G-invariante Morse-funktionen

If f is a Morse function on a smooth manifold M there exists a homotopy equivalence from M to a CW complex X such that the critical points of f with index are in a one-one correspondence to the -cells of X. In the equivariant case, a similar result holds for a special type of invariant Morse functions. In this paper we prove the existence of such special invariant Morse functions on compact smooth G-manifolds. As a consequence, any compact smooth G-manifold is homotopy equivalent to a G-CW complex. Other applications deal with the Euler number of the fixed point set and Morse inequalities in equivariant homology theory.     

The synthesis of N-substituted ureas II: Nucleophilic substitution of ureas at the carbonyl group

Summary N-Arylsubstituted ureas undergo exchange of the N-residue upon reaction with amines. Using kinetic measurements, investigation of product distribution, regioselectivity, catalysis, and substrate influences, it was shown that this reaction proceeds via a second order nucleophilic substitution at the urea carbonyl center. By means of semiempirical calculations using the MNDO method the alternative mechanism of fragmentation was investigated.

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Zur Synthese N-substituierter Harnstoffe II: Nucleophile Substitution von Harnstoffen an der Carbonylgruppe

Zusammenfassung N-Arylsubstituierte Harnstoffe erleiden bei der Reaktion mit Aminen einen Austausch des N-Restes. Durch kinetische Messungen, Untersuchung der Produktverteilung, Regioselektivität, Katalyse und des Einflusses des Edukts konnte abgeleitet werden, daß es sich hiebei um eine nucleophile Substitution zweiter Ordnung am Carbonylzentrum des Harnstoffs handelt. Durch semiempirische Rechnungen mit Hilfe der MNDO Methode wurde der alternative Reaktionsmechanismus einer Fragmentierung untersucht.

     

Beiträge zur Chemie der Pyrrolpigmente, 31. Mitt.: Die Spin-Gitter-Relaxation in den1H-NMR-Spektren von Bilatrienen-abc

The¹H-NMR spin lattice relaxation times of aetiobiliverdin-IV- and biliverdindimethylester were determined using the inversion recovery technique. The relaxation times of protons attached to the terminal rings A and D are longer than those situated at the rings B and C which points to a higher mobility of rings A and D. Moreover these measurements allowed an independent assignment of the¹H-NMR-signals of the methyl groups of biliverdindimethylester.

30. Mitt.:H. Falk undT. Schlederer, Ann. Chem., im Druck.     

A class of means and related inequalities

The aim of this paper is two-fold: First we describe a certain class of strictly positive, continuous functions u:I defined on certain intervals I]0,+[, and demonstrate that each function u of this class permits the definition of an associated mean M_u (a₁,...,a_n) for any finite number a₁,...,a_n of numbers in I. The arithmetic and the geometric mean are special cases of these u-means M_u. -Thereafter, we improve the classical inequality between the geometric and the arithmetic mean and derive from it a corresponding inequality between certain u-means and the arithmetic mean.