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Embedded systems have become ubiquitous in everyday life, and especially in the automotive industry. New applications challenge their design by introducing a new class of problems that are based on a detailed analysis of the environmental situation. Situation analysis systems rely on models and algorithms of the domain of computational geometry. The basic model is usually an Euclidean plane, which contains polygons to represent the objects of the environment. Usual implementations of computational geometry algorithms cannot be directly used for safety-critical systems. First, a strict analysis of their correctness is indispensable and second, nonfunctional requirements with respect to the limited resources must be considered. This thesis proposes a layered approach to a polygon-processing system. On top of rational numbers, a geometry kernel is formalised at first. Subsequently, geometric primitives form a second layer of abstraction that is used for plane sweep and polygon algorithms. These layers do not only divide the whole system into manageable parts but make it possible to model problems and reason about them at the appropriate level of abstraction. This structure is used for the verification as well as the implementation of the developed polygon-processing library.

On the Complexity of the Uncapacitated Single Allocation p-Hub Median Problem with Equal Weights
(2007)

The Super-Peer Selection Problem is an optimization problem in network topology construction. It may be cast as a special case of a Hub Location Problem, more exactly an Uncapacitated Single Allocation p-Hub Median Problem with equal weights. We show that this problem is still NP-hard by reduction from Max Clique.

Given an undirected connected network and a weight function finding a basis of the cut space with minimum sum of the cut weights is termed Minimum Cut Basis Problem. This problem can be solved, e.g., by the algorithm of Gomory and Hu [GH61]. If, however, fundamentality is required, i.e., the basis is induced by a spanning tree T in G, the problem becomes NP-hard. Theoretical and numerical results on that topic can be found in Bunke et al. [BHMM07] and in Bunke [Bun06]. In the following we present heuristics with complexity O(m log n) and O(mn), where n and m are the numbers of vertices and edges respectively, which obtain upper bounds on the aforementioned problem and in several cases outperform the heuristics of Schwahn [Sch05].

We derive some asymptotics for a new approach to curve estimation proposed by Mr'{a}zek et al. cite{MWB06} which combines localization and regularization. This methodology has been considered as the basis of a unified framework covering various different smoothing methods in the analogous two-dimensional problem of image denoising. As a first step for understanding this approach theoretically, we restrict our discussion here to the least-squares distance where we have explicit formulas for the function estimates and where we can derive a rather complete asymptotic theory from known results for the Priestley-Chao curve estimate. In this paper, we consider only the case where the bias dominates the mean-square error. Other situations are dealt with in subsequent papers.

The present work deals with the (global and local) modeling of the windfield on the real topography of Rheinland-Pfalz. Thereby the focus is on the construction of a vectorial windfield from low, irregularly distributed data given on a topographical surface. The developed spline procedure works by means of vectorial (homogeneous, harmonic) polynomials (outer harmonics) which control the oscillation behaviour of the spline interpoland. In the process the characteristic of the spline curvature which defines the energy norm is assumed to be on a sphere inside the Earth interior and not on the Earth’s surface. The numerical advantage of this method arises from the maximum-minimum principle for harmonic functions.

