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     

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.     

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.     

A Mets motif peptide found in copper transport proteins selectively binds Cu(I) with methionine-only coordination

Mets motifs, which refer to methionine-rich sequences found in the high-affinity copper transporter Ctr1, also appear in other proteins involved in copper trafficking and homeostasis, including other Ctrs as well as Pco and Cop proteins isolated from copper-resistant bacteria. To understand the coordination chemistry utilized by these proteins, we studied the copper binding properties of a peptide labeled Mets7-PcoC with the sequence Met-Thr-Gly-Met-Lys-Gly-Met-Ser. By comparing this sequence to a series of mutants containing noncoordinating norleucine in place of methionine, we confirm that all three methionine residues are involved in a thioether-only binding site that is selective for Cu(I). Two independent methods, one based on mass spectrometry and one based on rate differences for the copper-catalyzed oxidation of ascorbic acid, provide an effective K(D) of approximately 2.5 microM at pH 4.5 for the 1:1 complex of Mets7-PcoC with Cu(I). These results establish that a relatively simple peptide containing an MX(2)MX(2)M motif is sufficient to bind Cu(I) with an affinity that corresponds well with its proposed biological function of extracellular copper acquisition.     

Phase diagram of softly repulsive systems: the Gaussian and inverse-power-law potentials

We redraw, using state-of-the-art methods for free-energy calculations, the phase diagrams of two reference models for the liquid state: the Gaussian and inverse-power-law repulsive potentials. Notwithstanding the different behaviors of the two potentials for vanishing interparticle distances, their thermodynamic properties are similar in a range of densities and temperatures, being ruled by the competition between the body-centered-cubic (bcc) and face-centered-cubic (fcc) crystalline structures and the fluid phase. We confirm the existence of a reentrant bcc phase in the phase diagram of the Gaussian-core model, just above the triple point. We also trace the bcc-fcc coexistence line of the inverse-power-law model as a function of the power exponent n and relate the common features in the phase diagrams of such systems to the softness degree of the interaction.     

Synthesis of non-k-region ortho-quinones of polycyclic aromatic hydrocarbons from cyclic ketones

Non-K-region $\text{o}$-quinones of polycyclic aromatic hydrocarbons are prepared in four steps from cyclic ketones via dehydrogenation of tetrahydrodiols with 2,3-dichloro-5,6-dicyano-1,4-benzoquinone.     

Beiträge zur Chemie der Pyrrolpigmente, 26. Mitt.: Zur anaeroben Photochemie von Gallenpigmenten: Die Lumineszenz von Gallenpigment-Partialstruktursystemen und integralen Farbstoffen

The luminescence properties of about twentyfive model compounds representing the three main partial structures of bile pigments (namely pyrromethenes, pyrromethenones and methylenepyrrolylmethylenepyrrolinones) as well as tripyrrines and the geometrical isomers of aetiobiliverdin-IV- are reported. In these compounds there is usually only a very faint or even no fluorescence and phosphorescene as the pathway of deexcitation. Vibrational internal conversion and photoisomerizations at the exocyclic double bonds are the main anaerobic paths of radiationless decay of the excited states.

H. Falk, K. Grubmayr, E. Haslinger, T. Schlederer undK. Thirring, Mh. Chem.109, 1451 (1978).