1,3,6-Triphenyl-6-phenylazo-1,4,5,6-tetrahydropyridazin

Base induced 1.4-elimination of pyridine·HI from 1-(2-phenyl-2-phenylhydrazono-ethyl)-pyridinium iodide (6) yields 1.3.6-triphenyl-6-phenylazo-1.4.5.6-tetrahydropyridazine (8) the (4+2)-cyclodimer of the intermediate 1-phenyl-1-phenylazoethylene (7).8 can also be obtained by intramolecular oxidative cyclisation (with KMnO₄) of 1.4-diphenylbutane-1.4-dione bisphenylhydrazone (12). Spectroscopic data (ms,¹H-nmr, uv and ir/Raman) confirm the structure of8.     

Studium des gegenseitigen Einflusses der Bindungen in Thiocyanat-Kupfer(II)-Komplexen mit Methyl- und Dimethylpyridinen mittels Infrarotspektroskopie

The infrared spectra of thiocyanato-copper(II) complexes of the type Cu(NCS)₂ L ₂ with all isomeric picolines and lutidines (L) as well as those of the type Cu(NCS)₂ L ₃ withL=3- and 4-picoline, 3,4- and 3,5-lutidine were measured. The behaviour of the (CN) stretching vibrations of the Cu(NCS)₂ L ₂ complexes led to conclusions on the different kind of coordination of the NCS groups in dependence on the ligandL. The mutually conditioned strength of the Cu–NCS and Cu–N(L) bonds in the equatorial plane, especially in the presence of ligandsL with the steric effect, was determined from the frequency shift of the Cu–NCS and Cu–N(L) stretching vibrations with regard to the vibrations for Cu(NCS)₂(pyridine)₂.

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Die Massenspektren der Pyrrolidide einiger aliphatisch-alicyclischer Carbonsäuren

The mass spectra of the pyrrolidides of some long-chain carboxylic acids with alicyclic residues attached to their ω-end are discussed and compared with the spectra of the corresponding esters. Fragmentation triggered by the pyrrolidide group generates a series of peaks, which clearly exhibits the size and the structure of the carbon chain.     

Non relativistic continuum wave functions for two coulomb centres

We give the continuum wave function solutions to the Schrödinger equation for an electron moving field of two point nuclei, as an expansion in terms of one centre Coulomb wave functions in a prolate elliptical coordinate system. These solutions may be chosen to have a convenient asymptotic behaviour, and tend to the conventional solutions of the Helmholtz equation in the limit that the nuclear charge goes to zero. In symmetric systems, where both nuclei have the same charge the angular wave functions are found to be identical with those occurring in the free case, and the expansion coefficients for the corresponding radial solutions are given for selected values of electron energy and nuclear separation.[/p]     

X-ray diffraction and morphology of crystalline,hard, elastic materials

Summary X-ray diffraction and electron microscopic results on several crystalline polymers which demonstrate elastic properties (polypropylene, Celcon^®, poly-4-methyl-pentene) are reported. Photographic small angle X-ray diffraction techniques provided considerable qualitative information, concerning the morphological features of these elastic materials both as extruded, annealed and during extension. Lamellar thickness, thickness distribution and perfection of lamellae could be estimated. Lateral order features and orientation of the lamellar structures were obtainable from the sharpness and length of the equatorial wide angle diffraction arcs. Electron microscopic results essentially confirm the morphological features postulated on the basis of the X-ray results. These morphological features are discussed in terms of a general structural model which appears consistent with the mechanical properties of these materials.

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Zusammenfassung Röntgenbeugung und elektronenmikroskopische Daten von einigen kristallinen Polymerprodukten mit elastischen Eigenschaften (Polypropylen, Celcon, Poly-4-methylpenten) werden berichtet. Die photographische Röntgen-Kleinwinkelmethode liefert wichtige qualitative Messungen der morphologischen Struktur dieser elastischen Materialien in den Zuständen sowohl wie hergestellt als auch nach Tempern und während des Dehnungsprozesses. Die Dicke der Lamellen, ihre Dikkenverteilung und die Güte der Lamellen konnten abgeschätzt werden. Die laterale Ordnung und die Orientierung der Lamellen kann aus Weitwinkelbeugungsdaten abgeleitet werden. Die Elektronenmikroskopie bestätigt die Morphologie, die aus Röntgendaten folgt. Ein allgemeines Strukturmodel dieser Morphologie, das im Einklang mit den mechanischen Eigenschaften dieser Produkte steht, wird diskutiert.

