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In this study, 27 marine bacteria were screened for production of bioactive metabolites. Two strains from the surface of the soft coral Sinularia polydactyla, collected from the Red Sea, and three strains from different habitats in the North Sea were selected as a promising candidates for isolation of antimicrobial substances. A total of 50 compounds were isolated from the selected bacterial strains. From these metabolites 25 substances were known from natural sources, 10 substances were known as synthetic chemical and herein are reported as new natural products, and 13 metabolites are new. Two substances are still under elucidation. All new compounds were chemically and biologically characterized. Pseudoalteromonas sp. T268 produced simple phenol and oxindole derivatives. Production of homogentisic acid and WZ 268S-6 from this bacteria was affected by the salinity stress. WZ 268S-6 shows antimicrobial and cytotoxic activities. Its target is still unclear. Isolation of isatin from this strain points out for the possibility of using this substance as a chemotaxonomical marker for Alteromonas-like bacteria. A large number of nitro-substituted aromatic compounds were isolated from both Salegentibacter sp. T436 and Vibrio sp. WMBA1-4. They may be derived from metabolism of phenylalanine or tyrosine. From Salegentibacter sp. T436, 24 compounds were isolated, of which four compounds are new and six compounds were known as synthetic chemicals. WZ 436S-16 (dinitro-β-styrene) is the most potent antimicrobial and cytotoxic compound. It inhibits the oxygen uptake by N. coryli and causes apoptosis in the human promyelocytic leukaemia (HL-60 cells). From Vibrio sp. WMBA1-4, 13 new alkaloids were isolated, of which four were known as synthetic products and herein are reported as new substances from natural sources. The majority of these compounds show antimicrobial and cytotoxic activities. The cytotoxic activity of WMB4S-11 against the mouse lymphocytic leukaemia (L1210 cells) is due to the inhibition in the protein biosynthesis, while the remaining cytotoxic alkaloids have no effect on the synthesis of macromolecules in this cell line. The antibacterial activity of WMB4S-2, -11, -12, -13 and the antifungal activity of WMB4S-9 are not due to the inhibition in the macromolecules biosynthesis or in the oxygen uptake by the microorganisms. The biological activity of these nitro-aromatic compounds from Salegentibacter sp. T436 and Vibrio sp. WMBA1-4 is influenced by the presence of a nitro group and its position in respect to the hydroxyl group, number of the nitro groups, and the type of substitutions on the side chain. In diaryl-maleimide derivatives, types and position of substitution on the aryl rings, on the maleimide moity, and the hydrophobicity of the aryl ring itself lead to variations in the extent of the bioactivity of these derivatives. This is the first time that vibrindole (WMB4S-14) and turbomycin B or its noncationic form (WMB4S-15), isolated from Vibrio sp., are reported as cytotoxic compounds. WMB4S-15 inhibits the biosynthesis of macromolecules in L1210 cells. The structural similarity between some of the metabolites in this study and previously reported compounds from sponges, ascidians, and bryozoan indicates that the microbial origin of these compounds must be considered.

