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The thesis is concerned with the modelling of ionospheric current systems and induced magnetic fields in a multiscale framework. Scaling functions and wavelets are used to realize a multiscale analysis of the function spaces under consideration and to establish a multiscale regularization procedure for the inversion of the considered operator equation. First of all a general multiscale concept for vectorial operator equations between two separable Hilbert spaces is developed in terms of vector kernel functions. The equivalence to the canonical tensorial ansatz is proven and the theory is transferred to the case of multiscale regularization of vectorial inverse problems. As a first application, a special multiresolution analysis of the space of square-integrable vector fields on the sphere, e.g. the Earth’s magnetic field measured on a spherical satellite’s orbit, is presented. By this, a multiscale separation of spherical vector-valued functions with respect to their sources can be established. The vector field is split up into a part induced by sources inside the sphere, a part which is due to sources outside the sphere and a part which is generated by sources on the sphere, i.e. currents crossing the sphere. The multiscale technqiue is tested on a magnetic field data set of the satellite CHAMP and it is shown that crustal field determination can be improved by previously applying our method. In order to reconstruct ionspheric current systems from magnetic field data, an inversion of the Biot-Savart’s law in terms of multiscale regularization is defined. The corresponding operator is formulated and the singular values are calculated. Based on the konwledge of the singular system a regularzation technique in terms of certain product kernels and correponding convolutions can be formed. The method is tested on different simulations and on real magnetic field data of the satellite CHAMP and the proposed satellite mission SWARM.

In this paper, the reflection and refraction of a plane wave at an interface between .two half-spaces composed of triclinic crystalline material is considered. It is shown that due to incidence of a plane wave three types of waves namely quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH) will be generated governed by the propagation condition involving the acoustic tensor. A simple procedure has been presented for the calculation of all the three phase velocities of the quasi waves. It has been considered that the direction of particle motion is neither parallel nor perpendicular to the direction of propagation. Relations are established between directions of motion and propagation, respectively. The expressions for reflection and refraction coefficients of qP, qSV and qSH waves are obtained. Numerical results of reflection and refraction coefficients are presented for different types of anisotropic media and for different types of incident waves. Graphical representation have been made for incident qP waves and for incident qSV and qSH waves numerical data are presented in two tables.

UML and SDL are languages for the development of software systems that have different origins, and have evolved separately for many years. Recently, it can be observed that OMG and ITU, the standardisation bodies responsible for UML and SDL, respectively, are making efforts to harmonise these languages. So far, harmonisation takes place mainly on a conceptual level, by extending and aligning the set of language concepts. In this paper, we argue that harmonisation of languages can be approached both from a syntactic and semantic perspective. We show how a common syntactical basis can be derived from the analysis of the UML meta-model
and the SDL abstract grammar. For this purpose, conceptually sound and well-founded mappings from meta-models to abstract grammars and vice versa are defined and applied. On the semantic level, a comparison between corresponding language constructs is performed.

The goal of this thesis is a physically motivated and thermodynamically consistent formulation of higher gradient inelastic material behavior. Thereby, the influence of the material microstructure is incorporated. Next to theoretical aspects, the thesis is complemented with the algorithmic treatment and numerical implementation of the derived model. Hereby, two major inelastic effects will be addressed: on the one hand elasto-plastic processes and on the other hand damage mechanisms, which will both be modeled within a continuum mechanics framework.

In first part of this work, summaries of traditional Multiphase Flow Model and more recent Multiphase Mixture Model are presented. Attention is being paid to attempts include various heterogeneous aspects into models. In second part, MMM based differential model for two-phase immiscible flow in porous media is considered. A numerical scheme based on the sequential solution procedure and control volume based finite difference schemes for the pressure and saturation-conservation equations is developed. A computer simulator is built, which exploits object-oriented programming techniques. Numerical result for several test problems are reported.

We construct and study two surface measures on the space C([0,1],M) of paths in a compact Riemannian manifold M embedded into the Euclidean space R^n. The first one is induced by conditioning the usual Wiener measure on C([0,T],R^n) to the event that the Brownian particle does not leave the tubular epsilon-neighborhood of M up to time T, and passing to the limit. The second one is defined as the limit of the laws of reflected Brownian motions with reflection on the boundaries of the tubular epsilon-neighborhoods of M. We prove that the both surface measures exist and compare them with the Wiener measure W_M on C([0,T],M). We show that the first one is equivalent to W_M and compute the corresponding density explicitly in terms of the scalar curvature and the mean curvature vector of M. Further, we show that the second surface measure coincides with W_M. Finally, we study the limit behavior of the both surface measures as T tends to infinity.

