Properties and examples of FCR-algebras

An algebra A over a field k is FCR if every finite dimensional representation of A is completely reducible and the intersection of the kernels of these representations is zero. We give a useful characterization of FCR-algebras and apply this to C ^*-algebras and to localizations. Moreover, we show that “small” products and sums of FCR-algebras are again FCR. Received: 25 October 2000     

Inseparable Körpererweiterungen

Ohne Zusammenfassung     

Phases and solid structures by calcination of precursors for lead-magnesium-niobates

The preparation of powders for the manufacturing of high tech ceramics determines the quality of materials. Using the precursor for lead-magnesium-niobates (PMN), which was prepared from tartrate stabilized solutions of lead-acetate, magnesium-acetate and niobium-ammonium-oxalate in acetic acid by freeze-drying, both the mechanism of formation and the properties of products could be elucidated by X-ray diffraction, thermal analysis, determination of dispersity by laser diffraction particle sizing, mercury porosimetry and gas sorption measurement.     

About the influence of mechanical comminution processes on saturation magnetization of strontium ferrites

The influence of the mechanical comminution process on the coercive field of hardmagnetic ferrites is well known. But, there is a strong effect on the saturation magnetization of strontium ferrite as well. Using a special type of a vibration mill the saturation magnetization decreases to 0.084 T and increases up to 0.22 T by further enlarging the milling time. The saturation magnetization approaches up to 0.41 T again by subsequent annealing. Preliminary investigations aiming at an interpretation are given.     

On the geometry of conjugacy classes in classical groups

Summary We study closures of conjugacy classes in the Lie algebras of the orthogonal and symplectic groups and determine which ones are normal varieties. Furthermore we give a complete classification of the minimal singularities which arise in this context, i.e. the singularities which occur in the open classes in the boundary of a given conjugacy class. In contrast to the results for the general linear group ([KP1], [KP2]) there are classes with non normal closure; they are branched in a class of codimension two and give rise to normal minimal singularities. The methods used are (classical) invariant theory and algebraic geometry. Supported in part by the SFB Theoretische Mathematik, University of Bonn, and by the University of Hamburg     

Effect of the orientation of substituents on the chemical shifts of 13C. IV—13C NMR spectra of N,N-diisopropylamides and -thioamides

N,N-diisopropylamides and -thioamides show hindered rotation around the N? CH bonds, and the presence of mixtures of conformational isomers can be demonstrated at temperatures below 273 K in solution. ¹H and ¹³C NMR spectra of these conformers are measured and assigned. The ¹³C data serve to study through-space effects on ¹³C chemical shifts, which strongly depend on the conformations of the isopropyl groups. For amides, a through-space shielding of the N-methine carbons is found to exist only for conformers in which the methine hydrogen atom is spatially close to the oxygen atom. Chemical shift differences between amides and thioamides can be rationalized in terms of through-bond and through-space contributions, and serve for a better understanding of the shift differences in N,N-dialkylamides and -thioamides.     

Der Satz von Hahn-Banach und Fixpunktsätze in limitierten Vektorräumen

Ohne Zusammenfassung     

Synthese von Diterpenen als mögliche biogenetische Vorläufer des C20-Carotinoides Crocetin

Synthesis of Diterpenes as Possible Biogenetic Precursors of the C₂₀-Carotenoid Crocetin With regard to the investigation of the biosynthesis of the C₂₀-carotenoids in saffron the four diterpenes 6–9 were synthesized, who differ only in their degree of saturation. A detailed analysis of their ¹H- and ¹³C-NMR spectra has been achieved by their mutual comparison.