A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.

Konzeption eines generischen Vorgehensmodells zur strategieorientierten und partizipativen Einführung komplexer Softwaresysteme unter Berücksichtigung organisatorischer Gestaltungsprozesse

Die Dissertation befasst sich mit der Einführung komplexer Softwaresysteme, die, bestehend aus einer Kombination aus parametrisierter Standardsoftware gepaart mit Wettbewerbsvorteil sichernden Individualsoftwarekomponenten, keine Software-Engineering-Projekte im klassischen Sinn mehr darstellen, sondern einer strategieorientierten Gestaltung von Geschäftsprozessen und deren Implementierung in Softwaresystemen bedürfen. Die Problemstellung einer adäquaten Abwägung zwischen TCO-optimierender Einführung und einer gleichzeitigen vollständigen Unterstützung der kritischen Erfolgsfaktoren des Unternehmens ist hierbei von besonderer Bedeutung. Der Einsatz integrierter betriebswirtschaftlicher Standardsoftware, mit den Möglichkeiten einer TCO-Senkung, jedoch ebenfalls der Gefahr eines Verlustes von Alleinstellungsmerkmalen am Markt durch Vereinheitlichungstendenzen, stellt ein in Einführungsprojekten wesentliches zu lösendes Problem dar, um Suboptima zu vermeiden. Die Verwendung von Vorgehensmodellen, die sich oftmals an klassischen Softwareentwicklungsprojekten orientieren oder vereinfachte Phasenmodelle für das Projektmanagement darstellen, bedingt eine fehlende Situationsadäquanz in den Detailsituationen der Teilprojekte eines komplexen Einführungsprojektes. Das in dieser Arbeit entwickelte generische Vorgehensmodell zur strategieorientierten und partizipativen Einführung komplexer Softwaresysteme im betriebswirtschaftlichen Anwendungsbereich macht - aufgrund der besonders herausgearbeiteten Ansätze zu einer strategieorientierten Einführung, respektive Entwicklung derartiger Systeme sowie aufgrund der situationsadäquaten Vorgehensstrategien im Rahmen der Teilprojektorganisation � ein Softwareeinführungsprojekt zu einem Wettbewerbsfaktor stärkenden, strategischen Element im Unternehmen. Die in der Dissertation diskutierten Überlegungen lassen eine Vorgehensweise präferieren, die eine enge Verschmelzung des Projektes zur Organisationsoptimierung mit dem Softwareimplementierungsprozess impliziert. Eine Priorisierung der Geschäftsprozesse mit dem Ziel, zum einen bei Prozessen mit hoher wettbewerbsseitiger Priorität ein organisatorisches Suboptimum zu vermeiden und zum anderen trotzdem den organisatorischen Gestaltungs- und den Systemimplementierungsprozess schnell und ressourcenschonend durchzuführen, ist ein wesentliches Ergebnis der Ausarbeitungen. Zusätzlich führt die Ausgrenzung weiterer Prozesse vom Einführungsvorgang zunächst zu einem Produktivsystem, welches das Unternehmen in den wesentlichen Punkten abdeckt, das aber ebenso in späteren Projektschritten zu einem System erweitert werden kann, welches eine umfassende Funktionalität besitzt. Hieraus ergeben sich Möglichkeiten, strategischen Anforderungen an ein modernes Informationssystem, das die kritischen Erfolgsfaktoren eines Unternehmens konsequent unterstützen muss, gerecht zu werden und gleichzeitig ein so weit als möglich ressourcenschonendes, weil die Kostenreduktionsaspekte einer Standardlösung nutzend, Projekt durchzuführen. Ein weiterer wesentlicher Aspekt ist die situationsadäquate Modellinstanziierung, also die projektspezifische Anpassung des Vorgehensmodells sowie die situationsadäquate Wahl der Vorgehensweisen in Teilprojekten und dadurch Nutzung der Vorteile der verschiedenen Vorgehensstrategien beim konkreten Projektmanagement. Der Notwendigkeit der Entwicklung einer Projektorganisation für prototypingorientiertes Vorgehen wird in diesem Zusammenhang ebenfalls Rechnung getragen. Die Notwendigkeit der Unternehmen, sich einerseits mit starken Differenzierungspotenzialen am Markt hervorzuheben und andererseits bei ständig sinkenden Margen einer Kostenoptimierung nachzukommen, lässt auch in Zukunft das entwickelte Modell als erfolgreich erscheinen. Hinzu kommt die Tendenz zu Best-Of-Breed-Ansätzen und komponentenbasierten Systemen im Rahmen der Softwareauswahl, die eine ausgesprochen differenzierte Vorgehensweise in Projekten verstärkt notwendig machen wird. Durch die in das entwickelte Modell integrierten Prototyping-Ansätze wird der auch in Zukunft an Bedeutung gewinnenden Notwendigkeit der Anwenderintegration Rechnung getragen.

