An extension of a theorem of Gehring and Pommerenke

Gehring and Pommerenke have shown that if the Schwarzian derivativeSf of an analytic functionf in the unit diskD satisfies |Sf(z)|≤, 2(1 - |z|²)^–2 thenf(D) is a Jordan domain except whenf(D) is the image under a Möbius transformation of an infinite parallel strip. The condition |Sf(z)|≤ 2(1 - |z|²)^–2 is the classical sufficient condition for univalence of Nehari. In this paper we show that the same type of phenomenon established by Gehring and Pommerenke holds for a wider class of univalence criteria of the form|Sf(z)|≤p(|z|) also introduced by Nehari. These include|Sf((z)|≤π ²/2 and|Sf((z)|≤4(1-|z| ²)^–1. We also obtain results on Hölder continuity and quasiconformal extensions.     

Zweite Note über analytische Functionen mehrerer Veränderlichen

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Chloromethane surface chemistry on Fe3O4(1 1 1)-(2 × 2): A thermal desorption spectrometry comparison of CCl4, CBr2Cl2, and CH2Cl2

The surface chemistry of CBr₂Cl₂ on the Fe₃O₄(1 1 1)-(2 × 2) selvedge of single-crystal α-Fe₂O₃(0 0 0 1) has been investigated using temperature programmed reaction and desorption (TPR/D) measurements. The spectra obtained in this case show that strong chemisorption occurs and that a series of adsorbed halogenated reaction products are present. By comparison, studies of the adsorbed phase of CH₂Cl₂ show that only physisorption occurs. The TPR/D spectra of CBr₂Cl₂ show that dissociative formation of CCl₂ followed by its reaction with lattice oxygen is central to the monolayer reaction chemistry in this chloromethane. The branching ratios of the various desorbed products are compared with those obtained from CCl₄ adsorbed on the same (2 × 2) surface.     

High resolution electrospray ionization ion mobility spectrometry

Current commercially available ion mobility spectrometers are intended for the analysis of chemicals in the gas phase. Sample introduction methods, such as direct air sampling, a GC injector or a thermal desorber, are commonly an integral part of these instruments. This paper describes an electrospray ionization ion mobility spectrometer system that allows direct introduction samples in solution phase. This allows direct analysis of non-volatile organic and biological samples, and avoids decomposition of thermally liable samples, providing reliable chemical identification. In addition, the new ion mobility spectrometer allows mobility analysis with high resolving power. Commonly used commercial IMS systems provide resolving powers between 10 and 30; this new ion mobility spectrometer has resolving power greater than 60 for routine analysis. A high resolution instrument is necessary for many applications where a complex mixture needs to be separated and quantified. This paper demonstrates the advantages of using a high resolution ion mobility spectrometer and an electrospray ionization source for the analysis of non-volatile pharmaceuticals as well as dissolved explosive in solution phase.     

Tuning molecule-surface interactions with sub-nanometer-thick covalently bound organic monolayers

Measurements of the thermal desorption of methyl bromide (MeBr) from bare and RS-functionalized GaAs(110), where R = CH3 and CH3CH2, reveal marked systematic changes in molecule-surface interactions. As the thickness of the organic spacer layer is increased, the electrostatic MeBr-GaAs(110) interaction decreases, lowering the activation energy for desorption, Ed, as well as decreasing the critical coverage required for nucleation of bulklike MeBr. On the CH3CH2S-functionalized surface, Ed is lowered to a value roughly equal to that for desorption from three-dimensional (3-D) clusters; because the kinetics of desorption of isolated molecules differs from that for desorption from clusters, desorption of isolated molecules from the organic surface occurs at a lower temperature than desorption from the clusters. Thus, the "monolayer" desorption wave occurs at a lower temperature than the "multilayer" desorption wave. These results illustrate the role that organic chain length in nanometer-scale thin films can play in alteration of the delicate balance of interfacial interactions.