Symmetrien von Mannigfaltigkeiten und rationale Homotopietheorie

Ohne Zusammenfassung     

On the Navier–Stokes equations with free convection in three‐dimensional unbounded triangular channels

The quaternionic calculus is a powerful tool for treating the Navier–Stokes equations very elegantly and in a compact form, through the evaluation of two types of integral operators: the Teodorescu operator and the quaternionic Bergman projector. While the integral kernel of the Teodorescu transform is universal for all domains, the kernel function of the Bergman projector, called the Bergman kernel, depends on the geometry of the domain. In this paper, we use special variants of quaternionic‐holomorphic multiperiodic functions in order to obtain explicit formulas for unbounded three‐dimensional parallel plate channels, rectangular block domains and regular triangular channels. Copyright © 2007 John Wiley & Sons, Ltd.     

Runge–Kutta methods for affinely controlled nonlinear systems

Rooted tree analysis is adapted from stochastic differential equations to derive systematically general Runge–Kutta methods for deterministic affinely controlled nonlinear systems. Order conditions are found and some specific coefficients for second- and third-order methods are determined, which are then used for simulations compared with the Taylor methods for affinely controlled nonlinear systems derived by Grüne and Kloeden.     

Eigenvalue Inequalities and Schubert Calculus

Using techniques from algebraic topology we derive linear inequalities which relate the spectrum of a set of Hermitian matrices A₁,…, A_r ? ¢^n×n with the spectrum of the sum A₁ + … + A_r. These extend eigenvalue inequalities due to Freede-Thompson and Horn for sums of eigenvalues of two Hermitian matrices.