An algebra of meromorphic corner symbols

Operators on manifolds with corners that have base configurations with geometric singularities can be analysed in the frame of a conormal symbolic structure which is in spirit similar to the one for conical singularities of Kondrat'ev's work. Solvability of elliptic equations and asymptotics of solutions are determined by meromorphic conormal symbols. We study the case when the base has edge singularities which is a natural assumption in a number of applications. There are new phenomena, caused by a specific kind of higher degeneracy of the underlying symbols. We introduce an algebra of meromorphic edge operators that depend on complex parameters and investigate meromorphic inverses in the parameter-dependent elliptic case. Among the examples are resolvents of elliptic differential operators on manifolds with edges.     

Stability of translating solutions to mean curvature flow

We prove stability of rotationally symmetric translating solutions to mean curvature flow. For initial data that converge spatially at infinity to such a soliton, we obtain convergence for large times to that soliton without imposing any decay rates. The authors are members of SFB 647/B3 “Raum – Zeit – Materie: Singularity Structure, Long-time Behaviour and Dynamics of Solutions of Non-linear Evolution Equations”.     

Über die Dispersität von Metallen in Trägerkatalysatoren. II. Röntgenkleinwinkeluntersuchungen an Platin- und Palladium-Tonerde-Katalysatoren

On the Dispersion of Metals in Supported Catalysts. II. Small Angle X-ray Investigation. on Platinum/Alumina and Palladium/Alumina Catalysts The metal dispersion in 0.5% Pd/A1₂O₃. 0.5°% Pt/Al₂O₃ abd 1.5% Pt/Al₂O₃ catalysts was investigated by small angle X-ray scattering, Using a Kratky camera the difference scattering curves catalyst-carrier were evaluated. The assumption was made that the scattering centres are globular and that there is no interparticular scattering. From the Guinier approximation the Guinier radii R_G of the metal particles were determined. With the Pd catalyst always positive difference scattering curves were found, whereas negative values were found with the Pt catalysts at a scattering angle greater than 0.022 rad. Therefore only for the sample with 0.5% Pd the Porod invariant \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \tilde Q}$\end{document} and the Porod radius R_P could be determined. From R_G and R_P the parameters of a two- and of a one-parametric distribution were calculated. The results are in good agreement with data from wide angle X-ray diffraction measurements.     

Sorptionseffekte an Eisen(III)-hydroxid-F?llungen

Zusammenfassung Um Material zur Deutung des Mechanismus der Sorption von Sr²⁺-Ionen an Eisen(III)-hydroxid zu gewinnen, werden Meßreihen mitgeteilt, in denen die pH-Abhängigkeit der Sorption sowie deren Beeinflussung bei Fällung mit verschiedenen Basen (NaOH, Ammoniak, Trimethylamin, Benzylamin) untersucht wird. Aus den charakteristischen Unterschieden der Sorptionskurven muß gefolgert werden, daß die Art der Base für die Sorption eine wichtige Rolle spielt.

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Summary The sorption of Sr²⁺ ions on iron(III) hydroxide was studied as a function of the pH, of the precipitating reagent (NaOH, ammonium hydroxide, benzylamine, trimethylamine), of the temperature and of the total concentration.The curves of the relative sorption vs. pH are found to show characteristic differences which have to be explained in a detailed theory of the mechanism.

     

Zur Verbindungsbildung von MeO: M2O3. IV. Zur Struktur von monoklinem SrAl2O4

Einkristalle von SrAl₂O₄ wurden durch Hochtemperaturreaktionen von SrO mit Al₂O₃ dargestellt und röntgenographisch untersucht (a = 844,7; b = 881,6; c = 516,3 pm;β = 93,4₂°; Raumgruppe C–;P2₁, Z = 4). Die Tetraederabfolge in den Sechsringen dieser aufgefüllten Tridymit-Struktur wird mit der ähnlicher Oxometallate verglichen. Compound Formation MeO:M₂O₃. IV. Structure of Monoclinic SrAl₂O₄ Single crystals of SrAl₂O₄ were prepared by high temperature CO₂-LASER technique and investigated by X-ray methods. (a = 844.7; b = 881.6; c = 516.3 pm; β = 93.4₂°; space group C–P2₁, Z = 4). The orientation of the tetrahedra in this stuffed tridymite structure is discussed in comparison with related oxometallates.     

