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#### Faculty / Organisational entity

In this thesis viscoelastic material models are established to investigate the nature of continuous calving processes at Antarctic ice shelves. Physics-based descriptions of calving require appropriate fracture criteria to separate icebergs from the remaining ice shelf. Hence, criteria of the stress, the strain, and the self-similarity criterion are considered within finite-element computations. Crucial parameters in the models to determine the position of calving are the accurate knowledge of the geometry, especially the freeboard height, while the material parameters mainly influence the time span between two successive calving events. The extension to nonlinear material models is necessary to properly analyze the internal forces also for large deformations that occur for longer times of the viscous ice flow.

The main goal of this work was the study of the applicability of a polymer film heat exchanger concept for the applications in the chemical industry, such as the condensation of organic solvents. The polymer film heat exchanger investigated is a plate heat exchanger with very thin (0.025 – 0.1 mm) plates or films, which separate the fluids and enable the heat transfer. After a successful application of this concept to seawater desalination in a previous work, a further step is in chemical engineering, where the good chemical resistance of polymers in aggressive fluids is the challenge.
Two approaches were performed in this work. The first one was experimental and included the study of the chemical and mechanical resistance of preselected films, made of polymer materials, such as polyimide (PI), polyethylene terephthalate (PET) and polytetrafluoroethylene (PTFE). To simulate realistic operating conditions in a heat exchanger the films were exposed to a combined thermal (up to 90°C) and mechanical pressure loads (4-6 bar) with permanent contact with the relevant organic solvents, such as toluene, hexane, heptane and tetrahydrofuran (THF). Furthermore, a lab-scale apparatus and a full-scale demonstrator were manufactured in cooperation with two industrial partners. These were used for the investigation of the heat transfer performance for operating modes with and without phase change.
In addition to the experimental work, a coupled finite element –computational fluid dynamics (FEM-CFD)-model was developed, based on the fluid-structure-interaction (FSI). Two major tasks had to be solved here. The first one was the modelling of the condensation process, based on available mathematical models and energy balances. The second one was the consideration of the partially reversible deformation of the used film during operation. Since this deformation changes the geometry of the fluid channels also has an influence on the overall performance of the apparatus, a coupled FEM-CFD model was developed.
During the experimental study of the chemical resistance of the films, the PTFE film showed the best performance, and hence can be used for all four tested solvents. For the polyimide film, failures while exposed to THF were observed, and the PET film can only be used with water and hexane. With the used lab-scale heat exchanger and the full-scale demonstrator competitive overall heat transfer coefficients between 270 W/m²K and 700 W/m²K could be reached for the liquid-liquid (water-water, water-hexane) operation mode without phase change. For the condensation process, overall heat transfer coefficients of up to 1700/m²K could be obtained.
The numerical approach led to a well-functioning coupled model in a very small scale (1 cm²). An upscale, however, failed due to enormous hardware resources necessary required for the simulation of the entire full-scale demonstrator. The main reason for this is the very low thickness of the films, which leads to tiny mesh element sizes (<0.05 mm) necessary to model the deformation of the film. The modelling of the liquid-liquid heat transfer provided an acceptable accuracy (approx. 10%), but at very low rates the deviations were then higher (over 30%). The results of the condensation modelling were ambivalent. One the one hand a physically plausible model was developed, which could map the entire condensation process. On the other hand, the corresponding energy balance revealed major inaccuracy and hence could not be used for the determination of the overall heat transfer and showed the current limits of the FEM-CFD approach.

In this thesis we address two instances of duality in commutative algebra.
In the first part, we consider value semigroups of non irreducible singular algebraic curves
and their fractional ideals. These are submonoids of Z^n closed under minima, with a conductor and which fulfill special compatibility properties on their elements. Subsets of Z^n
fulfilling these three conditions are known in the literature as good semigroups and their ideals, and their class strictly contains the class of value semigroup ideals. We examine
good semigroups both independently and in relation with their algebraic counterpart. In the combinatoric setting, we define the concept of good system of generators, and we
show that minimal good systems of generators are unique. In relation with the algebra side, we give an intrinsic definition of canonical semigroup ideals, which yields a duality
on good semigroup ideals. We prove that this semigroup duality is compatible with the Cohen-Macaulay duality under taking values. Finally, using the duality on good semigroup ideals, we show a symmetry of the Poincaré series of good semigroups with special properties.
In the second part, we treat Macaulay’s inverse system, a one-to-one correspondence
which is a particular case of Matlis duality and an effective method to construct Artinian k-algebras with chosen socle type. Recently, Elias and Rossi gave the structure of the inverse system of positive dimensional Gorenstein k-algebras. We extend their result by establishing a one-to-one correspondence between positive dimensional level k-algebras and certain submodules of the divided power ring. We give several examples to illustrate
our result.

