Gültigkeitsbegriffe für Gleichungen in partiellen Algebren

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Der Beweis des Weierstraßschen approximationssatzes 1885 vor dem hintergrund der entwicklung der fourieranalysis

Eine bisher unveröffentlichte Ausarbeitung der Weierstraßschen Vorlesung “Ausgewählte Kapitel aus der Funktionenlehre” vom Sommersemester 1886 sowie verschiedene Briefwechsel aus jener Zeit gestatten es, Weierstraß' Verhältnis zur Theorie der Funktionen reeller Variablen näher zu beluechten. Es zeigt sich, daß Weierstraß den Beweis seines Approximationssatzes (1885) bewußt in die Traditionslinie der Fourieranalysis einordnete. Dies führte ihn zur Verallgemeinerung seines Satzes auf unstetige Funktionen mittels des Cantorschen Begriffs des (äußeren) Inhalts einer beschränkten Punktmenge.An unpublished autograph version of Weierstrass' lecture-course “Selected Chapters on Function Theory” (summer semester 1886) as well as several letters shed some light upon Weierstrass' position concerning the theory of functions of real variables. I show that Weierstrass considered his Approximation Theorem (1885) a part of the tradition of Fourier analysis. This led him to an extension of the theorem to the case of discontinuous functions by means of Cantor's concept of the outer content of a bounded point set.     

Traffic of Molecular Motors Through Tube-Like Compartments

The traffic of molecular motors through open tube-like compartments is studied using lattice models. These models exhibit boundary-induced phase transitions related to those of the asymmetric simple exclusion process (ASEP) in one dimension. The location of the transition lines depends on the boundary conditions at the two ends of the tubes. Three types of boundary conditions are studied: (A) Periodic boundary conditions which correspond to a closed torus-like tube. (B) Fixed motor densities at the two tube ends where radial equilibrium holds locally; and (C) Diffusive motor injection at one end and diffusive motor extraction at the other end. In addition to the phase diagrams, we also determine the profiles for the bound and unbound motor densities using mean field approximations and Monte Carlo simulations. Our theoretical predictions are accessible to experiments.     

Investigation of multi-layer coatings on cemented carbide cutting tools by analytical electron microscopy

Multi-layer coatings on cemented carbide substrates have been investigated by analytical electron microscopy (AEM). The samples were taken from cross-sections through the coating thus enabling a study of individual layers and interfaces. Various phenomena are shown: (1) tungsten diffusion and graphite inclusions in TiC layers, (2) oxygen impurities in Ti(C, N) coatings and (3) the occurrence of titanium oxinitrides in the interface between the Al₂O₃ and TiN-layers.Dedicated to Professor Günther Tölg on the occasion of his 60th birthday