Adaptive application of operators in standard representation

Recently adaptive wavelet methods have been developed which can be shown to exhibit an asymptotically optimal accuracy/work balance for a wide class of variational problems including classical elliptic boundary value problems, boundary integral equations as well as certain classes of noncoercive problems such as saddle point problems. A core ingredient of these schemes is the approximate application of the involved operators in standard wavelet representation. Optimal computational complexity could be shown under the assumption that the entries in properly compressed standard representations are known or computable in average at unit cost. In this paper we propose concrete computational strategies and show under which circumstances this assumption is justified in the context of elliptic boundary value problems. Dedicated to Charles A. Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 41A25, 41A46, 65F99, 65N12, 65N55. This work has been supported in part by the Deutsche Forschungsgemeinschaft SFB 401, the first and third author are supported in part by the European Community's Human Potential Programme under contract HPRN-CT-202-00286 (BREAKING COMPLEXITY). The second author acknowledges the financial support provided through the European Union's Human Potential Programme, under contract HPRN-CT-2002-00285 (HASSIP) and through DFG grant DA 360/4–1.     

Mehrfachbindungen zwischen Hauptgruppenelementen und Übergangsmetallen : XLIV. Synthesen von Hydrogensulfido- und Hydrogenselenido-Komplexen der Metalle Chrom, Molybdän und Wolfram

Hydrogenchalcogenido complexes of general composition (η⁵-C₅R₅)(CO)₃M(EH) (R = H, CH₃; M = Cr, Mo, W; E = S, Se) can be obtained by three different routes, sometimes in quite good yields. Thus, the sulfur and selenium derivatives can be synthesized by insertion of the respective elements into the metal-hydrogen bonds of the precursor compounds (η⁵-C₅R₅)(CO)₃MH. This species also reacts with potassium selenocyanate to yield the hydrogenselenido derivatives (η⁵-C₅R₅)(CO)₃M(SeH) which can also be obtained by treatment of the methyl complexes (η⁵-C₅R₅)(CO)₃M(CH₃ (M = Mo, W) with HBF₄ and Li[SeH]. The corresponding hydrogentellurido compounds are probably formed by these preparative methods but appear to be quickly converted into either the dinuclear tellurium bridge products (μ-Te)[(η⁵-C₅R₅)(CO)₃M]₂ (M = Mo) or into the hydrido complexes (η⁵-C₅R₅)(CO)₃MH (M= Mo, W) by release of elemental tellurium.     

A new microtensile tester for the study of MEMS materials with the aid of atomic force microscopy

An apparatus has been designed and implemented to measure the elastic tensile properties (Young's modulus and tensile strength) of surface micromachined polysilicon specimens. The tensile specimens are “dog-bone” shaped ending in a large “paddle” for convenient electrostatic or, in the improved apparatus, ultraviolet (UV) light curable adhesive gripping deposited with electrostatically controlled manipulation. The typical test section of the specimens is 400 μm long with 2 μm×50 μm cross section. The new device supports a nanomechanics method developed in our laboratory to acquire surface topologies of deforming specimens by means of Atomic Force Microscopy (AFM) to determine (fields of) strains via Digital Image Correlation (DIC). With this tool, high strength or non-linearly behaving materials can be tested under different environmental conditions by measuring the strains directly on the surface of the film with nanometer resolution.