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In recent years, the study of dynamical systems has developed into a central research area in mathematics. Actually, in combination with keywords such as "chaos" or "butterfly effect", parts of this theory have been incorporated in other scientific fields, e.g. in physics, biology, meteorology and economics. In general, a discrete dynamical system is given by a set X and a self-map f of X. The set X can be interpreted as the state space of the system and the function f describes the temporal development of the system. If the system is in state x âˆˆ X at time zero, its state at time n âˆˆ N is denoted by f^n(x), where f^n stands for the n-th iterate of the map f. Typically, one is interested in the long-time behaviour of the dynamical system, i.e. in the behaviour of the sequence (f^n(x)) for an arbitrary initial state x âˆˆ X as the time n increases. On the one hand, it is possible that there exist certain states x âˆˆ X such that the system behaves stably, which means that f^n(x) approaches a state of equilibrium for nâ†’âˆž. On the other hand, it might be the case that the system runs unstably for some initial states x âˆˆ X so that the sequence (f^n(x)) somehow shows chaotic behaviour. In case of a non-linear entire function f, the complex plane always decomposes into two disjoint parts, the Fatou set F_f of f and the Julia set J_f of f. These two sets are defined in such a way that the sequence of iterates (f^n) behaves quite "wildly" or "chaotically" on J_f whereas, on the other hand, the behaviour of (f^n) on F_f is rather "nice" and well-understood. However, this nice behaviour of the iterates on the Fatou set can "change dramatically" if we compose the iterates from the left with just one other suitable holomorphic function, i.e. if we consider sequences of the form (gâˆ˜f^n) on D, where D is an open subset of F_f with f(D)âŠ‚ D and g is holomorphic on D. The general aim of this work is to study the long-time behaviour of such modified sequences. In particular, we will prove the existence of holomorphic functions g on D having the property that the behaviour of the sequence of compositions (gâˆ˜f^n) on the set D becomes quite similarly chaotic as the behaviour of the sequence (f^n) on the Julia set of f. With this approach, we immerse ourselves into the theory of universal families and hypercyclic operators, which itself has developed into an own branch of research. In general, for topological spaces X, Y and a family {T_i: i âˆˆ I} of continuous functions T_i:Xâ†’Y, an element x âˆˆ X is called universal for the family {T_i: i âˆˆ I} if the set {T_i(x): i âˆˆ I} is dense in Y. In case that X is a topological vector space and T is a continuous linear operator on X, a vector x âˆˆ X is called hypercyclic for T if it is universal for the family {T^n: n âˆˆ N}. Thus, roughly speaking, universality and hypercyclicity can be described via the following two aspects: There exists a single object which allows us, via simple analytical operations, to approximate every element of a whole class of objects. In the above situation, i.e. for a non-linear entire function f and an open subset D of F_f with f(D)âŠ‚ D, we endow the space H(D) of holomorphic functions on D with the topology of locally uniform convergence and we consider the map C_f:H(D)â†’H(D), C_f(g):=gâˆ˜f|_D, which is called the composition operator with symbol f. The transform C_f is a continuous linear operator on the Fréchet space H(D). In order to show that the above-mentioned "nice" behaviour of the sequence of iterates (f^n) on the set D âŠ‚ F_f can "change dramatically" if we compose the iterates from the left with another suitable holomorphic function, our aim consists in finding functions g âˆˆ H(D) which are hypercyclic for C_f. Indeed, for each hypercyclic function g for C_f, the set of compositions {gâˆ˜f^n|_D: n âˆˆ N} is dense in H(D) so that the sequence of compositions (gâˆ˜f^n|_D) is kind of "maximally divergent" " meaning that each function in H(D) can be approximated locally uniformly on D via subsequences of (gâˆ˜f^n|_D). This kind of behaviour stands in sharp contrast to the fact that the sequence of iterates (f^n) itself converges, behaves like a rotation or shows some "wandering behaviour" on each component of F_f. To put it in a nutshell, this work combines the theory of non-linear complex dynamics in the complex plane with the theory of dynamics of continuous linear operators on spaces of holomorphic functions. As far as the author knows, this approach has not been investigated before.

