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.

Künstliche Randbedingungen und Algebraische Äquivalenzen in der Elastizitätstheorie

In dieser Arbeit werden zwei Aspekte bei Randwertproblemen der linearen Elastizitätstheorie untersucht: die Approximation von Lösungen auf unbeschränkten Gebieten und die Änderung von Symmetrieklassen unter speziellen Transformationen. Ausgangspunkt der Dissertation ist das von Specovius-Neugebauer und Nazarov in "Artificial boundary conditions for Petrovsky systems of second order in exterior domains and in other domains of conical type"(Math. Meth. Appl. Sci, 2004; 27) eingeführte Verfahren zur Untersuchung von Petrovsky-Systemen zweiter Ordnung in Außenraumgebieten und Gebieten mit konischen Ausgängen mit Hilfe der Methode der künstlichen Randbedingungen. Dabei werden für die Ermittlung von Lösungen der Randwertprobleme die unbeschränkten Gebiete durch das Abschneiden mit einer Kugel beschränkt, und es wird eine künstliche Randbedingung konstruiert, um die Lösung des Problems möglichst gut zu approximieren. Das Verfahren wird dahingehend verändert, dass das abschneidende Gebiet ein Polyeder ist, da es für die Lösung des Approximationsproblems mit üblichen Finite-Element-Diskretisierungen von Vorteil sei, wenn das zu triangulierende Gebiet einen polygonalen Rand besitzt. Zu Beginn der Arbeit werden die wichtigsten funktionalanalytischen Begriffe und Ergebnisse der Theorie elliptischer Differentialoperatoren vorgestellt. Danach folgt der Hauptteil der Arbeit, der sich in drei Bereiche untergliedert. Als erstes wird für abschneidende Polyedergebiete eine formale Konstruktion der künstlichen Randbedingungen angegeben. Danach folgt der Nachweis der Existenz und Eindeutigkeit der Lösung des approximativen Randwertproblems auf dem abgeschnittenen Gebiet und im Anschluss wird eine Abschätzung für den resultierenden Abschneidefehler geliefert. An die theoretischen Ausführungen schließt sich die Betrachtung von Anwendungsbereiche an. Hier werden ebene Rissprobleme und Polarisationsmatrizen dreidimensionaler Außenraumprobleme der Elastizitätstheorie erläutert. Der letzte Abschnitt behandelt den zweiten Aspekt der Arbeit, den Bereich der Algebraischen Äquivalenzen. Hier geht es um die Transformation von Symmetrieklassen, um die Kenntnis der Fundamentallösung der Elastizitätsprobleme für transversalisotrope Medien auch für Medien zu nutzen, die nicht von transversalisotroper Struktur sind. Eine allgemeine Darstellung aller Klassen konnte hier nicht geliefert werden. Als Beispiel für das Vorgehen wird eine Klasse von orthotropen Medien im dreidimensionalen Fall angegeben, die sich auf den Fall der Transversalisotropie reduzieren lässt.

Three-electron radiative transitions

A new type of many-electron radiative transitions involving three electrons is predicted. The results of their investigation by many-body perturbation theory are presented. New spectral lines observed in the wavelength range of 37.5 to 54.0 nm by means of photon-induced fluorescence spectroscopy (PIFS) following the excitation of the Kr I 3d{^-1}np resonances are reported and compared with the predictions.

Impact of sward type, cutting date and conditioning temperature on mass and energy flows in the integrated generation of solid fuel and biogas from semi-natural grassland

