Gorbitz ist ein Stadtteil, der von außen oft mit Klischees bedacht wird. Spricht man über kriminalitätsbezogene Herausforderungen in Dresdner Stadtteilen, wird Gorbitz oft an erster Stelle genannt. Die im Stadtteil vorhandenen Probleme stehen häufig im Fokus, während das Potential und das Engagement von Einwohnerinnen und Einwohnern, Vereinen und Einrichtungen nur selten wahrgenommen wird. Kommunale Kriminalprävention bedeutet in diesem Zusammenhang auch, den Blickwinkel auf einen Stadtteil zu verändern und diejenigen in den Fokus zustellen, die eng miteinander vernetzt im Stadtteil arbeiten und diesen positiv weiterentwickeln. Rückblickend auf das letzte Jahrzehnt lässt sich für Gorbitz anhand der Polizeilichen Kriminalstatistik (PKS)feststellen, dass der Stadtraum weniger von Kriminalität belastet war als die Stadt Dresden insgesamt. Erst in den letzten beiden Jahren ist ein Anstieg der Straftaten zu verzeichnen, 2019 wurden mehr Straftaten je 100.000 Einwohnerinnen und Einwohner registriert als in Dresden insgesamt. Die Gorbitzerinnen und Gorbitzer nehmen diesen Anstieg auch wahr: In einer postalischen Bürgerbefragung des SiQua-Projektesgaben71% der Befragten an, dass sich die Sicherheit in ihrem Wohngebiet während der letzten fünf Jahre verschlechtert hat. Vor allem nach Einbruch der Dunkelheit fühlen sie sich erheblich unsicherer als die Dresdnerinnen und Dresdner insgesamt. Das Vertrauen und der Zusammenhalt unter Nachbarn ist in Gorbitz deutlich geringer als in den meisten anderen Stadtteilen Dresdens Das ist ein wichtiger Grund für das geringe Sicherheitsgefühl. Ebenso lassen die Studienergebnisse aber auch die Potentiale des Stadtteils erkennen. So haben sich in Gorbitz während der letzten 5 Jahre fast genau so viele Einwohnerinnen und Einwohner ehrenamtlich für Geflüchtete engagiert, wie im restlichen Stadtgebiet (9%bzw.10%). Mit dem Blick auf mögliche Ansätze der kommunalen Präventionsarbeit zeigen sich die Gorbitzerinnen und Gorbitzer offen für unterschiedliche Lösungsansätze: Sieerachten sowohl härtere Strafen von Straftätern als auch mehr Angebote und Hilfen für Jugendliche für sinnvoll. Kritische Einstellungen lassen sich gegen über mehr privaten Wachdiensten feststellen.:1. Zusammenfassung der Situation in Gorbitz 2 2. Der Stadtraum Gorbitz 3 3. Überblick zur Lage im Stadtraum Gorbitz 4 a. Die objektive Sicherheitslage auf Basis der Polizeilichen Kriminalstatistik 4 b. Die Erfassung der Sicherheitswahrnehmung durch das Forschungsprojekt SiQua 5 4. Ausblick

Das Konzept von aktiven Brownschen Teilchen kann benutzt werden, um das Verhalten einfacher biologischer Organismen oder künstlicher Objekte, welche die Möglichkeit besitzen sich von selbst fortzubewegen zu beschreiben. Als Bewegungsgleichungen für aktive Brownsche Teilchen kommen Langevin Gleichungen zum Einsatz. In dieser Arbeit werden aktive Teilchen mit konstanter Geschwindigkeit diskutiert. Im ersten Teil der Arbeit wirkt auf die Bewegungsrichtung des Teilchen weißes alpha-stabiles Rauschen. Es werden die mittlere quadratische Verschiebung und der effektive Diffusionskoeffizient bestimmt. Eine überdampfte Beschreibung, gültig für Zeiten groß gegenüber der Relaxationszeit wird hergleitet. Als experimentell zugängliche Meßgröße, welche als Unterscheidungsmerkmal für die unterschiedlichen Rauscharten herangezogen werden kann, wird die Kurtose berechnet. Neben weißem Rauschen wird noch der Fall eines Ornstein-Uhlenbeck Prozesses angetrieben von Cauchy verteiltem Rauschen diskutiert. Während eine normale Diffusion mit zu weißem Rauschen