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.     

Justification of the Shallow-Water Limit for a Rigid-Lid Flow with Bottom Topography

The so-called lake equations arise as the shallow-water limit of the rigid-lid equations—three-dimensional Euler equations with a rigid-lid upper boundary condition—in a horizontally periodic basin with bottom topography. We prove an a priori estimate in the Sobolev space H ^m for m≥ 3 which shows that a solution to the rigid-lid equations can be approximated by a solution of the lake equations for an interval of time which can be estimated in terms of the initial deviation from a columnar configuration and the magnitude of the initial data in H ^m , the gradient of the bottom topography in H ^m+1 , and the aspect ratio of the basin. In particular, any solution to the lake equations remains close to some solution of the rigid-lid equations for an interval of time that can be made arbitrarily large by choosing the aspect ratio of the basin small. Received 10 October 1996 and accepted 15 May 1997     

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.

     

Dérivés propargyliques,XII et dérivés de la décahydroquinoléine,II Alkynyl-4, alkényl-4 et alkyl-4-décahydroquinolinols-4 N-substitués

The authors describe the synthesis of decahydro-4-quinolinones and N-substituted 4-alkynyl-, 4-allyl- and 4-alkyldecahydro-4-quinolinols and discuss the stereochemical problems of this compounds.     

Cyclisation par amination intramoléculaire dans la série de la pyrazine.

An original one-pot ayntheais of 4,7-diazaindoles is achieved by metalation of methylpyrazines or methylquinoxaline wich are then condensed with an aromatic nitrile: an intermediate imine-enamine is formed which leads, by intramolecular cyclization, to diazaindoles.     

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.     

Tensor products of contexts and complete lattices

Although the categoryCLC of complete lattices and complete homomorphisms does not possess arbitrary coproducts, we show that the tensor product introduced by Wille has the universal property of coproducts for so-called distributing families of morphisms (and only for these). As every family of morphisms into a completely distributive lattice is distributing, this includes the known fact that in the category of completely distributive lattices, arbitrary coproducts exist and coincide with the tensor products. Since the definition of tensor products is based on the notion of contexts and their concept lattices, many results on tensor products extend from complete lattices to contexts. Thus we introduce two kinds of tensor products for arbitrary families of contexts, a partial and a complete one, and establish universal properties of these tensor products.Presented by B. Jonsson.