Negative Größen bei Diophant?

In this paper we champion Diophantus of Alexandria and Isabella Basmakova against Norbert Schappacher. In two publications ([46] and [47]) he puts forward inter alia two propositions: Questioning Diophantus' originality he considers affirmatively the possibility, that the Arithmetica are the joint work of a team of authors like Bourbaki. And he calls Basmakova's claim (in [5]), that Diophantus uses negative numbers, a "nonsense", reproaching her for her "thoughtlessness". First, we disprove Schappacher's Bourbaki thesis. Second, we investigate the semantic meaning and historical significance of Diophantus' keywords leipsis and mparxis. Next, we discuss Schappacher's epistemology of the history of mathematics and defend Basmakova's methods. Furthermore, we give 33 places where Diophantus uses negative quantities as intermediate results; they appear as differences a - b of positive rational numbers, the subtrahend b being bigger than the minuend a; they each represent the (negative) basis (pleyra) of a square number (tetragonos), which is afterwards computed by the formula (a - b)^2 = a^2 + b^2 - 2ab. Finally, we report how the topic "Diophantus and the negative numbers" has been dealt with by translators and commentators from Maximus Planudes onwards.

Exact algorithms for p-adic fields and epsilon constant conjectures

We develop several algorithms for computations in Galois extensions of p-adic fields. Our algorithms are based on existing algorithms for number fields and are exact in the sense that we do not need to consider approximations to p-adic numbers. As an application we describe an algorithmic approach to prove or disprove various conjectures for local and global epsilon constants.

On Oseen Resolvent Estimates: A Negative Result

We consider the resolvent problem for the scalar Oseen equation in the whole space R^3. We show that for small values of the resolvent parameter it is impossible to obtain an L^2-estimate analogous to the one which is valid for the Stokes resolvent, even if the resolvent parameter has positive real part.

Application of biogas slurries from energy crops to arable soils and their impact on carbon and nitrogen dynamics

The use of renewable primary products as co-substrate or single substrate for biogas production has increased consistently over the last few years. Maize silage is the preferential energy crop used for fermentation due to its high methane (CH4) yield per hectare. Equally, the by-product, namely biogas slurry (BS), is used with increasing frequency as organic fertilizer to return nutrients to the soil and to maintain or increase the organic matter stocks and soil fertility. Studies concerning the application of energy crop-derived BS on the carbon (C) and nitrogen (N) mineralization dynamics are scarce. Thus, this thesis focused on the following objectives: I) The determination of the effects caused by rainfall patterns on the C and N dynamics from two contrasting organic fertilizers, namely BS from maize silage and composted cattle manure (CM), by monitoring emissions of nitrous oxide (N2O), carbon dioxide (CO2) and CH4 as well as leaching losses of C and N. II) The investigation of the impact of differences in soil moisture content after the application of BS and temperature on gaseous emissions (CO2, N2O and CH4) and leaching of C and N compounds. III) A comparison of BS properties obtained from biogas plants with different substrate inputs and operating parameters and their effect on C and N dynamics after application to differently textured soils with varying application rates and water contents. For the objectives I) and II) two experiments (experiment I and II) using undisturbed soil cores of a Haplic Luvisol were carried out. Objective III) was studied on a third experiment (experiment III) with disturbed soil samples. During experiment I three rainfall patterns were implemented including constant irrigation, continuous irrigation with periodic heavy rainfall events, and partial drying with rewetting periods. Biogas slurry and CM were applied at a rate of 100 kg N ha-1. During experiment II constant irrigation and an irrigation pattern with partial drying with rewetting periods were carried out at 13.5°C and 23.5°C. The application of BS took place either directly before a rewetting period or one week after the rewetting period stopped. Experiment III included two soils of different texture which were mixed with ten BS’s originating from ten different biogas plants. Treatments included low, medium and high BS-N application rates and water contents ranging from 50% to 100% of water holding capacity (WHC). Experiment I and II showed that after the application of BS cumulative N2O emissions were 4 times (162 mg N2O-N m-2) higher compared to the application of CM caused by a higher content of mineral N (Nmin) in the form of ammonium (NH4+) in the BS. The cumulative emissions of CO2, however, were on the same level for both fertilizers indicating similar amounts of readily available C after composting and fermentation of organic material. Leaching losses occurred predominantly in the mineral form of nitrate (NO3-) and were higher in BS amended soils (9 mg NO3--N m-2) compared to CM amended soils (5 mg NO3--N m-2). The rainfall pattern in experiment I and II merely affected the temporal production of C and N emissions resulting in reduced CO2 and enhanced N2O emissions during stronger irrigation events, but showed no effect on the cumulative emissions. Overall, a significant increase of CH4 consumption under inconstant irrigation was found. The time of fertilization had no effect on the overall C and N dynamics. Increasing temperature from 13.5°C to 23.5°C enhanced the CO2 and N2O emissions by a factor of 1.7 and 3.7, respectively. Due to the increased microbial activity with increasing temperature soil respiration was enhanced. This led to decreasing oxygen (O2) contents which in turn promoted denitrification in soil due to the extension of anaerobic microsites. Leaching losses of NO3- were also significantly affected by increasing temperature whereas the consumption of CH4 was not affected. The third experiment showed that the input materials of biogas plants affected the properties of the resulting BS. In particular the contents of DM and NH4+ were determined by the amount of added plant biomass and excrement-based biomass, respectively. Correlations between BS properties and CO2 or N2O emissions were not detected. Solely the ammonia (NH3) emissions showed a positive correlation with NH4+ content in BS as well as a negative correlation with the total C (Ct) content. The BS-N application rates affected the relative CO2 emissions (% of C supplied with BS) when applied to silty soil as well as the relative N2O emissions (% of N supplied with BS) when applied to sandy soil. The impacts on the C and N dynamics induced by BS application were exceeded by the differences induced by soil texture. Presumably, due to the higher clay content in silty soils, organic matter was stabilized by organo-mineral interactions and NH4+ was adsorbed at the cation exchange sites. Different water contents induced highest CO2 emissions and therefore optimal conditions for microbial activity at 75% of WHC in both soils. Cumulative nitrification was also highest at 75% and 50% of WHC whereas the relative N2O emissions increased with water content and showed higher N2O losses in sandy soils. In summary it can be stated that the findings of the present thesis confirmed the high fertilizer value of BS’s, caused by high concentrations of NH4+ and labile organic compounds such as readily available carbon. These attributes of BS’s are to a great extent independent of the input materials of biogas plants. However, considerably gaseous and leaching losses of N may occur especially at high moisture contents. The emissions of N2O after field application corresponded with those of animal slurries.