A generic formula for the values at the boundary points of monic classical orthogonal polynomials

In a previous paper we have determined a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type σ(x)y"n(x)+τ(x)y'n(x)-λnyn(x)=0. In this paper, we give another such formula which enables us to present a generic formula for the values of monic classical orthogonal polynomials at their boundary points of definition.

Design, implementation and application of a generic framework for integrated regional land-use modeling

Land use is a crucial link between human activities and the natural environment and one of the main driving forces of global environmental change. Large parts of the terrestrial land surface are used for agriculture, forestry, settlements and infrastructure. Given the importance of land use, it is essential to understand the multitude of influential factors and resulting land use patterns. An essential methodology to study and quantify such interactions is provided by the adoption of land-use models. By the application of land-use models, it is possible to analyze the complex structure of linkages and feedbacks and to also determine the relevance of driving forces. Modeling land use and land use changes has a long-term tradition. In particular on the regional scale, a variety of models for different regions and research questions has been created. Modeling capabilities grow with steady advances in computer technology, which on the one hand are driven by increasing computing power on the other hand by new methods in software development, e.g. object- and component-oriented architectures. In this thesis, SITE (Simulation of Terrestrial Environments), a novel framework for integrated regional sland-use modeling, will be introduced and discussed. Particular features of SITE are the notably extended capability to integrate models and the strict separation of application and implementation. These features enable efficient development, test and usage of integrated land-use models. On its system side, SITE provides generic data structures (grid, grid cells, attributes etc.) and takes over the responsibility for their administration. By means of a scripting language (Python) that has been extended by language features specific for land-use modeling, these data structures can be utilized and manipulated by modeling applications. The scripting language interpreter is embedded in SITE. The integration of sub models can be achieved via the scripting language or by usage of a generic interface provided by SITE. Furthermore, functionalities important for land-use modeling like model calibration, model tests and analysis support of simulation results have been integrated into the generic framework. During the implementation of SITE, specific emphasis was laid on expandability, maintainability and usability. Along with the modeling framework a land use model for the analysis of the stability of tropical rainforest margins was developed in the context of the collaborative research project STORMA (SFB 552). In a research area in Central Sulawesi, Indonesia, socio-environmental impacts of land-use changes were examined. SITE was used to simulate land-use dynamics in the historical period of 1981 to 2002. Analogous to that, a scenario that did not consider migration in the population dynamics, was analyzed. For the calculation of crop yields and trace gas emissions, the DAYCENT agro-ecosystem model was integrated. In this case study, it could be shown that land-use changes in the Indonesian research area could mainly be characterized by the expansion of agricultural areas at the expense of natural forest. For this reason, the situation had to be interpreted as unsustainable even though increased agricultural use implied economic improvements and higher farmers' incomes. Due to the importance of model calibration, it was explicitly addressed in the SITE architecture through the introduction of a specific component. The calibration functionality can be used by all SITE applications and enables largely automated model calibration. Calibration in SITE is understood as a process that finds an optimal or at least adequate solution for a set of arbitrarily selectable model parameters with respect to an objective function. In SITE, an objective function typically is a map comparison algorithm capable of comparing a simulation result to a reference map. Several map optimization and map comparison methodologies are available and can be combined. The STORMA land-use model was calibrated using a genetic algorithm for optimization and the figure of merit map comparison measure as objective function. The time period for the calibration ranged from 1981 to 2002. For this period, respective reference land-use maps were compiled. It could be shown, that an efficient automated model calibration with SITE is possible. Nevertheless, the selection of the calibration parameters required detailed knowledge about the underlying land-use model and cannot be automated. In another case study decreases in crop yields and resulting losses in income from coffee cultivation were analyzed and quantified under the assumption of four different deforestation scenarios. For this task, an empirical model, describing the dependence of bee pollination and resulting coffee fruit set from the distance to the closest natural forest, was integrated. Land-use simulations showed, that depending on the magnitude and location of ongoing forest conversion, pollination services are expected to decline continuously. This results in a reduction of coffee yields of up to 18% and a loss of net revenues per hectare of up to 14%. However, the study also showed that ecological and economic values can be preserved if patches of natural vegetation are conservated in the agricultural landscape. -----------------------------------------------------------------------

Generic Finite Element Model for Mechanically Consistent Scaling of Composite Beam-to-column Joint with Welded Connection

To study the behaviour of beam-to-column composite connection more sophisticated finite element models is required, since component model has some severe limitations. In this research a generic finite element model for composite beam-to-column joint with welded connections is developed using current state of the art local modelling. Applying mechanically consistent scaling method, it can provide the constitutive relationship for a plane rectangular macro element with beam-type boundaries. Then, this defined macro element, which preserves local behaviour and allows for the transfer of five independent states between local and global models, can be implemented in high-accuracy frame analysis with the possibility of limit state checks. In order that macro element for scaling method can be used in practical manner, a generic geometry program as a new idea proposed in this study is also developed for this finite element model. With generic programming a set of global geometric variables can be input to generate a specific instance of the connection without much effort. The proposed finite element model generated by this generic programming is validated against testing results from University of Kaiserslautern. Finally, two illustrative examples for applying this macro element approach are presented. In the first example how to obtain the constitutive relationships of macro element is demonstrated. With certain assumptions for typical composite frame the constitutive relationships can be represented by bilinear laws for the macro bending and shear states that are then coupled by a two-dimensional surface law with yield and failure surfaces. In second example a scaling concept that combines sophisticated local models with a frame analysis using a macro element approach is presented as a practical application of this numerical model.