Die Arbeit untersucht das Potential kleiner unbemannter Luftfahrtsysteme (UAS) in Landwirtschaft und Archäologie. Der Begriff UAS beinhaltet dabei: Fluggerät, Antriebsmechanismus, Sensorik, Bodenstation, Kommunikationsmittel zwischen Bodenstation und Fluggerät und weiteres Equipment. Aufgrund ihrer Flexibilität, fanden UAS seit der Jahrtausendwende eine blühende Entwicklung. Um die wachsende Weltbevölkerung zu ernähren, muss die landwirtschaftliche Produktion sensibel und nachhaltig intensiviert werden, um Nahrungssicherheit für alle zu gewährleisten und weitere Boden- und Landdegradation zu vermeiden. Präzisionslandwirtschaft umfasst technologische Verbesserungen hin zur effizienteren und weniger schädlichen landwirtschaftlichen Praxis. Hierbei ist die Verfügung über zeitnahe, leicht zugängliche hoch aufgelöste räumliche Daten eine Voraussetzung für die Nahrungsmittelproduktion. UAS schließen hier die Lücke zwischen Bodendaten und teuren bemannten Luftfahrtsysteme und selteneren Satellitenbildern. Die Vorteile der UAS-Daten liegen in der ad-hoc Akquisition großmaßstäbiger Fernerkundungsdaten, den geringeren Kosten gegenüber der bemannten Systeme und einer relativen Wetterunabhängigkeit, da auch unter Wolken geflogen werden kann. Den größten Anteil innerhalb der UAS stellen die Mini-UAS (Abfluggewicht von 5kg) und dabei vertikale Start- und Landesysteme. Diese können über Untersuchungsgebieten schweben, sind dadurch jedoch langsamer und eher geeignet für kleinere Flächen. Flugregularien und die Integration in den bemannten Luftraum werden derzeit europaweit harmonisiert und in den Mitgliedstaaten umgesetzt. Die Hauptziele dieser Arbeit lagen in der Evaluierung wie Schlüsselparametern landwirtschaftlicher Nutzpflanzen (Chlorophyll-, Stickstoffgehalt, Erntemenge, sonnendinduzierter Chlorophyll-Fluoreszenz) mittels UAS abgeleitet und wie UAS-Daten für archäologische Aufklärung genutzt werden können. Dazu wurde ein Quadrokopter (md4-1000, microdrones GmbH) mit einer digitalen Spiegelreflexkamera, einem Multispektralsensor (MiniMCA-6, Tetracam Inc.) und einer Thermalkamera (UCM, Zeiss) ausgestattet. Eine Sensitivitätsanalyse führte zur Ableitung geeigneter Wellenlängenbereiche und untersuchte bidirektionale und Flughöheneffekte auf das Multispektralsignal. Die Studie beschreibt außerdem die Vorgehensweise bei Bildaufnahme und Vorprozessierung mit besonderem Schwerpunkt auf die Multispektralkamera (530-900 nm). Die Vorprozessierung beinhaltet die Korrektur von Sensorfehlern (Linsenverzeichnung, Vignettierung, Kanalkalibrierung), die radiometrische Kalibrierung über eine empirische Korrektur mit Hilfe von Referenzspektren, Atmosphärenkorrektur und schließlich die geometrische Verarbeitung unter Verwendung von Structure from Motion Programme zur Generierung von Punktwolkenmodellen bis hin zum digitalen Orthophotomosaik und Höhenmodell in Zentimeterauflösung. In einer Weinbergsstudie (2011, 2012) wurden geeignete Beobachtungswinkel für die Untersuchung des Einflusses von Bodenbearbeitungsstrategien auf das Multispektralsignal evaluiert. Schrägichtaufnahmen von 45-° Beobachtungswinkel gegenüber Nadir waren am besten geeignet zur Ableitung pflanzenphysiolgischer Parameter und multispektraler Unterscheidung von Bodenbearbeitungstypen. So konnten Chlorophyll-Gehalte über Regressionsanalysen über mehrere saisonale Aufnahmen mit einem kreuzvalidierten R-² von 0.65, Stickstoffgehaltsindex von 0.76 (2012) und Ernte mit 0.84 (2011) und für verschiedene Zeitpunkte nach der Blüte (0.87) und während der Reifephase (0.73) ermittelt werden. Desweiteren wurde die (Fs) in einem Stickstoff-Düngung-Experiment bei Zuckerrüben von Multispektral-, Indizes und Thermaldaten untersucht (HyFlex-Kampagne 2012). Zuckerrübenvarietäten konnten spektral und thermal unterschieden werden, die Fluoreszenzindizes waren wetterbedingt, weniger erfolgreich. Außerdem konnte der Tagesgang der Fs trotz instabiler Einstrahlungsverhältnisse am Morgen abgeleitet werden. Die Werte waren jedoch gegenüber Bodenmessungen um ein Vielfaches erhöht. Archäologische Fernerkundung durch UAS wird bereits seit Jahren (z.B. mit Fesselballons) durchgeführt. Die Mustererkennung profitiert von der spektralen Ausdehnung vom menschlichen Auge hin zu multispektralen, neuerdings auch hyperspektralen Sensoren. Studien in Los BaÃ±ales, Spanien, zeigten die Möglichkeiten des Informationsgewinns durch Bildverarbeitung von UAS-Daten: vermutliche historische Siedlungsmuster konnten durch Landoberflächenklassifikation von Multispektraldaten mittels Support Vector Machines und Bestandsmusterdetektion beschrieben werden. Um qualitative hochwertige, hochaufgelöste UAS-Daten zu erhalten, sollten die Daten mit hoher Überlappung (80%) und auch Schrägsicht akquiriert und ggf. durch Referenzmessungen zur radiometrischen Kalibrierung und GPS-Messungen für geometrische Referenzierung ergänzt werden.