identischem Diffusionskoeffizienten bestimmt wird, kann die beobachtete Verteilung der Verschiebungen Nicht-Gaußförmig sein. Die Zeit für den Übergang zur Gaußverteilung kann deutlich größer als die Zeitskale Relaxationszeit und die Zeitskale des Ornstein-Uhlenbeck Prozesses sein. Eine Grenze der benötigten Zeit wird durch eine Näherung der Kurtosis ermittelt. Weiterhin werden die Grundlagen eines stochastischen Modells für lokale Suche gelegt. Lokale Suche ist die Suche in der näheren Umgebung eines bestimmten Punktes, welcher Haus genannt wird. Abermals diskutieren wir ein aktives Teilchen mit unveränderlichem Absolutbetrag der Geschwindigkeit und weißen alpha-stabilem Rauschen in der Bewegungsrichtungsdynamik. Die deterministische Bewegung des Teilchens wird analysiert bevor die Situation mit Rauschen betrachtet wird. Die stationäre Aufenthaltswahrscheinlichkeitsdichtefunktion wird bestimmt. Es wird eine optimale Rauschstärke für die lokale Suche, das heißt für das Auffinden eines neuen Ortes in kleinstmöglicher Zeit festgestellt. Die kleinstmögliche Zeit wird kaum von der Rauschart abhängen. Wir werden jedoch feststellen, dass die Rauschart deutlichen Einfluß auf die Rückkehrwahrscheinlichkeit zum Haus hat, wenn die Richtung des zu Hauses fehlerbehaftet ist. Weiterhin wird das Model durch eine an das Haus abstandsabhängige Kopplung erweitert werden. Zum Abschluß betrachten wir eine Gruppe von Suchern. / Active Brownian particles described by Langevin equations are used to model the behavior of simple biological organisms or artificial objects that are able to perform self propulsion. In this thesis we discuss active particles with constant speed. In the first part, we consider angular driving by white Levy-stable noise and we discuss the mean squared displacement and diffusion coefficients. We derive an overdamped description for those particles that is valid at time scales larger the relaxation time. In order to provide an experimentally accessible property that distinguishes between the considered noise types, we derive an analytical expression for the kurtosis. Afterwards, we consider an Ornstein-Uhlenbeck process driven by Cauchy noise in the angular dynamics of the particle. While, we find normal diffusion with the diffusion coefficient identical to the white noise case we observe a Non-Gaussian displacement at time scales that can be considerable larger than the relaxation time and the time scale provided by the Ornstein-Uhlenbeck process. In order to provide a limit for the time needed for the transition to a Gaussian displacement, we approximate the kurtosis. Afterwards, we lay the foundation for a stochastic model for local search. Local search is concerned with the neighborhood of a given spot called home. We consider an active particle with constant speed and alpha-stable noise in the dynamics of the direction of motion. The deterministic motion will be discussed before considering the noise to be present. An analytical result for the steady state spatial density will be given. We will find an optimal noise strength for the local search and only a weak dependence on the considered noise types. Several extensions to the introduced model will then be considered. One extension includes a distance dependent coupling towards the home and thus the model becomes more general. Another extension concerned with an erroneous understanding by the particle of the direction of the home leads to the result that the return probability to the home depends on the noise type. Finally we consider a group of searchers.