     

Über eine zum Kreisproblem verwandte Summe

An equivalent form of the classical circle problem is the unproved conjecture (3) . In this note the corresponding conjecture with _k (.) (the 1-periodic Bernoulli polynomials of orderk2) instead of ₁(.) is settled in an affirmative way (even with =0). Moreover, a generalized sum (6) is estimated by means of an analogue to a classical result due tovan der Corput.     

Relations between subclasses of greedoids

In previous papers many different classes and constructions of greedoids have been defined and studied. This paper documents inclusion relations among all subclasses of greedoids which are known so far. It will be shown that all inclusion relations are proper and that all but one subclasses of interval greedoids are distinct.

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Zusammenfassung In früheren Arbeiten wurden viele verschiedene Klassen und Konstruktionen für Greedoide eingeführt und studiert. In dieser Arbeit werden alle bekannten Inklusionsbeziehungen zwischen Unterklassen von Greedoiden dokumentiert. Es wird gezeigt, daß alle Inklusionsbeziehungen echt und alle Unterklassen mit einer Ausnahme tatsächlich verschieden sind.

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Supported by the joint research project Algorithmic Aspects of Combinatorial Optimization of the Hungarian Academy of Sciences (Magyar Tudományos Akadémia) and the German Research Association (Deutsche Forschungsgemeinschaft, SFB 21). Part of this research was done while the first author was visiting the Department of Combinatorics and Optimization, University of Waterloo.     

Nonlinear one-parametric bottleneck linear programming

We consider the one-parametric linear bottleneck problem min {c (x, t) ¦ x P (t)} where the bottleneck objectivec (x, t):=max {c_j (t) ¦ x_j>0} is minimized subject to linear constraints, i.e. P(t):={x ¦A (t) ·x=b (t), x0}. All coefficients are assumed to be continuous functions of one real parametert which varies in a real intervalS. A method is developed for constructing a partition ofS into subintervals on which either a basis stays optimal or the problem stays infeasible. Finiteness of the partition is due to certain finiteness assumptions on the zeroes of particular combinations of the coefficient functions. Using a lexicographic refinement of the objective function a characterization of the optimality interval of a fixed basis is derived which is independent on explicit information about other bases.

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Zusammenfassung Es werden einparametrische lineare Engpaßprobleme min {c (x, t) ¦x P (t)} betrachtet, wobei die Engpaßzielfunktionc (x, t):=max {c_j (t) ¦ x_j >0} unter linearen Nebenbedingungen, die durch P(t):={x ¦A (t) ·x=b (t), x0} gegeben sind, minimiert wird. Dabei wird angenommen, daß alle Koeffizienten stetige Funktionen eines reellen Parameterst aus einem IntervallS R sind. Es wird eine Methode entwickelt,S derart in Teilintervalle zu zerlegen, daß entweder eine Basis in solch einem Teilintervall optimal oder das Problem unzulässig bleibt. Die Endlichkeit dieser Partition vonS ergibt sich aus Endlichkeitsvoraussetzungen für die Nullstellen von Funktionen, die sich als gewisse Kombinationen der Koeffizientenfunktionen schreiben lassen. Durch eine lexikographische Verfeinerung der Zielfunktion gelingt es, das Intervall zu charakterisieren, in dem eine feste Basis optimal ist. Diese Charakterisierung ist unabhängig von expliziten Informationen über andere Basen.

     

Lösungsmitteleinfluß auf das Redoxverhalten von Bistriphenylphosphinquecksilber(II)-perchlorat

The influence of solvents on the redox behaviour of bistriphenylphosphinomercury perchlorate has been investigated by polarographic, voltammetric and potentiometric methods. The electrode process was found to be reversible in acetonitrile, propylene carbonate, N,N-dimethylformamide and dimethyl sulfoxide. An irreversible process was observed in nitromethane employing the dropping mercury electrode as well as in N,N-dimethylthioformamide and N-methyl-2-thiopyrrolidinone employing the rotating platinum electrode. Half wave potentials and diffusion coefficients have been measured. A linear relationship between theE _1/2 and the donor number (DN) of the solvent has been found for the reversible electrode reactions. Ligand replacement occurs in N,N-dimethylthioformamide and N-methyl-2-thiopyrrolidinone.

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The structure of defect Ru4Si3

The nature of the defect structure of Ru₄Si₃ has been studied with electron diffraction and electron microscopy methods. Lattice image pictures, interpreted with histogram analysis, reveal that planar defects of chemical twinning type are common in the crystals.