Zur Kenntnis der kolloidchemischen Eigenschaften des Humus

Ohne ZusammenfassungMeinem verehrten Lehrer, Herrn Prof. Dr. H. Pallmann — auf dessen Anregung diese Arbeit ausgeführt würde — möchte ich für die mir zuteil gewordene Förderung und die wertvollen Ratschläge bestens danken.     

Recombination of Au25+ with free electrons at low energies

The origin of the widely observed enhancement of rates for electron-ion recombination at very low energies is still unknown. We investigated the recombination of Au²⁵⁺ with free electrons in a merged-beams experiment at the UNILAC accelerator of the GSI in Darmstadt. At E _rel= 0 eV we found an enormous enhancement factor of 365 compared to the theory of radiative recombination. An increase of the electron density by a factor of 10 had not much influence on the measured rate coefficient. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Survey on Explicit Representation Formulae for Fundamental Solutions of Linear Partial Differential Operators

In the present article, we aim at treating the existence of fundamental solutions of linear partial differential operators with constant coefficients from the viewpoint of setting up explicit formulae yielding fundamental solutions.     

Amorphous chalcogenide AgSbS2 films prepared by pulsed laser deposition

The pulsed laser deposition technique has been applied to prepare amorphous ternary AgSbS films. The films were prepared from AgSbS₂ bulk glass using a KrF excimer laser. The composition of prepared films according to the results of the energy dispersive X-ray analysis and the Rutherford backscattering was close to bulk one. Optical transmission and spectral dependence of the refractive index proved the good optical quality of the films. The Ar⁺ ion laser dot exposures of the films show a potential applicability of the films as a new type of optical recording material. PACS 78.66.Jg; 81.15.Fg; 81.40.Wx     

A mixed‐FEM formulation for nonlinear incompressible elasticity in the plane

This article deals with an expanded mixed finite element formulation, based on the Hu‐Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a two‐fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babu?ka‐Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well‐known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank‐Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105–128, 2002     

Euler characteristic and related measures for random geometric sets

By an elementary calculation we obtain the exact mean values of Minkowksi functionals for a standard model of percolating sets. In particular, a recurrence theorem for the mean Euler characteristic recently put forward is shown to be incorrect. Related previous mathematical work is mentioned. We also conjecture bounds for the threshold density of continuum percolation, which are associated with the Euler characteristic.     

Beyond nanosizing: an approach to shape analysis of fluorescent nanostructures by SMI-microscopy

Using spatially modulated illumination (SMI) light microscopy it is possible to measure the sizes of fluorescent structures that have an extension far below the conventional optical resolution limit (“subresolution size”). Presently, the sizes are determined as the object extension along the optical axis of the SMI microscope. For this, however, “a priori” assumptions on the fluorochrome distribution (“shape”) within the examined fluorescent structure have to be made. Usually it is assumed that the fluorochrome follows a Gauss-distribution or a spherical distribution. In this report we overcome the necessity to make an assumption on the shape of the fluorochrome distribution. We introduce two new experimentally obtained parameters which allow the determination of a shape measure to describe the spatial distribution of the fluorescent dye. This becomes possible by independent measurements with different excitation wavelengths. As an example, we present shape parameter measurements on individual fluorescent microspheres with a nominal geometrical diameter (“size”) of 190 nm. In the case investigated, the experimental shape correlated well with a homogeneous fluorochrome distribution (“spherical shape”) but not with a variety of other “shapes”.