Effects of manure quality and application forms on soil C and N turnover of a subtropical oasis soil under laboratory conditions

Our knowledge of the agricultural sustainability of the millennia-old mountain oases in northern Oman is restricted in particular with respect to C and N turnover. A laboratory study was conducted (1) to analyse the effects of rewetting and drying on soil microorganisms after adding different manures, (2) to investigate the effects of mulching or incorporating of these manures, and (3) to evaluate the relationships between C and N mineralisation rates and manure quality indices. During the first 9-day rewetting and drying cycle, i.e. the “mulch” period, the content of extractable organic C decreased by approximately 40% in all four treatments. During the second 9-day rewetting and drying cycle, i.e. the “incorporation” period, this fraction decreased insignificantly in almost all treatments. The control and mature manure treatments form the first pair with a low percentage of total organic C evolved as CO2 (0.3% in 18 days) and a considerable percentage of total N mineralised as NH4 and NO3 (1% in 18 days), the fresh and immature manure treatments form the second pair with a higher amount of total organic C evolved as CO2 (0.5% in 18 days) and no net N mineralisation. During the first 9-day rewetting and drying cycle, the contents of microbial biomass C and biomass N increased by approximately 150% in all four treatments. During the second 9-day rewetting and drying cycle, no further increase was observed in the control and immature manure treatments and a roughly 30% increase in the other two treatments.

Applications and modelling in mathematics teaching

The aim of this paper is a comprehensive presentation of some important basic and general aspects of the topic applications and modelling, with emphasis on the secondary school level. Owing to the review character of this paper, some overlap with the survey paper Blum and Niss (1989) for ICME-6 in Budapest is inevitable. The paper will consist of three parts. In part 1, I shall try to clarify some basic concepts and remind the reader of a few application and modelling examples suitable for teaching. In part 2, I shall formulate some general aims for mathematics instruction and, on that basis, summarise the most important arguments for and against applications and modelling in mathematics teaching. Finally, in part 3, I shall discuss some relevant instructional aspects resulting from the considerations in part 2.

Mathematical modelling in mathematics education and instruction

This paper aims at giving a concise survey of the present state-of-the-art of mathematical modelling in mathematics education and instruction. It will consist of four parts. In part 1, some basic concepts relevant to the topic will be clarified and, in particular, mathematical modelling will be defined in a broad, comprehensive sense. Part 2 will review arguments for the inclusion of modelling in mathematics teaching at schools and universities, and identify certain schools of thought within mathematics education. Part 3 will describe the role of modelling in present mathematics curricula and in everyday teaching practice. Some obstacles for mathematical modelling in the classroom will be analysed, as well as the opportunities and risks of computer usage. In part 4, selected materials and resources for teaching mathematical modelling, developed in the last few years in America, Australia and Europe, will be presented. The examples will demonstrate many promising directions of development.

Analysis of applications and of conceptions for an application-oriented mathematics instruction

In connection with the (revived) demand for considering applications in the teaching of mathematics, various schemata or lists of criteria have been developed since the end of the sixties, which set up requirements about closeness to the real world or about the type of mathematics being used, and which have made it possible to analyze the available applications in their light. After having stated the problem (in section 1), we present (in section 2) a sketch of some of the best known of these and of some earlier schemata, although we are not aiming for a complete picture. Then (in section 3) we distinguish among different dimensions.in the analysis of applications. With this as a basis, we develop (in section 4) our own suggestion for categorizing types of applications and conceptions for an application-oriented mathematics instruction. Then (in section 5) we illustrate our schemata by some examples of performed evaluations. Finally (in section 6), we present some preliminary first results of the analysis of teaching conceptions.

