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The main aim of this work was to obtain an approximate solution of the seismic traveltime tomography problems with the help of splines based on reproducing kernel Sobolev spaces. In order to be able to apply the spline approximation concept to surface wave as well as to body wave tomography problems, the spherical spline approximation concept was extended for the case where the domain of the function to be approximated is an arbitrary compact set in R^n and a finite number of discontinuity points is allowed. We present applications of such spline method to seismic surface wave as well as body wave tomography, and discuss the theoretical and numerical aspects of such applications. Moreover, we run numerous numerical tests that justify the theoretical considerations.

In this paper we construct spline functions based on a reproducing kernel Hilbert space to interpolate/approximate the velocity field of earthquake waves inside the Earth based on traveltime data for an inhomogeneous grid of sources (hypocenters) and receivers (seismic stations). Theoretical aspects including error estimates and convergence results as well as numerical results are demonstrated.

Thermoelasticity represents the fusion of the fields of heat conduction and elasticity in solids and is usually characterized by a twofold coupling. Thermally induced stresses can be determined as well as temperature changes caused by deformations. Studying the mutual influence is subject of thermoelasticity. Usually, heat conduction in solids is based on Fourier’s law which describes a diffusive process. It predicts unnatural infinite transmission speed for parts of local heat pulses. At room temperature, for example, these parts are strongly damped. Thus, in these cases most engineering applications are described satisfactorily by the classical theory. However, in some situations the predictions according to Fourier’s law fail miserable. One of these situations occurs at temperatures near absolute zero, where the phenomenon of second sound1 was discovered in the 20th century. Consequently, non-classical theories experienced great research interest during the recent decades. Throughout this thesis, the expression “non-classical” refers to the fact that the constitutive equation of the heat flux is not based on Fourier’s law. Fourier’s classical theory hypothesizes that the heat flux is proportional to the temperature gradient. A new thermoelastic theory, on the one hand, needs to be consistent with classical thermoelastodynamics and, on the other hand, needs to describe second sound accurately. Hence, during the second half of the last century the traditional parabolic heat equation was replaced by a hyperbolic one. Its coupling with elasticity leads to non-classical thermomechanics which allows the modeling of second sound, provides a passage to the classical theory and additionally overcomes the paradox of infinite wave speed. Although much effort is put into non-classical theories, the thermoelastodynamic community has not yet agreed on one approach and a systematic research is going on worldwide.Computational methods play an important role for solving thermoelastic problems in engineering sciences. Usually this is due to the complex structure of the equations at hand. This thesis aims at establishing a basic theory and numerical treatment of non-classical thermoelasticity (rather than dealing with special cases). The finite element method is already widely accepted in the field of structural solid mechanics and enjoys a growing significance in thermal analyses. This approach resorts to a finite element method in space as well as in time.

The nowadays increasing number of fields where large quantities of data are collected generates an emergent demand for methods for extracting relevant information from huge databases. Amongst the various existing data mining models, decision trees are widely used since they represent a good trade-off between accuracy and interpretability. However, one of their main problems is that they are very instable, which complicates the process of the knowledge discovery because the users are disturbed by the different decision trees generated from almost the same input learning samples. In the current work, binary tree classifiers are analyzed and partially improved. The analysis of tree classifiers goes from their topology from the graph theory point of view to the creation of a new tree classification model by means of combining decision trees and soft comparison operators (Mlynski, 2003) with the purpose to not only overcome the well known instability problem of decision trees, but also in order to confer the ability of dealing with uncertainty. In order to study and compare the structural stability of tree classifiers, we propose an instability coefficient which is based on the notion of Lipschitz continuity and offer a metric to measure the proximity between decision trees. This thesis converges towards its main part with the presentation of our model ``Soft Operators Decision Tree\'\' (SODT). Mainly, we describe its construction, application and the consistency of the mathematical formulation behind this. Finally we show the results of the implementation of SODT and compare numerically the stability and accuracy of a SODT and a crisp DT. The numerical simulations support the stability hypothesis and a smaller tendency to overfitting the training data with SODT than with crisp DT is observed. A further aspect of this inclusion of soft operators is that we choose them in a way so that the resulting goodness function (used by this method) is differentiable and thus allows to calculate the best split points by means of gradient descent methods. The main drawback of SODT is the incorporation of the unpreciseness factor, which increases the complexity of the algorithm.

