Lattice Points in Three-Dimensional Convex Bodies with Points of Gaussian Curvature Zero at the Boundary

 In this article we investigate the number of lattice points in a three-dimensional convex body which contains non-isolated points with Gaussian curvature zero but a finite number of flat points at the boundary. Especially, in case of rational tangential planes in these points we investigate not only the influence of the flat points but also of the other points with Gaussian curvature zero on the estimation of the lattice rest. Received 19 June 2001; in revised form 17 January 2002 RID="a" ID="a" Dedicated to Professor Edmund Hlawka on the occasion of his 85th birthday     

The “Average” Work Function and Emission Area in the Fowler-Nordheim Equation

Derivation of the elementary Fowler-Nordheim equation is based on several strong physical assumptions (e.g. smooth flat surface and uniform work function across emitting surface, constant emission area and a uniform distribution of the applied field over it). A real emitter, however, definitely does not fulfill these assumptions. In spite of it the total emission current follows the FN equation and is frequently used for an estimation of the "average" work-function. The physical basis of this procedure and of the terms "average" work function and "emission area" are analyzed from the experimentalist's point of view. Thus some of the older - more or less intuitive - conclusions are substantiated.     

Synthesis of a giant 222 carbon graphite sheet

In this paper we present the synthesis and characterization of the so far largest polycyclic aromatic hydrocarbon (PAH), containing 222 carbon atoms or 37 separate benzene units. First a suitable three-dimensional oligophenylene precursor molecule is built up by a sequence of Diels-Alder and cyclotrimerization reactions and then planarized in the final step by oxidative cyclodehydrogenation to the corresponding hexagonal PAH. Structural proof is based on isotopically resolved MALDI-TOF mass spectra and electronic characteristics are studied by UV/Vis spectroscopy.     

Frequency characteristics of amplitude and phase of oscillating bubble systems in a closed measuring cell

The amplitude- and phase-frequency characteristics of oscillating bubble systems with a closed measuring cell are analyzed. The shape of the frequency characteristics is qualitatively different for bubbles smaller or larger than a hemisphere, respectively, and also for diluted and concentrated surfactant solutions. Moreover, the presence of a surfactant in the solution strongly influences the characteristic frequencies of the system. The experiments performed under ground and microgravity conditions show a good qualitative agreement with theoretically predicted amplitude- and phase-frequency characteristics and confirm the adequacy of the proposed theory. The comparison of high-frequency limits of the surface dilatational elasticity with the theoretical Gibbs elasticities calculated according to the respective adsorption isotherm shows good agreement for small surfactant concentrations. At higher concentrations large discrepancies are observed which can possibly be explained by the violation of the linearity condition for the surface layer.     

One-pot synthesis of 3,4-disubstituted 1H-pyrroles from 2-tropanones

3,4-Disubstituted pyrroles (2, 3) were prepared from 6/7-carboxyethyl-3-phenyl-3-tropen-2-ones (1) regioselectively and with high yields by using tosylmethyl isocyanide (TosMIC). This procedure enables the synthesis of pyrroles substituted with two distinct groups: a phenyl group and a substituted pyrrolidine analogue. The crystal structure of product 2a was determined, and the analogous derivatives were identified by (1)H and (13)C NMR spectroscopy.     

Acid-induced rearrangement reactions of reduced benzoquinone cyclopentadiene cycloadducts

Several Diels-Alder adducts between benzoquinones and cyclopentadiene were reduced to the corresponding diols 7a-c and 11. Treatment of these diols with strong acid triggered a skeletal rearrangement reaction resulting in compounds 8a-c and 12 that contain a 4,8-methanoazulene substructure. In addition, a dyotropic-like rearrangement of the tetracyclic lactone 13 to the spiro-lactone 18 was observed. Five of the structures were supported by X-ray analysis.     

Conjugation of linoleic acid over a hydrogen pre-activated heterogeneous catalyst

Development of a new heterogeneous catalytic pathway for isomerization of linoleic acid to conjugated linoleic acids at mild reaction conditions over Ni/H-MCM-41 in a soluted system.     

Solid supported fluoronitroaryl triazenes as immobilized and convertible Sanger reagents--synthesis and SNAr reactions towards a novel preparation of 1-alkyl-5-nitro-1H-benzotriazoles

Synthesis of novel fluoronitroaryl triazenes in liquid phase and on solid support have been described; mild displacement of the fluoride ion with various nucleophiles provides access to substituted arenes which in turn can be cleaved to provide a unique access to 1-alkyl-5-nitro-1H-benzotriazole.