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.

Solution properties of the de Branges differential recurrence equation

In this 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums thas was published by Askey and Gasper in 1976. The de Branges functions Tn/k(t) are defined as the solutions of a system of differential recurrence equations with suitably given initial values. The essential fact used in the proof of the Bieberbach and Milin conjectures is the statement Tn/k(t)<=0. In 1991 Weinstein presented another proof of the Bieberbach and Milin conjectures, also using a special function system Λn/k(t) which (by Todorov and Wilf) was realized to be directly connected with de Branges', Tn/k(t)=-kΛn/k(t), and the positivity results in both proofs Tn/k(t)<=0 are essentially the same. In this paper we study differential recurrence equations equivalent to de Branges' original ones and show that many solutions of these differential recurrence equations don't change sign so that the above inequality is not as surprising as expected. Furthermore, we present a multiparameterized hypergeometric family of solutions of the de Branges differential recurrence equations showing that solutions are not rare at all.

A semi-phenomenological approach to the structure and transport properties of macromolecules in solution

Motiviert durch die Lebenswissenschaften (Life sciences) haben sich Untersuchungen zur Dynamik von Makromolekülen in Lösungen in den vergangenen Jahren zu einem zukunftsweisenden Forschungsgebiet etabliert, dessen Anwendungen von der Biophysik über die physikalische Chemie bis hin zu den Materialwissenschaften reichen. Neben zahlreichen experimentellen Forschungsprogrammen zur räumlichen Struktur und den Transporteigenschaften grosser MolekÄule, wie sie heute praktisch an allen (Synchrotron-) Strahlungsquellen und den Laboren der Biophysik anzutreffen sind, werden gegenwärtig daher auch umfangreiche theoretische Anstrengungen unternommen, um das Diffusionsverhalten von Makromolekülen besser zu erklären. Um neue Wege für eine quantitative Vorhersagen des Translations- und Rotationsverhaltens grosser Moleküle zu erkunden, wurde in dieser Arbeit ein semiphänomenologischer Ansatz verfolgt. Dieser Ansatz erlaubte es, ausgehend von der Hamiltonschen Mechanik des Gesamtsystems 'Molekül + Lösung', eine Mastergleichung für die Phasenraumdichte der Makromoleküle herzuleiten, die den Einfluss der Lösung mittels effektiver Reibungstensoren erfasst. Im Rahmen dieses Ansatzes gelingt es z.B. (i) sowohl den Einfluss der Wechselwirkung zwischen den makromolekularen Gruppen (den sogenannten molekularen beads) und den Lösungsteilchen zu analysieren als auch (ii) die Diffusionseigen schaften für veschiedene thermodynamische Umgebungen zu untersuchen. Ferner gelang es auf der Basis dieser Näherung, die Rotationsbewegung von grossen Molekülen zu beschreiben, die einseitig auf einer Oberfläche festgeheftet sind. Im Vergleich zu den aufwendigen molekulardynamischen (MD) Simulationen grosser Moleküle zeichnet sich die hier dargestellte Methode vor allem durch ihren hohen `Effizienzgewinn' aus, der für komplexe Systeme leicht mehr als fünf Grössenordnungen betragen kann. Dieser Gewinn an Rechenzeit erlaubt bspw. Anwendungen, wie sie mit MD Simulationen wohl auch zukünftig nicht oder nur sehr zögerlich aufgegriffen werden können. Denkbare Anwendungsgebiete dieser Näherung betreffen dabei nicht nur dichte Lösungen, in denen auch die Wechselwirkungen der molekularen beads zu benachbarten Makromolekülen eine Rolle spielt, sondern auch Untersuchungen zu ionischen Flüssigkeiten oder zur Topologie grosser Moleküle.

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. -----------------------------------------------------------------------