Uwe Stephan Dissertation This work is concerned with methods and results for the calculation of electronic properties of amorphous carbon models (a-C). These investigations are based upon a very efficient non-selfconsistent ab-initio procedure for the evaluation of electronic states of extended systems using modified self- consistent DFT-LDA states and potentials of neutral atoms. Starting from the LCAO matrices constructed in this method, the electronic densities of states (DOS) of model systems are calculated by diagonalization or with use of the recursion method. Both techniques and, in particular, several versions of the recursion method will be investigated and compared with respect to their numerical efficiency and practical applicability. For DOS calculations in carbon systems a modification of the atomic SCF routine will be proposed and tested in application to the crystalline carbon allotropes diamond and graphite. In this work, the investigation of a-C structures is based on various structural models which have been generated in the author's research group by means of molecular-dynamics simulations using the empirical Tersoff potential as well as the just mentioned DFT-LDA approach. The total energy in this latter procedure is calculated as the sum of the band-structure energy and an empirical repulsive pair potential; contrary to the purely empirical approach, this scheme therefore includes pi-bonding effects and gives rise to a superior description of defect states in these models. As suggested by an analysis of the localization properties of the eigenstates, the defect structure in a-C models depends primarily on the ability of pi- and weak-sigma-bonded undercoordinated atoms to cluster. To investigate these clustering effects, a pi-bonding analysis will be proposed which enables the quantification and classification of the defect states and the estimation of gaps between pi bands. This procedure, which will be justified by local DOS calculations, provides essential structure-property correlations in dependence on the mass densities of the models. Within predominantly fourfold-coordinated models, the occurrence of a certain fraction of threefold-coordinated atoms turns out to stabilize the network by achieving optimum stress and defect minimization due to the preferred formation of pi-bonded atom pairs. Such models exhibit mass densities and pi gaps of about 3.0 g/cm^3 and 2.4 eV, respectively, in close agreement with recent experimental results.

The transition of the North African electricity system towards renewable energy technologies is analyzed in this thesis. Large potentials of photovoltaics (PV), concentrating solar power (CSP) and onshore wind power provide the opportunity to achieve a long-term shift from conventional power sources to a highly interconnected and sustainable electricity system based on renewable energy sources (RES). A multi-dimensional analysis evaluates the economic and technical effects on the electricity market as well as the socio-economic impact on manufacturing and employment caused by the large deployment of renewable energy technologies. The integration of renewable energy (RE) into the electricity system is modeled in a linear optimization model RESlion which minimizes total system costs of the long-term expansion planning and the hourly generation dispatch problem. With this model, the long-term portfolio mix of technologies, their site selection, required transmission capacities and the hourly operation are analyzed. The focus is set on the integration of renewable energy in the electricity systems of Morocco, Algeria, Tunisia, Libya and Egypt with the option to export electricity to Southern European countries. The model results of RESlion show that a very equal portfolio mix consisting of PV, CSP and onshore wind power is optimal in long-term scenarios for the electricity system. Until the year 2050, renewable energy sources dominate with over 70% the electricity generation due to their cost competiveness to conventional power sources. In the case of flexible and dispatchable electricity exports to Europe, all three RE technologies are used by the model at a medium cost perspective. The socio-economic impact of the scenarios is evaluated by a decision model (RETMD) for local manufacturing and job creation in the renewable energy sector which is developed by incorporating findings from expert interviews in the RE industry sector. The electricity scenarios are assessed regarding their potential to create local economic impact and local jobs in manufacturing RE components and constructing RE power plants. With 40,000 to 100,000 new jobs in the RE sector of North African countries, scenarios with substantial RE deployment can provide enormous benefits to the labor market and lead to additional economic growth. The deployment of renewable energy sources in North Africa is consequently accelerated and facilitated by finding a trade-off between an optimal technology portfolio from an electricity system perspective and the opportunities through