Computation of locally free class groups

We show that the locally free class group of an order in a semisimple algebra over a number field is isomorphic to a certain ray class group. This description is then used to present an algorithm that computes the locally free class group. The algorithm is implemented in MAGMA for the case where the algebra is a group ring over the rational numbers.

Church-Rosser groups and growing context-sensitive groups

A finitely generated group is called a Church-Rosser group (growing context-sensitive group) if it admits a finitely generated presentation for which the word problem is a Church-Rosser (growing context-sensitive) language. Although the Church-Rosser languages are incomparable to the context-free languages under set inclusion, they strictly contain the class of deterministic context-free languages. As each context-free group language is actually deterministic context-free, it follows that all context-free groups are Church-Rosser groups. As the free abelian group of rank 2 is a non-context-free Church-Rosser group, this inclusion is proper. On the other hand, we show that there are co-context-free groups that are not growing context-sensitive. Also some closure and non-closure properties are established for the classes of Church-Rosser and growing context-sensitive groups. More generally, we also establish some new characterizations and closure properties for the classes of Church-Rosser and growing context-sensitive languages.

Computations in Relative Algebraic K-Groups

Let G be finite group and K a number field or a p-adic field with ring of integers O_K. In the first part of the manuscript we present an algorithm that computes the relative algebraic K-group K_0(O_K[G],K) as an abstract abelian group. We solve the discrete logarithm problem, both in K_0(O_K[G],K) and the locally free class group cl(O_K[G]). All algorithms have been implemented in MAGMA for the case K = \IQ. In the second part of the manuscript we prove formulae for the torsion subgroup of K_0(\IZ[G],\IQ) for large classes of dihedral and quaternion groups.

Computation of relativistic symmetry orbitals for finite double point groups

A program is presented for the construction of relativistic symmetry-adapted molecular basis functions. It is applicable to 36 finite double point groups. The algorithm, based on the projection operator method, automatically generates linearly independent basis sets. Time reversal invariance is included in the program, leading to additional selection rules in the non-relativistic limit.

Agricultural practices and horizontal nutrient balances in urban gardens and the alternative use of urban agricultural land in Khartoum, Sudan