Status and Potential of Smallholder Livestock Production Systems in Xishuangbanna, southern P.R. China

With Chinas rapid economic development during the last decades, the national demand for livestock products has quadrupled within the last 20 years. Most of that increase in demand has been answered by subsidized industrialized production systems, while million of smallholders, which still provide the larger share of livestock products in the country, have been neglected. Fostering those systems would help China to lower its strong urban migration streams, enhance the livelihood of poorer rural population and provide environmentally save livestock products which have a good chance to satisfy customers demand for ecological food. Despite their importance, China’s smallholder livestock keepers have not yet gained appropriate attention from governmental authorities and researchers. However, profound analysis of those systems is required so that adequate support can lead to a better resource utilization and productivity in the sector. To this aim, this pilot study analyzes smallholder livestock production systems in Xishuangbanna, located in southern China. The area is bordered by Lao and Myanmar and geographically counts as tropical region. Its climate is characterized by dry and temperate winters and hot summers with monsoon rains from May to October. While the regionis plain, at about 500 m asl above sea level in the south, outliers of the Himalaya mountains reach out into the north of Xishuangbanna, where the highest peak reaches 2400 m asl. Except of one larger city, Jinghong, Xishuangbanna mainly is covered by tropical rainforest, areas under agricultural cultivation and villages. The major income is generated through inner-Chinese tourism and agricultural production. Intensive rubber plantations are distinctive for the lowland plains while small-scaled traditional farms are scattered in the mountane regions. In order to determine the current state and possible future chances of smallholder livestock production in that region, this study analyzed the current status of the smallholder livestock sector in the Naban River National Nature Reserve (NRNNR), an area which is largely representative for the whole prefecture. It covers an area of about 50square kilometer and reaches from 470 up to 2400 m asl. About 5500 habitants of different ethnic origin are situated in 24 villages. All data have been collected between October 2007 and May 2010. Three major objectives have been addressed in the study: 1. Classifying existing pig production systems and exploring respective pathways for development 2. Quantifying the performance of pig breeding systemsto identify bottlenecks for production 3. Analyzing past and current buffalo utilization to determine the chances and opportunities of buffalo keeping in the future In order to classify the different pig production s ystems, a baseline survey (n=204, stratified cluster sampling) was carried out to gain data about livestock species, numbers, management practices, cultivated plant species and field sizes as well associo-economic characteristics. Sampling included two clusters at village level (altitude, ethnic affiliation), resulting in 13 clusters of which 13-17 farms were interviewed respectively. Categorical Principal Component Analysis (CatPCA) and a two-step clustering algorithm have been applied to identify determining farm characteristics and assort recorded households into classes of livestock production types. The variables keep_sow_yes/no, TLU_pig, TLU_buffalo, size_of_corn_fields, altitude_class, size_of_tea_plantationand size_of_rubber_fieldhave been found to be major determinants for the characterization of the recorded farms. All farms have extensive or semi-intensive livestock production, pigs and buffaloes are predominant livestock species while chicken and aquaculture are available but play subordinate roles for livelihoods. All pig raisers rely on a single local breed, which is known as Small Ear Pig (SMEP) in the region. Three major production systemshave been identified: Livestock-corn based LB; 41%), rubber based (RB; 39%) and pig based (PB;20%) systems. RB farms earn high income from rubber and fatten 1.9 ±1.80 pigs per household (HH), often using purchased pig feed at markets. PB farms own similar sized rubber plantations