Part-time entrepreneurship has become increasingly popular and is a rather new field of research. Two important research topics are addressed in this dissertation: (a) the impact of culture on part-time and full-time entrepreneurship and (b) the motivational aspects of the transition from part-time to full-time entrepreneurship. Specifically, this dissertation advances prior research by highlighting the direct and indirect differential impact of macro-level societal culture on part-time and full-time entrepreneurship. Gender egalitarianism, uncertainty avoidance and future orientation have a significantly stronger impact on full-time than on part-time entrepreneurship. Furthermore the moderating impact of societal culture on micro-level relationships for both forms of entrepreneurship is explored. The age-old and well-established relationship between education and entrepreneurial activity is moderated by different forms of collectivism for part-time and full-time entrepreneurship. Regarding the motivation of part-time entrepreneurs to transition to full-time entrepreneurship, the entrepreneurial motives of self-realization and independence are significantly positively associated with the transition, whereas the entrepreneurial motives of income supplementation and recognition are significantly negatively associated with the transition. This dissertation advances academic research by indicating conceptual differences between part-time and full-time entrepreneurship in a multi country setting and by showing that both forms of entrepreneurship are impacted through different cultural mechanisms. Based on the findings, policy makers can identify the direct and indirect impact of societal culture on part-time and full-time entrepreneurship. As a result, policy makers can better target support and transition programs to foster entrepreneurial activity.

The present study covers the period from the late-ninth to the early-sixteenth centuries. Within this period, the late-thirteenth to mid-fourteenth centuries marked the decisive turning point, shaped more by attitudes and actions among the Christian majority than among Jewish agents. Our findings indicate an intensification of anti-Jewish tendencies, rooted in religious developments in Western Christendom. According to circumstances, however, these tendencies had a very varying impact across time and space. The frequent religious and ecclesiastical reform movements of Western Europe offer cases in point. In the 'German' Empire north of the Alps the monastic reforms of Saint Maximin and Gorze were by no means confined to the realm of monasticism; they were essential for shaping the historical circumstances in which the foundations of Ashkenazic Judaism were laid in the tenth and early-eleventh centuries. The concept of 'honor' was used by leading ecclesiastics such as bishop Rudiger of Speyer in 1084 to justify the settlement of Jews, but also by civic authorities such as those of Regensburg later on. It is significant for the long-term tendency, therefore, that the late-medieval expulsions from cities like Trier, Cologne, and Regensburg were eventually also legitimized by reference to the idea of honor.