Biological Photonic Crystals: Diatoms

The aim of this work was to produce a variety of fluorescent diatom cell wall material as a basis for spectroscopic investigations of the influence of the photonic structure on the emission of an incorporated laser dye. This goal was achieved by the method of in vivo-fluorochromation, in which the fluorescence dyes are incorporated by the diatom cells during cell wall formation. Several fluorescent dyes (mostly rhodamines) known as strong laser dyes, were tested for a possible application within this method. The results of this work show that half of the tested rhodamines can be applied for an in vivo-fluorochromation of diatom cells. For a successful incorporation into the diatom cell wall, a relatively low toxicity to diatom cells is necessary. Replacement of the carbon acid function at the carboxyphenyl ring of the rhodamine by a methyl or ethylester function showed to convert a rhodamine of relatively low toxicity to a rhodamine leading to severe lethal effects within the cells. In contrast to their carbon acid forms, which posses a net neutral charge of the molecule, rhodamine esters exhibit a net positive charge. The enhanced toxicological effects seem to be due to an increased accumulation of positive charged rhodamines within the mitochondria, an increased hydrophobicity due to the attachment of an alkyl substituent, an increased retention time of the dyes within the mitochondria and a therefore stronger negative effect on the mitochondrial membrane bound energy processes of the diatom cell. Therefore rhodamines with a positive net charge deriving from a methyl or ethylester function at the carboxy phenyl ring instead of a carbon acid substituent showed not to be suitable for long-term investigations/ biomineralization studies of diatoms. Investigations performed on diatom species of different orders showed that rhodamine 19, rhodamine B, and rhodamine 101 can presumably be successfully applied for in vivo-fluorochromation to all diatom species. The results obtained here can help to find further laser dyes for an in vivo-fluorochromation of diatom cells and therefore for the production of fluorescent nanostructural elements for a detailed optical investigation of the diatom cell wall. First optical measurements performed on in vivo-fluorochromated cell walls did not give any hints concerning the photonic structure of the diatom cell. Cell wall parts with different nanostructural elements were investigated and by comparison of the obtained fluorescence emission spectra, no special features that might derive from photonic structural effects could be observed. Results concerning the concentration dependent shifts within the emission spectra, as well as the decrease of fluorescence intensity of the stained cell wall structures with increasing dye concentration, depict that several effects occurring by interaction of the molecules within the cell wall can have an impact on the technical application of fluorescent cell walls. It can be assumed that the investigation of the photonic crystal behaviour and the possibility to achieve laser action within the diatom cell wall can be hampered by molecular interactions. The results give hints to prevent such obstacles. Comparison of the recent findings and state of the art of in vivo-fluorochromation of diatom cell wall material, make clear that the here presented results are of importance and can offer a considerable contribution to the development and establishment of new biosilification markers, for diatoms as well as for other biosilifying organisms.

Topics of divisibility

The set of integers forms a commutative ring whose elements admit a unique decomposition into primes. In this folder three lecture notes are bound, concerning topics, developed by dropping or replacing special properties of this most natural and most special ring. For short: investigated are groupoids w.r.t the interplay of multiplication - on the one hand - and divisibility, ideal decomposition and residuation, respectively, on the other hand.

Harmonische Funktionen auf dem Bruhat-Tits-Gebäude der PGL_3 über Funktionenkörpern

Harmonische Funktionen auf dem Bruhat-Tits-Gebäude der PGL(3) über Funktionenkörpern lassen sich als ein Analogon zu den auf der oberen Halbebene definierten klassischen Spitzenformen verstehen. An die Stelle des starken Abklingens der Spitzenformen tritt hier die Endlichkeit des Trägers modulo einer gewissen Untergruppe. Der erste Teil der vorliegenden Arbeit befaßt sich mit der Untersuchung und Charakterisierung dieses Trägers. Im weiteren Verlauf werden gewisse Konzepte der klassischen Theorie auf harmonische Funktionen übertragen. So wird gezeigt, daß diese sich ebenfalls als Fourierreihe darstellen lassen und es werden explizite Formeln für die Fourierkoeffizienten hergeleitet. Es stellt sich heraus, daß sich die Harmonizität in gewissen Relationen zwischen den Fourierkoeffizienten widerspiegelt und sich umgekehrt aus einem Satz passender Koeffizienten eine harmonische Funktion erzeugen läßt. Dies wird zur expliziten Konstruktion zweier quasi-harmonischer Funktionen genutzt, die ein Pendant zu klassischen Poincaré-Reihen darstellen. Abschließend werden Hecke-Operatoren definiert und Formeln für die Fourierkoeffizienten der Hecke-Transformierten einer harmonischen Funktion hergeleitet.