Die Geometrie unseres Anschauungsraumes – die euklidische Geometrie – ist für einen allgemeinbildenden Mathematikunterricht elementar. Seitens der Mathematiklehrkraft stellt grundsätzlich ihr Fachwissen das Fundament des Unterrichtens dar. Als Teil ihres Professionswissens sollten Mathematiklehrkräfte prinzipiell über ein Fachwissen verfügen, das in Bezug zur akademischen Mathematik den unterrichtlichen Anforderungen der schulischen Mathematik gerecht wird. Die im Rahmen der Dissertation entwickelte Theorie des metrisch-normalen euklidischen Raumes charakterisiert sich in ihrer perspektivischen Dualität, der mathematischen Stringenz eines axiomatisch-deduktiven Vorgehens auf der einen und der Berücksichtigung der fachdidaktischen Anforderungen an Mathematiklehrkräfte auf der anderen Seite; sie hebt sich darin von bestehenden Theorien ab.

In the last years, the public interest in epidemiology and mathematical modeling of disease spread has increased - mainly caused by the COVID-19 pandemic, which has emphasized the urgent need for accurate and timely modelling of disease transmission. However, even prior to that, mathematical modelling has been used for describing the dynamics and spread of infectious diseases, which is vital for developing effective interventions and controls, e.g., for vaccination campaigns and social restrictions like lockdowns. The forecasts and evaluations provided by these models influence political actions and shape the measures implemented to contain the virus. This research contributes to the understanding and control of disease spread, specifically for Dengue fever and COVID-19, making use of mathematical models and various data analysis techniques. The mathematical foundations of epidemiological modelling, as well as several concepts for spatio-temporal diffusion like ordinary differential equation (ODE) models, are presented, as well as an originally human-vector model for Dengue fever, and the standard (SEIR)-model (with the potential inclusion of an equation for deceased persons), which are suited for the description of COVID-19. Additionally, multi-compartment models, fractional diffusion models, partial differential equations (PDE) models, and integro-differential models are used to describe spatial propagation of the diseases. We will make use of different optimization techniques to adapt the models to medical data and estimate the relevant parameters or finding optimal control techniques for containing diseases using both Metropolis and Lagrangian methods. Reasonable estimates for the unknown parameters are found, especially in initial stages of pandemics, when little to no information is available and the majority of the population has not got in contact with the disease. The longer a disease is present, the more complex the modelling gets and more things (vaccination, different types, etc.) appear and reduce the estimation and prediction quality of the mathematical models. While it is possible to create highly complex models with numerous equations and parameters, such an approach presents several challenges, including difficulties in comparing and evaluating data, increased risk of overfitting, and reduced generalizability. Therefore, we will also consider criteria for model selection based on fit and complexity as well as the sensitivity of the model with respect to specific parameters. This also gives valuable information on which political interventions should be more emphasized for possible variations of parameter values. Furthermore, the presented models, particularly the optimization using the Metropolis algorithm for parameter estimation, are compared with other established methods. The quality of model calculation, as well as computational effort and applicability, play a role in this comparison. Additionally, the spatial integro-differential model is compared with an established agent-based model. Since the macroscopic results align very well, the computationally faster integro-differential model can now be used as a proxy for the slower and non-traditionally optimizable agent-based model, e.g., in order to find an apt control strategy.

Leitfrage: Inwieweit ist der Physikdidaktiker und Pädagoge Martin Wagenschein heute noch relevant? Antwort: Er ist!

Wie hingen Sprache und Gewalt im Nationalsozialismus zusammen? Ausgehend von der konstitutiven Sprachphilosophie des kanadischen Philosophen Charles Taylor untersucht die Dissertation die destruktive Wirkmacht der Sprache am Fall des Nationalsozialismus, der auf ungekannte Weise in die Sprache eingriff und damit Gewalt begünstigte, die bis heute ohnegleichen ist.

Efforts to induce customers to buy groceries through the Internet have existed for around twenty years. Early on, the market structures of the digital grocery trade were still strongly fragmented and poorly coordinated. Due to the technological advancement in the past decade, the digital purchase of groceries has become more attractive. The adoption rate of these services varies greatly between different regions. In Germany in particular, the digital grocery trade is stagnating at a comparatively low level. In this regard, this dissertation analyzes both the retail-side market structures and the expectations and obstacles of German consumers. The year 2020 connotes a turning point for the online grocery trade, as daily routines such as grocery shopping were subject to strict regulations imparted at a governmental level in order to reduce COVID-19 infections. At the same time, despite this opportunity, the digital grocery trade has not yet established itself nationwide in Germany. This can be attributed to a lack of investments, but also to inadequate digitization measures. A stronger synchronization between the digital and stationary offer, better integration of digital food services at a regional level as well as adapted, target group-appropriate digital solutions for the efficient breakdown of usage barriers will benefit service usage. The importance of stable food chains and distribution channels was illustrated by the COVID-19 pandemic. Further research should help to develop the digital food trade into a stable and sustainable supplementation of the stationary store.

