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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.

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.

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.

The last decades of stress research have yielded substantial advancements highlighting the importance of the phenomenon for basic psychological functions as well as physical health and well-being. Progress in stress research heavily relies on the availability of suitable and well validated laboratory stressors. Appropriate laboratory stressors need to be able to reliably provoke a response in the relevant parameters and be applicable in different research settings or experimental designs. This thesis focuses on the Cold Pressor Test (CPT) as a stress induction technique. Three published experiments are presented that show how the advantages of the CPT can be used to test stress effects on memory processes and how some of its disadvantages can be met by a simple modification that retains its feasibility and validity. The first experiment applies the CPT in a substantial sample to investigate the consolidation effects of post-learning sympathetic arousal. Stressed participants with high increases in heart rate during the CPT showed enhanced memory performance one day after learning compared to both the warm water control group and low heart rate responders. This finding suggests that beta-adrenergic activation elicited shortly after learning enhances memory consolidation and that the CPT induced heart rate response is a predictor for this effect. Moreover, the CPT proved to be an appropriate stressor to test hypothesis about endogenous adrenergic effects on memory processes. The second experiment addresses known practical limitations of the standard dominant hand CPT protocol. A bilateral feet CPT modification is presented, the elicited neuroendocrine stress response assessed and validated against the standard CPT in a within-subjects design. The bilateral feet CPT elicited a substantial neuroendocrine stress response. Moreover, with the exception of blood pressure responses, all stress parameters were enhanced compared to the standard CPT. This shows that the bilateral feet CPT is a valid alternative to the standard CPT. The third experiment further validates the bilateral feet CPT and its corresponding control procedure by employing it in a typical application scenario. Specifically, the bilateral feet CPT was used to modulate retrieval of event files in a distractor-response binding paradigm that required lateralized bimanual responses. Again, the bilateral feet CPT induced significant increases in heart rate, blood pressure and cortisol, no such increases could be observed in the warm water control condition. Moreover, stressed participants showed diminished retrieval compared to controls. These results provide further evidence for the feasibility and validity of the bilateral feet CPT and its warm water control procedure. Together the experiments presented here highlight the usefulness of the CPT as a tool in psychophysiological stress research. It is especially well suited to test hypothesis concerning stress effects on memory processes and its applicability can be further increased by the bilateral feet modification.

Climate change and habitat fragmentation modify the natural habitat of many wetland biota and lead to new compositions of biodiversity in these ecosystems. While the direct effects of climate are often well known, indirect effects due to biotic interactions remain poorly understood. The water meadow grasshopper, Chorthippus montanus, is a univoltine habitat specialist, which is adapted to permanently moist habitats. Land use change and drainage led to highly fragmented populations of this generally flightless species. In large parts of the Palaearctic Ch. montanus occurs sympatrically with its widespread congener, the meadow grasshopper Chorthippus parallelus. Due to their close relationship and their similar songs, hybridization is likely to occur in syntopic populations. Such a species pair of a habitat specialist and a habitat generalist represents an ideal model system to examine the role of ongoing climate change and an accumulation of extreme climatic events on the life history strategies, population dynamics and inter-specific interactions. In Chapter I a laboratory experiment was conducted to identify the impact of environmental factors on intra-specific life-history traits of Ch. montanus. Like other Orthoptera species, Ch. montanus follows a converse temperature size rule. In line with the dimorphic niche hypothesis, which states that sexual size dimorphism evolved in response to the different sexual reproductive roles, both sexes showed different responses to increasing density at lower temperatures. Males attained smaller body sizes at high densities, whereas females had a prolonged development time. This is the first evidence for a sex-specific phenotypic plasticity in Ch. montanus. Females benefit from the prolonged development as their reproductive success depends on the size and number of egg clutches they may produce. By contrast, the reproductive success of males depends on the chance to fertilize virgin females, which increases with faster development. This may become a disadvantage for Ch. montanus as an intraspecific phenology shift may increase hybridization risk with the sibling species. Despite the widespread assumption that hybridization between two sympatric species is rare due to complete reproductive barriers, the genetic analyses of 16 populations (Chapter II) provided evidence for wide prevalence of hybridization between both species in the wild. As no complete admixture was found in the examined population, it is assumed that hybridization only occurs in ecotones between wetlands and drier parts. Reproductive barriers (habitat isolation, behavior, phenology) seem to prevent the genetic swamping of Ch. montanus populations. Although a behavioral experiment showed that mate choice presents an important reproductive barrier between both species, the experiment also revealed that reproductive barriers could be altered by environmental change (e.g. increasing heterospecific frequency). Chapter III analyzes the impact of extreme climatic events on population dynamics and interspecific hybridization. A mark-recapture analysis combined with weather records over five years provides evidence that the embryonic development in Ch. montanus is vulnerable to extreme climatic events. Strong population declines in Ch. montanus lead to a disequilibrium between Ch. montanus and Ch. parallelus populations and increases the risk of hybridization. The highest hybridization risk was found in the first weeks of a season, when both species had an overlapping phenology. Furthermore, hybrids were generally localized at the edge of the Ch. montanus distribution with higher heterospecific encounter probabilities. The hybridization rate reached up to 19.6%. The genetic analyses in Chapter II and III show that hybridization differentially affects specialists and generalists. While generalists may benefit from hybridization by an increasing genetic diversity, such a positive correlation was not found for Ch. montanus. The results underline the importance of reproductive barriers for the co-existence of these sympatric species. However, climate change and other anthropogenic disturbances alter reproductive barriers and promote hybridization, which may threaten small populations by genetic displacement. As anthropogenic hybridization is recognized as a major threat to biodiversity, it should be considered in environmental law and policy. In Chapter IV the role of hybrids and hybridization in three levels of law and the historical backgrounds of hybrids becoming a part of legal instruments is analyzed. Due to legal uncertainties and the complexity of this topic a legal assessment of hybrids is challenging and argues for species-specific approaches. Nonetheless, existing legal norms provide a suitable basis, but need to be specified. Finally, this chapter discusses different opportunities for the management of hybrids and hybridization in a conservation perspective and their necessity.