Dipodal Ferrocene Derivatives for Nanostructured Redox-Functionalised Surfaces

Self-assembled monolayers (SAMs) on solid surfaces are of great current interest in science and nanotechnology. This thesis describes the preparation of several symmetrically 1,1’-substituted ferrocene derivatives that contain anchoring groups suitable for chemisorption on gold and may give rise to SAMs with electrochemically switchable properties. The binding groups are isocyano (-NC), isothiocyanato (-NCS), phosphanyl (-PPh2), thioether (-SR) and thienyl. In the context of SAM fabrication, isothiocyanates and phosphanes are adsorbate systems which, surprisingly, have remained essentially unexplored. SAMs on gold have been fabricated with the adsorbates from solution and investigated primarily by X-ray photoelectron spectroscopy and near-edge X-ray absorption fine structure spectroscopy. The results of these analytical investigations are presented and discussed in matters of the film quality and possible binding modes. The quality of self-assembled monolayers fabricated from 1,1’-diisocyanoferrocene and 1,1’-diisothiocyanatoferrocene turned out to be superior to that of films based on the other adsorbate species investigated. Films of those absorbates as well as of dppf afforded well-defined SAMs of good quality. All other films of this study based on sulfur containing anchoring groups exhibit chemical inhomogeneity and low orientational order of the film constituents and therefore failed to give rise to well-defined SAMs. Surface coordination chemistry is naturally related to molecular coordination chemistry. Since all SAMs described in this thesis were prepared on gold (111) surfaces, the ferrocene-based ligands of this study have been investigated in their ability for complexation towards gold(I). The sulfur-based ferrocene ligands [fc(SR)2] failed to give stable gold(I) complexes. In contrast, 1,1’-diisocyanoferrocene (1) proved to be an excellent ligand for the complexation of gold(I). Several complexes were prepared and characterised utilising a series of gold(I) acetylides. These complexes show interesting structural motifs in the solid state, since intramolecular aurophilic interactions lead to a parallel orientation of the isocyano moieties, combined with an antiparallel alignment of neighbouring units. The reaction of 1 with the gold(I) acetylide [Au(C≡C–Fc)]n turned out to be very unusual, since the two chemically equivalent isocyano groups undergo a different reaction. One group shows an ordinary coordination and the other one undergoes an extraordinary 1,1-insertion into the Au-C bond. As a sideline of the research of this thesis several ferrocene derivatives have been tested for their suitability for potential surface reactions. Copper(I) mediated 1,3-dipolar cycloadditions of azidoferrocene derivatives with terminal alkynes appeared very promising in this context, but failed to a certain extent in terms of ‘click’ chemistry, since the formation of the triazoles depended on the strict exclusion of oxygen and moisture and yields were only moderate. Staudinger reactions between dppf and azidoferrocene derivatives were also tested. The nucleophilic additions of secondary amines to 1,1’-diisothiocyanatoferrocene led to the respective thiourea derivatives in quantitative yields.

Solution of the Hartree-Fock equations for atoms and diatomic molecules with the finite element method

The finite element method (FEM) is now developed to solve two-dimensional Hartree-Fock (HF) equations for atoms and diatomic molecules. The method and its implementation is described and results are presented for the atoms Be, Ne and Ar as well as the diatomic molecules LiH, BH, N_2 and CO as examples. Total energies and eigenvalues calculated with the FEM on the HF-level are compared with results obtained with the numerical standard methods used for the solution of the one dimensional HF equations for atoms and for diatomic molecules with the traditional LCAO quantum chemical methods and the newly developed finite difference method on the HF-level. In general the accuracy increases from the LCAO - to the finite difference - to the finite element method.

Finite element method for the accurate solution of diatomic molecules

We present the Finite-Element-Method (FEM) in its application to quantum mechanical problems solving for diatomic molecules. Results for Hartree-Fock calculations of H_2 and Hartree-Fock-Slater calculations of molecules like N_2 and C0 have been obtained. The accuracy achieved with less then 5000 grid points for the total energies of these systems is 10_-8 a.u., which is demonstrated for N_2.

Solution of the Hartree-Fock-Slater equations for diatomic molecules by the finite-element method

We present the finite-element method in its application to solving quantum-mechanical problems for diatomic molecules. Results for Hartree-Fock calculations of H_2 and Hartree-Fock-Slater calculations for molecules like N_2 and CO are presented. The accuracy achieved with fewer than 5000 grid points for the total energies of these systems is 10^-8 a.u., which is about two orders of magnitude better than the accuracy of any other available method.

Ions of the superheavy elements in vacuum and in solution

The extension of the Periodic Table into the range of unknown atomic numbers of above one hundred requires relativistic calculations. The results of the latter are used to indicate probable values for X-ray transition lines which will be useful for identification of the atomic species formed during collision between accelerated ions and the target. If the half-lives of the isotopes are long, then the chemistry of these new species becomes an important question which is reviewed for E110, E 111 and E112. The possible structural chemistry of the elements E108 to E112 is suggested. Finally the effects of solvation on ions of the actinide and superheavy elements have been studied.

Solution of the time dependent Dirac-Fock-Slater equation for many-electron collisions systems using a time window method

We present a new scheme to solve the time dependent Dirac-Fock-Slater equation (TDDFS) for heavy many electron ion-atom collision systems. Up to now time independent self consistent molecular orbitals have been used to expand the time dependent wavefunction and rather complicated potential coupling matrix elements have been neglected. Our idea is to minimize the potential coupling by using the time dependent electronic density to generate molecular basis functions. We present the first results for 16 MeV S{^16+} on Ar.