local manufacturing. By developing two model approaches for evaluating the effects of renewable energy technologies in the electricity system and in the industrial sector, this thesis contributes to the literature on energy economics and energy policy for the large-scale integration of renewable energy in North Africa.:Abstract iii Acknowledgement iv Table of contents v List of tables ix List of figures xii List of abbreviations xvi 1 Introduction 1 1.1 Renewable energy in North Africa 2 1.2 Research questions and aim of this thesis 3 1.2.1 Modeling of electricity systems 4 1.2.2 Modeling of manufacturing and employment impact 6 1.2.3 Optimal renewable energy scenarios 6 1.3 Related research 7 1.4 Structure of thesis 7 2 Modeling fundamentals for electricity systems with renewable energy sources 9 2.1 Energy system modeling 9 2.2 Electricity models 16 2.2.1 Classifications and taxonomy 17 2.2.2 Differences between operation models and planning models 20 2.2.3 Typical modeling approaches 21 2.3 Optimization models 23 2.3.1 Basic model structure 23 2.3.2 Objective functions of electricity models 24 2.3.3 Technical aspects of electricity systems as models constraints 26 2.3.4 Combining different objectives in energy scenarios 27 2.4 Models for high shares of renewable energy 28 2.5 Models for North African electricity systems 31 2.6 Conclusions for model development 34 3 Electricity system of North Africa 36 3.1 Market structure 36 3.2 National targets for renewable energy 40 3.2.1 Morocco 40 3.2.2 Algeria 41 3.2.3 Tunisia 42 3.2.4 Libya 42 3.2.5 Egypt 43 3.3 Long-term development of electricity demand 44 3.4 Electricity exports to Europe 47 3.5 Geopolitical risks for the electricity system 51 4 Development of the electricity market model RESlion 53 4.1 Model requirements and modeling goals 53 4.2 Modeling of renewable energy technologies 56 4.2.1 Onshore wind power plants and wind resources 59 4.2.2 PV power plants and solar resources 61 4.2.3 CSP plants and solar resources 63 4.2.4 Hydro power plants and energy storage systems 65 4.3 General model approach of RESlion 65 4.4 Model description of RESlion 69 4.4.1 Introduction to the model structure 69 4.4.2 Temporal coverage 70 4.4.3 Objective function 72 4.4.4 Technology independent model constraints 74 4.4.5 Regional electricity exchange: Transmission lines 76 4.4.6 Renewable energy technologies 78 4.4.7 Hydro and storage power plants 80 4.4.8 Uncertainty of input parameters and assumptions 81 4.5 Modeling of expansion planning 83 4.6 Modeling of detailed hourly generation dispatch 83 4.7 Extension options to a Mixed Integer Linear Programming model 84 4.8 Solver selection and implementation environment 85 5 Model-based analysis of future electricity scenarios for North Africa 86 5.1 Scenario assumptions 86 5.2 Scenario definition 89 5.3 Technical and economic input data 94 5.4 Model adjustment 99 5.4.1 Electricity generation in reference year 2010 99 5.4.2 Testing of results with detailed hourly generation dispatch 100 5.5 Electricity scenarios for North Africa by 2050 102 5.5.1 Development of the generation system 102 5.5.2 System and generation costs 106 5.5.3 Site selection of RES generation capacities 108 5.5.4 Regional transmission lines 114 5.5.5 Energy storage systems 118 5.5.6 Technology specific generation 119 5.5.7 CO2 emissions 126 5.6 Sensitivity analyses 126 5.6.1 Adaption of market conditions: Split of electricity markets 127 5.6.2 Technology focus 127 5.6.3 Adaption of cost trends for fossil fuels, transmission lines and storage systems 129 5.7 Technology specific findings for CSP, PV and wind power 131 5.7.1 Typical sites and locations for electricity generation from RES 131 5.7.2 Influence of wind speeds and solar irradiation 131 5.7.3 Interactions with conventional power plants 132 5.8 Electricity scenarios with export to Europe 133 5.9 Discussion of RESlion model and its results 139 6 Model development for socio-economic impact analysis 142 6.1 The idea of combining a cost-optimized electricity system with a socio-economic analysis 142 6.2 Literature review and terminology 145 6.3 Data acquisition and further studies 148 6.4 Model description of RETMD 151 6.4.1 Model objectives 151 6.4.2 Model structure and decision modeling 152 6.4.3 Model limitations and uncertainties 156 6.5 Data input of RETMD 157 6.5.1 Construction of reference power plants 157 6.5.2 Operation of reference power plants 159 6.5.3 Status quo of local manufacturing in recent RE projects 160 6.6 Sensitivity of RETMD on market size and know-how 161 6.7 Discussion of model achievements 163 7 Manufacturing and employment impact of optimized electricity scenarios 165 7.1 Demand scenarios for the RE markets from 2012 to 2030 165 7.2 Economic impact and employment creation 166 7.3 Technology specific development of local manufacturing 168 7.4 Country specific development of local manufacturing 172 7.5 Potentials of local manufacturing in each scenarios 174 7.6 Local economic impact 176 7.7 Local employment impact 177 7.8 Evaluation of scenario results 181 7.9 Electricity system analysis and RE manufacturing: Results and discussion of the combined analysis 183 8 Conclusions and outlook 186 8.1 Conclusion on model developments 186 8.2 Conclusion on renewable energy in North Africa 187 8.3 Outlook and further research 189 9 Bibliography 191 10 Appendix 210