The fast development of the financial markets in the last decade has lead to the creation of a variety of innovative interest rate related products that require advanced numerical pricing methods. Examples in this respect are products with a complicated strong path-dependence such as a Target Redemption Note, a Ratchet Cap, a Ladder Swap and others. On the other side, the usage of the standard in the literature one-factor Hull and White (1990) type of short rate models allows only for a perfect correlation between all continuously compounded spot rates or Libor rates and thus are not suited for pricing innovative products depending on several Libor rates such as for example a "steepener" option. One possible solution to this problem deliver the two-factor short rate models and in this thesis we consider a two-factor Hull and White (1990) type of a short rate process derived from the Heath, Jarrow, Morton (1992) framework by limiting the volatility structure of the forward rate process to a deterministic one. In this thesis, we often choose to use a variety of modified (binomial, trinomial and quadrinomial) tree constructions as a main numerical pricing tool due to their flexibility and fast convergence and (when there is no closed-form solution) compare their results with fine grid Monte Carlo simulations. For the purpose of pricing the already mentioned innovative short-rate related products, in this thesis we offer and examine two different lattice construction methods for the two-factor Hull-White type of a short rate process which are able to deal easily both with modeling of the mean-reversion of the underlying process and with the strong path-dependence of the priced options. Additionally, we prove that the so-called rotated lattice construction method overcomes the typical for the existing two-factor tree constructions problem with obtaining negative "risk-neutral probabilities". With a variety of numerical examples, we show that this leads to a stability in the results especially in cases of high volatility parameters and negative correlation between the base factors (which is typically the case in reality). Further, noticing that Chan et al (1992) and Ritchken and Sankarasubramanian (1995) showed that option prices are sensitive to the level of the short rate volatility, we examine the pricing of European and American options where the short rate process has a volatility structure of a Cheyette (1994) type. In this relation, we examine the application of the two offered lattice construction methods and compare their results with the Monte Carlo simulation ones for a variety of examples. Additionally, for the pricing of American options with the Monte Carlo method we expand and implement the simulation algorithm of Longstaff and Schwartz (2000). With a variety of numerical examples we compare again the stability and the convergence of the different lattice construction methods. Dealing with the problems of pricing strongly path-dependent options, we come across the cumulative Parisian barrier option pricing problem. We notice that in their classical form, the cumulative Parisian barrier options have been priced both analytically (in a quasi closed form) and with a tree approximation (based on the Forward Shooting Grid algorithm, see e.g. Hull and White (1993), Kwok and Lau (2001) and others). However, we offer an additional tree construction method which can be seen as a direct binomial tree integration that uses the analytically calculated conditional survival probabilities. The advantage of the offered method is on one side that the conditional survival probabilities are easier to calculate than the closed-form solution itself and on the other side that this tree construction is very flexible in the sense that it allows easy incorporation of additional features such as e.g a forward starting one. The obtained results are better than the Forward Shooting Grid tree ones and are very close to the analytical quasi closed form solution. Finally, we pay our attention to pricing another type of innovative interest rate alike products - namely the Longevity bond - whose coupon payments depend on the survival function of a given cohort. Due to the lack of a market for mortality, for the pricing of the Longevity bonds we develop (following Korn, Natcheva and Zipperer (2006)) a framework that contains principles from both Insurance and Financial mathematic. Further on, we calibrate the existing models for the stochastic mortality dynamics to historical German data and additionally offer new stochastic extensions of the classical (deterministic) models of mortality such as the Gompertz and the Makeham one. Finally, we compare and analyze the results of the application of all considered models to the pricing of a Longevity bond on the longevity of the German males.

This thesis deals with modeling aspects of generalized Newtonian and of non-Newtonian fluids, as well as with development and validation of algorithms used in simulation of such fluids. The main contribution in the modeling part are the introduction and analysis of a new model for the generalized Newtonian fluids, where constitutive equation is of an algebraic form. Distinction between shear and extensional viscosities leads to anisotropic viscosity model. It can be considered as a natural extension of the well known (isotropic viscosity) Carreau model, which deals only with shear viscosity properties of the fluid. The proposed model takes additionally into account extensional viscosity properties. Numerical results show that the anisotropic viscosity model gives much better agreement with experimental observations than the isotropic one. Another contribution of the thesis consists of the development and analysis of robust and reliable algorithms for simulation of generalized Newtonian fluids. For such fluids the momentum equations are strongly coupled through mixed derivatives appearing in the viscous term (unlike the case of Newtonian fluids). It is shown in this thesis, that a careful treatment of those derivatives is essential in deriving robust algorithms. A modification of a standard SIMPLE-like algorithm is given, where all the viscous terms from the momentum equations are discretized in an implicit manner. Moreover, it is shown that a block diagonal preconditioner to the viscous operator is good enough to be used in simulations. Furthermore, different solution techniques, namely projection type methods (consists of solving momentum equations and pressure correction equation) and fully coupled methods (momentum and continuity equations are solved together), are compared. It is shown, that explicit discretization of the mixed derivatives lead to stability problems. Further, analytical estimates of eigenvalue distribution for three different preconditioners, applied to the transformed system arising after discretization and linearization of the momentum and continuity equations, are provided. We propose to apply a block Gauss-Seidel preconditioner to the transformed system. The analysis shows, that this preconditioner is able to cluster eigenvalues around unity independent of the transformation step. It is not the case for other preconditioners applied to the transformed system as discussed in the thesis. The block Gauss-Seidel preconditioner has also shown the best behavior (among all preconditioners discussed in the thesis) in numerical experiments. Further contribution consists of comparison and validation of numerical algorithms applied in simulations of non-Newtonian fluids modeled by time integral constitutive equations. Numerical results from simulations of dilute polymer solutions, described by the integral Oldroyd B model, have shown very good quantitative agreement with the results obtained by differential Oldroyd B counterpart in 4:1 planar contraction domain at low Weissenberg numbers. In this case, the Weissenberg number is changed by changing the relaxation time. However, contrary to the differential Oldroyd B model, the integral one allows to perform stable simulations also in the range of high Weissenberg numbers. Moreover, very good agreement with experimental observations has been achieved. Simulations of concentrated polymer solutions (polystyrene and polybutadiene solutions), modeled by the integral Doi Edwards model, supplemented by chain length fluctuations, have shown very good qualitative agreement with the results obtained by its differential approximation in 4:1:4 constriction domain. Again, much higher Weissenberg numbers can be achieved when the integral model is used. Moreover, very good quantitative results with experimental data of polystyrene solution for the first normal stress difference and shear viscosity defined here as the quotient of a shear stress and a shear rate. Finally, comparison of the two methods used for approximating the time integral constitutive equation, namely Deformation Field Method (DFM) and Backward Lagrangian Particle Method (BLPM), is performed. In BLPM the particle paths are recalculated at every time step of the simulations, what has never been tried before. The results have shown, that in the considered geometries both methods give similar results.