Evapotranspiration (ET) is one of the most important variables in hydrological studies. In the ET process, energy exchange and water transfer are involved. ET consists of transpiration and evaporation. The amount of plants transpiration dominates in ET. Especially in the forest regions, the ratio of transpiration to ET is in general 80-90 %. Meteorological variables, vegetation properties, precipitation and soil moisture are critical influence factors for ET generation. The study area is located in the forest area of Nahe catchment (Rhineland-Palatinate, Germany). The Nahe catchment is highly wooded. About 54.6 % of this area is covered by forest, with deciduous forest and coniferous forest are two primary types. A hydrological model, WaSiM-ETH, was employed for a long-term simulation from 1971-2003 in the Nahe catchment. In WaSiM-ETH, the potential evapotranspiration (ETP) was firstly calculated by the Penman-Monteith equation, and subsequently reduced according to the soil water content to obtain the actual evapotranspiration (ETA). The Penman-Monteith equation has been widely used and recommended for ETP estimation. The difficulties in applying this equation are the high demand of ground-measured meteorological data and the determination of surface resistance. A method combined remote sensing images with ground-measured meteorological data was also used to retrieve the ETA. This method is based on the surface properties such as surface albedo, fractional vegetation cover (FVC) and land surface temperature (LST) to obtain the latent heat flux (LE, corresponding to ETA) through the surface energy balance equation. LST is a critical variable for surface energy components estimation. It was retrieved from the TM/ETM+ thermal infrared (TIR) band. Due to the high-quality and cloudy-free requirements for TM/ETM+ data selection as well as the overlapping cycle of TM/ETM+ sensor is 16 days, images on only five dates are available during 1971-2003 (model ran) " May 15, 2000, July 05, 2001, July 19, August 04 and September 21 in 2003. It is found that the climate conditions of 2000, 2001 and 2003 are wet, medium wet and dry, respectively. Therefore, the remote sensing-retrieved observations are noncontinuous in a limited number over time but contain multiple climate conditions. Aerodynamic resistance and surface resistance are two most important parameters in the Penman-Monteith equation. However, for forest area, the aerodynamic resistance is calculated by a function of wind speed in the model. Since transpiration and evaporation are separately calculated by the Penman-Monteith equation in the model, the surface resistance was divided into canopy surface resistance rsc and soil surface resistance rse. rsc is related to the plants transpiration and rse is related to the bare soil evaporation. The interception evaporation was not taken into account due to its negligible contribution to ET rate under a dry-canopy (no rainfall) condition. Based on the remote sensing-retrieved observations, rsc and rse were calibrated in the WaSiM-ETH model for both forest types: for deciduous forest, rsc = 150 smâˆ’1, rse = 250 smâˆ’1; for coniferous forest, rsc = 300 smâˆ’1, rse = 650 smâˆ’1. We also carried out sensitivity analysis on rsc and rse. The appropriate value ranges of rsc and rse were determined as (annual maximum): for deciduous forest, [100,225] smâˆ’1 for rsc and [50,450] smâˆ’1 for rse; for coniferous forest, [225,375] smâˆ’1 for rsc and [350,1200] smâˆ’1 for rse. Due to the features of the observations that are in a limited number but contain multiple climate conditions, the statistical indices for model performance evaluation are required to be sensitive to extreme values. In this study, boxplots were found to well exhibit the model performance at both spatial and temporal scale. Nush-Sutcliffe efficiency (NSE), RMSE-observations standard deviation ratio (RSR), percent bias (PBIAS), mean bias error (MBE), mean variance of error distribution (S2d), index of agreement (d), root mean square error (RMSE) were found as appropriate statistical indices to provide additional evaluation information to the boxplots. The model performance can be judged as satisfactory if NSE > 0.5, RSR â‰¤ 0.7, PBIAS < -±12, MBE < -±0.45, S2d < 1.11, d > 0.79, RMSE < 0.97. rsc played a more important role than rse in ETP and ETA estimation by the Penman-Monteith equation, which is attributed to the fact that transpiration dominates in ET. The ETP estimation was found the most correlated to the relative humidity (RH), followed by air temperature (T), relative sunshine duration (SSD) and wind speed (WS). Under wet or medium wet climate conditions, ETA estimation was found the most correlated to T, followed by RH, SSD and WS. Under a water-stress condition, there were very small correlations between ETA and each meteorological variable.

Death is perceived as a severe threat to the self. Although it is certain that everyone has to die, people usually don"t think about the finiteness of their life. Everything reminding of death is ignored, rationalized and death-related thoughts and fears are pushed out of mind (TMT; Pyszczynski et al., 1999). However, people differ in their ability to regulate negative affect and to access their self-system (Kuhl, 2001). As death is assumed to arouse existential fears, the ability to regulate such fears is particularly important, higher self-access could be relevant in defending central personal values. This thesis aimed at showing existential fears under mortality salience and effects of self-regulation of affect under mortality salience. In two studies (Chapter 2) implicit negative affect under mortality salience was demonstrated. An additional study (Chapter 3) shows the effects of self-regulation on implicit negative affect, whereas four studies in Chapter 4 displayed differences in self-access under mortality salience depending on people- ability of self-regulating negative affect.

