Computations in Relative Algebraic K-Groups

Let G be finite group and K a number field or a p-adic field with ring of integers O_K. In the first part of the manuscript we present an algorithm that computes the relative algebraic K-group K_0(O_K[G],K) as an abstract abelian group. We solve the discrete logarithm problem, both in K_0(O_K[G],K) and the locally free class group cl(O_K[G]). All algorithms have been implemented in MAGMA for the case K = \IQ. In the second part of the manuscript we prove formulae for the torsion subgroup of K_0(\IZ[G],\IQ) for large classes of dihedral and quaternion groups.

Fluoreszenzspektroskopische Untersuchungen von Autoionisations- und Photodissoziationsprozessen des Stickstoffmoleküls nach monochromatischer Synchrotronstrahlanregung

Autoionisations- und Photodissoziationsprozesse von molekularem Stickstoff wurden mit Hilfe der photoneninduzierten Fluoreszenzspektroskopie nach Anregung von monochromatisierter Synchrotronstrahlung untersucht. Dabei wurden zwei Anregungsprozesse untersucht. Die Anregung eines Sub-Valenzschalenelektrons diente zum Studium des Photodissoziationsverhaltens von hochangeregten Zuständen ("super-excited-states") und die aus den Experimenten gewonnenen partiellen Emissionsquerschnitte wurden absolut normiert. Durch Anregen eines Innerschalenelektrons wurde die 1s^{-1}pi* Resonanz schwingungsselektiv angeregt und die darauf folgende Autoionisation in den N_2^+ C ^2\Sigma_u^+ (v)-Zustand und dessen Relaxation durch Fluoreszenzemission in den Grundzustand des Stickstoffions untersucht. Erstmalig wurden partielle Emissionsquerschnitte nach Photodissoziation in neutrale Fragmente von hochangeregten Zuständen von atomaren Stickstoff im Anregungsenergiebereich zwischen 23eV und 26,7eV und im Fluoreszenzwellenläneninterval zwischen 80nm und 150nm absolut bestimmt. Die schwingungsselektive Besetzung der Innerschalenresonanz des Stickstoffmoleküls ermöglichte eine detaillierte Analyse des Autoionisationsverhaltens der Innerschalenresonanz in den N_2^+ C-Zustand durch Analyse der nachfolgenden Relaxation durch molekulare Fluoreszenz in den Grundzustand des Molekülions.

Numerical Methods for Non-Stationary Stokes Flow

We consider a first order implicit time stepping procedure (Euler scheme) for the non-stationary Stokes equations in smoothly bounded domains of R3. Using energy estimates we can prove optimal convergence properties in the Sobolev spaces Hm(G) (m = 0;1;2) uniformly in time, provided that the solution of the Stokes equations has a certain degree of regularity. For the solution of the resulting Stokes resolvent boundary value problems we use a representation in form of hydrodynamical volume and boundary layer potentials, where the unknown source densities of the latter can be determined from uniquely solvable boundary integral equations’ systems. For the numerical computation of the potentials and the solution of the boundary integral equations a boundary element method of collocation type is used. Some simulations of a model problem are carried out and illustrate the efficiency of the method.

Freiraumqualität statt Abstandsgrün. - Band 1

Deutsche Forschungsgemeinschaft

Approximate solutions and error estimates for a Stokes boundary value problem

The aim of this paper is the numerical treatment of a boundary value problem for the system of Stokes' equations. For this we extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the system of Stokes' equations in two dimensions. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.