Energy production from biomass and the conservation of ecologically valuable grassland habitats are two important issues of agriculture today. The combination of a bioenergy production, which minimises environmental impacts and competition with food production for land with a conversion of semi-natural grasslands through new utilization alternatives for the biomass, led to the development of the IFBB process. Its basic principle is the separation of biomass into a liquid fraction (press fluid, PF) for the production of electric and thermal energy after anaerobic digestion to biogas and a solid fraction (press cake, PC) for the production of thermal energy through combustion. This study was undertaken to explore mass and energy flows as well as quality aspects of energy carriers within the IFBB process and determine their dependency on biomass-related and technical parameters. Two experiments were conducted, in which biomass from semi-natural grassland was conserved as silage and subjected to a hydrothermal conditioning and a subsequent mechanical dehydration with a screw press. Methane yield of the PF and the untreated silage was determined in anaerobic digestion experiments in batch fermenters at 37°C with a fermentation time of 13-15 and 27-35 days for the PF and the silage, respectively. Concentrations of dry matter (DM), ash, crude protein (CP), crude fibre (CF), ether extract (EE), neutral detergent fibre (NDF), acid detergent fibre (ADF), acid detergent ligning (ADL) and elements (K, Mg, Ca, Cl, N, S, P, C, H, N) were determined in the untreated biomass and the PC. Higher heating value (HHV) and ash softening temperature (AST) were calculated based on elemental concentration. Chemical composition of the PF and mass flows of all plant compounds into the PF were calculated. In the first experiment, biomass from five different semi-natural grassland swards (Arrhenaterion I and II, Caricion fuscae, Filipendulion ulmariae, Polygono-Trisetion) was harvested at one late sampling (19 July or 31 August) and ensiled. Each silage was subjected to three different temperature treatments (5°C, 60°C, 80°C) during hydrothermal conditioning. Based on observed methane yields and HHV as energy output parameters as well as literature-based and observed energy input parameters, energy and green house gas (GHG) balances were calculated for IFBB and two reference conversion processes, whole-crop digestion of untreated silage (WCD) and combustion of hay (CH). In the second experiment, biomass from one single semi-natural grassland sward (Arrhenaterion) was harvested at eight consecutive dates (27/04, 02/05, 09/05, 16/05, 24/05, 31/05, 11/06, 21/06) and ensiled. Each silage was subjected to six different treatments (no hydrothermal conditioning and hydrothermal conditioning at 10°C, 30°C, 50°C, 70°C, 90°C). Energy balance was calculated for IFBB and WCD. Multiple regression models were developed to predict mass flows, concentrations of elements in the PC, concentration of organic compounds in the PF and energy conversion efficiency of the IFBB process from temperature of hydrothermal conditioning as well as NDF and DM concentration in the silage. Results showed a relative reduction of ash and all elements detrimental for combustion in the PC compared to the untreated biomass of 20-90%. Reduction was highest for K and Cl and lowest for N. HHV of PC and untreated biomass were in a comparable range (17.8-19.5 MJ kg-1 DM), but AST of PC was higher (1156-1254°C). Methane yields of PF were higher compared to those of WCD when the biomass was harvested late (end of May and later) and in a comparable range when the biomass was harvested early and ranged from 332 to 458 LN kg-1 VS. Regarding energy and GHG balances, IFBB, with a net energy yield of 11.9-14.1 MWh ha-1, a conversion efficiency of 0.43-0.51, and GHG mitigation of 3.6-4.4 t CO2eq ha-1, performed better than WCD, but worse than CH. WCD produces thermal and electric energy with low efficiency, CH produces only thermal energy with a low quality solid fuel with high efficiency, IFBB produces thermal and electric energy with a solid fuel of high quality with medium efficiency. Regression models were able to predict target parameters with high accuracy (R2=0.70-0.99). The influence of increasing temperature of hydrothermal conditioning was an increase of mass flows, a decrease of element concentrations in the PC and a differing effect on energy conversion efficiency. The influence of increasing NDF concentration of the silage was a differing effect on mass flows, a decrease of element concentrations in the PC and an increase of energy conversion efficiency. The influence of increasing DM concentration of the silage was a decrease of mass flows, an increase of element concentrations in the PC and an increase of energy conversion efficiency. Based on the models an optimised IFBB process would be obtained with a medium temperature of hydrothermal conditioning (50°C), high NDF concentrations in the silage and medium DM concentrations of the silage.

Leguminous cover crops differentially affect maize yields in three contrasting soil types of Kakamega, Western Kenya

Maize production in smallholder farming systems in Kenya is largely limited by low soil fertility. As mineral fertilizer is expensive, green manuring using leguminous cover crops could be an alternative strategy for farmers to enhance farm productivity. However due to variability in soil type and crop management, the effects of green manure are likely to differ with farms. The objectives of this study were to evaluate Mucuna pruriens and Arachis pintoi on (i) biomass and nitrogen fixation (^15N natural abundance), (ii) soil carbon and nitrogen stocks and (iii) their effects on maize yields over two cropping seasons in Kakamega, Western Kenya. Mucuna at 6 weeks accumulated 1–1.3 Mg ha^{-1} of dry matter and 33–56 kg ha^{-1} nitrogen of which 70% was nitrogen derived from the atmosphere (Ndfa). Arachis after 12 months accumulated 2–2.7 Mg ha^{-1} of dry matter and 51–74 kg N ha^{-1} of which 52-63 % was from Ndfa. Soil carbon and nitrogen stocks at 0–15 cm depth were enhanced by 2-4 Mg C ha^{-1} and 0.3–1.0 Mg N ha^{-1} under Mucuna and Arachis fallow, irrespective of soil type. Maize yield increased by 0.5-2 Mg ha^{-1} in Mucuna and 0.5–3 Mg ha^{-1} in Arachis and the response was stronger on Nitisol than on Acrisol or Ferralsol. We concluded that leguminous cover crops seem promising in enhancing soil fertility and maize yields in Kenya, provided soil conditions and rainfall are suitable.