Knowledge Building in Landscape Architecture

The objective of this study was to develop an internet-based seminar framework applicable for landscape architecture education. This process was accompanied by various aims. The basic expectation was to keep the main characteristics of landscape architecture education also in the online format. On top of that, four further objectives were anticipated: (1) training of competences for virtual team work, (2) fostering intercultural competence, (3) creation of equal opportunities for education through internet-based open access and (4) synergy effects and learning processes across institutional boundaries. This work started with the hypothesis that these four expected advantages would compensate for additional organisational efforts caused by the online delivery of the seminars and thus lead to a sustainable integration of this new learning mode into landscape architecture curricula. This rationale was followed by a presentation of four areas of knowledge to which the seminar development was directly related (1) landscape architecture as a subject and its pedagogy, (2) general learning theories, (3) developments in the ICT sector and (4) wider societal driving forces such as global citizenship and the increase of open educational resources. The research design took the shape of a pedagogical action research cycle. This approach was constructive: The author herself is teaching international landscape architecture students so that the model could directly be applied in practice. Seven online seminars were implemented in the period from 2008 to 2013 and this experience represents the core of this study. The seminars were conducted with varying themes while its pedagogy, organisation and the technological tools remained widely identical. The research design is further based on three levels of observation: (1) the seminar design on the basis of theory and methods from the learning sciences, in particular educational constructivism, (2) the seminar evaluation and (3) the evaluation of the seminars’ long term impact. The seminar model itself basically consists of four elements: (1) the taxonomy of learning objectives, (2) ICT tools and their application and pedagogy, (3) process models and (4) the case study framework. The seminar framework was followed by the presentation of the evaluation findings. The major findings of this study can be summed up as follows: Implementing online seminars across educational and national boundaries was possible both in term of organisation and technology. In particular, a high level of cultural diversity among the seminar participants has definitively been achieved. However, there were also obvious obstacles. These were primarily competing study commitments and incompatible schedules among the students attending from different academic programmes, partly even in different time zones. Both factors had negative impact on the individual and working group performances. With respect to the technical framework it can be concluded that the majority of the participants were able to use the tools either directly without any problem or after overcoming some smaller problems. Also the seminar wiki was intensively used for completing the seminar assignments. However, too less truly collaborative text production was observed which could be improved by changing the requirements for the collaborative task. Two different process models have been applied for guiding the collaboration of the small groups and both were in general successful. However, it needs to be said that even if the students were able to follow the collaborative task and to co-construct and compare case studies, most of them were not able to synthesize the knowledge they had compiled. This means that the area of consideration often remained on the level of the case and further reflections, generalisations and critique were largely missing. This shows that the seminar model needs to find better ways for triggering knowledge building and critical reflection. It was also suggested to have a more differentiated group building strategy in future seminars. A comparison of pre- and post seminar concept maps showed that an increase of factual and conceptual knowledge on the individual level was widely recognizable. Also the evaluation of the case studies (the major seminar output) revealed that the students have undergone developments of both the factual and the conceptual knowledge domain. Also their self-assessment with respect to individual learning development showed that the highest consensus was achieved in the field of subject-specific knowledge. The participants were much more doubtful with regard to the progress of generic competences such as analysis, communication and organisation. However, 50% of the participants confirmed that they perceived individual development on all competence areas the survey had asked for. Have the additional four targets been met? Concerning the competences for working in a virtual team it can be concluded that the vast majority was able to use the internet-based tools and to work with them in a target-oriented way. However, there were obvious differences regarding the intensity and activity of participation, both because of external and personal factors. A very positive aspect is the achievement of a high cultural diversity supporting the participants’ intercultural competence. Learning from group members was obviously a success factor for the working groups. Regarding the possibilities for better accessibility of educational opportunities it became clear that a significant number of participants were not able to go abroad during their studies because of financial or personal reasons. They confirmed that the online seminar was to some extent a compensation for not having been abroad for studying. Inter-institutional learning and synergy was achieved in so far that many teachers from different countries contributed with individual lectures. However, those teachers hardly ever followed more than one session. Therefore, the learning effect remained largely within the seminar learning group. Looking back at the research design it can be said that the pedagogical action research cycle was an appropriate and valuable approach allowing for strong interaction between theory and practice. However, some more external evaluation from peers in particular regarding the participants’ products would have been valuable.