Some New Classes of Orthogonal Polynomials and Special Functions

In dieser Dissertation präsentieren wir zunächst eine Verallgemeinerung der üblichen Sturm-Liouville-Probleme mit symmetrischen Lösungen und erklären eine umfassendere Klasse. Dann führen wir einige neue Klassen orthogonaler Polynome und spezieller Funktionen ein, welche sich aus dieser symmetrischen Verallgemeinerung ableiten lassen. Als eine spezielle Konsequenz dieser Verallgemeinerung führen wir ein Polynomsystem mit vier freien Parametern ein und zeigen, dass in diesem System fast alle klassischen symmetrischen orthogonalen Polynome wie die Legendrepolynome, die Chebyshevpolynome erster und zweiter Art, die Gegenbauerpolynome, die verallgemeinerten Gegenbauerpolynome, die Hermitepolynome, die verallgemeinerten Hermitepolynome und zwei weitere neue endliche Systeme orthogonaler Polynome enthalten sind. All diese Polynome können direkt durch das neu eingeführte System ausgedrückt werden. Ferner bestimmen wir alle Standardeigenschaften des neuen Systems, insbesondere eine explizite Darstellung, eine Differentialgleichung zweiter Ordnung, eine generische Orthogonalitätsbeziehung sowie eine generische Dreitermrekursion. Außerdem benutzen wir diese Erweiterung, um die assoziierten Legendrefunktionen, welche viele Anwendungen in Physik und Ingenieurwissenschaften haben, zu verallgemeinern, und wir zeigen, dass diese Verallgemeinerung Orthogonalitätseigenschaft und -intervall erhält. In einem weiteren Kapitel der Dissertation studieren wir detailliert die Standardeigenschaften endlicher orthogonaler Polynomsysteme, welche sich aus der üblichen Sturm-Liouville-Theorie ergeben und wir zeigen, dass sie orthogonal bezüglich der Fisherschen F-Verteilung, der inversen Gammaverteilung und der verallgemeinerten t-Verteilung sind. Im nächsten Abschnitt der Dissertation betrachten wir eine vierparametrige Verallgemeinerung der Studentschen t-Verteilung. Wir zeigen, dass diese Verteilung gegen die Normalverteilung konvergiert, wenn die Anzahl der Stichprobe gegen Unendlich strebt. Eine ähnliche Verallgemeinerung der Fisherschen F-Verteilung konvergiert gegen die chi-Quadrat-Verteilung. Ferner führen wir im letzten Abschnitt der Dissertation einige neue Folgen spezieller Funktionen ein, welche Anwendungen bei der Lösung in Kugelkoordinaten der klassischen Potentialgleichung, der Wärmeleitungsgleichung und der Wellengleichung haben. Schließlich erklären wir zwei neue Klassen rationaler orthogonaler hypergeometrischer Funktionen, und wir zeigen unter Benutzung der Fouriertransformation und der Parsevalschen Gleichung, dass es sich um endliche Orthogonalsysteme mit Gewichtsfunktionen vom Gammatyp handelt.

Capturing Emergent Semantics from Social Annotation Systems

The ongoing growth of the World Wide Web, catalyzed by the increasing possibility of ubiquitous access via a variety of devices, continues to strengthen its role as our prevalent information and commmunication medium. However, although tools like search engines facilitate retrieval, the task of finally making sense of Web content is still often left to human interpretation. The vision of supporting both humans and machines in such knowledge-based activities led to the development of different systems which allow to structure Web resources by metadata annotations. Interestingly, two major approaches which gained a considerable amount of attention are addressing the problem from nearly opposite directions: On the one hand, the idea of the Semantic Web suggests to formalize the knowledge within a particular domain by means of the "top-down" approach of defining ontologies. On the other hand, Social Annotation Systems as part of the so-called Web 2.0 movement implement a "bottom-up" style of categorization using arbitrary keywords. Experience as well as research in the characteristics of both systems has shown that their strengths and weaknesses seem to be inverse: While Social Annotation suffers from problems like, e. g., ambiguity or lack or precision, ontologies were especially designed to eliminate those. On the contrary, the latter suffer from a knowledge acquisition bottleneck, which is successfully overcome by the large user populations of Social Annotation Systems. Instead of being regarded as competing paradigms, the obvious potential synergies from a combination of both motivated approaches to "bridge the gap" between them. These were fostered by the evidence of emergent semantics, i. e., the self-organized evolution of implicit conceptual structures, within Social Annotation data. While several techniques to exploit the emergent patterns were proposed, a systematic analysis - especially regarding paradigms from the field of ontology learning - is still largely missing. This also includes a deeper understanding of the circumstances which affect the evolution processes. This work aims to address this gap by providing an in-depth study of methods and influencing factors to capture emergent semantics from Social Annotation Systems. We focus hereby on the acquisition of lexical semantics from the underlying networks of keywords, users and resources. Structured along different ontology learning tasks, we use a methodology of semantic grounding to characterize and evaluate the semantic relations captured by different methods. In all cases, our studies are based on datasets from several Social Annotation Systems. Specifically, we first analyze semantic relatedness among keywords, and identify measures which detect different notions of relatedness. These constitute the input of concept learning algorithms, which focus then on the discovery of synonymous and ambiguous keywords. Hereby, we assess the usefulness of various clustering techniques. As a prerequisite to induce hierarchical relationships, our next step is to study measures which quantify the level of generality of a particular keyword. We find that comparatively simple measures can approximate the generality information encoded in reference taxonomies. These insights are used to inform the final task, namely the creation of concept hierarchies. For this purpose, generality-based algorithms exhibit advantages compared to clustering approaches. In order to complement the identification of suitable methods to capture semantic structures, we analyze as a next step several factors which influence their emergence. Empirical evidence is provided that the amount of available data plays a crucial role for determining keyword meanings. From a different perspective, we examine pragmatic aspects by considering different annotation patterns among users. Based on a broad distinction between "categorizers" and "describers", we find that the latter produce more accurate results. This suggests a causal link between pragmatic and semantic aspects of keyword annotation. As a special kind of usage pattern, we then have a look at system abuse and spam. While observing a mixed picture, we suggest that an individual decision should be taken instead of disregarding spammers as a matter of principle. Finally, we discuss a set of applications which operationalize the results of our studies for enhancing both Social Annotation and semantic systems. These comprise on the one hand tools which foster the emergence of semantics, and on the one hand applications which exploit the socially induced relations to improve, e. g., searching, browsing, or user profiling facilities. In summary, the contributions of this work highlight viable methods and crucial aspects for designing enhanced knowledge-based services of a Social Semantic Web.

