the octahedral case.     

Asymmetric organocatalysis of the addition of acetone to 2-nitrostyrene using N-diphenylphosphinyl-1,2-diphenylethane-1,2-diamine (PODPEN)

The highly enantioselective addition of acetone to 2-nitrostyrene, using N-diphenylphosphinyl-trans-1,2-diphenylethane-1,2-diamine (PODPEN) as a catalyst, is described.