Die vorliegende Arbeit befasst sich mit der Untersuchung von Absorptionseigenschaften und elektronischer Kurzzeit-Dynamik von organischen Farbstoffmolekülen und supramolekularen Photokatalysatoren in der Gasphase. Dabei wurde erstmals sehr intensiv ein eine relativ unbekannte experimentelle Methode eingesetzt, nämlich die zeitaufgelöste, pump-probe (Anregung-Abfrage) Photofragmentations-Spektroskopie. Die Kombination eines kommerziellen Quadrupol Ionenfallen Massenspektrometers mit einem Femtosekunden Lasersystem erlaubt es die intrinsischen, elektronischen Eigenschaften molekularer, ionischer Systeme abzubilden. Neben Populationsdynamik angeregter Zustände wurden erstmals Schwingungs- und Rotationswellenpaket-Dynamik mit dieser Methode beobachtet und dokumentiert.
Im ersten Teil der Arbeit werden die Ergebnisse der Untersuchungen an einigen ausgewählten Fluoresecein-Derivaten und eines Carbocyanin-Farbstoffes präsentiert. Obwohl diese Modellsysteme zunächst nur dem Zweck dienen sollten die Möglichkeiten des experimentellen Aufbaus zu evaluieren, ergaben die Untersuchungen weiterhin tiefgreifende Einblicke in die elektronische Struktur isolierter organischer Farbstoffe, die bis heute in Literatur nicht dokumentiert worden sind.
Der zweite Teil befasst sich mit der Untersuchung an drei supramolekularen, ionischen Systemen zur photokatalytischen Wasserstofferzeugung. Dabei dienten wieder zwei der Systeme dem Zweck den experimentellen Aufbau zu evaluieren. Neben der elektronischen Populationsdynamik wurde mittels polarisationsabhängiger Messungen weitere Einblicke in den Elektronentransferprozess erhalten – ein Kernpunkt in der Wirkweise supramolekularer Katalysatoren. Die neugewonnen Erkenntnisse wurden schließlich verwendet um einen neuartigen Katalysator zu untersuchen. Dabei stellte sich heraus, dass die Labilität der Ligandensphäre am katalytischen Metallzentrum Untersuchungen am intakten System in Lösung stark beeinträchtigt und somit nur aussagekräftige Ergebnisse mittels einer Gasphasen Methode, einer wie der hier verwendeten, erhalten werden können.
Die experimentellen Ergebnisse werden unterstützt durch quantenchemische Berechnungen von energetischen Minimum-Strukturen, den Strukturen von Übergangszuständen, sowie der Berechnung von Schwingungs- und UV/Vis-Absorptionsspektren mittels (zeitabhängiger) Dichtefunktionaltheorie (DFT & TD-DFT).

In this dissertation convergence of binomial trees for option pricing is investigated. The focus is on American and European put and call options. For that purpose variations of the binomial tree model are reviewed.
In the first part of the thesis we investigated the convergence behavior of the already known trees from the literature (CRR, RB, Tian and CP) for the European options. The CRR and the RB tree suffer from irregular convergence, so our first aim is to find a way to get the smooth convergence. We first show what causes these oscillations. That will also help us to improve the rate of convergence. As a result we introduce the Tian and the CP tree and we proved that the order of convergence for these trees is \(O \left(\frac{1}{n} \right)\).
Afterwards we introduce the Split tree and explain its properties. We prove the convergence of it and we found an explicit first order error formula. In our setting, the splitting time \(t_{k} = k\Delta t\) is not fixed, i.e. it can be any time between 0 and the maturity time \(T\). This is the main difference compared to the model from the literature. Namely, we show that the good properties of the CRR tree when \(S_{0} = K\) can be preserved even without this condition (which is mainly the case). We achieved the convergence of \(O \left(n^{-\frac{3}{2}} \right)\) and we typically get better results if we split our tree later.

Wie Proteine sich innerhalb weniger Millisekunden korrekt falten können, ist eine der fundamentalen Fragen in der Biochemie. Ein beim Faltungsprozess durchlaufener Übergangszustand ist der molten globule Zustand (MG Zustand), der sich unter bestimmten Bedingungen stabilisieren und untersuchen lässt. In diesem Zustand ähnelt die Sekundärstruktur dem nativen Zustand, während die Tertiärstruktur eher dem vollständig entfalteten Zustand entspricht. In dieser Arbeit wurde der MG Zustand am Beispiel des Maltose bindenden Proteins (MBP) untersucht. Dazu wurde MBP bei pH 3,2 im MG-Zustand stabilisiert und dies mittels Fluoreszenz Spektroskopie bestätigt. Die Abstände zwischen definierten Aminosäuren im MG Zustand wurden durch Spinlabels, die an gezielt mutierten Cysteinpaaren angebracht wurden, mittels Elektronenspinresonanz (EPR) gemessen und mit den Abständen derselben Aminosäuren im nativen Zustand verglichen. Anhand von sieben verschiedenen Doppelmutanten wurde die periphere Struktur mittels gepulster EPR analysiert, zwei weitere Doppelmutanten dienten dazu, die Struktur der molekularen Bindungstasche von MBP mittels CW EPR zu untersuchen. Die Anwesenheit von Maltose führte im MG Zustand zu einer deutlichen Veränderung der Abstände bestimmter Spinlabels in der peripheren Struktur. Dies deutet darauf hin, dass MBP Maltose sogar im MG Zustand binden kann. Durch isotherme Titrationskalorimetrie (ITC) wurde diese Vermutung bestätigt: die Ergebnisse zeigen jedoch, dass der Bindungsprozess zwischen MBP und Maltose im MG Zustand mit 11 fach geringerer Bindungsenthalpie erfolgt wie im nativen Zustand. Die Abstände der Spinlabel Paare neben der Bindungstasche von MBP unterschieden sich im MG Zustand vom nativen Zustand weder mit noch ohne Maltose. Diese Ergebnisse weisen darauf hin, dass MBP im MG Zustand rund um die Bindungstasche bereits eine klar ausgebildete Tertiärstruktur besitzt. Um diese Befunde zu bestätigen, sollten nun Untersuchungen anhand weiterer Doppelmutanten und mittels empfindlicherer Messungen wie z.B. DQC durchgeführt werden.