Traffic flow on road networks has been a continuous source of challenging mathematical problems. Mathematical modelling can provide an understanding of dynamics of traffic flow and hence helpful in organizing the flow through the network. In this dissertation macroscopic models for the traffic flow in road networks are presented. The primary interest is the extension of the existing macroscopic road network models based on partial differential equations (PDE model). In order to overcome the difficulty of high computational costs of PDE model an ODE model has been introduced. In addition, steady state traffic flow model named as RSA model on road networks has been dicsussed. To obtain the optimal flow through the network cost functionals and corresponding optimal control problems are defined. The solution of these optimization problems provides an information of shortest path through the network subject to road conditions. The resulting constrained optimization problem is solved approximately by solving unconstrained problem invovling exact penalty functions and the penalty parameter. A good estimate of the threshold of the penalty parameter is defined. A well defined algorithm for solving a nonlinear, nonconvex equality and bound constrained optimization problem is introduced. The numerical results on the convergence history of the algorithm support the theoretical results. In addition to this, bottleneck situations in the traffic flow have been treated using a domain decomposition method (DDM). In particular this method could be used to solve the scalar conservation laws with the discontinuous flux functions corresponding to other physical problems too. This method is effective even when the flux function presents more than one discontinuity within the same spatial domain. It is found in the numerical results that the DDM is superior to other schemes and demonstrates good shock resolution.

For the last decade, optimization of beam orientations in intensity-modulated radiation therapy (IMRT) has been shown to be successful in improving the treatment plan. Unfortunately, the quality of a set of beam orientations depends heavily on its corresponding beam intensity profiles. Usually, a stochastic selector is used for optimizing beam orientation, and then a single objective inverse treatment planning algorithm is used for the optimization of beam intensity profiles. The overall time needed to solve the inverse planning for every random selection of beam orientations becomes excessive. Recently, considerable improvement has been made in optimizing beam intensity profiles by using multiple objective inverse treatment planning. Such an approach results in a variety of beam intensity profiles for every selection of beam orientations, making the dependence between beam orientations and its intensity profiles less important. This thesis takes advantage of this property to accelerate the optimization process through an approximation of the intensity profiles that are used for multiple selections of beam orientations, saving a considerable amount of calculation time. A dynamic algorithm (DA) and evolutionary algorithm (EA), for beam orientations in IMRT planning will be presented. The DA mimics, automatically, the methods of beam's eye view and observer's view which are recognized in conventional conformal radiation therapy. The EA is based on a dose-volume histogram evaluation function introduced as an attempt to minimize the deviation between the mathematical and clinical optima. To illustrate the efficiency of the algorithms they have been applied to different clinical examples. In comparison to the standard equally spaced beams plans, improvements are reported for both algorithms in all the clinical examples even when, for some cases, fewer beams are used. A smaller number of beams is always desirable without compromising the quality of the treatment plan. It results in a shorter treatment delivery time, which reduces potential errors in terms of patient movements and decreases discomfort.

This thesis introduces so-called cone scalarising functions. They are by construction compatible with a partial order for the outcome space given by a cone. The quality of the parametrisations of the efficient set given by the cone scalarising functions are then investigated. Here, the focus lies on the (weak) efficiency of the generated solutions, the reachability of effiecient points and continuity of the solution set. Based on cone scalarising functions Pareto Navigation a novel, interactive, multiobjective optimisation method is proposed. It changes the ordering cone to realise bounds on partial tradeoffs. Besides, its use of an equality constraint for the changing component of the reference point is a new feature. The efficiency of its solutions, the reachability of efficient solutions and continuity is then analysed. Potential problems are demonstrated using a critical example. Furthermore, the use of Pareto Navigation in a two-phase approach and for nonconvex problems is discussed. Finally, its application for intensity-modulated radiotherapy planning is described. Thereby, its realisation in a graphical user interface is shown.