Today’s agriculture heavily relies on pesticides to manage diverse pests and maximise crop yields. Despite elaborate regulation of pesticide use based on a complex environmental risk assessment (ERA) scheme, the widespread use of these biologically active compounds has been shown to be a threat to the environment. For surface waters, pesticide exposure has been observed to exceed safe concentration levels and negatively impact stream ecology leading to the question whether current ERA schemes ensure a sustainable use of pesticides. To answer this, the large-scale “Kleingewässer-Monitoring” (KgM) assessed the occurrence of pesticides and related effects in 124 streams throughout Germany, Central Europe, in 2018 and 2019. Based on five scientific publications originating from the KgM, this thesis evaluated pesticide exposure in streams, ecological effects and the regulatory implications. More than 1,000 water samples were analysed for over 100 pesticide analytes to characterise occurrence patterns (publication 1). Measured concentrations and effects were used to validate the exposure and effect concentrations predicted in the ERA (publication 2). By jointly analysing real-world pesticide application data and measured pesticide mixtures in streams, the disregard of environmental pesticide mixtures in the ERA was evaluated (publication 3). The toxic potential of mixtures in stream water was additionally investigated using suspect screening for 395 chemicals and a battery of in-vitro bioassays (publication 4). Finally, the results from the KgM stream monitoring were used to assess the capability to identify pesticide risks in governmental monitoring programmes (publication 5). The results of this thesis reveal the widespread occurrence of pesticides in non-target stream ecosystems. The water samples contained a variety of pesticides occurring in complex mixtures predominantly in short-term peaks after rainfall events (publications 1 & 4). Respective pesticide concentration maxima were linked to declines in vulnerable invertebrate species and exceeded regulatory acceptable concentrations in about 80% of agricultural streams, while these thresholds were still estimated partly insufficient to protect the invertebrate community (publication 2). The co-occurrence of pesticides in streams led to a risk underestimated in the single substance-oriented ERA by a factor of about 3.2 in realistic worst-case scenarios, which is further exacerbated by a high frequency at which non-target organism are exposed to pesticides (publication 3). Stream water samples taken after rainfall caused distinct effects in bioassays which were only explainable to a minor extent by the many analytes, indicating the relevance of unknown chemical or biological mixture components (publication 4). Finally, the regulatory monitoring of surface waters under the Water Framework Directive (WFD) was found to significantly underestimate pesticide risks, as about three quarters of critical pesticides and more than half of streams at risk were overlooked (publication 5). Essentially, this thesis involves a new level of validation of the ERA of pesticides in aquatic ecosystems by assessing pesticide occurrence and environmental impacts at a scale so far unique. The overall results demonstrate that the current agricultural use of pesticides leads to significant impacts on stream ecology that go beyond the level tolerated under the ERA. This thesis identified the underestimation of pesticide exposure, the potential insufficiency of regulatory thresholds and the general inertia of the authorisation process as the main causes why the ERA fails to meet its objectives. To achieve a sustainable use of pesticides, the thesis proposes substantial refinements of the ERA. Adequate monitoring programmes such as the KgM, which go beyond current government monitoring efforts, will continue to be needed to keep pesticide regulators constantly informed of the validity of their prospective ERA, which will always be subject to uncertainty.