The thesis deals with the subgradient optimization methods which are serving to solve nonsmooth optimization problems. We are particularly concerned with solving large-scale integer programming problems using the methodology of Lagrangian relaxation and dualization. The goal is to employ the subgradient optimization techniques to solve large-scale optimization problems that originated from radiation therapy planning problem. In the thesis, different kinds of zigzagging phenomena which hamper the speed of the subgradient procedures have been investigated and identified. Moreover, we have established a new procedure which can completely eliminate the zigzagging phenomena of subgradient methods. Procedures used to construct both primal and dual solutions within the subgradient schemes have been also described. We applied the subgradient optimization methods to solve the problem of minimizing total treatment time of radiation therapy. The problem is NP-hard and thus far there exists no method for solving the problem to optimality. We present a new, efficient, and fast algorithm which combines exact and heuristic procedures to solve the problem.

The main two problems of continuous-time financial mathematics are option pricing and portfolio optimization. In this thesis, various new aspects of these major topics of financial mathematics will be discussed. In all our considerations we will assume the standard diffusion type setting for securitiy prices which is today well-know under the term "Black-Scholes model". This setting and the basic results of option pricing and portfolio optimization are surveyed in the first chapter. The next three chapters deal with generalizations of the standard portfolio problem, also know as "Merton's problem". Here, we will always use the stochastic control approach as introduced in the seminal papers by Merton (1969, 1971, 1990). One such problem is the very realistic setting of an investor who is faced with fixed monetary streams. More precisely, in addition to maximizing the utility from final wealth via choosing an investment strategy, the investor also has to fulfill certain consumption needs. Also the opposite situation, an additional income stream can now be taken into account in our portfolio optimization problem. We consider various examples and solve them on one hand via classical stochastic control methods and on the other hand by our new separation theorem. This together with some numerical examples forms Chapter 2. Chapter 3 is mainly concerned with the portfolio problem if the investor has different lending and borrowing rates. We give explicit solutions (where possible) and numerical methods to calculate the optimal strategy in the cases of log utility and HARA utility for three different modelling approaches of the dependence of the borrowing rate on the fraction of wealth financed by a credit. The further generalization of the standard Merton problem in Chapter 4 consists in considering simultaneously the possibilities for continuous and discrete consumption. In our general approach there is a possibility for assigning the different consumption times different weights which is a generalization of the usual way of making them comparable via discounting. Chapter 5 deals with the special case of pricing basket options. Here, the main problem is not path-dependence but the multi-dimensionality which makes it impossible to give usuefull analytical representations of the option price. We review the literature and compare six different numerical methods in a systematic way. Thereby we also look at the influence of various parameters such as strike, correlation, forwards or volatilities on the erformance of the different numerical methods. The problem of pricing Asian options on average spot with average strike is the topic of Chapter 6. We here apply the bivariate normal distribution to obtain an approximate option price. This method proves to be very reliable and e±cient for the valuation of different variants of Asian options on average spot with average strike.

SST (satellite-to-satellite tracking) and SGG (satellite gravity gradiometry) provide data that allows the determination of the first and second order radial derivative of the earth's gravitational potential on the satellite orbit, respectively. The modeling of the gravitational potential from such data is an exponentially ill-posed problem that demands regularization. In this paper, we present the numerical studies of an approach, investigated in [24] and [25], that reconstructs the potential with spline smoothing. In this case, spline smoothing is not just an approximation procedure but it solves the underlying compact operator equation of the SST-problem and the SGG-problem. The numerical studies in this paper are performed for a simplified geometrical scenario with simulated data, but the approach is designed to handle first or second order radial derivative data on a real satellite orbit.

In this paper we consider set covering problems with a coefficient matrix almost having the consecutive ones property, i.e., in many rows of the coefficient matrix, the ones appear consecutively. If this property holds for all rows it is well known that the set covering problem can be solved efficiently. For our case of almost consecutive ones we present a reformulation exploiting the consecutive ones structure to develop bounds and a branching scheme. Our approach has been tested on real-world data as well as on theoretical problem instances.