Stabilität starkstetiger,positiver Operatorhalbgruppen aufC*-Algebren

Ohne Zusammenfassung     

Mean curvature flow of monotone Lagrangian submanifolds

We use holomorphic disks to describe the formation of singularities in the mean curvature flow of monotone Lagrangian submanifolds in . Supported by DFG, priority program SPP 1154, SM 78/1-1, SCHW 892/1-1.     

[P3Se4]+: A Binary Phosphorus–Selenium Cation

Although a fairly large number of binary group 15/16 element cations have been reported, no example involving phosphorus in combination with a group 16 element has been synthesized and characterized to date. In this contribution is reported the synthesis and structural characterization of the first example of such a cation, namely a nortricyclane‐type [P₃Se₄]⁺. This cation has been independently discovered by three groups through three different synthetic routes, as described herein. The molecular and electronic structure of the [P₃Se₄]⁺ cage and its crystal properties in the solid state have been characterized comprehensively by using X‐ray diffraction, Raman, and nuclear magnetic resonance spectroscopies, as well as quantum chemical calculations.     

Ripple formation in weakly turbulent flow

The formation of granular ripples under liquid shear flow in an annular channel is studied experimentally. The erodible granular bed is subject to weakly turbulent flows without a defined sharp boundary layer close to the granular bed. The flow field and the degree of turbulence is characterized quantitatively by using a particle image velocimeter and a laser-Doppler velocimeter, respectively. A new range of particle Reynolds numbers at the lower limit of the Shields diagram were explored. Quantitative measurements of the granular flow on the surface reveal that the threshold for particle motion coincides within the order of one percent with the threshold for ripple formation. In fully developed ripples it was found that on the leeward side of the ripples regions of low-velocity gradients exist where granular motion is scarce, indicating that the coupling between the ripples is mainly caused by the flow field of the liquid.     

Polymer Optical Fibers and Nonlinear Optical Device Principles

Basic principles of the present optoelectronic research activities at Hoechst AG are presented in this contribution. Within the diversified broad band spectrum of optoelectronic materials and applications our interest is focused on new types of polymer optical fibers and nonlinear optical device principles using organic Langmuir–Blodgett films and electrically poled polymers. The basic principles and the limits of the present research and development activities which have a high market potential are outlined.