Effects of transformation processes in 'jubraka' agroforestry systems of the Nuba Mountains, Sudan, on nutrient fluxes

Intensification processes in homegardens of the Nuba Mountains, Sudan, raise concerns about strongly positive carbon (C) and nutrient balances which are expected to lead to substantial element losses from these agroecosystems, in particular via soil gaseous emissions. Therefore, this thesis aimed at the quantification of C, nitrogen (N), phosphorus (P) and potassium (K) input and output fluxes with a special focus on soil gaseous losses, and the calculation of respective element balances. A further focus in this thesis was rainfall, a valuable resource for rain-fed agriculture in the Nuba Mountains. To minimize negative consequences of the high variability of rainfall, risk reducing mechanisms were developed by rain-fed farmers that may lose their efficacy in the course of climate change effects predicted for East Africa. Therefore, the second objective of this study was to examine possible changes in rainfall amounts during the last 60 years and to provide reliable risk and probability statements of rainfall-induced events of agricultural importance to rain-fed farmers in the Nuba Mountains. Soil gaseous emissions of C (in form of CO2) and N (in form of NH3 and N2O) of two traditional and two intensified homegardens were determined with a portable dynamic closed chamber system. For C gaseous emission rates reached their peak at the onset of the rainy season (2,325 g CO2-C ha-1 h-1 in an intensified garden type) and for N during the rainy season (16 g NH3-N ha-1 h-1 and 11.3 g N2O-N ha-1 h-1, in a traditional garden type). Data indicated cumulative annual emissions of 5,893 kg CO2-C ha-1, 37 kg NH3-N ha-1, and 16 kg N2O-N ha-1. For the assessment of the long-term productivity of the two types of homegardens and the identification of pathways of substantial element losses, a C and nutrient budget approach was used. In three traditional and three intensified homegardens observation plots were selected. The following variables were quantified on each plot between June and December in 2010: soil amendments, irrigation, biomass removal, symbiotic N2 fixation, C fixation by photosynthesis, atmospheric wet and dry deposition, leaching and soil gaseous emissions. Annual balances for C and nutrients amounted to -21 kg C ha-1, -70 kg N ha-1, 9 kg P ha-1 and -117 kg K ha-1 in intensified homegardens and to -1,722 kg C ha-1, -167 kg N ha-1, -9 kg P ha-1 and -74 kg K ha-1 in traditional homegardens. For the analysis of rainfall data, the INSTAT+ software allowed to aggregate long-term daily rainfall records from the Kadugli and Rashad weather stations into daily, monthly and annual intervals and to calculate rainfall-induced events of agricultural importance. Subsequently, these calculated values and events were checked for possible monotonic trends by Mann-Kendall tests. Over the period from 1970 to 2009, annual rainfall did not change significantly for either station. However, during this period an increase of low rainfall events coinciding with a decline in the number of medium daily rainfall events was observed in Rashad. Furthermore, the availability of daily rainfall data enabled frequency and conditional probability calculations that showed either no statistically significant changes or trends resulting only in minor changes of probabilities.

Wastewater usage in urban and peri-urban agricultural production systems: scenarios from India

The role urban and peri-urban agriculture (UPA) plays in reducing urban poverty and ensuring environmental sustainability was recognized by the Millennium Development Goals (MGDs). India is the world’s largest democratic nation with a population of 1.2 billion. The rapid urbanization and high proportion of people below the poverty line along with higher migration to urban areas make India vulnerable to food crisis and urbanization of poverty. Ensuring jobs and food security among urban poor is a major challenge in India. The role of UPA can be well explained and understood in this context. This paper focuses on the current situation of UPA production in India with special attention to wastewater irrigation. This question is being posed about the various human health risks from wastewater irrigation which are faced by farmers and labourers, and, secondly by consumers. The possible health hazards involve microbial pathogens as well as helminth (intestinal parasites). Based on primary and secondary data, this paper attempts to confirm that UPA is one of the best options to address increasing urban food demand and can serve to complement rural supply chains and reduce ecological food prints in India. “Good practice urban and peri-urban agriculture” necessitates an integrated approach with suitable risk reduction mechanisms to improve the efficiency and safety of UPA production.