Stability and interface quality of GeO2 films grown on Ge by atomic oxygen assisted deposition

The composition of GeO(2) films grown on Ge has been studied for different molecular deposition processes and after exposure to ambient air. The stoichiometry, the interaction with moisture, and the interfacial details of the films are shown to be dramatically process dependent.     

On the maximal number of coprime subdegrees in finite primitive permutation groups

We compute the divisor class group of the general hypersurface Y of a complex projective normal variety X of dimension at least four containing a fixed base locus Z. We deduce that completions of normal local complete intersection domains of finite type over C of dimension ≥ 4 are completions of UFDs of finite type over C.     

NON-FUCHSIAN SINGULARITIES IN QUANTUM MECHANICS

A modification of the spiked harmonic oscillator is studied in the case for which the perturbation potential contains both an inverse power and a linear term. It is then possible to evaluate trial functions by solving an integral equation due to the occurrence of the linear term. The general form of such integral equation is obtained by using a Green-function method, and adding a modified Bessel function of second kind which solves an homogeneous problem with Dirichlet boundary condition at the origin.     

Failure of n‐uniqueness: a family of examples

In this paper, the connections between model theory and the theory of infinite permutation groups (see 11 ) are used to study the n‐existence and the n‐uniqueness for n‐amalgamation problems of stable theories. We show that, for any n ? 2, there exists a stable theory having (k + 1)‐existence and k‐uniqueness, for every k ? n, but has neither (n + 2)‐existence nor (n + 1)‐uniqueness. In particular, this generalizes the example, for n = 2, due to Hrushovski given in 3 . © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Nanoscale Imaging and Stabilization of Silica Nanospheres in Liquid Phase Transmission Electron Microscopy

Liquid phase transmission electron microscopy (LP‐TEM) is a novel and highly promising technique for the in situ study of important nanoscale processes, in particular the synthesis and modification of various nanostructures in a liquid. Destabilization of the samples, including reduction, oxidation, or dissolution by interactions between electron beam, liquid, and sample, is still one of the main challenges of this technique. This work focuses on amorphous silica nanospheres and the phenomena behind their reshaping and dissolution in LP‐TEM. It is proposed that silica degradation is primarily the result of reducing radical formation in the liquid phase and the subsequent accelerated hydroxylation of the silica, while alterations in silica solid structure, pH, and oxidizing species formation had limited influence. Furthermore, the presence of water vapor instead of liquid water also results in degradation of silica. Most importantly however, it is shown that the addition of scavengers for reducing radicals significantly improved amorphous silica stability during LP‐TEM imaging. Devising such methods to overcome adverse effects in LP‐TEM is of the utmost importance for further development and implementation of this technique in studies of nanoscale processes in liquid.     

Similarity solutions in space dependent extended kinetic theory

Summary An exact analytical solution to a simple problem of extended kinetic theory for a spatially inhomogeneous binary gas mixture is determined in this paper by resorting to Lie group theoretical methods. It is shown that there are cases in which the nonlinear evolution equations for the densities allow transformation groups of infinite order, where the corresponding similarity solution actually represents the general solution to the problem. Results are then briefly commented on.

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Zusammenfassung In dieser Abhandlung wird eine exakte analytische Lösung für ein einfaches Problem aus der erweiterten kinetischen Theorie räumlich inhomogener binärer Gasmischungen angegeben. Es wird gezeigt, daß die nichtlinearen Evolutionsgleichungen für die Dichten in bestimmten Fällen Lie-Gruppen von unendlicher Ordnung zulassen. Die zugehörigen Similarity-Lösungen stellen dann allgemeine Lösungen des zugrundeliegenden Problems dar. Die Ergebnisse werden kurz erläutert.

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On leave from: Institute of Mathematical Physics, University of Ulm, Oberer Eselsberg, 7900 Ulm, F.R.G.     

Covariant polarization bases for spin=12, 1, 32 particles and their use

A simple method is presented for evaluating transition amplitudes between massive states with $\text{spin}\text{=}\text{1}\text{2}\text{, 1}$ and definite polarization. The $\text{spin}\text{-}\text{3}\text{2}$ case is also briefly discussed. Applications to testing the decay and production of vector bosons are considered.     

On a nonlinear evolution problem of particle transport theory with nonconstant collision frequencies

The spatially homogeneous nonlinear integrodifferential Boltzmann equation for test particles interacting between themselves and with a background host medium through scattering and removal collisions is solved analytically in physical conditions in which some of the cross sections do not obey the classical inverse speed law, and the relevant collision frequencies are not constant. Results for the distribution function and the total density are illustrated and commented on.

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Riassunto L'equazione integrodifferenziale nonlineare di Boltzmann per la funzione di distribuzione di un gas di particelle interagenti tra loro e con un prefissato mezzo ospite mediante collisioni binarie di scattering e rimozione è risolta analiticamente in alcuni casi fisici con frequenze di collisione non costanti. I risultati sono brevemente illustrati e commentati.