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.     

Accreditation of reference material producers: the example of IRMM's Reference Materials Unit

The potential approaches for third-party assessment of reference material producers are revisited and the activities of the Reference Materials (RM) Unit of the Institute for Reference Materials and Measurements (IRMM) to obtain accreditation to ISO Guide 34 and ISO 17025 are described. Accreditation was related to the Unit as all matrix RM activities of the institute are concentrated there. A management system was established that allows sufficient flexibility to be applicable to a wide range of RMs while being precise enough to ensure compliance with ISO Guides 30, 31 and especially 34 and 35. Accreditation was achieved in 2004 with independent scopes for testing and RM production and was confirmed and extended in 2005. The key aspects of the RM Unit's management system for RM production are presented. Presented at BERM-10, April 2006, Charleston, SC, USA     

Magnetism of metal cyanide networks assembled at interfaces

Studies of metal cyanide thin films prepared directly at interfaces are reviewed. The systems range from monolayers, single-layer analogs of Prussian blue-like networks, to bulk powders prepared as thin films. Monolayer networks are prepared at the air/water interface and transferred to solid supports using Langmuir-Blodgett film methods. Films of bulk materials are prepared directly on solid surfaces using a templated sequential deposition procedure. The magnetic properties of the films have been explored, and in some cases, these monolayers and surface films give rise to new behavior that is only possible because of the fabrication method or thin film architecture. The methods of synthesis can generate oriented samples, even when the materials are poorly crystalline. Furthermore, the interface-assembled networks are inherently anisotropic, leading to phenomena not present in the solid-state analogs, such as anisotropic photomagnetism in a thin film of Rb_jCo_k[Fe(CN)₆]_l·nH₂O.     

Über lokalarchimedische Anordnungen projektiver Ebenen

The question, whether the Archimedean ordering of only one of the ternary rings of a projective plane implies that is Archimedean, i.e. that every ternary ring of is Archimedean, is answered in the negative by the construction of local-Archimedean orderings of free planes. There exists even Archimedean affine planes with non-Archimedean associated projective planes.