Temporal Data Management and Incremental Data Recomputation with Wide-column Stores and MapReduce
(2017)

In recent years, ”Big Data” has become an important topic in academia
and industry. To handle the challenges and problems caused by Big Data,
new types of data storage systems called ”NoSQL stores” (means ”Not-only-
SQL”) have emerged.
”Wide-column stores” are one kind of NoSQL stores. Compared to relational database systems, wide-column stores introduce a new data model,
new IRUD (Insert, Retrieve, Update and Delete) semantics with support for
schema-flexibility, single-row transactions and data expiration constraints.
Moreover, each column stores multiple data versions with associated time-
stamps. Well-known examples are Google’s ”Big-table” and its open sourced
counterpart ”HBase”. Recently, such systems are increasingly used in business intelligence and data warehouse environments to provide decision support, controlling and revision capabilities.
Besides managing the current values, data warehouses also require management and processing of historical, time-related data. Data warehouses
frequently employ techniques for processing changes in various data sources
and incrementally applying such changes to the warehouse to keep it up-to-
date. Although both incremental data warehousing maintenance and temporal data management have been the subject of intensive research in the
relational database and finally commercial database products have picked up
the ability for temporal data processing and management, such capabilities
have not been explored systematically for today’s wide-column stores.
This thesis helps to address the shortcomings mentioned above. It care-
fully analyzes the properties of wide-column stores and the applicability
of mechanisms for temporal data management and incremental data ware-
house maintenance known from relational databases, extends well-known approaches and develops new capabilities for providing equivalent support in
wide-column stores.

In the present work the concept of decarboxylative couplings and the strategy to use carboxylates as directing groups for C-H functionalizations have been decisively improved in three ways. These concepts emphasize the multifaceted nature of aromatic carboxylic acids as expedient starting materials in homogeneous catalysis to construct highly desirable molecular scaffolds in a straightforward fashion.
In the first project, the restriction of decarboxylative biaryl synthesis to exclusively couple aryl halides with ortho-substituted benzoic acids has been overcome by a holistic optimization of a Cu/Pd bimetallic catalyst system. Long ago postulated, this is now the proof that decarboxylative cross-couplings are not intrinsically limited to different decarboxylation propensities of benzoic acids or hampered by excess halides, accessing for the first time the entire spectrum of aromatic carboxylic acids as starting materials for the decarboxylative biaryl synthesis. The second project uses the carboxyl moiety as directing group for the ortho-arylation with aryl bromides and -chlorides catalyzed by comparatively inexpensive ruthenium. The carboxylic acid group remains untouched after the ortho-functionalization giving the possibility to a wealth of further diversifications via decarboxylative ipso-substitutions. Within the same project, a Cu/Ru bimetallic catalyst system was found to be able to switch the decarboxylative biaryl coupling from the ipso- to the ortho-position, complementing the Cu/Pd system developed in the first project. In a third project, a redox neutral C-C bond formation revealed the full synthetic potential of the carboxyl group. The COOH moiety acts as a classical directing group for the C-H hydroarylation of internal alkynes to form highly desirable 2-vinyl benzoic acids. With propargylic alcohols the hydroarylation is followed by an in situ esterification, showing that after easing the C-H cleavage, the directing group can be transformed into another functional group, thus, acting as a transformable directing group. Most importantly, a new fascinating reaction mode is activated by embedding the decarboxylation within the C-H functionalization event. This mode of action is capable to solve regioselectivity issues that inherently occur when dealing with carboxylates as directing groups. A so-called deciduous directing group is cast off simultaneously within the C-H functionalization event, resulting in an inherently monoselective pathway.
These methods were developed with the permanent goal of ensuring high sustainability. They do require neither pre-functionalized starting materials nor additional oxidants and provide access to a number of chemically relevant molecules from abundant, inexpensive and toxicologically innocuous educts.

