In situ formation of ligand and catalyst--application in ruthenium-catalyzed enantioselective reduction of ketones

The direct in situ formation of highly efficient ruthenium-catalysts for the asymmetric reduction of ketones was obtained by combining chiral ligand building blocks with a ruthenium precursor.     

Novel simple and highly modular ligands for efficient asymmetric transfer-hydrogenation of ketones

Novel simple and highly modular dipeptide-analogue ligands combined with [RuCl2(p-cymene)]2 were demonstrated to efficiently catalyze the reduction of ketones under hydrogen transfer conditions with enantioselectivities up to 96%.     

Reentrant phase transition in granular superconductors

The conditions for the appearance of a reentrant superconducting phase in granular materials are studied in mean field approximation applied to periodic models. We assume that the relevant low-lying excitation is the transfer of a Cooper pair from a grain to one of its neighbours, and neglect pair breaking. Both on-grain (U) and nearest neighbour (V) Coulomb interactions are taken into account, and the Coulomb problem is treated in Bethe-Peierls approximation. WhenV/U is not too large, reentrance is predicted ifV/U>(4+3z)^?1/2 wherez is the coordination number. This result is different from a recent criterion suggested by ?imánek, which allows reentrance only in the immediate vicinities of certain discrete values ofV/U. For strong enoughV/U, the models treated here show a transition to an ionic-salt-like charge-ordered state. Reentrant superconductivity is shown to occur also on an ionic background. In actual systems, close-packing effects partially frustrate the ionic ordering and enhance the reentrant feature.     

Step Fluctuations for a Faceted Crystal

A statistical mechanics model for a faceted crystal is the 3D Ising model at zero temperature. It is assumed that in one octant all sites are occupied by atoms, the remaining ones being empty. Allowed atom configurations are such that they can be obtained from the filled octant through successive removals of atoms with breaking of precisely three bonds. If V denotes the number of atoms removed, then the grand canonical Boltzmann weight is q ^V , 0<q<1. As shown by Cerf and Kenyon, in the limit q1 a deterministic shape is attained, which has the three facets (100), (010), (001), and a rounded piece interpolating between them. We analyse the step statistics as q1. In the rounded piece it is given by a determinantal process based on the discrete sine-kernel. Exactly at the facet edge, the steps have more space to meander. Their statistics is again determinantal, but this time based on the Airy-kernel. In particular, the border step is well approximated by the Airy process, which has been obtained previously in the context of growth models. Our results are based on the asymptotic analysis for space-time inhomogeneous transfer matrices.     

The mass enhancement and the specific heat of disordered and amorphous metals

The reduction of the mean free path in metals causes a change of the electronphonon interaction and the Eliashberg function α²(Ω)F(Ω). The values of α²(Ω)F(Ω) for pure, disordered and amorphous lead are used to calculate the enhancement of the density of states and the electronic specific heat in these materials. In pure lead the cyclotron mass (1+λ) has a maximum at 11 °K and the Sommerfeld constant (γ) has a maximum at 5 °K. In disordered lead with a mean free path of about 70 Å, both, 1+λ and γ are almost constant in this temperature range. For amorphous lead there is no temperature range where 1+λ and γ are sufficiently constant. A measurement of the specific heat in disordered non-superconducting metals could answer the question whether these metals are closer to the superconducting state when their mean free path is reduced, a fact which is true for all weak-coupling superconductors.     

Enhanced self‐ordering of anodic ZrO2 nanotubes in inorganic and organic electrolytes using two‐step anodization

This work reports on the optimized growth of self‐ordered ZrO₂ nanotubes in inorganic water‐based and organic electrolyte systems containing small amounts of fluoride employing a two‐step anodization process. We show how surface pretreatments of the metallic Zr substrate can drastically improve the growth and morphology of the resulting anodic ZrO₂ nanotube arrays. Using two step anodization and employing organic electrolytes, highly regular and ordered nanotubular ZrO₂ oxide layers can be grown to significantly increased tube lengths compared with aqueous electrolytes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Towards ideal hexagonal self‐ordering of TiO2 nanotubes

The present work reports on key factors that influence the degree of order in anodic TiO₂ nanotube layers. We show that the anodization voltage and the Ti purity are of crucial importance for the ideality of self‐organization within the nanotube layers and that repeated anodization can significantly improve hexagonal ordering. Optimizing each factor significantly reduces the variation in the average pore diameter and strongly reduces the areal density of polygon ordering/packing errors. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A combinatorial proof of associativity of Ore extensions

We use a counting argument to show that Ore extensions are associative.     

Partial category actions on sets and topological spaces

We introduce (continuous) partial category actions on sets (topological spaces) and show that each such action admits a universal globalization. Thereby, we obtain a simultaneous generalization of corresponding results for groups, by Abadie, and Kellendonk and Lawson, and for monoids, by Megrelishvili and Schröder. We apply this result to the special case of partial groupoid actions where we obtain a sharpening of a result by Gilbert, concerning ordered groupoids, in the sense that mediating functions between universal globalizations always are injective.