The provision of quality-of-service (QoS) on the network layer is a major challenge in communication networks. This applies particularly to mobile ad-hoc networks (MANETs) in the area of Ambient Intelligence (AmI), especially with the increasing use of delay and bandwidth sensitive applications. The focus of this survey lies on the classification and analysis of selected QoS routing protocols in the domain of mobile ad-hoc networks. Each protocol is briefly described and assessed, and the results are summarized in multiple tables.

Calibration of robots has become a research field of great importance over the last decades especially in the field industrial robotics. The main reason for this is that the field of application was significantly broadened due to an increasing number of fully automated or robot assisted tasks to be performed. Those applications require significantly higher level of accuracy due to more delicate tasks that need to be fulfilled (e.g. assembly in the semiconductor industry or robot assisted medical surgery). In the past, (industrial) robot calibration had to be performed manually for every single robot under lab conditions in a long and cost intensive process. Expensive and complex measurement systems had to be operated by highly trained personnel. The result of this process is a set of measurements representing the robot pose in the task space (i.e. world coordinate system) and as joint encoder values. To determine the deviation, the robot pose indicated by the internal joint encoder values has to be compared to the physical pose (i.e. external measurement data). Hence, the errors in the kinematic model of the robot can be computed and therefore later on compensated. These errors are inevitable and caused by varying manufacturing tolerances and other sources of error (e.g. friction and deflection). They have to be compensated in order to achieve sufficient accuracy for the given tasks. Furthermore for performance, maintenance, or quality assurance reasons the robots may have to undergo the calibration process in constant time intervals to monitor and compensate e.g. ageing effects such as wear and tear. In modern production processes old fashioned procedures like the one mentioned above are no longer suitable. Therefore a new method has to be found that is less time consuming, more cost effective, and involves less (or in the long term even no) human interaction in the calibration process.

Guaranteeing correctness of compilation is a ma jor precondition for correct software. Code generation can be one of the most error-prone tasks in a compiler. One way to achieve trusted compilation is certifying compilation. A certifying compiler generates for each run a proof that it has performed the compilation run correctly. The proof is checked in a separate theorem prover. If the theorem prover is content with the proof, one can be sure that the compiler produced correct code. This paper presents a certifying code generation phase for a compiler translating an intermediate language into assembler code. The time spent for checking the proofs is the bottleneck of certifying compilation. We exhibit an improved framework for certifying compilation and considerable advances to overcome this bottleneck. We compare our implementation featuring the Coq theorem prover to an older implementation. Our current implementation is feasible for medium to large sized programs.

Abstraction is intensively used in the verification of large, complex or infinite-state systems. With abstractions getting more complex it is often difficult to see whether they are valid. However, for using abstraction in model checking it has to be ensured that properties are preserved. In this paper, we use a translation validation approach to verify property preservation of system abstractions. We formulate a correctness criterion based on simulation between concrete and abstract system for a property to be verified. For each distinct run of the abstraction procedure the correctness is verified in the theorem prover Isabelle/HOL. This technique is applied in the verification of embedded adaptive systems. This paper is an extended version a previously published work.

In this thesis we classify simple coherent sheaves on Kodaira fibers of types II, III and IV (cuspidal and tacnode cubic curves and a plane configuration of three concurrent lines). Indecomposable vector bundles on smooth elliptic curves were classified in 1957 by Atiyah. In works of Burban, Drozd and Greuel it was shown that the categories of vector bundles and coherent sheaves on cycles of projective lines are tame. It turns out, that all other degenerations of elliptic curves are vector-bundle-wild. Nevertheless, we prove that the category of coherent sheaves of an arbitrary reduced plane cubic curve, (including the mentioned Kodaira fibers) is brick-tame. The main technical tool of our approach is the representation theory of bocses. Although, this technique was mainly used for purely theoretical purposes, we illustrate its computational potential for investigating tame behavior in wild categories. In particular, it allows to prove that a simple vector bundle on a reduced cubic curve is determined by its rank, multidegree and determinant, generalizing Atiyah's classification. Our approach leads to an interesting class of bocses, which can be wild but are brick-tame.

In this paper, a stochastic model [5] for the turbulent fiber laydown in the industrial production of nonwoven materials is extended by including a moving conveyor belt. In the hydrodynamic limit corresponding to large noise values, the transient and stationary joint probability distributions are determined using the method of multiple scales and the Chapman-Enskog method. Moreover, exponential convergence towards the stationary solution is proven for the reduced problem. For special choices of the industrial parameters, the stochastic limit process is an Ornstein{Uhlenbeck. It is a good approximation of the fiber motion even for moderate noise values. Moreover, as shown by Monte{Carlo simulations, the limiting process can be used to assess the quality of nonwoven materials in the industrial application by determining distributions of functionals of the process.