Nonwoven materials are used as filter media which are the key component of automotive filters such as air filters, oil filters, and fuel filters. Today, the advanced engine technologies require innovative filter media with higher performances. A virtual microstructure of the nonwoven filter medium, which has similar filter properties as the existing material, can be used to design new filter media from existing media. Nonwoven materials considered in this thesis prominently feature non-overlapping fibers, curved fibers, fibers with circular cross section, fibers of apparently infinite length, and fiber bundles. To this end, as part of this thesis, we extend the Altendorf-Jeulin individual fiber model to incorporate all the above mentioned features. The resulting novel stochastic 3D fiber model can generate geometries with good visual resemblance of real filter media. Furthermore, pressure drop, which is one of the important physical properties of the filter, simulated numerically on the computed tomography (CT) data of the real nonwoven material agrees well (with a relative error of 8%) with the pressure drop simulated in the generated microstructure realizations from our model.
Generally, filter properties for the CT data and generated microstructure realizations are computed using numerical simulations. Since numerical simulations require extensive system memory and computation time, it is important to find the representative domain size of the generated microstructure for a required filter property. As part of this thesis, simulation and a statistical approach are used to estimate the representative domain size of our microstructure model. Precisely, the representative domain size with respect to the packing density, the pore size distribution, and the pressure drop are considered. It turns out that the statistical approach can be used to estimate the representative domain size for the given property more precisely and using less generated microstructures than the purely simulation based approach.
Among the various properties of fibrous filter media, fiber thickness and orientation are important characteristics which should be considered in design and quality assurance of filter media. Automatic analysis of images from scanning electron microscopy (SEM) is a suitable tool in that context. Yet, the accuracy of such image analysis tools cannot be judged based on images of real filter media since their true fiber thickness and orientation can never be known accurately. A solution is to employ synthetically generated models for evaluation. By combining our 3D fiber system model with simulation of the SEM imaging process, quantitative evaluation of the fiber thickness and orientation measurements becomes feasible. We evaluate the state-of-the-art automatic thickness and orientation estimation method that way.

In this thesis, we consider a problem from modular representation theory of finite groups. Lluís Puig asked the question whether the order of the defect groups of a block \( B \) of the group algebra of a given finite group \( G \) can always be bounded in terms of the order of the vertices of an arbitrary simple module lying in \( B \).
In characteristic \( 2 \), there are examples showing that this is not possible in general, whereas in odd characteristic, no such examples are known. For instance, it is known that the answer to Puig's question is positive in case that \( G \) is a symmetric group, by work of Danz, Külshammer, and Puig.
Motivated by this, we study the cases where \( G \) is a finite classical group in non-defining characteristic or one of the finite groups \( G_2(q) \) or \( ³D_4(q) \) of Lie type, again in non-defining characteristic. Here, we generalize Puig's original question by replacing the vertices occurring in his question by arbitrary self-centralizing subgroups of the defect groups. We derive positive and negative answers to this generalized question.
\[\]
In addition to that, we determine the vertices of the unipotent simple \( GL_2(q) \)-module labeled by the partition \( (1,1) \) in characteristic \( 2 \). This is done using a method known as Brauer construction.

We introduce and investigate a product pricing model in social networks where the value a possible buyer assigns to a product is influenced by the previous buyers. The selling proceeds in discrete, synchronous rounds for some set price and the individual values are additively altered. Whereas computing the revenue for a given price can be done in polynomial time, we show that the basic problem PPAI, i.e., is there a price generating a requested revenue, is weakly NP-complete. With algorithm Frag we provide a pseudo-polynomial time algorithm checking the range of prices in intervals of common buying behavior we call fragments. In some special cases, e.g., solely positive influences, graphs with bounded in-degree, or graphs with bounded path length, the amount of fragments is polynomial. Since the run-time of Frag is polynomial in the amount of fragments, the algorithm itself is polynomial for these special cases. For graphs with positive influence we show that every buyer does also buy for lower prices, a property that is not inherent for arbitrary graphs. Algorithm FixHighest improves the run-time on these graphs by using the above property.
Furthermore, we introduce variations on this basic model. The version of delaying the propagation of influences and the awareness of the product can be implemented in our basic model by substituting nodes and arcs with simple gadgets. In the chapter on Dynamic Product Pricing we allow price changes, thereby raising the complexity even for graphs with solely positive or negative influences. Concerning Perishable Product Pricing, i.e., the selling of products that are usable for some time and can be rebought afterward, the principal problem is computing the revenue that a given price can generate in some time horizon. In general, the problem is #P-hard and algorithm Break runs in pseudo-polynomial time. For polynomially computable revenue, we investigate once more the complexity to find the best price.
We conclude the thesis with short results in topics of Cooperative Pricing, Initial Value as Parameter, Two Product Pricing, and Bounded Additive Influence.