This thesis discusses methods for the classification of finite projective planes via exhaustive search. In the main part the author classifies all projective planes of order 16 admitting a large quasiregular group of collineations. This is done by a complete search using the computer algebra system GAP. Computational methods for the construction of relative difference sets are discussed. These methods are implemented in a GAP-package, which is available separately. As another result --found in cooperation with U. Dempwolff-- the projective planes defined by planar monomials are classified. Furthermore the full automorphism group of the non-translation planes defined by planar monomials are classified.

Nowadays piezoelectric and ferroelectric materials are becoming more and more an interesting part of smart materials in scientific and engineering applications. Precision machining in manufacturing, micropositioning in metrology, common rail systems with piezo fuel injection control in automobile industry, and ferroelectric random access memories (FRAM) in microelectromechanical systems (MEMS) besides commercial piezo actuators and sensors can be very good examples for the application of piezoceramic and ferroelectric materials. In spite of having good characteristics, piezoelectric and ferroelectric materials have significant nonlinearities, which limit the applications in high performance usage. Domain switching (ferroelastic or ferroelectric) is the main reason for the nonlinearity of ferroelectric materials. External excessive electromechanical loads (mechanical stress and electric field) are driving forces for domain switching. In literature, various important experiments related to the non-linear properties of piezoelectric and ferroelectric materials are reported. Simulations of nonlinear properties of piezoelectric and ferroelectric materials based on physical insights of the material have been performed during the last two decades by using micromechanical and phenomenological models. The most significant experiments and models are deeply discussed in the literature survey. In this thesis the nonlinear behaviour of tetragonal perovskite type piezoceramic materials is simulated theoretically using two and three dimensional micromechanical models which are based on physical insights of the material. In the simulations a bulk piezoceramic material which has numerous grains is considered. Each grain has random orientation in properties of polarization and strain. Randomness of orientations is given by Euler angles equally distributed between \(0\) and \(2\pi\). Each element in the micromechanical model has been assumed to have the same properties of the real piezoelectric grain. In the first part of the simulations, quasi-static characteristics of piezoelectric materials are investigated by applying cyclic, rate independent, bipolar, uni-axial and external electrical loading with an amplitude of 2 kV/mm gradually starting from zero value in virgin state. Moreover, the simulations are undertaken for these materials which are subjected to quasi-static, uni-polar, uni-axial mechanical stress, namely compressive stress. The calculations are performed at each element based on linear constitutive equations, nonlinear domain switching and a probability theory for domain switching. In order to fit the simulations to the experimental data, some parameters such as spontaneous polarization, spontaneous strain, piezoelectric and dielectric constants are chosen from literature. The domain switching of each grain is determined by an electromechanical energy criterion. Depending on the actual energy related to a critical energy a certain probability is introduced for domain switching of the polarization direction. Same energy levels are assumed in the electromechanical energy relation for different types of domain switching like 90º and 180º for perovskite type tetragonal or 70.5º and 109.5º for rhombohedral microstructures. It is assumed that intergranular effects between grains can be modelled by such probability functions phenomenologically. The macroscopic response of the material to the applied electromechanical loading is calculated by using Euler transformations and averaging the individual grains. Properties of piezoelectric materials under fixed mechanical stresses are also investigated by applying constant compressive stress in addition to cyclic electrical loading in the simulations. Compressive stress is applied and kept constant before cyclic bipolar electrical loading is implemented. In the following chapters, a three-dimensional micromechanical model is extended for the simulation of the rate dependent properties of certain perovskite type tetragonal piezoelectric materials. The frequency dependent micromechanical model is now not only based on linear constitutive and nonlinear domain switching but also linear kinetics theories. The material is loaded both electrically and mechanically in separate manner with an alternating electrical voltage and mechanical stress values of various moderate frequencies, which are in the order of 0.01 Hz to 1 Hz. Electromechanical energy equation in combination with a probability function is again used to determine the onset of the domain switching inside the grains. The propagation of the domain wall during the domain switching process in grains is modelled by means of linear kinetics relations after a new domain nucleates. Electric displacement versus electric field hysteresis loops, mechanical strain versus mechanical stress and electric displacement versus mechanical stress for different frequencies and amplitudes of the alternating electric fields and compressive stresses are simulated and presented. A simple micromechanical model without using probabilistic approach is compared with the one that takes it into account. Both models give important insights into the rate dependency of piezoelectric materials, which was observed in some experiments reported in the literature. Intergranular effects are other significant factors for nonlinearities of polycrystalline ferroelectric materials. Even piezoelectric actuators and sensors show nonlinearities when they are operated with electrical loading, which is much lower than the coercive electric field level. Intergranular effects are the main cause of such small hysteresis loops. In the corresponding chapter, two basic field effects which are electrical and mechanical are taken into account for the consideration of intergranular effects micromechanically in the simulations of the two dimensional model. Therefore, a new electromechanical energy equation for the threshold of domain switching is introduced to explain nonlinearities stemming from both domain switching and intergranular effects. The material parameters like coercive electric field and critical spontaneous polarization or strain quantities are not implemented in the electromechanical energy relation. But, this relation contains new parameters which consider both mechanical and electrical field characteristics of neighbouring elements. By using this new model, mechanical strain versus electric field butterfly curves under small electrical loading conditions are also simulated. Hence, a rate dependent concept is applied in butterfly curves by means of linear kinetics model. As a result, the simulations have better matching with corresponding experiments in literature. In the next step, the model can be extended in three dimensional case and the parameters of electromechanical energy relation can be improved in order to get better simulations of nonlinear properties of polycrystalline piezoelectric materials.

