Invariant Manifolds in Dissipative Dynamical Systems

Invariant manifolds like tori, spheres and cylinders play an important part in dynamical systems. In engineering, tori correspond with the important phenomenon of multi-frequency oscillations. Normal hyperbolicity guarantees the robustness of these manifolds but in many applications weaker forms of hyperbolicity present more realistic cases and interesting phenomena. We will review the theory and present a number of examples using normalization-averaging techniques.Dedicated to nonlinear scientist Ale Tondl on his 80th birthdayMathematics Subject Classifications (2000) 34C30, 34C20.     

Thiamorphinans. I

The present paper deals with the synthesis of 5,5a,6,7,8,9-hexahydro-5,9a-iminoethano-4H-naphtho[2,1-b] -thiophenes (I) as derivatives of the first of three novel isomeric S-heterocycles with morphinan-like structure (“thiamorphinans”).     

Extraction chromatography using chelating agents

The separation of Zn?Cd, Ag?Hg, Cd?Ag and Pb?Bi?Po by extraction chromatography in the system dithizone-carbon tetrachloride is reported. It is shown that it is possible to calculate optimum conditions for the separation of the metals from the extraction constants of the metal chelates and the stability constants of the metal complexes with masking agents.     

Étude de quelques dérivés de la pyrazoline-2: Spectres infrarouge et methode CNDO/2

The infrared spectra of some derivatives of 2-pyrazoline have been studied in the region of the CN and N-H stretching bands.The N-H stretching frequency seems to be related to Taft's σ^* constants of the substituents bound to the intracyclic carbon atoms. The “acidity” of this group seems to be considerably less than in pyrrole or in carboxylic amides.Absorption spectra of the pure compounds or of moderately concentrated solutions suggest the existence of intermolecular hydrogen bonding.The hybridization state of nitrogen atom (1) seems to be approximatively sp³, without any noticeable conjugation with the CN(2) double bond. In those cases where two conformers could be assumed to exist only one has been observed.These results are in accordance with those of a molecular orbital calculation by the CNDO/2 method. This calculation suggests that in 5-methyl-2-pyrazoline, the hydrogen atom bound to N(1) is trans with respect to the methyl group.     

Projective planes over rings of stable rank 2

This paper gives an axiomatic characterization of projective planes over rings of stable rank 2. These rings, which are known from algebraic K-theory, beautifully reflect simple geometric properties. The basic relations in the plane are incidence and the neighbor relation. The axioms consist of a number of axioms expressing elementary relations between points and lines such as, e. g., the existence of a unique line joining any two non-neighboring points, and a couple of axioms ensuring the existence of transvections and dilatations.     

A Stereocontrolied Entry to Racemic Eremophilane and Valencane Sesquiterpenes via an Intramolecular Diels-Alder Reaction

A stereocontrolied route to racemic eremophilane and valencane sesquiterpenes is described via a common intermediate 15 , accessible from an intramolecular Diels-Alder reaction. ¹³ C - NMR .-shift assignments of the bicyclic intermediates and products are presented.