We discuss the portfolio selection problem of an investor/portfolio manager in an arbitrage-free financial market where a money market account, coupon bonds and a stock are traded continuously. We allow for stochastic interest rates and in particular consider one and two-factor Vasicek models for the instantaneous
short rates. In both cases we consider a complete and an incomplete market setting by adding a suitable number of bonds.
The goal of an investor is to find a portfolio which maximizes expected utility
from terminal wealth under budget and present expected short-fall (PESF) risk
constraints. We analyze this portfolio optimization problem in both complete and
incomplete financial markets in three different cases: (a) when the PESF risk is
minimum, (b) when the PESF risk is between minimum and maximum and (c) without risk constraints. (a) corresponds to the portfolio insurer problem, in (b) the risk constraint is binding, i.e., it is satisfied with equality, and (c) corresponds
to the unconstrained Merton investment.
In all cases we find the optimal terminal wealth and portfolio process using the
martingale method and Malliavin calculus respectively. In particular we solve in the incomplete market settings the dual problem explicitly. We compare the
optimal terminal wealth in the cases mentioned using numerical examples. Without
risk constraints, we further compare the investment strategies for complete
and incomplete market numerically.

Redox-neutral decarboxylative coupling reactions have emerged as a powerful strategy for C-C bond formation. However, the existing reaction conditions possess limitations, such as the coupling of aryl halides restricted to ortho-substituted benzoic acids; alkenyl halides were not applicable in decarboxylative coupling reaction. Within this thesis, the developments of Pd/Cu bimetallic catalyst systems are presented to overcome the limitations.
In the first part of the PhD work, a customized bimetallic PdII/CuI catalyst system was successfully developed to facilitate the decarboxylative cross-coupling of non-ortho-substituted aromatic carboxylates with aryl chlorides. The restriction of decarboxylative cross-coupling reactions to ortho-substituted or heterocyclic carboxylate substrates was overcome by holistic optimization of this bimetallic Cu/Pd catalyst system. All kinds of benzoic acids regardless of their substitution pattern now can be applied in decarboxylative cross-coupling reaction. This confirms prediction by DFT studies that the previously observed limitation to certain activated carboxylates is not intrinsic. The catalyst system also presents higher performance in the coupling of ortho-substituted benzoates, giving much higher yields than those previously reported. ortho-Methyl benzoate and ortho-phenyl benzoate which have never before been converted in decarboxylative coupling reactions, gave reasonable yields. These together further confirm the superiority of the new protocol.
In the second part of the PhD work, arylalkenes syntheses via two different Pd/Cu bimetallic-catalyzed decarboxylative couplings have been developed. This part consists of two projects: 2a) decarboxylative coupling of alkenyl halides; 2b) decarboxylative Mizoroki-Heck coupling of aryl halides with α,β-unsaturated carboxylic acids.
In project 2a, widely available, inexpensive, bench-stable aromatic carboxylic acids are used as nucleophile precursors instead of expensive and sensitive organometallic reagents that are commonly used in previously reported transition-metal catalyzed cross-couplings of alkenyl halides. With this protocol, alkenyl halides for the first time are used in decarboxylative coupling reaction, allowing regiospecific synthesis of a broad range of (hetero)arylalkenes in high yields. Unwanted double bond isomerization, a common side reaction in the alternative Heck reactions especially in the coupling of cycloalkenes or aliphatic alkenes, did not take place in this decarboxylative coupling reaction. Polysubstituted alkenes that hard to access with Heck reaction are also produced in good yields. The reaction can easily be scaled up to gram scale. The synthetic utility of this reaction was also demonstrated by synthesizing an important intermediate of fungicidal compound in high yield within 2 steps.
In project 2b, a Cu/Pd bimetallic catalyzed decarboxylative Mizoroki-Heck coupling of aryl halides with α, β-unsaturated carboxylic acids was successfully developed in which the carboxylate group directs the arylation into its β-position before being tracelessly removed via protodecarboxylation. It opens up a convenient synthesis of unsymmetrical 1,1-disubstituted alkenes from widely available precursors. This reaction features good regioselectivity, which is complementary to that of traditional Heck reactions, and also presents excellent functional group tolerance. Moreover, a one-pot 3-step 1,1-diarylethylene synthesis from methyl acrylate was achieved, where solvent changes or isolation of intermediates are not required. This subproject presents an example of carboxylic acids utility in synthesizing valuable compounds which are hard to access via conventional methodologies.

Novel Pseudocyclopeptides Containing 1,4-Disubstituted 1,2,3-Triazole Subunits for Anion Recognition
(2017)