Biological Soil Crusts (BSCs), composed of lichens, mosses, green algae, microfungi and cyanobacteria are an ecological important part of the perennial landcover of many arid and semiarid regions (Belnap et al. 2001a), (Büdel 2002). In many arid and hyperarid areas BSCs form the only perennial "vegetation cover" largely due to their extensive resistance to drought (Lange et al. 1975). For the Central Namib Desert (Namibia), BSCs consisting of extraordinary vast lichen communities were recently mapped and classified into six morphological classes for a coastal area of 350 km x 60 km. Embedded into the project "BIOTA" (www.biota-africa.org) financed by the German Federal Ministry of Education and Research the study was undertaken in the framework of the PhD thesis by Christoph Schultz. Some of these lichen communities grouped together in so called "lichen fields" have already been studied concerning their ecology and diversity in the past (Lange et al. 1994), (Loris & Schieferstein 1992), (Loris et al. 2004), (Ullmann & Büdel 2001a), (Wessels 1989). Multispectral LANDSAT 7 ETM+ and LANDSAT 5 TM satellite imagery was utilized for an unitemporal supervised classification as well as for the establishment of a monitoring based on a combined retrospective supervised classification and change detection approach (Bock 2003), (Weiers et al. 2003). Results comprise the analysis of the mapped distribution of lichen communities for the Central Namib Desert as of 2003 as well as reconstructed distributions for the years 2000, 1999, 1992 and 1991 derived from retrospective supervised classification. This allows a first monitoring of the disturbance, destruction and recovery of the lichen communities in these arid environments including the analysis of the major abiotic processes involved. Further analysis of these abiotic processes is key for understanding the influence of Namib lichen communities on overall aeolian and water induced erosion rates, nutrient cycles, water balance and pedogenic processes (Belnap & Gillette 1998), (Belnap et al. 2001b), (Belnap 2001c), (Evans & Lange 2001), (McKenna Neumann & Maxwell 1999). In order to aid the understanding of these processes SRTM digital elevation model data as well as climate data sets were used as reference. Good correlation between geomorphological form elements as well as hydrological drainage system and the disturbance patterns derived from individual post classification change comparisons between the timeframes could be observed. Conjoined with the climate data sets sporadic foehn-like windstorms as well as extraordinary precipitation events were identified to largely affect the distribution patterns of lichen communities. Therefore the analysis and monitoring of the diversity, distribution and spatiotemporal change of Central Namib BSCs with the means of Remote Sensing and GIS applications proof to be important tools to create further understanding of desertification and degradation processes in these arid regions.

The new international capital standard for credit institutions (“Basel II”) allows banks to use internal rating systems in order to determine the risk weights that are relevant for the calculation of capital charge. Therefore, it is necessary to develop a system that enfolds the main practices and methods existing in the context of credit rating. The aim of this thesis is to give a suggestion of setting up a credit rating system, where the main techniques used in practice are analyzed, presenting some alternatives and considering the problems that can arise from a statistical point of view. Finally, we will set up some guidelines on how to accomplish the challenge of credit scoring. The judgement of the quality of a credit with respect to the probability of default is called credit rating. A method based on a multi-dimensional criterion seems to be natural, due to the numerous effects that can influence this rating. However, owing to governmental rules, the tendency is that typically one-dimensional criteria will be required in the future as a measure for the credit worthiness or for the quality of a credit. The problem as described above can be resolved via transformation of a multi-dimensional data set into a one-dimensional one while keeping some monotonicity properties and also keeping the loss of information (due to the loss of dimensionality) at a minimum level.