The surge in the urban population evident in most developing countries is a worldwide phenomenon, and often the result of drought, conflicts, poverty and the lack of education opportunities. In parallel with the growth of the cities is the growing need for food which leads to the burgeoning expansion of urban and peri-urban agriculture (UPA). In this context, urban agriculture (UA) contributes significantly to supplying local markets with both vegetable and animal produce. As an income generating activity, UA also contributes to the livelihoods of poor urban dwellers. In order to evaluate the nutrient status of urban soils in relation to garden management, this study assessed nutrient fluxes (inputs and outputs) in gardens on urban Gerif soils on the banks of the River Nile in Khartoum, the capital city of Sudan. To achieve this objective, a preliminary baseline survey was carried out to describe the structure of the existing garden systems. In cooperation with the author of another PhD thesis (Ms. Ishtiag Abdalla), alternative uses of cow dung in brick making kilns in urban Khartoum were assessed; and the socio-economic criteria of the brick kiln owners or agents, economical and plant nutritional value of animal dung and the gaseous emission related to brick making activities were assessed. A total of 40 household heads were interviewed using a semi-structured questionnaire to collect information on demographic, socio-economic and migratory characteristics of the household members, the gardening systems used and the problems encountered in urban gardening. Based on the results of this survey, gardens were divided into three groups: mixed vegetable-fodder gardens, mixed vegetable-subsistence livestock gardens and pure vegetable gardens. The results revealed that UA is the exclusive domain of men, 80% of them non-native to Khartoum. The harvested produce in all gardens was market oriented and represented the main source of income for 83% of the gardeners. Fast growing leafy vegetables such as Jew’s mallow (Corchorous olitorius L.), purslane (Portulaca oleracea L.) and rocket (Eruca sativa Mill.) were the dominant cultivated species. Most of the gardens (95%) were continuously cultivated throughout the year without any fallow period, unless they were flooded. Gardeners were not generally aware of the importance of crop diversity, which may help them overcome the strongly fluctuating market prices for their produce and thereby strengthen the contributions of UA to the overall productivity of the city. To measure nutrient fluxes, four gardens were selected and their nutrients inputs and outputs flows were monitored. In each garden, all plots were monitored for quantification of nutrient inputs and outputs. To determine soil chemical fertility parameters in each of the studied gardens, soil samples were taken from three selected plots at the beginning of the study in October 2007 (gardens L1, L2 and H1) and in April 2008 (garden H2) and at the end of the study period in March 2010. Additional soil sampling occurred in May 2009 to assess changes in the soil nutrient status after the River Nile flood of 2008 had receded. Samples of rain and irrigation water (river and well-water) were analyzed for nitrogen (N), phosphorus (P), potassium (K) and carbon (C) content to determine their nutrient inputs. Catchment traps were installed to quantify the sediment yield from the River Nile flood. To quantify the nutrient inputs of sediments, samples were analyzed for N, P, K and organic carbon (Corg) content, cation exchange capacity (CEC) and the particle size distribution. The total nutrient inputs were calculated by multiplying the sediment nutrient content by total sediment deposits on individual gardens. Nutrient output in the form of harvested yield was quantified at harvest of each crop. Plant samples from each field were dried, and analyzed for their N, P, K and Corg content. Cumulative leaching losses of mineral N and P were estimated in a single plot in garden L1 from December 1st 2008 to July 1st 2009 using 12 ion exchange resins cartridges. Nutrients were extracted and analyzed for nitrate (NO3--N), ammonium (NH4+-N) and phosphate PO4-3-P. Changes in soil nutrient balance were assessed as inputs minus outputs. The results showed that across gardens, soil N and P concentrations increased from 2007 to 2009, while particle size distribution remained unchanged. Sediment loads and their respective contents of N, P and Corg decreased significantly (P < 0.05) from the gardens of the downstream lowlands (L1 and L2) to the gardens of the upstream highlands (H1 and H2). No significant difference was found in K deposits. None of the gardens received organic fertilizers and the only mineral fertilizer applied was urea (46-0-0). This equaled 29, 30, 54, and 67% of total N inputs to gardens L1, L2, H1, and H2, respectively. Sediment deposits of the River Nile floods contributed on average 67, 94, 6 and 42% to the total N, P, K and C inputs in lowland gardens and 33, 86, 4 and 37% of total N, P, K and C inputs in highland gardens. Irrigation water and rainfall contributed substantially to K inputs representing 96, 92, 94 and 96% of total K influxes in garden L1, L2, H1 and H2, respectively. Following the same order, total annual DM yields in the gardens were 26, 18, 16 and 1.8 t ha-1. Annual leaching losses were estimated to be 0.02 kg NH4+-N ha-1 (SE = 0.004), 0.03 kg NO3--N ha-1 (SE = 0.002) and 0.005 kg PO4-3-P ha-1 (SE = 0.0007). Differences between nutrient inputs and outputs indicated negative nutrient balances for P and K and positive balances of N and C for all gardens. The negative balances in P and K call for adoptions of new agricultural techniques such as regular manure additions or mulching which may enhance the soil organic matter status. A quantification of fluxes not measured in our study such as N2-fixation, dry deposition and gaseous emissions of C and N would be necessary to comprehensively assess the sustainability of these intensive gardening systems. The second part of the survey dealt with the brick making kilns. A total of 50 brick kiln owners/or agents were interviewed from July to August 2009, using a semi-structured questionnaire. The data collected included general information such as age, family size, education, land ownership, number of kilns managed and/or owned, number of months that kilns were in operation, quantity of inputs (cow dung and fuel wood) used, prices of inputs and products across the production season. Information related to the share value of the land on which the kilns were built and annual income for urban farmers and annual returns from dung for the animal raisers was also collected. Using descriptive statistics, budget calculation and Gini coefficient, the results indicated that renting the land to brick making kilns yields a 5-fold higher return than the rent for agriculture. Gini coefficient showed that the kiln owners had a more equal income distribution compared to farmers. To estimate emission of greenhouse gases (GHGs) and losses of N, P, K, Corg and DM from cow dung when used in brick making, samples of cow dung (loose and compacted) were collected from different kilns and analyzed for their N, P, K and Corg content. The procedure modified by the Intergovernmental Panel on Climate Change (IPCC, 1994) was used to estimate the gaseous emissions of cow dung and fuel wood. The amount of deforested wood was estimated according to the default values for wood density given by Dixon et al. (1991) and the expansion ratio for branches and small trees given by Brown et al. (1989). The data showed the monetary value of added N and P from cow dung was lower than for mineral fertilizers. Annual consumption of compacted dung (381 t DM) as biomass fuel by far exceeded the consumption of fuel wood (36 t DM). Gaseous emissions from cow dung and fuel wood were dominated by CO2, CO and CH4. Considering that Gerif land in urban Khartoum supports a multifunctional land use system, efficient use of natural resources (forest, dung, land and water) will enhance the sustainability of the UA and brick making activities. Adoption of new kilns with higher energy efficiency will reduce the amount of biomass fuels (cow dung and wood) used the amount of GHGs emitted and the threat to the few remaining forests.

