Multiplicity results for a class of quasilinear eigenvalue problems on unbounded domains

Using a recent result of Ricceri [10] we prove a multiplicity result for a class of quasilinear eigenvalue problems with nonlinear boundary conditions on an unbounded domain. Our paper completes previous results obtained by Carstea and Rădulescu [4], Chabrowski [1], [2], Kandilakis and Lyberopoulos [6] and Pflüger [7]. Received: 17 April 2007     

Photoemission of spinpolarized electrons from strained GaAsP

Strained layer GaAs_.95P_.05 photo cathodes are presented, which emit electron beams spinpolarized to a degree of P = 75% typically. Quantum yields around QE = 0.4% are observed routinely. The figure of merit P² × QE = 2.3 × 10^–3 is comparable to that of the best strained layer cathodes reported in literature. The optimum wavelength of irradiating light around 830 nm is in convenient reach of Ti:sapphire lasers or diode lasers respectively. The cathodes are produced using MOCVD-techniques. A GaAs_.55P_.45-GaAs_.85P_.15 superlattice structure prevents the migration of dislocations from the substrate and bottom layers to the strained overlayer. The surface is protected by an arsenic layer so that no chemical cleaning is necessary before installation into vacuum. The source of polarized electrons attached to the Mainz race track microtron MAMI works with such cathodes now. More than 1000 hours beamtime have been performed successfully.     

Approximation of Stochastic Nonlinear Equations of Schrödinger Type by the Splitting Method

In this article, we construct a splitting method for nonlinear stochastic equations of Schrödinger type. We approximate the solution of our problem by the sequence of solutions of two types of equations: one without stochastic integral term, but containing the Laplace operator and the other one containing only the stochastic integral term. The two types of equations are connected to each other by their initial values. We prove that the solutions of these equations both converge strongly to the solution of the Schrödinger type equation.     

Formation of Fluorinated Amido Esters through Unexpected C3−C4 Bond Fission in 4‐Trifluoromethyl‐3‐oxo‐β‐lactams

4‐Trifluoromethyl‐3‐oxo‐β‐lactams were unexpectedly transformed into 2‐[(2,2‐difluorovinyl)amino]‐2‐oxoacetates as major products, accompanied by minor amounts of 2‐oxo‐2‐[(2,2,2‐trifluoroethyl)amino]acetates, upon treatment with alkyl halides and triethylamine in DMSO. This peculiar C3?C4 bond fission reactivity was investigated in‐depth, from both an experimental and a computational point of view, in order to shed light on the underlying reaction mechanism.     

Development of a method for direct determination of solids as thin films by energy dispersive X-ray fluorescence analysis

Solid samples can be analysed as without a prior decomposition step, if they are pulverized and then embedded in a thin layer of a cold-setting polymer. This method is very appropriate for materials which are difficult to decompose or which can be easily contaminated. The sample components are evenly distributed in a thin layer, which improves considerably the signal-tonoise-ratio, and this leads to a decrease of the limits of detection. The reproducibility of the method was tested with cobalt oxide and yttrium oxide and also a mixture of these with silver oxide and manganese dioxide. Between 20 and 60 ng of these elements can be determined without difficulty, with a precision of ± 2–4%. The correlation coefficients found for the calibration graphs were between 0.994 and 0.999.     

Strukturelle Abwandlungen an N-Acetylneuraminsäuren, 8 Synthese von 7-, 8-, 9-Desoxy- und 4,7-Didesoxyneuraminsäure

The 7- and 8-Iodnonulosonic acid derivatives1 and2 react with tributyltinhydride-AIBN to the 7- and 8-deoxy-N-acetylneuraminic acid derivatives3 a and4 a which after hydrolysis give the 7-deoxy-N-acetylneuraminic acid3 b (5-N-acetamido-3,5,7-trideoxy--D-galacto-2-nonulopyranosidonic acid=7-Deoxy-Neu5Ac) and 8-deoxy-N-acetylneuraminic acid4 b (5-N-acetamido-3,5,8-trideoxy--D-galacto-2-nonulopyranosidonic acid=8-Deoxy-Neu5Ac). The 4,8,9-tris-(t-butyldimethylsilyl)-N-acetylneuraminic acid derivative5 a yields after transformation to the 7-O-acetyl compound5 b and partial removing of the protecting groups the derivative5 c. Further reaction with theMitsunobu-reagent and methyliodide affords the 9-Iodocompound6 a which turned to the 8-O-acetylderivative6 b. Subsequent reduction by means of tributyltinhydride yields first the 9-deoxyderivative7 a and after hydrolysis the 9-deoxy-N-acetylneuraminic acid7 b (5-N-acetyl amido-3,5,9-trideoxy-D-glycero--d-galacto-2-nonulopy-ranosidonic acid=9-Deoxy-Neu5Ac). Another synthesis of7 b follows the route8 f 8 g 7 c. The Deoxy-N-acetylneuraminic acid3 b could be prepared also by an alternative procedure using the methyl--8,9-methylethylen-4-O-t-butyldimethylsilyl-N-acetylneuraminic acid methylester8 a via the intermediate compounds8 d and8 e. Application of the 8,9-O-methylethyliden-N-acetylneuraminic acid derivative8 opens an approach to the xanthogenates8 a and8 b which could be reduced to the deoxy-N-acetylneuraminic acid derivatives9 a and10 a. Hydrolysis of10 a yields the 4,7-dideoxy-N-acetylneuraminic acid10 b (5-N-acetamido-3,4,5,7-tetradeoxy--D-lyxo-2-nonulopyranosidonic acid=4,7-Dideoxy-Neu5Ac).