Functional calculus for non-commuting operators with real spectra via an iterated Cauchy formula

We define a smooth functional calculus for a non-commuting tuple of (unbounded) operators A_j on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also extended to tuples of more general operators allowing smooth functional calculii. We also discuss the relation to the case with commuting operators.     

Small models for chain algebras

Supported by the Deutsche Forschungsgemeinschaft under a Heisenberg grant     

Asymmetric hydrogenation of alkyl(vinyl)thioethers: a promising approach to α-chiral thioethers

This paper describes the enantioselective hydrogenation of vinylthioethers. We show that thioether derivatives of maleic esters can be hydrogenated with full conversion and up to 60% ee, and that α-thioether cinnamic acids can be hydrogenated in 51% ee with modest conversion.     

Characterisation of adsorbed layers on sulphide minerals by photoelectron spectroscopy

The systems galena/2-mercaptobenzothiazole (MBT) and pyrite/MBT have been studied using synchrotron radiation excited photoelectron spectroscopy (SRXPS). The chemisorption of MBT and the multilayer formation of 2,2′-dithiobis(benzothiazole) (BBTD) are evidenced by additional structures, observed beside the substrate signals, in the S2p-spectra of cleaved mineral surfaces after adsorption of MBT. The amount of the complex remains constant at concentrations as high as 10^–5 mol/L whereas the amount of BBTD increases. From the dependence of the adsorbate intensities on the excitation energy the conclusion can be drawn that an overlayer of BBTD on a chemisorbed layer of MBT is formed. The very weak adsorption of MBT on pyrite in alkaline solutions may explain the selective flotation of galena from pyrite in alkaline media.     

Contingent epiderivatives and set-valued optimization

In this paper we introduce the concept of the contingent epiderivative for a set-valued map which modifies a notion introduced by Aubin [2] as upper contingent derivative. It is shown that this kind of a derivative has important properties and is one possible generalization of directional derivatives in the single-valued convex case. For optimization problems with a set-valued objective function optimality conditions based on the concept of the contingent epiderivative are proved which are necessary and sufficient under suitable assumptions.     

Interplay of charge, spin, orbital and lattice correlations in colossal magnetoresistance manganites

We derive a realistic microscopic model for doped colossal magnetoresistance manganites, which includes the dynamics of charge, spin, orbital and lattice degrees of freedom on a quantum mechanical level. The model respects the SU(2) spin symmetry and the full multiplet structure of the manganese ions within the cubic lattice. Concentrating on the hole doped domain ( 0≤x≤0.5) we study the influence of the electron-lattice interaction on spin and orbital correlations by means of exact diagonalisation techniques. We find that the lattice can cause a considerable suppression of the coupling between spin and orbital degrees of freedom and show how changes in the magnetic correlations are reflected in dynamic phonon correlations. In addition, our calculation gives detailed insights into orbital correlations and demonstrates the possibility of complex orbital states. Received 4 September 2002 / Received in final form 8 November 2002 Published online 31 December 2002