Quenched asymptotics of the ground state energy of random Schrödinger operators with scaled Gibbsian potentials

 This article describes the almost sure infinite volume asymptotics of the ground state energy of random Schr?dinger operators with scaled Gibbsian potentials. The random potential is obtained by distributing soft obstacles according to an infinite volume grand canonical tempered Gibbs measure with a superstable pair interaction. There is no restriction on the strength of the pair interaction: it may be taken, e.g., at a critical point. The potential is scaled with the box size in a critical way, i.e. the scale is determined by the typical size of large deviations in the Gibbsian cloud. The almost sure infinite volume asymptotics of the ground state energy is described in terms of two equivalent deterministic variational principles involving only thermodynamic quantities. The qualitative behaviour of the ground state energy asymptotics is analysed: Depending on the dimension and on the H?lder exponents of the free energy density, it is identified which cases lead to a phase transition of the asymptotic behaviour of the ground state energy. Received: 24 June 2002 / Revised version: 17 February 2003 Published online: 12 May 2003 Mathematics Subject Classification (2000): Primary 82B44; Secondary 60K35 Key words or phrases: Gibbs measure – H?lder exponents – Random Schr?dinger operator – Ground state – Large deviations     

Photopolymers for Rapid Prototyping of Soluble Mold Materials and Molding of Cellular Biomaterials

To substitute cross-linked photopolymers in rapid prototyping of mold materials and therefore extend the range of materials which can be casted, organo-soluble photopolymers were developed. Branched bisalkylacrylamides were suitable as base component for such formulations, due to their high reactivity, good mechanical properties, and excellent solubility of the formed polymers. These molding materials were used to prepare cellular biocompatible materials which could be used as bone replacement materials. Biocompatible crosslinkers based on methacrylates from hydrolyzed gelatine or lactic acid ethyleneglycol blockcopolymers and commercially available reactive diluents are the base components of such a formulation. Biocompatibility was investigated by osteoblast-like cells. Cellular biocompatible parts were obtained by thermal polymerization in soluble mould materials prepared by 3D-photoshaping.     

Interpolatory properties of best rationalL 1-approximations

In this paper the distribution of the zeros of the error function for bestL ₁-approximation by rational functions fromR _n,m is considered. It is shown that the maximal distance between such zeros isO(1/(n–m)), ifn > m.Communicated by Edward B. Saff.     

Die Bestimmung von Glyoxal und Glyoxyls?ure

Zusammenfassung Es werden Methoden beschrieben, mit deren Hilfe Glyoxal und Glyoxylsäure nebeneinander bestimmt werden können. Die Summe der Carbonylverbindungen wird mit einer bekannten Menge Semicarbazid zu den Semicarbazonen umgesetzt und das überschüssige Semicarbazid jodometrisch bestimmt. Glyoxal allein wird in einer zweiten Bestimmung mit Lauge nach Cannizzaro in glykolsaures Natrium umgesetzt und der dafür erforderliche Laugeverbrauch titrimetrisch bestimmt. Aus der Summe Glyoxal + Glyoxylsäure einerseits und der Glyoxalbestimmung andererseits läßt sich der Glyoxylsäuregehalt berechnen.     

Stereoselective synthesis of cis-p-menth-8-ene-1,7-diol, cis-p-menthane-1,7-diol, and cis-p-menthane-1,7,8-triol

The natural products cis-p-menthane-1,7-diol (cis-IV), cis-p-menth-8-ene-1,7-diol (cis-I) and cis-p-menthane-1,7,8-triol (cis-II) are obtained starting from the corresponding cis-cyanohydrins, cis-2 and cis-7, respectively, by chemical transformation of the cyano into the hydroxymethyl group. The key step of the synthesis is the very high cis-selectivity (> or = 96 %) of the MeHNL-catalyzed HCN addition to 4-alkylcyclohexanones. From 4-isopropylcyclohexanone (1) the cyanohydrin cis-2 and from 4-(1-methylvinyl)cyclohexanone (6) the cyanohydrin cis-7 result almost quantitatively. Regioselective hydroxylation of cis-I affords the triol cis-II. X-ray crystal structure determinations of the final products confirm their cis-configuration.