We consider immersed hypersurfaces in euclidean $R^{n+1}$ which are stable with respect to an elliptic parametric functional with integrand $F=F(N)$ depending on normal directions only. We prove an integral curvature estimate provided that $F$ is sufficiently close to the area integrand, extending the classical curvature estimate of Schoen, Simon and Yau for stable minimal hypersurfaces in $R^{n+1}$. As a crucial point of our analysis we derive a generalized Simons inequality for the laplacian of the length of a weighted second fundamental form with respect to an abstract metric associated with $F$. Using Moser's iteration technique we finally prove a pointwise curvature estimate for $n leq 5$. As an application we obtain a new Bernstein result for complete stable hypersurfaces of dimension $n leq 5$.

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This thesis deals with the structure of the no-wait job-shop problem as well as the derivation of fast approximation algorithms. These algorithms are based on a decomposition approach into a sequencing and a timetabling problem that was initially introduced by Macchiaroli et al. (1999). In the thesis the problems are derived from a mixed integer formulation of the original problem and proved to be NP-hard in the strong sense. After presenting a fast heuristic approach for the timetabling problem, the focus lies on the sequencing problem for which several local search algorithms are presented. The algorithms are tested on a wide variety of benchmark problems for the classical job-shop problem. Among the algorithms, the tabu search approach outperforms all other algorithms that can be found in the literature in objective value as well as computation time.

Stochastic programming offers a way to treat uncertainty in decision problems. In particular, it allows the minimization of risk. We consider mean-risk models involving deviation measures, as for instance the standard deviation and the semideviation, and discuss these risk measures in the framework of stochastic dominance as well as in the framework of coherent risk measures. We derive statements concerning the structure and the stability of the resulting optimization problems whereby we emphasize on models including integrality requirements on some decision variables. Then we propose decomposition algorithms for the mean-risk models under consideration and present numerical results for two stochastic programming applications.

This thesis deals with regualrity questions of elliptic and parabolic systems of partial differential equations of second order. With the help of a Harnack inequality it is shown that bounded weak solutions of certain parabolic systems are Hölder continous. In the second chapter we prove regularity theorems for weak harmonic mappings in the interior and at the boundary, an important tool for these theorems are again two Harnack inequalities. The last two chapters deal with degenerate elliptic systems, for certain degenerate elliptic coefficients (e.g. in the Muckenhouptclass A2) we prove two Harnack inequalities and show with these inequalities some regularity theorems for degenerate elliptic systems.

In order to develop and evaluate characteristics of ideal-typical patterns of private additional lessons in mathematics, I refer to investigations on mathematics school lessons of Hans Freudenthal, Hans Werner Heymann, Alan H. Schoenfeld, and Heinrich Winter. Their ideal-typical patterns are equally represented in the six fundamental dimensions independent work, subject orientation, process and problem oriented interactions, structural thinking, discovering education processes, and application orientation. For private additional lessons, the content of the six dimensions is determined by case studies, consisting of the execution and analysis of remedial teaching, and evaluated by synopsis to the characteristics of school teaching. As an outlook I present a concept of school-organized remedial teaching.

The presented dissertation is concerned with anisotropic curvature motion of two-dimensional parametric surfaces as well as their application in surface fairing and surface restauration. Mainly the so called anisotropic mean curvature motion (AMCM) and the anisotropic Willmore-flow are being treated. These flows are generalizations of the classical mean curvature flow and the classical Willmore-flow, respectively. The anisotropies are induced by positive, 1-homogenous and convex functions, which can be regarded as support functions of convex bodies, so called Wulff-shapes. Being a method of fourth order of differentiation in the surface coordinates, the anisotropic Willmore-flow allows the prescription of boundary values for the position of the boundary itself as well as for the surface normals on the boundary of a surface patch under consideration. Hence it is an appropriate method for the reconstruction of partially destroyed surfaces. In this work a numerical scheme for the anisotropic Willmore-flow is presented, which is based on an operator splitting of the fourth order evolution equation into two weak equations of first order of differentiation, which is discretized using linear finite elements in space. In particular the discretization of the AMCM turns out to be one of these equations. Based on the AMCM a method for the fairing of surfaces with crystalline edges is developed. Modifications of the discrete AMCM are also used for surface modeling purposes. Schemes for the artificial aging and for virtual engraving of surfaces are presented. Further on a subdivision scheme based on the isotropic mean curvature motion is introduced. Finally, the isotropic as well as the anisotropic Willmore-flow is employed for the restauration of partially destroyed triangulated surfaces.

We study a class of filtered flat vector bundles of rank 2 which we call pseudo-eeliptic bundles. We construct pseudo-elliptic bundles starting from a deformation datum defined over the function field of a curve over an algebraically closed field of positive characteristic. This leads us to study a variant of Dwork's accessary parameter problem. We give applications of our results to Galois theory.