Anion recognition is one of the most rapidly growing areas in the field of Supramolecular Chemistry due to the vital role of anions in the environment, in biology and in industry. The development of new anion binding motifs that can also be combined with known ones in a novel receptor is a timely topic. In this context, we have synthesized three cyclic pseudopeptides 16, 17 and 18, containing conventional H-bond donors (amide) in combination with, respectively, triazole C–H or triazole C–I functions.
All three receptors were synthesized by using a combination of peptide and click chemistry. Structural studies show that all three pseudopeptides adopt conformations with the triazole C-H or C-I groups pointing into the cavity center to allow them to contribute to binding. Quantitative binding studies showed that the cyclic pseudohexapeptide 1 coordinates to oxoanions (sulfate, dihydrogenphosphate, and hydrogenpyrophosphate) with different binding strengths and complex stoichiometries in 2.5 vol% water/DMSO.
Anion selectivity of 16 significantly changes when the cavity size of this pseudopeptide is increased to obtain the larger analog 17. This pseudooctapeptide forms well defined complexes with protonated phosphate anions. The complexation involves sandwiching of a cyclic tetramer of dihydrogenphosphate or a dimer of dihydrogenpyrophosphate anions by two pseudopeptide rings. Both complexes were characterized structurally in the solid state. They are stable in solution (2.5 vol% water/DMSO) as result of the interaction between hydrogen bond donors of 17 and the oxygen atoms of the anionic aggregates. The complexes can also be transferred to the gas phase without decomposition.
Anion selectivity of 16 was further altered by introducing iodine atom in the C5 position of the 1,4-disubstituted 1,2,3-triazole units. The corresponding cyclic pseudohexapeptide 18 features a smaller cavity diameter than 17 as a result of the iodide atoms and was therefore found to only coordinate to smaller spherical anions such as chloride. It forms 1:1 complexes with chloride, bromide and iodide in 2.5 vol% water/DMSO. Among the halides, 18 has highest affinity for chloride followed by bromide and iodide. The same stability trend was also observed in the gas phase by ESI/MS.
Concluding, I prepared three new macrocyclic pseudopeptides during my PhD and characterized their complexes with anions in terms of structure and affinity. All of these pseudopeptides were shown to interact with phosphate-derived anions, which renders them unique among the anion receptors developed in the Kubik group before.

The thesis studies change points in absolute time for censored survival data with some contributions to the more common analysis of change points with respect to survival time. We first introduce the notions and estimates of survival analysis, in particular the hazard function and censoring mechanisms. Then, we discuss change point models for survival data. In the literature, usually change points with respect to survival time are studied. Typical examples are piecewise constant and piecewise linear hazard functions. For that kind of models, we propose a new algorithm for numerical calculation of maximum likelihood estimates based on a cross entropy approach which in our simulations outperforms the common Nelder-Mead algorithm.
Our original motivation was the study of censored survival data (e.g., after diagnosis of breast cancer) over several decades. We wanted to investigate if the hazard functions differ between various time periods due, e.g., to progress in cancer treatment. This is a change point problem in the spirit of classical change point analysis. Horváth (1998) proposed a suitable change point test based on estimates of the cumulative hazard function. As an alternative, we propose similar tests based on nonparametric estimates of the hazard function. For one class of tests related to kernel probability density estimates, we develop fully the asymptotic theory for the change point tests. For the other class of estimates, which are versions of the Watson-Leadbetter estimate with censoring taken into account and which are related to the Nelson-Aalen estimate, we discuss some steps towards developing the full asymptotic theory. We close by applying the change point tests to simulated and real data, in particular to the breast cancer survival data from the SEER study.