Experimental and CFD study on low temperature drying of loose and compressed bulks

Die Trocknung ist eines der am häufigsten verwendeten Verfahren, um die Haltbarkeit von landwirtschaftlichen Gütern zu verlängern. Von den vielen gebräuchlichen Trocknungsarten ist die Konvektionstrocknung, die Luft als Energie- und Feuchteträger verwendet, weiterhin die wichtigste. Trotz ihrer Nachteile und ihres hohen spezifischen Energieverbrauchs sind Satztrockner für die Getreide-, Kräuter- und Heutrocknung noch weit verbreitet. Ferner werden Konvektionstrockner gemeinhin zur künstlichen Trocknung eingesetzt. Diese Arbeit ist Teil eines Forschungsprojekts, welches eine sorptionsgestützte solare Trocknung von landwirtschaftlichen Gütern untersucht. Bei dieser wird kühle feuchte Luft in Kontakt mit einer konzentrierten hygroskopischen Salzlösung gebracht. Während dieses Prozesses wird die Luft entfeuchtet und mit Hilfe der freigesetzten Verdampfungsenthalpie erwärmt. Die Anwendung dieses Verfahrens zur Trocknung landwirtschaftlicher Güter ist besonders interessant für Produkte, die bei niedrigen Temperaturen verarbeitet werden, um ihre Qualität nicht negativ zu beeinflussen. Bei allen energieintensiven Prozessen und vor allem bei der Verwendung von Solarenergie ist ein effizienter Energieverbrauch äußerst wichtig für den technischen und ökonomischen Erfolg. Eine ungleichmäßige Trocknung ist oftmals bei Satztrocknern zu beobachten, was die Energieeffizienz negativ beeinflusst. Aus diesem Grund lag im agrartechnischen Teil des Projekts der Schwerpunkt auf der Trocknung bei niedrigen Temperaturen und geringer Luftfeuchte, die der Sorptionsprozess liefert, sowie auf der Verbesserung der Luftverteilung und der Gleichmäßigkeit der Trocknung in lockeren und verdichteten Schüttungen. Es wurden Dünnschicht-Trocknungsexperminente für Blattsellerie bei unterschiedlichen Lufttemperaturen und unterschiedlicher relativer Luftfeuchte durchgeführt. Die Ergebnisse zeigen eindeutig, dass nicht nur die Lufttemperatur einen großen Einfluss auf die Trocknungsgeschwindigkeit hat, sondern auch die relative Luftfeuchte. Dies ist vor allem bei niedrigen Temperaturen, wie sie vom Sorptionssystem geliefert werden, der Fall. Um die Luftverteilung und Gleichmäßigkeit der Trocknung lockerer Schüttungen zu untersuchen, wurde ein Kistentrockner experimentell und in Strömungssimulationen getestet. Die Leistung des ursprünglichen Trockners wurde signifikant durch einfache Veränderungen des Designs verbessert. Diese stellten einen gleichmäßigeren Luftstrom durch das Produkt sicher. Die Trocknung von Heu-Rundballen stellt eine Herausforderung dar, da diese sehr stark verdichtet sind und die Dichte innerhalb eines Ballens stark schwankt. Strömungs- und Trocknungssimulationen so wie experimentelle Messungen zeigten, dass das Trocknerdesign einen großen Einfluss auf die Gleichmäßigkeit der Trocknung hat. Bei den einfachsten Trocknervarianten war die Verteilung auch bei optimal gepressten Ballen unzureichend, während komplexere Trockner eine gleichmäßigere Trocknung erzielten. Jedoch werden auch hier die Ergebnisse stark von der Verteilung der Dichte im Ballen beeinflusst, welche in der Praxis weiterhin nicht ideal ist. Abschließend wurde, um den Trocknungsfortschritt zu überwachen, eine Methodik getestet, bei der zur Messung des durchschnittlichen aktuellen Feuchtegehalts des Produktes psychrometrische Messungen und Messungen des Luftstroms in kurzen Abständen durchgeführt wurden. Die Menge des tatsächlich entfernten Wassers stimmte in den meisten Fällen gut mit der geschätzten Menge überein. Jedoch hängt der Erfolg dieser Methode stark von der Genauigkeit der Messfühler ab.