Notiz zur quantitativen Bestimmung von Si-H- und Si-Si-Gruppen

Zusammenfassung Eine einfache und genaue Methode zur Bestimmung von Si-H- und Si-Si-Gruppen wird vorgeschlagen, die auf alkalischer Hydrolyse der Substanz in einem verschlossenen und evakuierten Kolben und AuswÄgen des dem entwickelten Wasserstoff entsprechenden Wasservolumens beruht. Bei H-Gehalten von 1–2% betrÄgt die Genauigkeit ± 0,03% (abs.).

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Note on the quantitative determination of Si-H- and Si-Si-groups

A simple, robust and surprisingly exact method for the quantitative determination of Si-H- or Si-Si-groups is based on alkaline hydrolysis of the Si-H- or Si-Si-containing substances in a sealed and evacuated vessel and weighing of the volume of water equivalent to the developed volume of hydrogen. The accuracy is ± 0.03% (abs.) with H contents of 1–2%.

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Herrn Prof. Dr. E. Asmus zum 60. Geburtstag gewidmet.     

Trace element analysis of high-purity copper

Summary In copper samples trace impurities of the elements As, Bi, Cr, Fe, Pb, Sb, Se and Te in the low g/g range were coprecipitated with lanthanum hydroxide and determined by flame AAS (Fe) and electrothermal AAS (other elements). Reduction of the sample weight results in a considerable saving of time compared to elder procedures and allows to apply centrifugation instead of filtration as separation technique, by which the risk of contamination is decreased. The completeness of separation was examined by analyzing standard solutions. Additionally radio tracer experiments were employed with Sb and Se. Based on recovery data, a classification scheme was set up with regard to adsorption behaviour. High-purity copper samples were analyzed by the procedure described; INAA and ICP-MS were used as comparison methods. Parameters affecting the precision were examined; the main influence was caused by the separation step. The procedure is well suitable for the determination of 2–10 g/g As, Cr and Pb and 5–50 g/g Fe in high-purity copper.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday     

Zum mechanismus des strahlenchemischen abbaus von polytetrafluorethylen

The present work studies the changes in polymer structure and the mechanism of the decomposition of polytetrafluoroethylene resin (PTFE) exposed to high energy radiation (electron beam). Spectroscopic and kinetic observations are used to interpret the degradation process. For the first time the decomposition of PTFE has been carried out on a preparative scale and new results obtained by analysing the degradation products. The radiation-induced degradation of PTFE is accompanied by thermal degradation under certain irradiation conditions. This is due to an increase in temperature of the polymer caused by retardation of highly accelerated electrons (heat accumulation effect).The kinetics are discussed in terms of the reactions and recombination of radicals produced by high-energy radiation both in the polymer melt and the polymer surface. These are related to the overall rate of decomposition.The primary radicals formed by decomposition of PTFE in an inert atmosphere (N₂, Ar) react to produce perfluorinated alkanes and alkenes. In the presence of reactive gases the decomposition fragments originated will react rapidly; e.g. if oxygen is present in the reactive area the radicals form perflourinated peroxyl and oxyl radicals which finally stabilize themselves by CC-scission to perfluorocarbon acid fluorides and carbonyldifluorides.     

The identification of nitrated polycyclic aromatic hydrocarbons in diesel particulate extracts and their potential formation as artifacts during particulate collection

Summary The highly complex matrix of diesel particulate extracts was analyzed for nitrated polycyclic aromatic hydrocarbons (nitro-PAH) using fused-silica capillary-column gas chromatography along with a thermionic nitrogen-phosphorus detector (TID) and high-performance liquid chromatography followed by on-line catalytic reduction of the nitro-PAH to amino-PAH and subsequent fluorescence detection. Positive isomer identification and quantitation of nitro-PAH are from retention times of authentic standards and their mass spectra. The ease of nitro-PAH formation by nitration of PAH raises the question regarding the origin of these species, whether they are produced as “native” products during the engine combustion process and/or in the exhaust, or instead, formed as the result of chemical conversion to produce artifacts during the sampling procedure. This problem is assessed examing 1-nitropyrene-concentration in particulates of three light-duty diesel engines for different sampling times. 1-Nitropyrene concentrations show only a moderate increase with sampling time under average sampling conditions. Presented at the 15th International Symposium on Chromatography, Nürnberg, October 1984