In this thesis I investigate several aspects of local quantum criticality, a concept of key importance in a number of physical contexts ranging from critical heavy fermion compounds to quantum dot systems. Quantum critical points are associated with second order phase transitions at zero temperature. In contrast to their finite-temperature counterparts, the zero-point motion cannot be neglected near a quantum critical point. As a result, the incorporation of quantum dynamics leads to an effective dimension larger than the spatial dimension of the system for the order parameter fluctuations within the Ginzburg-Landau-Wilson treatment of criticality. This so-called quantum-to-classical mapping works well for the critical properties in insulating systems but apparently fails in systems containing gapless fermions. This has been experimentally most clearly been demonstrated within a particular class of intermetallic compounds called heavy fermions. A particular way in which the Ginzburg-Landau-Wilson paradigm fails is for critical Kondo destruction that seems to underlie the unconventional quantum criticality seen in the heavy fermions. I focus on studying the properties of critical Kondo destruction and the emergence of energy-over-temperature-scaling in systems without spatial degrees of freedom, i.e., so-called quantum impurity systems. In particular, I employ large-N techniques to address critical properties of this class of quantum phase transitions in and out of equilibrium. As quantum critical systems are characterized by a scale-invariant spectrum with many low-lying excitations, it may appear that any perturbation can lead to a response beyond the linear response regime. Understanding what governs the non-linear response regime near quantum criticality is an interesting area. Here, I first present a path integral version of the Schrieffer-Wolff transformation which relates the functional integral form of the partition function of the Anderson model to that of its effective low-energy model. The equivalence between the low-energy sector of the Anderson model in the Kondo regime and the spin-isotropic Kondo model is usually established via a canonical transformation performed on the Hamiltonian, followed by a projection. The resulting functional integral assumes the form of a spin path integral and includes a geometric phase factor, i.e. a Berry phase. The approach stresses the underlying symmetries of the model and allows for a straightforward generalization of the transformation to more involved models. As an example of the efficiency of the approach I apply it to a single electron transistor attached to ferromagnetic leads and derive the effective low-energy model of such a magnetic transistor. As Kondo screening is a local phenomenon, it and its criticality can be studied using the appropriate impurity model. A general impurity model to study critical Kondo destruction is the pseudogap Bose-Fermi Kondo model. Here, I concentrate on the multi-channel version of the model using the dynamical large-N study. This model allows to study the non-trivial interplay between two different mechanisms of critical Kondo destruction. The interplay of two processes that can each by itself lead to critical Kondo destruction. The zero-temperature residual entropy at various fixed points for the model is also discussed. The two channel Anderson model exhibits several continuous quantum phase transitions between weak- and strong-coupling phases. The non-crossing approximation (NCA) is believed to give reliable results for the standard two-channel Anderson model of a magnetic impurity in a metal. I revisit the reliability of the NCA for the standard two channel Anderson model (constant conduction electron density of states) and investigate its reliability for the two-channel pseudogap Anderson model. This is done by comparing finite-temperature, finite-frequency solutions of the NCA equations and asymptotically exact zero-temperature NCA solutions with numerical renormalization-group calculations. The phase diagram of this model is well established. The focus here will be on the dynamical scaling properties obtained within the NCA. Finally, I study the thermal and non-thermal steady state scaling functions and the steady-state dynamics of the pseudogap Kondo model. This model allows us to study the concept of effective temperatures near fully interacting as well as weak-coupling fixed points and compare the out-of-equilibrium scaling properties of critical Kondo destruction to those of the traditional spin-density wave (SDW) scenario. The differences I identify can be experimentally probed. This may be helpful in identifying the nature of the quantum critical points observed in certain heavy fermion compounds.

