Analyticity and naturality of the multi-variable functional calculus

Mackey-complete complex commutative continuous inverse algebras generalize complex commutative Banach algebras. After constructing the Gelfand transform for these algebras, we develop the functional calculus for holomorphic functions on neighbourhoods of the joint spectra of finitely many elements and for holomorphic functions on neighbourhoods of the Gelfand spectrum. To this end, we study the algebra of holomorphic germs in weak^*${\mathrm{weak}}^{*}$-compact subsets of the dual. We emphasize the simultaneous analyticity of the functional calculus in both the function and its arguments and its naturality. Finally, we treat systems of analytic equations in these algebras.     

Continuous time simulation of transient polymer networks: Rheological properties

In this work the rheological properties of a concentrated polymer solution or melt are investigated. The polymeric material is described as a transient network and the specific model is of the Yamamoto type with configuration dependent creation and loss rates. For the solution of the model a continuous time simulation approach is used which is based on the stochastic interpretation of the fundamental equations of the theory. The qualitative predictions for the rheological behaviour turn out to be very good. For a quantitative test the unknown configuration dependence of the loss rate function is extracted from experimental data as the solution of an inverse problem. The comparison of experimental data for planar elongational flow with the simulation results using the fitted loss rate function shows that the agreement is satisfactory, but not yet perfect. A possible reason for this finding is given.     

Brownian dynamics simulation of a bead-spring chain model with configuration-dependent anisotropic mobility

The paper presents numerical studies of a bead-spring chain model for concentrated polymer solutions and melts. Anisotropic configuration-dependent mobility tensors determine the interaction forces between the molecular chains. The analysis consists of the solution of the Langevin equation in which the Brownian forces are numerically simulated. For a chain of 10 beads connected by Hookean springs the rheological properties are studied for the case of a sudden onset of a steady shear. The results flow illustrate the effects of the anisotropy of the forces on the beads and of different shear rates. The experimentally observed overshoot in the shear growth function and the first normal stress function is simulated by the model, albeit not quantitavely.     

Enantioselective Total Synthesis of the Lignan (+)‐Linoxepin

An enantioselective total synthesis of the natural (+)‐linoxepin ( 1 ) was accomplished in eleven steps from bromovanin ( 24 ). Key steps are a domino carbopalladation/ Mizoroki–Heck reaction with the formation of a pentacyclic system, an asymmetric hydroboration as well as an oxidative lactonization.     

Frequency dependent conductivity for asymmetric hopping in one dimension

The frequency dependent conductivity for one dimensional disordered classical systems is considered in the presence of an external static electric field which acts as a bias for the hopping rates. In the high frequency limit one obtains an expansion in inverse frequencies for the conductivity, whereas for low frequencies an expansion in the inverse moments of the distribution of the random transition rates is derived. The lowest order contributions of these expansions are explicitely evaluated and compared with recent calculations by Derrida and Orbach. The method is restricted to systems with nonsingular distributions of the transfer rates.     

The proline-catalyzed direct asymmetric three-component Mannich reaction: scope, optimization, and application to the highly enantioselective synthesis of 1,2-amino alcohols

We have developed proline-catalyzed direct asymmetric three-component Mannich reactions of ketones, aldehydes, and amines. Several of the studied reactions provide beta-amino carbonyl compounds (Mannich products) in excellent enantio-, diastereo-, regio-, and chemoselectivities. The scope of each of the three components and the influence of the catalyst structure on the reaction are described. Reaction conditions have been optimized, and the mechanism and source of asymmetric induction are discussed. We further present application of our reaction to the highly enantioselective synthesis of 1,2-amino alcohols.     

A graphics display-oriented strategy for the amino acid sequencing of peptides by tandem mass spectrometry

Summary A graphics display-oriented method for the computer-aided interpretation of the mass spectrum of a peptide in terms of its amino acid sequence is presented. The spectrum is obtained by collision induced decomposition of the protonated molecular ion (M+H)⁺ of the peptide generated by fast atom bombardment in the first double focussing mass analyzer of a tandem mass spectrometer and the product ion mass spectrum (CID spectrum) recorded by the second double focussing mass analyzer. The algorithm displays all series of peaks differing by the mass of -NH-CHR-CO- for the various amino acids. This display, which is very fast and can be augmented through interrogation by the user, greatly facilitates the determination of the amino acid sequence. The method is demonstrated on the spectra of a undecapeptide of (M+H)⁺ m/z = 1208.2 and a tetradecapeptide of (M+H)⁺ m/z = 1758.9.

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Bestimmung der Aminosäure-Sequenz von Peptiden durch Tandem-Massenspektrometrie mit Hilfe eines graphischen Display

     

Über die Temperaturabhängigkeit des komplexen Elastizitätsmoduls von Kupfer

Copper single crystals of various orientations were investigated by means of the resonant bar method. The measurements were performed between 9 and 17 kc/s. The amplitude-independent internal friction and the Young's modulus were determined between ?180 and +200 °C.