The present thesis deals with multi-user mobile radio systems, and more specifically, the downlinks (DL) of such systems. As a key demand on future mobile radio systems, they should enable highest possible spectrum and energy efficiency. It is well known that, in principle, the utilization of multi-antennas in the form of MIMO systems, offers considerable potential to meet this demand. Concerning the energy issue, the DL is more critical than the uplink. This is due to the growing importance of wireless Internet applications, in which the DL data rates and, consequently, the radiated DL energies tend to be substantially higher than the corresponding uplink quantities. In this thesis, precoding schemes for MIMO multi-user mobile radio DLs are considered, where, in order to keep the complexity of the mobile terminals as low as possible, the rationale receiver orientation (RO) is adopted, with the main focus to further reduce the required transmit energy in such systems. Unfortunately, besides the mentioned low receiver complexity, conventional RO schemes, such as Transmit Zero Forcing (TxZF), do not offer any transmit energy reductions as compared to conventional transmitter oriented schemes. Therefore, the main goal of this thesis is the design and analysis of precoding schemes in which such transmit energy reductions become feasible - under virtually maintaining the low receiver complexity - by means of replacing the conventional unique mappings by the selectable representations of the data. Concerning the channel access scheme, Orthogonal Frequency Division Multiplex (OFDM) is presently being favored as the most promising candidate in the standardization process of the enhanced 3G and forthcoming 4G systems, because it allows a very flexible resource allocation and low receiver complexity. Receiver oriented MIMO OFDM multi-user downlink transmission, in which channel equalization is already performed in the transmitter of the access point, further contributes to low receiver complexity in the mobile terminals. For these reasons, OFDM is adopted in the target system of the considered receiver oriented precoding schemes. In the precoding schemes considered the knowledge of channel state information (CSI) in the access point in the form of the channel matrix is essential. Independently of the applied duplexing schemes FDD or TDD, the provision of this information to the access point is always erroneous. However, it is shown that the impact of such deviations not only scales with the variance of the channel estimation errors, but also with the required transmit energies. Accordingly, the reduced transmit energies of the precoding schemes with selectable data representation also have the advantage of a reduced sensitivity to imperfect knowledge of CSI. In fact, these two advantages are coupled with each other.

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.

Elastomeric and other rubber-like materials are often simultaneously exposed to short- and long-time loads within engineering applications. When aiming at establishing a general simulation tool for viscoelastic media over these different time scales, a suitable material model and its corresponding material parameters can only be determined if an appropriate number of experimental data is taken into account. In this work an algorithm for the identification of material parameters for large strain viscoelasticity is presented. Thereby, data of multiple experiments are considered. Based on this method the experimental loading intervals for long-time experiments can be shortened in time and the parameter identification procedure is now referred to experimental data of tests under short- and long-time loads without separating the parameters due to these different time scales. The employed viscoelastic material law is based on a nonlinear evolution law and valid far from thermodynamic equilibrium. The identification is carried out by minimizing a least squares functional comparing inhomogeneous displacement fields from experiments and FEM simulations at given (measured) force loads. Within this optimization procedure all material parameters are identified simultaneously by means of a gradient based method for which a semi-analytical sensitivity analysis is calculated. Representative numerical examples are referred to measured data for different polyurethanes. In order to show the general applicability of the identification method for multiple tests, in the last part of this work the parameter identification for small strain plasticity is presented. Thereby three similar test programs on three specimen of the aluminum alloy AlSi9Cu3 are analyzed, and the parameter sets for the respective individual identifications, and for the combination of all tests in one identification, is compared.

The main goal of this work is to examine various aspects of `inelastic continuum mechanics': first, fundamental aspects of a general finite deformation theory based on a multiplicative decomposition of the deformation gradient with special emphasis on the incompatibility of the so-called intermediate configuration are discussed in detail. Moreover, various balance of linear momentum representations together with the corresponding volume forces are derived in a configurational mechanics context. Subsequent chapters are consequently based on these elaborations so that the applied multiplicative decomposition generally serves as a fundamental modelling concept in this work; after generalised strain measures are introduced, a kinematic hardening model coupled with anisotropic damage, a substructure evolution framework as well as two different growth and remodelling formulations for biological tissues are presented.

Modelling languages are important in the process of software development. The suitability of a modelling language for a project depends on its applicability to the target domain. Here, domain-specific languages have an advantage over more general modelling languages. On the other hand, modelling languages like the Unified Modeling Language can be used in a wide range of domains, which supports the reuse of development knowledge between projects. This thesis treats the syntactical and semantical harmonisation of modelling languages and their combined use, and the handling of complexity of modelling languages by providing language subsets - called language profiles - with tailor-made formal semantics definitions, generated by a profile tool. We focus on the widely-used modelling languages SDL and UML, and formal semantics definitions specified using Abstract State Machines.