This cumulative dissertation aims to complement existing literature with insights on two topics gaining strong importance in the Private Equity Industry: 1) cross-border investments and 2) co-investments with portfolio firm management in times of uncertainty. Results in paper on cross-border investments suggest that the physical presence of a local office of PE firms can actually make a difference for foreign investments. With a local office, operating performance of PE firms is higher after the buyouts. Local offices are especially beneficial for performance the higher the perceived foreignness between PE firm and portfolio firm is. In addition, PE firms increase deal flow after a local office opening, do less syndicates and have higher deal volumes. Respective results imply it is worth in future research to differentiate between pure cross-border deals and deals operated through a local office. The forth paper sheds light on the positive relationship between management buyouts (MBOs) and economic policy uncertainty. Analyses indicate that access to information is a relevant channel for higher propensity of MBOs in uncertain times.:1 Introduction 1.1 Trends in private equity industry 1.2 Overview of essays 2 The Cross-Border Buyout Next Door 2.1 Introduction 2.2 Theoretical background 2.3 Data 2.4 Operating performance results 2.5 Insights from semi-structured interviews 2.6 Conclusion 3 Opening a Local Office - PE Firms' Engine for International Expansion? 3.1 Introduction 3.2 Theoretical background 3.3 Sample and data 3.4 Determinants of office openings 3.5 Impact of local offices 3.6 Conclusion 3.A Appendices 4 Entrepreneurial Activity in Times of Uncertainty: The Case of Management Buyouts 4.1 Introduction 4.2 Literature review and hypotheses 4.3 Material and methods 4.4 Results and discussion 4.5 Conclusions 4.A Appendices References

Die Arbeit beschreibt ein Modell, dass den Materialfluss in Transport- und Puffersystemen mit Hilfe eines agenten-basierten Ansatzes realistisch abbildet. Auf der Basis von Produktionsprogrammen werden individuelle Güter in beliebigen Netzwerkstrukturen mit Hilfe direkter und indirekter Interaktionen behinderungsvermeidend gesteuert. / The thesis describes a model that realistically illustrates the material flow in transport and buffer systems by means of an agent-based approach. Individual goods are steered hindrance-avoiding in arbitrary network structures based on production programs by means of direct and indirect interactions.

Im ersten Teil wird eine neue Konstruktion der parabolischen Induktion für pro-p Iwahori-Heckemoduln gegeben. Dabei taucht eine neue Klasse von Algebren auf, die in gewisser Weise als Interpolation zwischen der pro-p Iwahori-Heckealgebra einer p-adischen reduktiven Gruppe $G$ und derjenigen einer Leviuntergruppe $M$ von $G$ gedacht werden kann. Für diese Algebren wird ein Induktionsfunktor definiert und eine Transitivitätseigenschaft bewiesen. Dies liefert einen neuen Beweis für die Transitivität der parabolischen Induktion für Moduln über der pro-p Iwahori-Heckealgebra. Ferner wird eine Funktion auf einer parabolischen Untergruppe untersucht, die als Werte nur p-Potenzen annimmt. Es wird gezeigt, dass sie eine Funktion auf der (pro-p) Iwahori-Weylgruppe von $M$ definiert, und dass die so definierte Funktion monoton steigend bzgl. der Bruhat-Ordnung ist und einen Vergleich der Längenfunktionen zwischen der Iwahori-Weylgruppe von $M$ und derjenigen der Iwahori-Weylgruppe von $G$ erlaubt. Im zweiten Teil wird ein allgemeiner Zerlegungssatz für Polynome über der sphärischen (parahorischen) Heckealgebra einer p-adischen reduktiven Gruppe $G$ bewiesen. Diese Zerlegung findet über einer parabolischen Heckealgebra statt, die die Heckealgebra von $G$ enthält. Für den Beweis des Zerlegungssatzes wird vorausgesetzt, dass die gewählte parabolische Untergruppe in einer nichtstumpfen enthalten ist. Des Weiteren werden die nichtstumpfen parabolischen Untergruppen von $G$ klassifiziert. / The first part deals with a new construction of parabolic induction