Über Primzahldarstellungen durch binäre quadratische Formen

Ohne Zusammenfassung     

Strong rightD-domains

An integral domainR is called rightD-domain if its lattice of all right ideals is distributive. In § 2 a sufficient condition for an integral domainR is given such thatR is a rightD-domain if and only ifR is a leftD-domain. For example each integral domain which is algebraic over its center satisfies this criterion. Furthermore, a rightD-domain is called strong if its lattice of all fractional right ideals is distributive. Examples of strong rightD-domains are given in §4. Each overring of a strong rightD-domain is also a strong rightD-domain whereas arbitrary rightD-domains may have overrings which are no rightD-domains. Section 3 is mainly concerned with the set * of all left invertible fractional right ideals and the mapping :**,II _l ^–1 whereI _l ^–1 denotes the left inverse ofI. For example, equivalent conditions are given for * to be a sublattice of and it is shown that is bijective if and only if (IJ)=(I)+(J) holds for allI,J*. Finally, §5 deals with (right)D-domains which are algebraic over their centersC. It is proved thatR is invariant if and only ifC is a commutative Prüfer domain andR the integral closure ofC inQ(R).     

Characterization of modified glassy carbon films

The composition and structure of the thin conversion films at pre- and breakdown state are investigated. The breakdown leads to a modified structure and composition. Raman spectra of modified films show the formation of glassy carbon with a defined size of crystallites. A typical morphology characterized by a strong structured surface indicates this breakdown state. Electron diffraction patterns of the pre-breakdown state show the presence of titanium nitride, titanium carbide and titanium oxide.Dedicated to Professor Dr. rer. nat. Dr. h.c. Hubertus Nickel on the occasion of his 65th birthday     

Partial Purification and Characterization of Raucaffricine β-D-Glucosidase from Plant Cell-Suspension Cultures of Rauwolfia serpentina BENTH

A novel highly substrate-specific Rauwolfia enzyme, raucaffricine β-D -glucosidase, was isolated from cell-suspension cultures of R. serpentina. The enzyme has been purified ca. 1350-fold, its major characteristics such as M_r = 66600 ± 5%, pH optimum 5.1, temperature optimum 38°, and inhibition of its activity by glucose and fructose were investigated. Its limited distribution in different cell cultures and differentiated plants indicates that the enzyme is present in significant amounts exclusively in cultured Rauwolfia cells.     

Polymer fibers as carriers for homogeneous catalysts

This paper describes a polymer fiber-based approach for the immobilization of homogeneous catalysts. The goal is to generate products that are free of catalysts which would be of great importance for the development of optoelectronic or pharmaceutical compounds. Electrospinning was employed to prepare the non-woven fiber assembly composed of polystyrene. The homogeneous catalyst scandium triflate was immobilized on the polystyrene fibers during electrospinning and on corresponding core shell fibers using a fiber template approach. An imino aldol and an aza-Diels-Alder model reaction were carried out with each fibrous catalytic system. This resulted in the immobilization of homogeneous catalysts in a polymer environment without loss of their catalytic activity and may even be enhanced when compared with reactions carried out in homogeneous solutions.     

Diffusion-Limited Reactions and Mortal Random Walkers in Confined Geometries

Motivated by the diffusion-reaction kinetics on interstellar dust grains, we study a first-passage problem of mortal random walkers in a confined two-dimensional geometry. We provide an exact expression for the encounter probability of two walkers, which is evaluated in limiting cases and checked against extensive kinetic Monte Carlo simulations. We analyze the continuum limit which is approached very slowly, with corrections that vanish logarithmically with the lattice size. We then examine the influence of the shape of the lattice on the first-passage probability, where we focus on the aspect ratio dependence: Distorting the lattice always reduces the encounter probability of two walkers and can exhibit a crossover to the behavior of a genuinely one-dimensional random walk. The nature of this transition is also explained qualitatively.     

Drazin-monotonicity characterizations for property-n matrices

A square matrix A is said to have property n if there exists a nonnegative power of A. In this paper, necessary and sufficient conditions for such matrices to have a nonnegative Drazin inverse are presented.