The classic Capital Asset Pricing Model and the portfolio theory suggest that investors hold the market portfolio to diversify idiosyncratic risks. The theory predicts that expected return of assets is positive and that reacts linearly on the overall market. However, in reality, we observe that investors often do not have perfectly diversified portfolios. Empirical studies find that new factors influence the deviation from the theoretical optimal investment. In the first part of this work (Chapter 2) we study such an example, namely the influence of maximum daily returns on subsequent returns. Here we follow ideas of Bali et al. (2011). The goal is to find cross-sectional relations between extremely positive returns and expected average returns. We take account a larger number of markets worldwide. Bali et al. (2011) report with respect to the U.S. market a robust negative relation between MAX (the maximum daily return) and the expected return in the subsequent time. We extent substantially their database to a number of other countries, and also take more recent data into account (until end of 2009). From that we conclude that the relation between MAX and expected returns is not consistent in all countries. Moreover, we test the robustness of the results of Bali et al. (2011) in two time-periods using the same data from CRSP. The results show that the effect of extremely positive returns is not stable over time. Indeed we find a negative cross-sectional relation between the extremely positive returns and the average returns for the first half of the time series, however, we do not find significant effects for the second half. The main results of this chapter serve as a basis for an unpublished working paper Yuan and Rieger (2014b). While in Chapter 2 we have studied factors that prevent optimal diversification, we consider in Chapter 3 and 4 situations where the optimal structure of diversification was previously unknown, namely diversification of options (or structured financial products). Financial derivatives are important additional investment form with respect to diversification. Not only common call and put options, but also structured products enable investors to pursue a multitude of investment strategies to improve the risk-return profile. Since derivatives become more and more important, diversification of portfolios with dimension of derivatives is of particularly practical relevance. We investigate the optimal diversification strategies in connection with underlying stocks for classical rational investors with constant relative risk aversion (CRRA). In particular, we apply Monte Carlo method based on the Black-Scholes model and the Heston model for stochastic volatility to model the stock market processes and the pricing of the derivatives. Afterwards, we compare the benchmark portfolio which consists of derivatives on single assets with derivatives on the index of these assets. First we compute the utility improvement of an investment in the risk-free assets and plain-vanilla options for CRRA investors in various scenarios. Furthermore, we extend our analysis to several kinds of structured products, in particular capital protected notes (CPNs), discount certificates (DCs) and bonus certificates (BCs). We find that the decision of an investor between these two diversification strategies leads to remarkable differences. The difference in the utility improvement is influenced by risk-preferences of investors, stock prices and the properties of the derivatives in the portfolio. The results will be presented in Chapter 3 and are the basis for a yet unpublished working paper Yuan and Rieger (2014a). To check furthermore whether underlyings of structured products influence decisions of investors, we discuss explicitly the utility gain of a stock-based product and an index-based product for an investor whose preferences are described by cumulative prospect theory (CPT) (Chapter 4, compare to Yuan (2014)). The goal is that to investigate the dependence of structured products on their underlying where we put emphasis on the difference between index-products and single-stock-products, in particular with respect to loss-aversion and mental accounting. We consider capital protected notes and discount certificates as examples, and model the stock prices and the index of these stocks via Monte Carlo simulations in the Black-Scholes framework. The results point out that market conditions, particularly the expected returns and volatility of the stocks play a crucial role in determining the preferences of investors for stock-based CPNs and index-based CPNs. A median CPT investor prefers the index-based CPNs if the expected return is higher and the volatility is lower, while he prefers the stock-based CPNs in the other situation. We also show that index-based DCs are robustly more attractive as compared to stock-based DCs for CPT investors.