Mathematics - General

Powerful optimization algorithms are key ingredients in science and engineering applications. In this thesis, we develop a novel class of discrete-time, derivative-free optimization algorithms relying on gradient approximations based on non-commutative maps - inspired by Lie bracket approximation ideas in control systems. Those maps...

The main focus of this thesis is the discussion of stability of an objective (atomic) structure consisting of single atoms which interact via a potential. We define atomistic stability using a second derivative test. More precisely, atomistic stability is equivalent to a vanishing first...

The classical exponential polynomials, today commonly named after E., T. Bell, have a wide range of remarkable applications in Combinatorics, Algebra, Analysis, and Mathematical Physics. Within the algebraic framework presented in this book they appear as structural coefficients in finite expansions of certain higher-order...

During the last century, navigation systems have become ubiquitous and guide drivers, cyclists, and pedestrians towards their desired destinations. While operating worldwide, they rely on line-of-sight conditions towards satellites and are thus limited to outdoor areas. However, finding a gate within an airport, a...

To further improve the NLOS detection and mitigation performance for Ultra-wideband (UWB) system, this thesis systematically investigates the UWB LOS/NLOS errors. The LOS errors are evaluated in different environments and with different distances. Different blockage materials and blockage conditions are considered for NLOS errors....

An ensemble system is a collection of nearly identical dynamical systems which admit a certain degree of heterogeneity, and which are subject to the restriction that they may only be manipulated or observed as a whole. This thesis presents analysis and control methods for...

The Simplex algorithm is one of the most important algorithms in discrete optimization, and is the most used algorithm for solving linear programs in practice. In the last 50 years, several pivot rules for this algorithm have been proposed and studied. For most deterministic...

In the first part of this thesis we extend the theory of anisotropic Triebel-Lizorkin spaces to time-periodic functions. In particular, the spatial trace space is determined together with the existence of extension operators. Additionally, some results regarding pointwise multiplication are provided. As a preparation...

A classical problem in the field of mathematical fluid mechanics is the flow of a viscous incompressible fluid past a rigid body. In his doctoral thesis, Thomas Walter Eiter investigates time-periodic solutions to the associated Navier-Stokes equations when the body performs a non-trivial translation....

Since the 1980s the coorbit theory has provided a powerful tool for analyzing function spaces. It allows to define certain function spaces, so-called coorbit spaces, by means of representations of groups in Hilbert spaces, and offers a uniform strategy to discretize these spaces. The...

This thesis is concerned with the numerical treatment of hyperbolic conservation laws. These play an important role in describing many natural phenomena. Challenges in their theoretical as well as numerical study stem from the fact that spontaneous shock discontinuities can arise in their solutions,...

This thesis contributes to an acceleration of the manufacturing process of composite components from hybrid textiles, which contain reinforcement fibres and polymer matrix fibres from high-performance thermoplastics. Hybrid textiles distinguish in terms of drapeability compared to thermoplastic tapes. A comprehensive material characterisation of two...

Software testing is becoming increasingly important because more and more products are software-intensive. Cars, for example, contain more and more control software (ECUs) that are networked with each other. With new rail vehicles, software problems delay commissioning by months, even years, because the different...

This book provides a comprehensive methodology for multiscale simulation of degradation in lithium-ion batteries. The work helps to understand battery degradation processes by revealing complex multiscale effects, which cannot be taken into account by single-scale models. A novel numerical method is presented, which dynamically...

In this thesis, a novel framework for the construction and analysis of strong linearizations for matrix polynomials is presented. Strong linearizations provide the standard means to transform polynomial eigenvalue problems into equivalent generalized eigenvalue problems while preserving the complete finite and infinite eigenstructure of...

Our world today is becoming increasingly complex, and technical devices are getting ever smaller and more powerful. The high density of electronic components together with high clock frequencies leads to unwanted side-effects like crosstalk, delayed signals and substrate noise, which are no longer negligible...

In the context of advanced driver-assistance systems (ADAS), vehicles are equipped with multiple sensors to record the vehicle's environment and use intelligent algorithms to understand the data. This study contributes to the research in modern ADAS on different aspects. Methods deployed in ADAS must...

In the first part of this thesis we established a maximal regularity result to the Stokes equations in exterior domains with moving boundary. This leads to existence of solutions to the Navier-Stokes equations globally in time for small data. Secondly, we consider Leray's problem...

This thesis is concerned with the linear-quadratic optimal control and model order reduction (MOR) of large-scale linear time-varying (LTV) control systems. In the first two parts, particular attention is paid to a tracking-type finite-time optimal control problem with application to an inverse heat conduction...

The amazing success of computational mathematical optimization over the last decades has been driven more by insights into mathematical structures than by the advance of computing technology. In this vein, Jonas Schweiger addresses applications, where nonconvexity in the model and uncertainty in the data...

It is known that a continuous linear operator T defined on a Banach function space X(mu) (over a finite measure space (Omega, igma, mu) and with values in a Banach space X can be extended to a sort of optimal domain. Indeed, under certain...

In the calculus of variations, the goal is to explore extrema of a given integral functional. From origins of the problem, it might be expected that the functional can be adequately simplified by neglecting some small quantities. A way to rigorously justify such an...

The rise of Information and Communication Technology (ICT) in the second half of the 20th century became the dominant force in economics. Its rise accelerates in the first 15 years of this century at an astonishing speed. The world of ICT right now is...

We consider expensive optimization problems, that is to say problems where each evaluation of the objective function is expensive in terms of computing time, consumption of resources, or cost. This often happens in situations where the objective function is not available in analytic form,...

In recent papers, Wied and his coauthors have introduced change-point procedures to detect and estimate structural breaks in the correlation between time series. To prove the asymptotic distribution of the test statistic and stopping time as well as the change-point estimation rate, they use...