Due to their superior weight-specific mechanical properties, carbon fibre epoxy composites (CFRP) are commonly used in aviation industry. However, their brittle failure behaviour limits the structural integrity and damage tolerance in case of impact (e.g. tool drop, bird strike, hail strike, ramp collision) or crash events. To ensure sufficient robustness, a minimum skin thickness is therefore prescribed for the fuselage, partially exceeding typical service load requirements from ground or flight manoeuvre load cases. A minimum skin thickness is also required for lightning strike protection purposes and to enable state-of-the-art bolted repair technology. Furthermore, the electrical conductivity of CFRP aircraft structures is insufficient for certain applications; additional metal components are necessary to provide electrical functionality (e.g. metal meshes on the outer skin for lightning strike protection, wires for electrical bonding and grounding, overbraiding of cables to provide electromagnetic shielding). The corresponding penalty weights compromise the lightweight potential that is actually given by the structural performance of CFRP over aluminium alloys.
Former research attempts tried to overcome these deficits by modifying the resin system (e.g. by addition of conductive particles or toughening agents) but could not prove sufficient enhancements. A novel holistic approach is the incorporation of highly conductive and ductile continuous metal fibres into CFRP. The basic idea of this hybrid material concept is to take advantage of both the electrical and mechanical capabilities of the integrated metal fibres in order to simultaneously improve the electrical conductivity and the damage tolerance of the composite. The increased density of the hybrid material is over-compensated by omitting the need for additional electrical system installation items and by the enhanced structural performance, enabling a reduction of the prescribed minimum skin thickness. Advantages over state-of-the-art fibre metal laminates mainly arise from design and processing technology aspects.
In this context, the present work focuses on analysing and optimising the structural and electrical performance of such hybrid composites with shares of metal fibres up to 20 vol.%. Bundles of soft-annealed austenitic steel or copper cladded low carbon steel fibres with filament diameters of 60 or 63 µm are considered. The fibre bundles are distinguished by high elongation at break (32 %) and ultimate tensile strength (900 MPa) or high electrical conductivity (2.4 × 10^7 S/m). Comprehensive researches are carried out on the fibre bundles as well as on unidirectional and multiaxial laminates. Both hybrid composites with homogeneous and accumulated steel fibre arrangement are taken into account. Electrical in-plane conductivity, plain tensile behaviour, suitability for bolted joints as well as impact and perforation performance of the composite are analysed. Additionally, a novel non-destructive testing method based on measurement of deformation-induced phase transformation of the metastable austenitic steel fibres is discussed.
The outcome of the conductivity measurements verifies a correlation of the volume conductivity of the composite with the volume share and the specific electrical resistance of the incorporated metal fibres. Compared to conventional CFRP, the electrical conductivity in parallel to the fibre orientation can be increased by one to two orders of magnitude even for minor percentages of steel fibres. The analysis, however, also discloses the challenge of establishing a sufficient connection to the hybrid composite in order to entirely exploit its electrical conductivity.
In case of plain tensile load, the performance of the hybrid composite is essentially affected by the steel fibre-resin-adhesion as well as the laminate structure. Uniaxial hybrid laminates show brittle, singular failure behaviour. Exhaustive yielding of the embedded steel fibres is confined to the arising fracture gap. The high transverse stiffness of the isotropic metal fibres additionally intensifies strain magnification within the resin under transverse tensile load. This promotes (intralaminar) inter-fibre-failure at minor composite deformation. By contrast, multiaxial hybrid laminates exhibit distinctive damage evolution. After failure initiation, the steel fibres extensively yield and sustain the load-carrying capacity of angularly (e.g. ±45°) aligned CFRP plies. The overall material response is thus not only a simple superimposition but a complex interaction of the mechanical behaviour of the composite’s constituents. As a result of this post-damage performance, an ultimate elongation of over 11 % can be proven for the hybrid laminates analysed in this work. In this context, the influence of the steel fibre-resin adhesion on the failure behaviour of the hybrid composite is explicated by means of an analytical model. Long term exposure to corrosive media has no detrimental effect on the mechanical performance of stainless steel fibre reinforced composites. By trend, water uptake increases the maximum elongation at break of the hybrid laminate.
Moreover, the suitability of CFRP for bolted joints can partially be improved by the integration of steel fibres. While the bearing strength basically remains nearly unaffected, the bypass failure behaviour (ε_{max}: +363 %) as well as the head pull-through resistance (E_{a,BPT}: +81 %) can be enhanced. The improvements primarily concern the load-carrying capacity after failure initiation. Additionally, the integrated ductile steel fibres significantly increase the energy absorption capacity of the laminate in case of progressive bearing failure by up to 63 %.
However, the hybrid composite exhibits a sensitive low velocity/low mass impact behaviour. Compared to conventional CFRP, the damage threshold load of very thin hybrid laminates is lower, making them prone for delamination at minor, non-critical impact energies. At higher energy levels, however, the impact-induced delamination spreads less since most of the impact energy is absorbed by yielding of the ductile metal fibres instead of crack propagation. This structural advantage compared to CFRP gains in importance with increasing impact energy. The plastic deformation of the metastable austenitic steel fibres is accompanied by a phase transformation from paramagnetic γ-austenite to ferromagnetic α’-martensite. This change of the magnetic behaviour can be used to detect and evaluate impacts on the surface of the hybrid composite, which provides a simple non-destructive testing method. In case of low velocity/high mass impact, integration of ductile metal fibres into CFRP enables to address spacious areas of the laminate for energy absorption purposes. As a consequence, the perforation resistance of the hybrid composite is significantly enhanced; by addition of approximately 20 vol.% of stainless steel fibres, the perforation strength can be increased by 61 %, while the maximum energy absorption capacity rises by 194 %.

Non–woven materials consist of many thousands of fibres laid down on a conveyor belt
under the influence of a turbulent air stream. To improve industrial processes for the
production of non–woven materials, we develop and explore novel mathematical fibre and
material models.
In Part I of this thesis we improve existing mathematical models describing the fibres on the
belt in the meltspinning process. In contrast to existing models, we include the fibre–fibre
interaction caused by the fibres’ thickness which prevents the intersection of the fibres and,
hence, results in a more accurate mathematical description. We start from a microscopic
characterisation, where each fibre is described by a stochastic functional differential
equation and include the interaction along the whole fibre path, which is described by a
delay term. As many fibres are required for the production of a non–woven material, we
consider the corresponding mean–field equation, which describes the evolution of the fibre
distribution with respect to fibre position and orientation. To analyse the particular case of
large turbulences in the air stream, we develop the diffusion approximation which yields a
distribution describing the fibre position. Considering the convergence to equilibrium on
an analytical level, as well as performing numerical experiments, gives an insight into the
influence of the novel interaction term in the equations.
In Part II of this thesis we model the industrial airlay process, which is a production method
whereby many short fibres build a three–dimensional non–woven material. We focus on
the development of a material model based on original fibre properties, machine data and
micro computer tomography. A possible linking of these models to other simulation tools,
for example virtual tensile tests, is discussed.
The models and methods presented in this thesis promise to further the field in mathematical
modelling and computational simulation of non–woven materials.

