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- Wavelet Analysis of the Geomagnetic Field Within Source Regions of Ionospheric and Magnetospheric Currents (1999)
- A multiscale method is introduced using spherical (vector) wavelets for the computation of the earth's magnetic field within source regions of ionospheric and magnetospheric currents. The considerations are essentially based on two geomathematical keystones, namely (i) the Mie representation of solenoidal vector fields in terms of toroidal and poloidal parts and (ii) the Helmholtz decomposition of spherical (tangential) vector fields. Vector wavelets are shown to provide adequate tools for multiscale geomagnetic modelling in form of a multiresolution analysis, thereby completely circumventing the numerical obstacles caused by vector spherical harmonics. The applicability and efficiency of the multiresolution technique is tested with real satellite data.

- Optimal Order Results for a Class of Regularizazion Methodes Using Unbounded Operators (1999)
- A class of regularization methods using unbounded regularizing operators is considered for obtaining stable approximate solutions for ill-posed operator equations. With an a posteriori as well as an priori parameter choice strategy, it is shown that the method yields optimal order. Error estimates have also been obtained under stronger assumptions on the the generalized solution. The results of the paper unify and simplify many of the results available in the literature. For example, the optimal results of the paper includes, as particular cases for Tikhonov regularization, the main result of Mair (1994) with an a priori parameter choice and a result of Nair (1999) with an a posteriori parameter choice. Thus the observations of Mair (1994) on Tikhonov regularization of ill-posed problems involving finitely and infinitely smoothing operators is applicable to various other regularization procedures as well. Subsequent results on error estimates include, as special cases, an optimal result of Vainikko (1987) and also recent results of Tautenhahn (1996) in the setting Hilbert scales.

- Möglichkeiten einer eigenständigen Alterssicherung für Frauen (1999)
- Im Rahmen dieser Arbeit wird gezeigt, daß Frauen sowohl durch die Gesetzgebung als auch durch arbeitsmarktpolitische und steuerliche Rahmenbedingungen benachteiligt werden. Es stellt sich die Frage, inwieweit eine Verbesserung der Altersversorgung für die Frau vorgenommen werden kann. Dabei muß eine verbesserte und an die Bedürfnisse der Frauen angepaßte Altersvorsorge nicht unbedingt auf die bestehende gesetzliche Rentenversicherung (GRV) aufbauen.

- On the Analysis of Spatial Binary Images (1999)
- This paper deals with the characterization of microscopically heterogeneous, but macroscopically homogeneous spatial structures. A new method is presented which is strictly based on integral-geometric formulae such as Crofton's intersection formulae and Hadwiger's recursive de nition of the Euler number. The corresponding algorithms have clear advantages over other techniques. As an example of application we consider the analysis of spatial digital images produced by means of Computer Assisted Tomo- graphy.

- On the Construction of Discrete Equilibrium Distributions for Kinetic Schemes (1999)
- A general approach to the construction of discrete equilibrium dis- tributions is presented. Such distribution functions can be used to set up Kinetic Schemes as well as Lattice Boltzmann methods. The general principles are also applied to the construction of Chapman Enskog dis- tributions which are used in Kinetic Schemes for compressible Navier Stokes equations.

- A new discrete velocity method for Navier-Stokes equations (1999)
- The relation between the Lattice Boltzmann Method, which has re- cently become popular, and the Kinetic Schemes, which are routinely used in Computational Fluid Dynamics, is explored. A new discrete velocity model for the numerical solution of Navier-Stokes equations for incom- pressible uid ow is presented by combining both the approaches. The new scheme can be interpreted as a pseudo-compressibility method and, for a particular choice of parameters, this interpretation carries over to the Lattice Boltzmann Method.

- On Center Cycles in Grid Graphs (1998)
- Finding "good" cycles in graphs is a problem of great interest in graph theory as well as in locational analysis. We show that the center and median problems are NP hard in general graphs. This result holds both for the variable cardinality case (i.e. all cycles of the graph are considered) and the fixed cardinality case (i.e. only cycles with a given cardinality p are feasible). Hence it is of interest to investigate special cases where the problem is solvable in polynomial time. In grid graphs, the variable cardinality case is, for instance, trivially solvable if the shape of the cycle can be chosen freely. If the shape is fixed to be a rectangle one can analyse rectangles in grid graphs with, in sequence, fixed dimension, fixed cardinality, and variable cardinality. In all cases a com plete characterization of the optimal cycles and closed form expressions of the optimal objective values are given, yielding polynomial time algorithms for all cases of center rectangle problems. Finally, it is shown that center cycles can be chosen as rectangles for small cardinalities such that the center cycle problem in grid graphs is in these cases completely solved.

- Least-squares Geopotential Approximation by Windowed Fourier and Wavelet Transform (1999)
- Two possible substitutes of the Fourier transform in geopotential determination are windowed Fourier transform (WFT) and wavelet transform (WT). In this paper we introduce harmonic WFT and WT and show how it can be used to give information about the geopotential simultaneously in the space domain and the frequency (angular momentum) domain. The counterparts of the inverse Fourier transform are derived, which allow us to reconstruct the geopotential from its WFT and WT, respectively. Moreover, we derive a necessary and sufficient condition that an otherwise arbitrary function of space and frequency has to satisfy to be the WFT or WT of a potential. Finally, least - squares approximation and minimum norm (i.e. least - energy) representation, which will play a particular role in geodetic applications of both WFT and WT, are discussed in more detail.