The Approach Towards Equilibrium in a Reversible Ising Dynamics Model: An Information-Theoretic Analysis Based on an Exact Solution

We study the approach towards equilibrium in a dynamic Ising model, the Q2R cellular automaton, with microscopic reversibility and conserved energy for an infinite one-dimensional system. Starting from a low-entropy state with positive magnetisation, we investigate how the system approaches equilibrium characteristics given by statistical mechanics. We show that the magnetisation converges to zero exponentially. The reversibility of the dynamics implies that the entropy density of the microstates is conserved in the time evolution. Still, it appears as if equilibrium, with a higher entropy density is approached. In order to understand this process, we solve the dynamics by formally proving how the information-theoretic characteristics of the microstates develop over time. With this approach we can show that an estimate of the entropy density based on finite length statistics within microstates converges to the equilibrium entropy density. The process behind this apparent entropy increase is a dissipation of correlation information over increasing distances. It is shown that the average information-theoretic correlation length increases linearly in time, being equivalent to a corresponding increase in excess entropy.     

EPR and ENDOR investigations of Ge,Sn and Pb impurities in CdSe

Electron paramagnetic resonance (EPR) experiments of light activated Ge, Sn and Pb impurities in wurtzite type CdSe crystals are presented. These²S_1/2 centres exhibit a large hyperfine structure which shows a variation with temperature. 25 shells of neighbour nuclei are resolved for CdSeSn by means of the Electron nuclear double resonance (ENDOR) technique. All shells belong to one of three distinct shell symmetries of the lattice thus confirming a high symmetry defect. Additional Sn respectively Ge related spectra are described and interpreted as complex centres correlated with lithium.     

On pseudoparticle solutions in Yang's theory of gravity

Within the framework of differential geometry, Yang's parallel-displacement gauge theory is considered with respect to pure gravitational fields. In afour-dimensional Riemannian manifold it is shown that thedouble self-dual solutions obey Einstein's vacuum equations with the cosmological term, whereas the doubleanti-self-dual configurations satisfy the Rainich conditions of Wheeler'sgeometrodynamics. Conformal methods reveal that the gravitational analog of the instanton or pseudoparticle solution of Yang-Mills theory was already known to Riemann.     

Phase-Transfer Catalyzed Two-Phase Reactions in Preparative Organic Chemistry

Quaternary ammonium and phosphonium salts catalyze reactions between substances located partly in an aqueous and partly in an organic phase. Use of such phase-transfer catalysts simplifies and accelerates numerous reactions traditionally conducted in nonaqueous media. These reactions include carbene reactions, nucleophilic substitutions, alkylations of ketones and nitriles, Wittig and Darzens reactions, formation of ethers and esters. Other reactions such as hydrolysis and oxidation can be accelerated.     

Nachweisgrenzen proteolytischer Aktivitäten

Zusammenfassung Verschiedene Methoden der Bestimmung von Proteaseaktivitäten warden jeweils am gleichen Protease-Präparat (Bromelin, Trypsin,-Chymotrypsin, Pepsin) geprüft, um die Erfassungsgrenzen zu ermitteln. Wie erwartet, erhöhen längere Inkubationszeiten die Empfindlichkeit der Methoden, jedoch können auch schon bei Inkubationszeiten von nur 1 Minute beispielsweise noch Trypsinkonzentrationen von ca. 100 ng/ml gemessen werden. Unerwartet war das Ergebnis, daß sich auch mit relativ einfachen Mitteln (Milch als Substrat, Messung der freigesetzten Aminogruppen mit TNBS) noch sehr geringe Enzymkonzentrationen erfassen lassen. Da diese Methode praktisch für alle untersuchten Proteasen von optimaler Empfindlichkeit ist, dürfte sie insbesondere für die Untersuchung von Proteasen unbekannter Natur von Bedeutung sein.

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Detection limits for proteases

Summary Different methods for the assay of protease activities are compared with the same protease preparation (bromelin, trypsin, -chymotrypsin, pepsin) in order to find out the limits of detection. As expected the sensitivity of the methods rises with the longer incubation times, but in spite of this incubations as short as 1 minute may be sufficient in the determination of e. g. trypsin at a level of 100 ng/ml. Unexpected was the result that with a rather simple method (milk as substrate, determination of free amino groups with trinitrobenzenesulfonic acid) very small concentrations of enzyme may be measured. As this method practically gives optimal sensitivity for all proteases studied, it may be of special value for the assay of proteases whose nature is unknown.

     

13C-NMR-spektroskopische und stereochemische Untersuchungen: XI—Konformationen von Bicyclo[3.3.1]nonanen und ihre Unterscheidbarkeit durch lanthanideninduzierte Verschiebungen

The ¹³C chemical shifts of bicyclo[3.3.1]nonane and of the corresponding 9-hydroxy- and 9-oxo- derivatives are compared with chemical shifts calculated on the basis of stereospecific shift increments. These results as well as the ¹H n.m.r. spectrum of the ketone indicate a predominant chair-chair conformation CC. A low temperature ¹³C n.m.r. study as well as an analysis of the temperature dependence of ¹³C chemical shifts in bicyclo[3.3.1]nonane furnish a limit for the free energy difference between CC and BC conformations of ΔG ≧ 5,85 kJ mol^?1. The distinction between CC, BC and BB provides a test for the applicability of lanthanide-induced ¹H and ¹³C shifts for the assignment of flexible geometries. The typical occurrence of several and/or flat minima in the LIS geometry analysis allows only the exclusion of boat–boat conformations.     

Conformal changes of metrics and the initial-value problem of general relativity

Conformal techniques are reviewed with respect to applications to the initial-value problem of general relativity. Invariant transverse traceless decompositions of tensors, one of its main tools, are related to representations of the group of conformeomorphisms acting on the space of all Riemannian metrics onM. Conformal vector fields, a kernel in the decomposition, are analyzed on compact manifolds with constant scalar curvature. The realization of arbitrary functions as scalar curvature of conformally equivalent metrics, a generalization of Yamabe's conjecture, is applied to the Hamiltonian constraint and to the issue of positive energy of gravitational fields. Various approaches to the solution of the initial-value equations produced by altering the scaling behavior of the second fundamental form are compared.     

The eightfold way to color geometrodynamics

Color models of strong interactions are generalized to aGL(8,) ^f GL(8,) ^c gauge theory incorporating space-time curvature and Cartan's torsion. Following Salam, the dynamics is determined by an Einstein-Dirac-type Lagrangian. The resulting field equations are anonlinear (due to the torsion) Heisenberg-Pauli-Weyl equation for the fundamental spinor fields and a generalized Einstein equation for the background metric of hadronic dimensions. According to this model baryonic quarks are confined ingeon (black soliton)-type objects by the tensor gluons ofstrong gravity. This approach also leads to a black soliton mass formula which is in qualitative agreement with part of the baryon spectrum. Hadronic mesons are interpreted as gluon strings trapped in a multiconnected space-time. Interrelations of color geometrodynamics with other bag models are pointed out. Finally, the conceptual origin of this space-time foundation of quark confinement is presented.