This dissertation describes an indoor localization system based on oscillating magnetic fields and the underlying processing architecture. The system consists of several fixed anchor points, generating the magnetic fields (transmitter), and wearable magnetic field measurement units, whose position should be determined (receiver). The system is evaluated in different environments and application areas. Additionally, various fields of application are discussed and assessed in ubiquitous and pervasive computing and Ambient Assisted Living. The fusion of magnetic field-based distance information and positions derived from LIDAR distance measurements is described and evaluated.
The system architecture consists of three layers, a physical layer, a layer for position and distance estimation between a magnetic field transmitter and a receiver, and a layer which uses several measurements to different transmitters to estimate the overall position of a wearable measurement unit.
Each layer covers different aspects which have to be taken care of when magnetic field information is processed. Especially the properties of the generated magnetic field information are considered in the processing algorithms.
The physical layer covers the magnetic field generation and magnetic Field-Based information transfer, synchronization of a transmitter and the receivers and the description of the locally measured magnetic fields on the receiver side. After a transfer of this information to a central processing unit, the hardware specific signal levels are transformed to the levels of the theoretical magnetic field models. The values are then used to estimate candidate positions and distances. Due to symmetrical effects of the magnetic fields, it is only possible to reduce the receiver position to 8 points around the transmitter (one position in each of the octants of the coordinate system). The determined positions have a mean error of 108 cm, the average error of the distance is 40 cm.
On top of this, the distance and position information against different transmitters are fused, this covers clock synchronization of transmitters, triggering and scheduling sequences and distance and position based localization and tracking algorithms. The magnetic-field-based indoor localization system has been evaluated in different applications and environments; the mean position error is 60 cm to 70 cm depending on the environment. A comparison against an RF-based indoor localization system shows the robustness of magnetic fields against RF shadows caused by big metal objects.
We additionally present algorithms for regions of interest detection, working on raw magnetic field information and transformed position and distance information. Setups in larger areas can distinguish regions which are further than 50 cm apart, small scale coil setups (3 transmitters in 2m^3) allow to resolve regions below 20 cm.
In the end, we describe a fusion algorithm for a wearable localization system based on 4 LIDAR distance measurement units and magnetic field-based distance estimation. The magnetic field indoor localization system provides distance proximity information which is used to resolve ambiguous position estimates of the LIDAR system. In a room (8m × 10m), we achieve a mean error of 8 cm.

Magnetic and Structural Characterization of Isolated Gaseous Ions by XMCD and IRMPD Spectroscopy
(2017)

This thesis comprises four independent research studies on the magnetic and structural characterization of isolated ions in the gas phase. The electrospray ionization (ESI) technique is used for the transfer of (multi-)metallic complexes and organic molecules from solution into the gas phase. The subsequent storage of molecular ions in ion traps allows for a variety of spectroscopic methods in order to investigate the intrinsic properties of the isolated species void of solvent, crystal lattice, bulk or supporting surface effects. The magnetic properties of metal complexes are elucidated by gas phase X-ray magnetic circular dichroism (XMCD) spectroscopy. The element selective technique in combination with sum rule analysis allows for a separate determination of spin and orbital magnetic moments at different metal centers. Structural investigations on isolated molecular ions in terms of coordination sphere, binding motifs and hydrogen bonds are conducted using infrared multiple photon dissociation (IRMPD) spectroscopy. A resonant two color IRMPD technique serves to increase fragmentation yields, overcome dissociation bottlenecks and reveal otherwise dark bands. Comparison of experimental IRMPD spectra with calculated harmonic absorption spectra by density functional theory (DFT) provides structural assignments for a profound understanding of intra- and intermolecular interactions.

Following the ideas presented in Dahlhaus (2000) and Dahlhaus and Sahm (2000) for time series, we build a Whittle-type approximation of the Gaussian likelihood for locally stationary random fields. To achieve this goal, we extend a Szegö-type formula, for the multidimensional and local stationary case and secondly we derived a set of matrix approximations using elements of the spectral theory of stochastic processes. The minimization of the Whittle likelihood leads to the so-called Whittle estimator \(\widehat{\theta}_{T}\). For the sake of simplicity we assume known mean (without loss of generality zero mean), and hence \(\widehat{\theta}_{T}\) estimates the parameter vector of the covariance matrix \(\Sigma_{\theta}\).
We investigate the asymptotic properties of the Whittle estimate, in particular uniform convergence of the likelihoods, and consistency and Gaussianity of the estimator. A main point is a detailed analysis of the asymptotic bias which is considerably more difficult for random fields than for time series. Furthemore, we prove in case of model misspecification that the minimum of our Whittle likelihood still converges, where the limit is the minimum of the Kullback-Leibler information divergence.
Finally, we evaluate the performance of the Whittle estimator through computational simulations and estimation of conditional autoregressive models, and a real data application.