Lifschitz tails for the Anderson model

We present, in an expository way, an elementary rigorous proof (patterned after an argument of Kirsch-Martinelli) that the Anderson model has Lifschitz tails in very great generality.Research partially supported by USNSF Grant No. MCS-81-20833.     

Pointwise bounds on eigenfunctions and wave packets inN-body quantum systems

By using Agmon's geodesic ideas to single out particular regions in path space, we obtain optimal lower bounds on the leading behavior for the fall off of the ground state of multiparticle system.Research partially supported by UNSF Grant MCS-78-01885On leave from: Départment de Mathématiques, Université de Saint Etienne, 23 rue P. Mìchelon, F-42023 Saint Etienne Cédex, France     

Rate constants for photochemically induced hydrogen abstraction calculated from spin trapping rates

ESR spin trapping method has been applied to calculate the rate constant for -hydrogen abstraction from ethylbenzene by triplet anthraquinone: k₁=1.1×10⁷ M^–1 s^–1 (error of estimation 25%).

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( ) -CH : k₁=1.1×10⁷ M^–1–1 ( 25%)

     

Ermittlung von Bildungskurven nach J. Bjerrum mittels differenzieller Dampfdruckosmometrie

Determination of Bjerrum Formation Curves by Differential Vapour Pressure Osmometry . A differential vapour pressure osmometry method for the determination of Bjerrum formation curves is described. This technique allows the determination of formation constants in nonaqueous solvent systems.     

Generation of ester enolates by reductive a-deacetoxylation

Diethyl allylmalonates or 2-arylalkanoic esters are prepared in good yield by reductive α-deoxygenation of the corresponding α-acetoxy or α-alkony esters. Since the intermediate ester enolates are generated under aprotic conditions, a one pot reductive-alkylation is also possible. One application of this procedure allows diethyl oxomalonate to serve as a conjunctive reagent for stitching together an alkene and an alkyl halide with a malonyl group as linchpin.     

Einsatz gas-chromatographischer Kolonnen hoher Trennleistung in direkter Kombination mit Massenspektrometer

A routine instrument for the combination of a single focusing mass spectrometer with high efficiency tubular as well as packed GC columns using a molecule separator is described. The application of the unit in the analysis of cigarette smoke is given.     

Anwendungen der De Rhamschen Zerlegung auf Probleme der lokalen Flächentheorie

Various questions of classical differential geometry lead to the problem of determining all those hypersurfaces of euclidean space for which the covariant derivative of the second fundamental form vanishes identically. In the first part of this note, we investigate these hypersurfaces; the result is summarized in the theorem of the opening paragraph, whose proof is based in the decomposition theorem of De Rham (see e.g. [6], pp. 180–186). Applying this result in the second part of the note, we give local characterizations of the Euclidean sphere.