This thesis was motivated by the need to advance the knowledge on the variability and dynamics of energy fluxes in lakes and reservoirs, as well as about the physical processes that regulate the fluxes at both the air and water side of the air-water interface. In the first part, I re-examine how mechanical energy, resulting from its major source – the vertical wind energy flux - distributes into the various types of water motions, including turbulent flows and surface and internal waves. Although only a small fraction of the wind energy flux from the atmosphere is transferred to the water, it is crucial for physical, biogeochemical and ecological processes in lentic ecosystems. Based on extensive air- and water-side measurements collected at two small water bodies (< 10 km2), we estimated the energy fluxes and energy content in surface and in internal waves. Overall, the estimated energy fluxes and energy content agree well with results reported for larger water bodies, suggesting that the energetics driving the water motions in enclosed basins is similar, independently of the basin size. Our findings highlight the importance of the surface waves that receive the largest fraction of the wind energy flux, which strongly nonlinearly increases for wind speeds exceeding 3 m s-1. We found that the existing parameterization of the wave height as a function of wind speed and fetch length did not reproduce the measured wave amplitude in lakes. On average, the highest energy content was observed in basin-scale internal waves, together with high-frequency internal waves exhibiting seasonal variability and varies among the aquatic systems. During our analysis, we discovered the diurnal variability of the energy dissipation rates in the studied lake, suggesting biogenic turbulence generation, which appears to be a widespread phenomenon in lakes and reservoirs. In the second part of the thesis, I addressed current knowledge gaps related to the bulk transfer coefficients (also known as the drag coefficient, the Stanton number and the Dalton number), which are of a particular importance for the bulk estimation of the surface turbulent fluxes of momentum, sensible and latent heat in the atmospheric boundary layer. Their inaccurate representation may lead to significant errors in flux estimates, affecting, for example, the weather and climate predictions or estimations of the near-surface current velocities in lake hydrodynamic models. Although the bulk transfer coefficients have been extensively studied over the past several decades (mainly in marine and large-lake environments), there has been no systematic analysis of measurements obtained at lakes of different size. A significant increase of the transfer coefficients at low wind speeds (< 3 m s-1) has been observed in several studies, but, to date, it has remained unexplained. We evaluated the bulk transfer coefficients using flux measurements from 31 lakes and reservoirs. The estimates were generally within the range reported in previous studies for large lakes and oceans. All transfer coefficients increased substantially at low wind speeds, which was found to be associated with the presence of gusts and capillary waves (except the Dalton number). We found that the Stanton number is systematically higher than the Dalton number. This challenges the assumption made in the Bowen-ratio method, which is widely used for estimating evaporation rates from micrometeorological measurements. We found that the variability of the transfer coefficients among the lakes could be associated with lake surface area. In flux parameterizations at lake surfaces, it is recommended to consider variations in the drag coefficient and the Stanton number due to wind gustiness and capillary wave roughness while the Dalton number could be considered as constant at all wind speeds. In the third part of the thesis, I address the key drivers of the near-surface turbulence that control the gas exchange in a large regulated river. As all inland waters, rivers are an important natural source of greenhouse gases. The effects of the widespread alteration and regulation of river flow for human demands on gas exchange is largely unknown. In particular, the near-surface turbulence in regulated rivers has been rarely measured and its drivers have not been identified. While in lakes and reservoirs, near-surface turbulence is mainly related to atmospheric forcing, in shallow rivers and streams it is generated by bottom friction of the gravity-forced flow. The studied large regulated river represents a transition between these two cases. Atmospheric forcing and gravity were the dominant drivers of the near-surface turbulence for a similar fraction of the measurement period. Based on validated scalings, we derived a simple model for estimating the relative contributions of wind and bottom friction to near-surface turbulence in lotic ecosystems with different flow depths. Large diel variability in the near-surface energy dissipation rates due to flow regulation leads to the same variability in gas exchange. This suggests that estimates of gas fluxes from rivers are biased by measurements performed predominantly during daytime. In addition, the novelty in all the analyses described above is the use of the turbulent surface fluxes measured directly by the eddy-covariance technique – at the moment of writing, the most advanced method. Overall, this thesis is of a potential interest for a broad range of scientific disciplines, including limnology, micrometeorology and open channel hydraulics.