The reactive scattering for H- + H_2 and H+ + H_2 and its isotopologues were investigated using different methods. The studies aimed at providing insights into elementary reactions, and go beyond these to more complexchemical reactions. By comparison of the reaction probabilities of H+...

A systems biological approach towards cellular networks promises a better understanding of how these systems work. The development of mathematical models is however inherently complicated, as the involved molecules and their interactions are mostly difficult to measure. Focusing on gene regulation networks, this work...

This thesis is dedicated to the problem of object recognition in the three-dimensional space. Instead of using exclusively the information typically transported by a two-dimensional image, the concept of this work additionally incorporates the third dimension, namely the depth. The depth data itself is...

This thesis contributes to the development of a cooperative control theory for homogeneous and heterogeneous multi-agent systems consisting of identical and non-identical dynamical agents, respectively. The goal is to explain fundamental effects of non-identical agent dynamics on the behavior of a distributed system and,...

TFast and Approximate Computation of Laplace and Fourier Transforms Aby Ines Melzer DIn this thesis, we treat the computation of transforms with asymptotically smooth and oscillatory kernels. We introduce the discrete Laplace transform in a modern form including a generalization to more general kernel...

Der Expression von Genen liegen stochastische Prozesse zu Grunde, die zu Fluktuationen in der Menge von Proteinen eines jeden Gens fuhren. Zu starke Fluktuationen in Proteinmengen konnen fur Organismen schadlich sein, da die meisten zellularen Prozesse auf der prazisen Wechselwirkung von Proteinen beruhen. Diese...

The discipline of mixed-integer nonlinear programming (MINLP) deals with finite-dimensional optimization problems featuring both discrete choices and nonlinear functions. By this combination, it facilitates more accurate models of real-world systems than possible with purely continuous or purely linear models alone. This book presents new...

The problem of jointly designing a robust controller and an intelligent scheduler for networked control systems (NCSs) is addressed in this thesis. NCSs composing of multiple plants that share a single channel communication network with uncertain time-varying transmission times are modeled as switched polytopic...

This thesis presents the foundations, the initial state, and the progress made in modelling and implementing a real-world and real-time online microscopic traffic simulation system for highway traffic. To successfully model and implement such a simulation system, this thesis recommends the use of a...

This thesis is concerned with the numerical solution of boundary value problems (BVPs) governed by nonlinear elliptic partial differential equations (PDEs). To iteratively solve such BVPs, it is of primal importance to develop efficient schemes that guarantee convergence of the numerically approximated PDE solutions...

This thesis considers the linear-quadratic optimal control problem for differential-algebraic systems. In this first part, a complete theoretical analysis of this problem is presented. The basis is a new differential-algebraic version of the Kalman-Yakubovich-Popov (KYP) lemma. One focus is the analysis of the solution...

Vehicle accelerations affect the human body in various ways. In some cases, accelerations cause involuntary motions of limbs like arms and hands. If someone is engaged in a manual control task at the same time, these involuntary limb motions can lead to involuntary control...

This work deals with the mathematical modelling of material behaviour of steel during heat treatment. In the case of inelastic material behaviour, the underlying system of equations is non-linear and its equations are coupled. Therefore, the description and modelling of inelastic phenomena is especially...

In this thesis, we show that every regular singular holonomic D-module in Cn whose singular locus is a normal crossing is isomorphic to a quiver D-module -- a D-module whose definition is based on certain representations of the hypercube quiver. To be more precise...

Adaptive wavelet methods have recently proven to be a very powerful instrument for the numerical treatment of nonlinear partial differential equations. In many cases, these methods can be shown to converge with an optimal rate with respect to the degrees of freedom and in...

In this thesis, the authors develops a way of examining the Stokes structure of certain irregular singular mathcal D- modules, namely the direct image of exponentially twisted meromorphic connections with regular singularities, in a topological point of view. This topological description is used to...

A thorough understanding of crack formation in brittle materials is of great interest in both experimental sciences and theoretical studies. Such materials show an elastic response to very small displacements and develop cracks already at moderately large strains. Typically there is no plastic regime...

In this thesis simulation models have been developed and validated to investigate the protein-lipid interaction mechanisms at the trans-Golgi network (TGN) of mammalian cells. In two systems biological studies, ordinary differential equation models were used to examine the interactions between the lipids involved in...

Modern control systems are usually realized as embedded systems. This typically leads to resource-constrained control systems due to constraints on computing speed, memory size or communication bandwidth. In this thesis, scheduling and control strategies as well as event-triggered control strategies are addressed for handling...

These Lecture Notes provide an introduction to the modern theory of classical finite-dimensional integrable systems. The first chapter focuses on some classical topics of differential geometry. This should help the reader to get acquainted with the required language of smooth manifolds, Lie groups and...

Regular languages have a wide area of applications. This makes it an important task to convert between different forms of regular language representations, and to compress the size of such representations. This book studies modern aspects of compressions and conversions of regular language representations....

The quantitative understanding of changes in cell types, referred to as cell type transitions, is fundamental to advance fields such as stem cell research, immunology, and cancer therapies. This thesis provides a mathematical modeling framework to simulate and analyze cell type transitions. The novel...

This work considers the problem of decentralized controller and network design under communication constraints. Traditionally, this problem is solved in a two-step approach by first deciding on a topology and then designing the dynamical couplings. Presented in this thesis is a new approach by...

This work considers the problem of identifying the fault in a faulty dynamical system on the basis of the system's input and output signals only. For this purpose, a model-based method for the design of diagnostic tests which consist of specific input signals and...

Large systems of particles interacting via the laws of classical mechanics are widely used models in material science and statistical mechanics. A major topic in this context is the relation between the dynamics of these large, but microscopic systems and a behavior that is...