Parallel load balancing is studied for problems with certain bisection properties. A class of problems has bisectors if every problem p of weight w(p) in the class can be subdivided into two subproblems whose weight (load) is at least an -fraction of the original problem. A problem p is to be split into N subproblems such that the maximum weight among them is as close to w(p)=N as possible. It ...

We deal with different properties of a smooth and strictly convex body that depend on the behavior of the planar sections of the body parallel to and close to a given tangent plane. The first topic is boundary points where any given convex domain in the tangent plane can be approximated by a sequence of suitably rescaled planar sections (so-called p-universal points). In the second topic, the g...

We have obtained ultra-high quality spectra (R = 180, 000; S/N > 300) with unprecedented wavelength coverage (4400 to 7400 Å) for a number of stars covering most of the HR diagram in order to test the predictions of models of stellar surface convection. Line bisectors and core wavelength shifts are both measured and modeled, allowing us to validate and/or reveal the limitations of state-of-the-...

Generic singularities of line fields have been studied for lines of principal curvature of embedded surfaces. In this paper we propose an approach to classify generic singularities of general line fields on 2D manifolds. The idea is to identify line fields as bisectors of pairs of vector fields on the manifold, with respect to a given conformal structure. The singularities correspond to the zer...

There are many problems and configurations in Euclidean geometry that were never extended to the framework of (normed or) finite dimensional real Banach spaces, although their original versions are inspiring for this type of generalization, and the analogous definitions for normed spaces represent a promising topic. An example is the geometry of simplices in non-Euclidean normed spaces. We pres...

In parallel computation we often need an algorithm for dividing one computationally expensive job into a xed number, say N , of subjobs, which can be processed in parallel (with reasonable overhead due to additional communication). In practice it is often easier to repeatedly bisect jobs, i.e., split one job into exactly two subjobs, than to generate N subjobs at once. In order to balance the l...

Dissertation zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften

This paper describes SCSolver, a geometric constraint solver based on adaptive sampling of an underlying constraint space. The solver is demonstrated on the computation of the offset to a surface as well as the computation of the bisector between two surfaces. The adaptive constraint sampling generates a solution manifold through a generalized dual-contouring approach appropriate for higher-dim...