This dissertation is dedicated to a new concept for capturing renunciation-oriented attitudes and beliefs — sufficiency orientation. Sufficiency originates in the interdisciplinary sustain-ability debate. In contrast to efficiency and consistency, sufficiency considers human behaviour as the cause of socio-ecological crises and strives for a reduction in consumption respecting the planetary boundaries. The present work places sufficiency in a psychological research context and explores it qualitatively and quantitatively. On the basis of five manuscripts, the overarching question pursued is to what extent sufficiency orientation contributes to socio-ecological transformation. Based on one qualitative study and five further quantitative studies, sufficiency orientation is investigated in different behavioural contexts that are of particular importance with regard to CO2 emissions. In addition, sufficiency orientation is linked to a wider range of psychologically relevant theories that help gain an overview of correlates and possible causes for the development of a sufficiency orientation. Manuscript 1 uses expert interviews (N = 21) to develop a heuristic framework on a transformation towards societal sufficiency orientation including barriers and enablers, as well as ambiguities on such a change. The derived elements are interpreted in the light of the leverage points approach. This framework can serve as a heuristic for future research and to develop measures concerning sufficiency orientation. As part of an online study (N = 648), Manuscript 2 examines the extent to which sufficiency orientation can be embedded in classic models for explaining pro-environmental intentions and behaviour (Theory of Planned Behaviour, Norm Activation Model), and showed a significant contribution to the explanation of intentions and behaviour in the field of plastic consumption. Manuscript 3 reports two framing experiments (Study 1, N = 123, Study 2, N = 330) to investigate how pro-social justice sensitivity contributes to making sufficiency orientation more salient and promoting it. While sufficiency orientation and pro-social facets of justice sensitivity were positively related to each other, there was no effect of the framing intervention in the hypothesised direction. The results indicate that justice-related information at least in the presented manner is more likely to generate reactance. Manuscript 4 presents an online study (N = 317) and targets the importance of sufficiency orientation for predicting actual greenhouse gas emissions in relation to flight behav-iour and policy support for the decarbonisation of mobility. In addition, the connection between sufficiency orientation and global identity is examined. It turns out that sufficiency orientation is superior to global identity in predicting actual emissions and decarbonisation policies. Contrary to expectations, sufficiency orientation and the form of global identity operationalised in the presented study shows a positive correlation and are compatible. Manuscript 5 reports a reflective diary intervention (N = 252) that should lead to a short- and long-term increase in sufficiency orientation by satisfying basic psychological needs through induced self-reflection. For both groups with or without the intervention, sufficiency orientation increased slightly but significantly. Although no specific effect of the manipulation was found, basic psychological need satisfaction turns out to be the largest predictor for sufficiency orientation. Subjective well-being is positively associated with sufficiency orientation, while time affluence shows no clear associations in the study. Overall, the results highlight the relevance of sufficiency orientation in relation to socio-ecological transformation and actual behavioural change. Sufficiency orientation is related to low-emission behaviour and support for political measures to decarbonize infrastructures. These results contribute to the discussion on the intention-behaviour gap in regard to impact-relevant behaviour, i.e. behaviour producing high emissions. The present findings suggest, that sufficiency orientation could be related to a strong intention-behavioural consistency. However, further research is needed to validate these results and improve the measurement of sufficiency orientation. Furthermore, the studies provided insights on correlates of sufficiency orientation: justice sensitivity, global identity, subjective well-being and left-wing liberal political ideologies are all found to be positively related to sufficiency orien-tation. Moreover, basic psychological need satisfaction was identified as a potential mechanism that can support the emergence of sufficiency orientation, however, causality remains unclear. From these findings, the work derives practical implications how to possibly strengthen sufficiency orientation on the micro, meso and macro levels of society. Taken together, the dissertation provides important insights into a new and still developing concept, and shows its connectivity to psychological theories. However, future research is required in order to grasp more precisely the complexity of sufficiency orientation and to understand origins and predictors of sufficiency orientation. This work contributes to the interdisciplinary debate on socio-ecological transformation and points out that sufficiency orientation can serve to a future worth living as being related to reduced consumption.

This study examines the contribution of saving and credit cooperatives (SACCOS) on the improvement of members‘ socio economic development in Rwanda: Opportunities and challenges‖, Evidence from Umwalimu SACCO- Huye District‖. The appearance of saving and credit cooperatives or credit unions has been known as remedy for social ills rooted in poverty because of its efficiency in loans or credits dispensation, social equality for enhancement and reduction of poverty amongst low income earners. Therefore, millions and millions of poor people and non-bankable in developing countries (or third world countries) have been provided access to formal financial services through saving and credit cooperatives‘ programs. The targeted population concerned by the study was 1,940 members of USACCO from which a sample of 92 respondents was purposively selected. The study has adopted a combination of correlation and descriptive research design. It has employed both quantitative and qualitative approaches. The study used both primary and secondary data. The primary data was collected using questionnaire and interview and, while secondary data was collected using documentations techniques whereby, Manual of procedures and Credit policies of USACCO and financial reports have been consulted. The analysis of data was done using SPSS version 21. The data was presented in form of tables, charts and graphs designed by SPSS v. 21. The bio-characteristics of respondents showed that, the majority of respondents were women with 55.4%, majority of respondents‘ age is between 26 to 45 years Furthermore, and majority 77.20% of respondents were married. 100% of respondents attended school, where the majority of respondents attended secondary school with certificate A2. The study has revealed that Umwalimu SACCO services offered to its members have a positive effect on the improvement of members‘ welfare. It was found that USACCO services have slightly affected income level of members, assets acquired, access to education and medical care as well as small income generating activities established by members in Huye District. The analysis of data also revealed that there are some variables which have effected USACCO members‘ socio-economic status, these were listed as: Education background of a member, number of dependents, the occupation of a member, and number of loans got from USACCO, government programs against teachers‘ welfare, and membership duration played very important role on the improvement of standard living of teachers. All these variables were found to have positive effects on teachers‘ socio-economic status, except the family size of respondents. In addition, the findings showed that, the majority of respondents confirmed that, they did not find opportunities to save with other financial institutions, and other respondents did not have access to loan from other financial institutions due to complicated loan requirements. In addition, after they have joined USACCO, their deplorable status somewhat changed, both socially and economically which has contributed to the improvement of their welfare. Therefore, the study testified that, the welfare of USACCO members in terms of assets acquired, income increased was improved compared to situation before joining USACCO. The study concludes that ―the level of improvement of living conditions of teachers depends largely to the level of loan granted by USACCO to teachers and membership duration. If the level of teachers‘ loan and saving increases, there will be also improvement of teachers‘ wellbeing‖ and finally, USACCO financial service is a veritable instrument for better improvement of economic and social conditions of teachers. The study recommends that, USACCO should provide frequent and regular trainings on business management game to their members. This could help members for good management of their loans and reducing loan defaulters‘ cases observed at USACCO. Challenges observed were lack of physical collateral security required by USACCO, complicated loan requirements terms and conditions and insufficient trainings on business management game.