for modules over the pro-p Iwahori-Hecke algebra. This construction exhibits a new class of algebras that can be thought of as an interpolation between the pro-p Iwahori-Hecke algebra of a p-adic reductive group $G$ and the corresponding algebra of a Levi subgroup $M$ of $G$. For these algebras we define a new induction functor and prove a transitivity property. This gives a new proof of the transitivity of parabolic induction for modules over the pro-p Iwahori-Hecke algebra. Further, a function on a parabolic subgroup with p-power values is studied. We show that it induces a function on the (pro-p) Iwahori-Weyl group of $M$, that it is monotonically increasing with respect to the Bruhat order, and that it allows to compare the length function on the Iwahori-Weyl group of $M$ with the one on the Iwahori-Weyl group of $G$. In the second part a general decomposition theorem for polynomials over the spherical (parahoric) Hecke algebra of a p-adic reductive group $G$ is proved. The proof requires that the chosen parabolic subgroup is contained in a non-obtuse one. Moreover, we give a classification of non-obtuse parabolic subgroups of $G$.

We revisit in L2-spaces the autoconvolution equation x ∗ x = y with solutions which are real-valued or complex-valued functions x(t) defined on a finite real interval, say t ∈ [0,1]. Such operator equations of quadratic type occur in physics of spectra, in optics and in stochastics, often as part of a more complex task. Because of their weak nonlinearity deautoconvolution problems are not seen as difficult and hence little attention is paid to them wrongly. In this paper, we will indicate on the example of autoconvolution a deficit in low order convergence rates for regularized solutions of nonlinear ill-posed operator equations F(x)=y with solutions x† in a Hilbert space setting. So for the real-valued version of the deautoconvolution problem, which is locally ill-posed everywhere, the classical convergence rate theory developed for the Tikhonov regularization of nonlinear ill-posed problems reaches its limits if standard source conditions using the range of F (x† )∗ fail. On the other hand, convergence rate results based on Hölder source conditions with small Hölder exponent and logarithmic source conditions or on the method of approximate source conditions are not applicable since qualified nonlinearity conditions are required which cannot be shown for the autoconvolution case according to current knowledge. We also discuss the complex-valued version of autoconvolution with full data on [0,2] and see that ill-posedness must be expected if unbounded amplitude functions are admissible. As a new detail, we present situations of local well-posedness if the domain of the autoconvolution operator is restricted to complex L2-functions with a fixed and uniformly bounded modulus function.

In zukünftigen Elektroenergiesystemen wird die dezentrale, häufig auf erneuerbaren Quellen basierende Energieversorgung eine große Bedeutung einnehmen. Die wachsende Präsenz der dezentralen Erzeugung in verschiedenen Spannungsebenen des elektrischen Netzes erfordert neue Konzepte zur Regelung des elektrischen Energieversorgungssystems. Insbesondere gibt es eine Tendenz auch kleine Netzbereiche autonome, d.h. vom Verbundnetz unabhängig zu betreiben. In diesem Zusammenhang müssen die Stabilitäts- und Regelungsaspekte immer stärker berücksichtigt werden. Die vorliegende Untersuchung konzentriert sich auf die Beurteilung und die Verbesserung der Stabilität von Windkraftanlagen (WKA). Die Integration von WKA zur dezentralen Energieversorgung in lokale Energienetze unter besonderer Berücksichtigung der Systemsstabilität ist das Ziel dieser Arbeit. Hierfür muss die Analyse der Stabilität einer WKA sowohl qualitativ als auch quantitativ durchgeführt werden, um die Faktoren zu ermitteln, die zur Verbesserung der Systemsstabilität beitragen. Der darauf basierte Entwurf von Regelstrategien für ein verbessertes dynamisches und transientes Verhalten wird theoretisch und durch numerische Simulationen validiert.