Matching problems with additional resource constraints are generalizations of the classical matching problem. The focus of this work is on matching problems with two types of additional resource constraints: The couple constrained matching problem and the level constrained matching problem. The first one is a matching problem which has imposed a set of additional equality constraints. Each constraint demands that for a given pair of edges either both edges are in the matching or none of them is in the matching. The second one is a matching problem which has imposed a single equality constraint. This constraint demands that an exact number of edges in the matching are so-called on-level edges. In a bipartite graph with fixed indices of the nodes, these are the edges with end-nodes that have the same index. As a central result concerning the couple constrained matching problem we prove that this problem is NP-hard, even on bipartite cycle graphs. Concerning the complexity of the level constrained perfect matching problem we show that it is polynomially equivalent to three other combinatorial optimization problems from the literature. For different combinations of fixed and variable parameters of one of these problems, the restricted perfect matching problem, we investigate their effect on the complexity of the problem. Further, the complexity of the assignment problem with an additional equality constraint is investigated. In a central part of this work we bring couple constraints into connection with a level constraint. We introduce the couple and level constrained matching problem with on-level couples, which is a matching problem with a special case of couple constraints together with a level constraint imposed on it. We prove that the decision version of this problem is NP-complete. This shows that the level constraint can be sufficient for making a polynomially solvable problem NP-hard when being imposed on that problem. This work also deals with the polyhedral structure of resource constrained matching problems. For the polytope corresponding to the relaxation of the level constrained perfect matching problem we develop a characterization of its non-integral vertices. We prove that for any given non-integral vertex of the polytope a corresponding inequality which separates this vertex from the convex hull of integral points can be found in polynomial time. Regarding the calculation of solutions of resource constrained matching problems, two new algorithms are presented. We develop a polynomial approximation algorithm for the level constrained matching problem on level graphs, which returns solutions whose size is at most one less than the size of an optimal solution. We then describe the Objective Branching Algorithm, a new algorithm for exactly solving the perfect matching problem with an additional equality constraint. The algorithm makes use of the fact that the weighted perfect matching problem without an additional side constraint is polynomially solvable. In the Appendix, experimental results of an implementation of the Objective Branching Algorithm are listed.

Auf der Grundlage großer Datensätze bereits behandelter Psychotherapiepatienten werden typische Veränderungsmuster identifiziert, die Therapeuten dabei unterstützen sollen, den beobachteten Verlauf ihrer Patienten besser einordnen und Erfolgswahrscheinlichkeiten ableiten zu können. Dabei werden Unterschiede und Gemeinsamkeiten dieser Muster und deren Implikationen in Bezug auf Therapieerfolg und -länge für verschiedene Störungsbilder, Erhebungsinstrumente, Therapiephasen und Untersuchungsdesigns herausgearbeitet sowie rechenintensive Identifikationsmethoden mit einfacheren verglichen.

In the first part of this work we generalize a method of building optimal confidence bounds provided in Buehler (1957) by specializing an exhaustive class of confidence regions inspired by Sterne (1954). The resulting confidence regions, also called Buehlerizations, are valid in general models and depend on a designated statistic'' that can be chosen according to some desired monotonicity behaviour of the confidence region. For a fixed designated statistic, the thus obtained family of confidence regions indexed by their confidence level is nested. Buehlerizations have furthermore the optimality property of being the smallest (w.r.t. set inclusion) confidence regions that are increasing in their designated statistic. The theory is eventually applied to normal, binomial, and exponential samples. The second part deals with the statistical comparison of pairs of diagnostic tests and establishes relations 1. between the sets of lower confidence bounds, 2. between the sets of pairs of comparable lower confidence bounds, and 3. between the sets of admissible lower confidence bounds in various models for diverse parameters of interest.

Floods are hydrological extremes that have enormous environmental, social and economic consequences.The objective of this thesis was a contribution to the implementation of a processing chain that integrates remote sensing information into hydraulic models. Specifically, the aim was to improve water elevation and discharge simulations by assimilating microwave remote sensing-derived flood information into hydraulic models. The first component of the proposed processing chain is represented by a fully automated flood mapping algorithm that enables the automated, objective, and reliable flood extent extraction from Synthetic Aperture Radar images, providing accurate results in both rural and urban regions. The method operates with minimum data requirements and is efficient in terms of computational time. The map obtained with the developed algorithm is still subject to uncertainties, both introduced by the flood mapping algorithm and inherent in the image itself. In this work, particular attention was given to image uncertainty deriving from speckle. By bootstrapping the original satellite image pixels, several synthetic images were generated and provided as input to the developed flood mapping algorithm. From the analysis performed on the mapping products, speckle uncertainty can be considered as a negligible component of the total uncertainty. In the final step of the proposed processing chain real event water elevations, obtained from satellite observations, were assimilated in a hydraulic model with an adapted version of the Particle Filter, modified to work with non-Gaussian distribution of observations. To deal with model structure error and possibly biased observations, a global and a local weight variant of the Particle Filter were tested. The variant to be preferred depends on the level of confidence that is attributed to the observations or to the model. This study also highlighted the complementarity of remote sensing derived and in-situ data sets. An accurate binary flood map represents an invaluable product for different end users. However, deriving from this binary map additional hydraulic information, such as water elevations, is a way of enhancing the value of the product itself. The derived data can be assimilated into hydraulic models that will fill the gaps where, for technical reasons, Earth Observation data cannot provide information, also enabling a more accurate and reliable prediction of flooded areas.