The presented study was motivated by the dynamic phenomena observed in basic catalytic surface reactions, especially by bi- and tristability, and the interactions between these stable states. In this regard, three reaction-diffusion models were developed and examined using bifurcation theory and numerical simulations. A first model was designed to extend the bistable CO oxidation on Ir(111) to include hydrogen and its oxidation. The differential equation system was analyzed within the framework of bifurcation theory, revealing three branches of stable solutions. One state is characterized by high formation rates (upper rate state, UR), while the other two branches display low formation rates (lower rate (LR) \& very low rate (VLR) states). The overlapping branches form the shape of a `swallowtail', the curve of saddle-node bifurcations forming two cusps. Increasing the temperature leads to a subsequent unfolding and hence decreases the system complexity. A series of numerical simulations representing possible experiments was conducted to illustrate the experimental accessibility (or the lack) of said states. Relaxation experiments show partially long decay times. Quasistatic scanning illustrates the existence of all three states within the tristable regime and their respective conversion once crossing a fold. A first attempt regarding the state dominance in reaction-diffusion fronts was done. While UR seems to dominate in 1D, a 2D time-evolution shows that LR invades the interphase between UR and VLR. Subsequently, a generic monospecies mock model was used for the comprehensive study of reaction-diffusion fronts. A quintic polynomial as reaction term was chosen, derived by the sixth-order potential associated with the `butterfly bifurcation'. This ensures up to three stable solutions($u_{0}$,$u_{1}$,$u_{2}$), depending on the four-dimensional parameter space. The model was explored extensively, identifying regions with similar behaviors. A term for the front velocity connecting two stable states was derived, depending only on the relative difference of the states' potential wells. Equipotential curves were found, where the front velocity vanishes of a given front. Numerical simulations on a two-dimensional, finite disk using a triangulated mesh supported these findings. Additionally, the front-splitting instability was observed for certain parameters. The front solution $u_{02}$ becomes unstable and divides into $u_{01}$ and $u_{12}$, exhibiting different front velocities. A good estimate for the limit of the front splitting region was given and tested using time evolutions. Finally, the established mock model was modified from continuous to discrete space, utilizing a simple domain in 1D and three different lattices in 2D (square, hexagonal, triangular). For low diffusivities or large distances between coupling nodes, fronts can become pinned, if the parameters are within range of the equipotential lines. This phenomenon is known as propagation failure and its extent in parameter space was explored in 1D. In 2D, an estimate was given for remarkable front orientations respective to the lattice using a pseudo-2D approximation. Near the pinning region, front velocities differ significantly from the continuous expectation as the shape of the curve potential becomes significant. Factors that decide the size and shape of the pinning regions are the coupling strength, the lattice, the front orientation relative to the lattice, and the front itself. The bifurcation diagram shows a snaking curve in the pinning region, each alternating branch representing a stable or unstable frozen front solution. Numerical simulations supported the observations concerning propagation failure and lattice dependence. Furthermore, the influence of front orientation on the front velocity was explored in greater detail, showing that fronts with certain lattice-dependent orientations are more or less prone to propagation failure. This leads to the possibility of pattern formation, reflecting the lattice geometry. An attempt to quantify the front movement depending on angular front orientation has shown reasonable results and good agreement with the pseudo-2D approach.