Constructing a ‘moment of crisis’ and its adequate solution

The rejection of the European Constitution marks an important crystallization point for debate about the European Union (EU) and the integration process. The European Constitution was envisaged as the founding document of a renewed and enlarged European Union and thus it was rather assumed to find wide public support. Its rejection was not anticipated. The negative referenda in France and the Netherlands therefore led to a controversial debate about the more fundamental meaning and the consequences of the rejection both for the immediate state of affairs as well as for the further integration process. The rejection of the Constitution and the controversy about its correct interpretation therefore present an intriguing puzzle for political analysis. Although the treaty rejection was taken up widely in the field of European Studies, the focus of existing analyses has predominantly been on explaining why the current situation occurred. Underlying these approaches is the premise that by establishing the reasons for the rejection it is possible to derive the ‘true’ meaning of the event for the EU integration process. In my paper I rely on an alternative, discourse theoretical approach which aims to overcome the positivist perspective dominating the existing analyses. I argue that the meaning of the event ‘treaty rejection’ is not fixed or inherent to it but discursively constructed. The critical assessment of this concrete meaning-production is of high relevance as the specific meaning attributed to the treaty rejection effectively constrains the scope for supposedly ‘reasonable’ options for action, both in the concrete situation and in the further European integration process more generally. I will argue that the overall framing suggests a fundamental technocratic approach to governance from part of the Commission. Political struggle and public deliberation is no longer foreseen as the concrete solutions to the citizens’ general concerns are designed by supposedly apolitical experts. Through the communicative diffusion and the active implementation of this particular model of governance the Commission shapes the future integration process in a more substantial way than is obvious from its seemingly limited immediate problem-solving orientation of overcoming the ‘constitutional crisis’. As the European Commission is a central actor in the discourse production my analysis focuses on the specific interpretation of the situation put forward by the Commission. In order to work out the Commission’s particular take on the event I conducted a frame analysis (according to Benford/Snow) on a body of key sources produced in the context of coping with the treaty rejection.

On Solution Sets of Information Inequalities

We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce important properties of Bayesian networks, which is important within causal inference.

Biofuel as the solution of alternative energy production?

There have being increasing debate on the prospects of biofuel becoming the next best alternative to solving the problem of CO2 emission and the escalating fuel prices, but the question is whether this assertion is true and also if it comes without any cost to pay. This paper seeks to find out whether this much praised alternative to solving these problems is a better option or another way for the developed countries to find more areas where they could get cheap land, labour and raw materials for the production of biofuel. This will focus mainly on some effects the growing biofuel production has on food security, livelihood of people, the environment and some land conflicts developing as a result of land grabbing for biofuel production in the developing countries.

Exact Solution of the Nonlinear Dynamics of Recurrent Neural Mechanisms for Direction Selectivity

Different theoretical models have tried to investigate the feasibility of recurrent neural mechanisms for achieving direction selectivity in the visual cortex. The mathematical analysis of such models has been restricted so far to the case of purely linear networks. We present an exact analytical solution of the nonlinear dynamics of a class of direction selective recurrent neural models with threshold nonlinearity. Our mathematical analysis shows that such networks have form-stable stimulus-locked traveling pulse solutions that are appropriate for modeling the responses of direction selective cortical neurons. Our analysis shows also that the stability of such solutions can break down giving raise to a different class of solutions ("lurching activity waves") that are characterized by a specific spatio-temporal periodicity. These solutions cannot arise in models for direction selectivity with purely linear spatio-temporal filtering.

Characterization of ZnO Nanorods Grown on GaN Using Aqueous Solution Method

Uniformly distributed ZnO nanorods with diameter 70-100 nm and 1-2μm long have been successfully grown at low temperatures on GaN by using the inexpensive aqueous solution method. The formation of the ZnO nanorods and the growth parameters are controlled by reactant concentration, temperature and pH. No catalyst is required. The XRD studies show that the ZnO nanorods are single crystals and that they grow along the c axis of the crystal plane. The room temperature photoluminescence measurements have shown ultraviolet peaks at 388nm with high intensity, which are comparable to those found in high quality ZnO films. The mechanism of the nanorod growth in the aqueous solution is proposed. The dependence of the ZnO nanorods on the growth parameters was also investigated. While changing the growth temperature from 60°C to 150°C, the morphology of the ZnO nanorods changed from sharp tip (needle shape) to flat tip (rod shape). These kinds of structure are useful in laser and field emission application.