Residues of regular and meromorphic differential forms

Dedicated to E. Kunz on the occasion of his sixtieth birthday     

Zur Synthese von isocamphananalogem Ephedrin

The synthesis of two new bicyclic phenylethylamine derivatives with potentially simpathomimetic effects is described. The synthesis of the isocamphane analogous apoephedrine (4) starts from the bicyclic methylketone5 and leads via its -bromoderivative6 and the corresponding tosylamidoketone8 to4. The synthesis of the title compound2 has been accomplished by preparing the -oximinoketone19 from the bicyclic ethylketone15 with subsequent reduction to the amino alcohol derivative20 and final selective monomethylation by theJohnstone procedure via the corresponding trifluoroacetamide.

Herrn Prof. Dr.K. Kratzl mit den besten Wünschen zum 70. Geburtstag gewidmet.     

Extraktive Anreicherung von Gold an mit phosphororganischen Verbindungen modifizierten Kohlepasteelektroden

Zusammenfassung Gold(III) kann aus saurer, chloridhaltiger Lösung mit einer mit Tri-n-octylphosphinoxid (TOPO) oder Tri-n-butylphosphat (TBP) modifizierten Kohlepasteelektrode extraktiv angereichert werden. Als voltammetrische Bestimmung eignet sich für quantitative analytische Zwecke die kathodische Differentialpulsvoltammetrie (CDPV). Die Abhängigkeit der Anreicherung von methodischen Parametern (Acidität, Anreicherungszeit usw.) wie auch Fremdioneneinflüsse werden untersucht.

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Extractive preconcentration of gold with carbon paste electrodes modified with organophosphorous compounds

Summary Gold(III) can be preconcentrated from acidic chloride-containing solution at a carbon paste electrode chemically modified with tri-n-octylphosphine oxide (TOPO) or tri-n-butylphosphate (TBP). For quantitative analytical purposes cathodic differential pulse voltammetry (CDPV) can be applied. The dependence of the preconcentration on methodical parameters (acidity, preconcentration time etc.) as well as interferences with other extractable ions have been investigated.

     

Polyminimaxgruppen

Ohne Zusammenfassung     

Composite wavelet bases for operator equations

This paper is concerned with the construction of biorthogonal wavelet bases defined on a union of parametric images of the unit -cube. These bases are to satisfy certain requirements imposed by applications to a class of operator equations acting on such domains. This covers also elliptic boundary value problems, although this study is primarily motivated by our previous analysis of wavelet methods for pseudo-differential equations with special emphasis on boundary integral equations. In this case it is natural to model the boundary surface as a union of parametric images of the unit cube. It will be shown how to construct wavelet bases on the surface which are composed of wavelet bases defined on each surface patch. Here the relevant properties are the validity of norm equivalences in certain ranges of Sobolev scales, as well as appropriate moment conditions.

     

Explicit Green operators for quantum mechanical Hamiltonians. I. The hydrogen atom

We study a new approach to determine the asymptotic behaviour of quantum many-particle systems near coalescence points of particles which interact via singular Coulomb potentials. This problem is of fundamental interest in electronic structure theory in order to establish accurate and efficient models for numerical simulations. Within our approach, coalescence points of particles are treated as embedded geometric singularities in the configuration space of electrons. Based on a general singular pseudo-differential calculus, we provide a recursive scheme for the calculation of the parametrix and corresponding Green operator of a nonrelativistic Hamiltonian. In our singular calculus, the Green operator encodes all the asymptotic information of the eigenfunctions. Explicit calculations and an asymptotic representation for the Green operator of the hydrogen atom and isoelectronic ions are presented.     

Synthesis of Poly(Ethylene Glycol)–Supported (R)-BINOL Derivatives and Their First Application in Enantioselective Mukaiyama Aldol Reactions

The Mukaiyama aldol reaction of 2-styryl-oxazole-4-carbaldehyde (1) as model substrate with S-ketene silyl acetal 2 catalyzed by poly(ethylene glycol)-supported binaphthyl-derived chiral titanium(IV) complexes afforded the corresponding aldol product in good to excellent yields and enantioselectivities up to 94% ee. The chemical yields and/or the enantioselectivities are enhanced by generating the active catalyst from Ti(OiPr)₄, polymer-supported ligands (R)-6 or (R)-8, and chiral or achiral promoters. Pyrrolidine derivative (S)-13 and trifluoromethyl-substituted phenol 12 are the most efficient additives found.     

A multi-configuration reference CEPA method based on pair natural orbitals

Summary A multi-reference CI scheme is proposed which is aiming at a considerable reduction of the generally very large number of configurations of CI expansions in multi-configuration reference cases. This reduction is achieved by combining the idea of internal contraction, the concept of pair natural orbitals (PNO's) and CEPA (coupled electron pair) type approximations for the contributions of higher than double excitations. This latter estimate leads to size consistent results and also permits to employ reference wavefunctions that contain only the dominantly occupied configurations of the considered system. Applications to two test cases, the lowest states (³ P,¹ D and¹ S) of the carbon atom and the symmetry forbiddenC _2v insertion reaction of Be and H₂, show that our method is able to truncate CI expansions to lengths of no more than 10³–10⁴ without losing more than 1–2% of the correlation energy. The calculated excitation energies and energy barriers agree with the full CI results in the respective basis within about 1 kcal/mol. Thus the MC-CEPA-PNO method presents a very efficient way to obtain chemical accuracy in CI-calculations for molecular systems.Dedicated to Prof. Dr. W. Kutzelnigg on the occasion of his 60th birthday     

Trace Element Determination in Diesel Particulates by Total-Reflection X-Ray Fluorescence Analysis

 Particulate matter of Diesel emissions collected from diluted exhaust during standard test runs with two Diesel fuels of different sulfur content was analysed by total-reflection X-ray fluorescence (TXRF). The trace elements determined were S, Ca, Cr, Mn, Fe, Ni, Cu, Zn and Pb. Additionally, some filter materials were tested with respect to their applicability for sample collection. Quartz fibre filters were found to be most suitable, both from a technical and a chemical point of view. A clear reduction of total particulate emissions during the whole test was observed when the fuel with very low sulfur content was used. In addition, it was found that the wear metal content of particulate matter emitted by a cold engine was higher than that observed during normal engine working temperature. Received September 10, 1998. Revision March 2, 1999