A Unified Constructive Approach to the Topological Degree in Rn

The paper gives an approach to the topological degree in Rⁿ which takes into account numerical requirements and permits derivation of the known degree computation formulas in a simple way. The new approach subsumes several earlier approaches and represents a general principle of construction of degree computation formulas. The basic idea consists of computing the degree of a continuous function relative to a bounded open subset Ω of Rⁿ by means of an auxiliary function which is defined on a polyhedron approximating Ω and maps into a known fixed convex polyhedron containing the origin of Rⁿ. It is further shown that the topological degree of a continuous function relative to an n-dimensional polyhedron P can be computed alone by means of a subset of the boundary of P .     

Extrusion of pastes with a piston extruder for the determination of the local solid and fluid concentration, the local porosity and saturation and displacement profiles by means of NMR imaging

 Nuclear Magnetic Resonance (NMR) was used to investigate the extrusion behaviour of PTFE pastes in a ram extruder. By means of ¹H-NMR imaging (MRI) it is possible to determine the local proton density and therefore, the local fluid concentration. The ¹⁹F-MRI provides the local solid concentration. Thus the local saturation and the local porosity can be calculated with the information of the local fluid and solid concentration. Furthermore displacement profiles can be derived from NMR images by means of correlation techniques without any preparation or marking of the pastes. Received: 8 May 2000   Accepted: 1 May 2001     

The canonical solution operator of $ {\bar \partial } $ on weighted spaces with holomorphic coefficients

On weighted spaces with strictly plurisubharmonic weightfunctions the canonical solution operator of and the ‐Neumann operator are bounded. In this paper we find a class of strictly plurisubharmonic weightfunctions with certain growth conditions, so that they are Hilbert‐Schmidt operators between weighted spaces with different weightfunctions, if they are restricted to forms with holomorphic coefficients. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ground-state complex formation of perylene with pyromellitic dianhydride studied by static fluorescence quenching

The association of complex formation with static quenching in CT systems was investigated. Evaluation of the data made evident that the inner filter effect must be allowed for. Time-resolved and temperature-dependent stationary measurements of fluorescence led to the separation of dynamic and static quenching components. The static quenching constant is discussed with respect to the equilibrium constant of complex formation determined by absorption spectroscopy.     

Laser systems specialized for laser spectroscopy at storage rings

Laser spectroscopy at storage rings often suffers from a limited resolution due to Doppler-broadened resonances. Broadening is caused by the velocity spread of the ions stored in the beam. In the following, the present status of our work on laser systems specialized on the specific needs of laser spectroscopy at storage rings is reported. Two pulsed laser systems were developed. One is a dye laser whose spectral bandwidth can be switched by inserting different Littrow-prisms into the resonator. An increase in bandwidth up to a factor of 45 was achieved. This laser was used for fast qualitative scans and high resolution measurements. The other laser system is a Nd : YAG laser pumped optical parametric oscillator. It is a tunable laser system covering the spectral range from 410 to 4000 nm. Furthermore, a continuous wave laser with a frequency shifted feedback cavity is described. It shows broadband emission with an adjustable bandwidth of up to 4.5 GHz. This laser can be advantageous for laser cooling of ion beams. This revised version was published online in August 2006 with corrections to the Cover Date.     

Alkenylidenes in Organic Synthesis

Alkenylidenes R₂C?C: (= alkylidene carbenes) undergo regio- and stereoselective intramolecular C? H insertion reactions that are excellently suited for the synthesis of cyclopentenes. The 1, 2-shifts occurring with R?H and R?Ar are useful for the preparation of alkynes. Alkenylidenes are efficiently generated from carbonyl compounds by diazomethylation, from vinyl halides by α-elimination, from alkynyliodonium salts by addition of nucleophiles, and from alkynes by retro-1, 2-shifts. Specific applications of the various methods, particularly in the synthesis of natural products, are discussed.