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.

     

Application of the NDDO method to transition metal compounds

The NDDO method has been extended to include elements withd-orbitals. A parametrization for the first-row transition metals is given, which has been worked out to describe structural properties of transition metal complexes. Applications of the method to the Jahn-Teller distortions of tetrachloro complexes are presented. The NDDO results are compared with those from CNDO and INDO calculations. It turns out that the NDDO method seems to be the most sensitive among the ZDO procedures.     

Synthesis and structural characterization of neutral higher-coordinate silicon(IV) complexes with tridentate dianionic chelate ligands

The neutral pentacoordinate silicon(IV) complexes 8 and 9 with an SiO2N3 skeleton and the neutral hexacoordinate silicon(IV) complex 10.1/2 CH3CN with an SiO4N2 skeleton were synthesized, starting from tetra(cyanato-N)silane or tetra(thiocyanato-N)silane. Compounds 8 and 9 contain one tridentate dianionic ligand derived from 4-[(2-hydroxyphenyl)amino]pent-3-en-2-one and two monodentate singly charged cyanato-N or thiocyanato-N ligands bound to the silicon(IV) coordination center, whereas the silicon(IV) center of 10 is coordinated by two of these tridentate dianionic ligands. All compounds were characterized by single-crystal X-ray diffraction and solid-state and solution NMR spectroscopy. To get more information about the stereochemistry of the compounds studied, the experimental investigations were complemented by computational studies.     

Characterization of multilayers by means of EDXS in the analytical TEM

Referring to the characterization of nanoscale multilayers in cross section, the resolution limits of the EDXS method have been investigated. For that purpose EDXS line scan profiles of nanoscale Fe-Cr multilayers have been calculated assuming an increased specimen thickness and different tilts between electron beam and layer interface. The resolution limit seems to be greater than 2 nm layer thickness for regular multilayers. Experimentally a limit of 5 nm was reached. Received: 30 July 1997 / Accepted: 2 February 1998     

Synthesen und Kristallstrukturanalysen neuer zwitterionischer spirocyclischer (Ammonioorganyl)bis[vic-arendiolato(2–)]silicate: Untersuchungen zur Struktur der λ5Si-Koordinationspolyeder

Syntheses and Crystal Structure Analyses of New Zwitterionic Spirocyclic (Ammonioorganyl)bis[vic-arenediolato(2–)]silicates: Studies on the Structure of the λ⁵Si Coordination Polyhedra A new crystallographic modification ( 1-II ) of the zwitterionic λ⁵Si-spirosilicate [2-(pyrrolidinio)ethyl]bis[3,4,5,6-tetrabromobenzene-1,2-diolato(2 – )]silicate ( 1 ) was synthesized. In addition, two solvent-free crystallographic modifications ( 2-I, 2-II ) and two solvates ( 2 · Me₂CO, 2 λ MeNO₂) of the zwitterionic λ⁵Si-spirosilicate [(morpholinio)methyl]bis[2,3-naphthalenediolato(2 – )]silicate ( 2 ) were prepared. All new compounds were studied by ²⁹Si-CP/MAS NMR spectroscopy and compounds 1-II (Pna2₁), 2 · Me₂CO (P2₁/c), and 2 · MeNO₂ (P2₁/n) were structurally characterized by single-crystal X-ray diffraction.     

Derivate des Sila-Mephenhydramins und Sila-Chlorphenoxamins

DerivativesA andB of the two sila-antihistamines silamephenhydramine and sila-chlorphenoxamine were synthesized for the first time by the steps shown in scheme 1. They and their precursors III and IV were characterized by their physical (Table 1) and chemical properties and their structures confirmed by NMR and mass spectroscopy (Tables 2 and 3). Their pharmacological effects were investigated and compared with those of the corresponding sila-antihistamines.

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4. Mitt.:R. Tacke undU. Wannagat,107, 449 (1976).

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Mit Auszügen aus der DissertationR. Tacke, Techn. Univ. Braunschweig 1974.     

Syntheses of enantiopure Si-centrochiral silicon-based muscarinic antagonists using an enantioselective enzymatic esterification as the key step

The muscarinic antagonists (R)-cyclopentyl(hydroxymethyl)phenyl[2-(piperidin-1-yl)ethyl]silane[(R)-1] and(R)-1-{2-[cyclopentyl(hydroxymethyl)phenylsilyl]ethyl}-1-methylpiperidinium iodide [(R)-2] were synthesized using anenantioselective enzymatic transformation as the key step. Apapain-catalyzed (E.C. 3.4.22.2) esterification ofrac-cyclopentyl(hydroxymethyl)phenyl(vinyl)silane(rac-3) with 5-phenylpentanoic acid afforded(R)-cyclopentyl(phenyl)[(5-phenylpentanoyloxy)methyl]vinylsilane[(R)-4] which upon chemical hydrolysis gave enantiomericallyenriched (R)-3 (68% ee). Repetition of thisesterification/hydrolysis sequence, starting from enantiomericallyenriched (R)-3, finally gave the enantiopure silane (R)-3(98% ee) which served as the starting material for thesubsequent chemical synthesis of (R)-1 and (R)-2{(R)-3 (R)-cyclopentyl(phenyl)[(trimethylsilyloxy)methyl]vinylsilane[(R)-5] (R)-1 (R)-2}.