and raise 4.7 ±2.77 pigs per HH, with fodder mainly being cultivated and collected in theforest. LB farms grow corn, rice and tea and keep 4.6 ±3.32 pigs per HH, also fed with collected and cultivated fodder. Only 29% of all pigs were marketed (LB: 20%; RB: 42%; PB: 25%), average annual mortality was 4.0 ±4.52 pigs per farm (LB: 4.6 ±3.68; RB: 1.9 ±2.14; PB: 7.1 ±10.82). Pig feed mainly consists of banana pseudo stem, corn and rice hives and is prepared in batches about two to three times per week. Such fodder might be sufficient in energy content but lacks appropriate content of protein. Pigs therefore suffer from malnutrition, which becomes most critical in the time before harvest season around October. Farmers reported high occurrences of gastrointestinal parasites in carcasses and often pig stables were wet and filled with manure. Deficits in nutritional and hygienic management are major limits for development and should be the first issues addressed to improve productivity. SME pork was found to be known and referred by local customers in town and by richer lowland farmers. However, high prices and lacking availability of SME pork at local wet-markets were the reasons which limited purchase. If major management constraints are overcome, pig breeders (PB and LB farms) could increase the share of marketed pigs for town markets and provide fatteners to richer RB farmers. RB farmers are interested in fattening pigs for home consumption but do not show any motivation for commercial pig raising. To determine the productivity of input factors in pig production, eproductive performance, feed quality and quantity as well as weight development of pigs under current management were recorded. The data collection included a progeny history survey covering 184 sows and 437 farrows, bi-weekly weighing of 114 pigs during a 16-months time-span on 21 farms (10 LB and 11 PB) as well as the daily recording of feed quality and quantity given to a defined number of pigs on the same 21 farms. Feed samples of all recorded ingredients were analyzed for their respective nutrient content. Since no literature values on thedigestibility of banana pseudo stem – which is a major ingredient of traditional pig feed in NRNNR – were found, a cross-sectional digestibility trial with 2x4 pigs has been conducted on a station in the research area. With the aid of PRY Herd Life Model, all data have been utilized to determine thesystems’ current (Status Quo = SQ) output and the productivity of the input factor “feed” in terms of saleable life weight per kg DM feed intake and monetary value of output per kg DM feed intake.Two improvement scenarios were simulated, assuming 1) that farmers adopt a culling managementthat generates the highest output per unit input (Scenario 1; SC I) and 2) that through improved feeding, selected parameters of reproduction are improved by 30% (SC II). Daily weight gain averaged 55 ± 56 g per day between day 200 and 600. The average feed energy content of traditional feed mix was 14.92 MJ ME. Age at first farrowing averaged 14.5 ± 4.34 months, subsequent inter-farrowing interval was 11.4 ± 2.73 months. Littersize was 5.8 piglets and weaning age was 4.3 ± 0.99 months. 18% of piglets died before weaning. Simulating pig production at actualstatus, it has been show that monetary returns on inputs (ROI) is negative (1:0.67), but improved (1:1.2) when culling management was optimized so that highest output is gained per unit feed input. If in addition better feeding, controlled mating and better resale prices at fixed dates were simulated, ROI further increased to 1:2.45, 1:2.69, 1:2.7 and 1:3.15 for four respective grower groups. Those findings show the potential of pork production, if basic measures of improvement are applied. Futureexploration of the environment, including climate, market-season and culture is required before implementing the recommended measures to ensure a sustainable development of a more effective and resource conserving pork production in the future. The two studies have shown that the production of local SME pigs plays an important role in traditional farms in NRNNR but basic constraints are limiting their productivity. However, relatively easy approaches are sufficient for reaching a notable improvement. Also there is a demand for more SME pork on local markets and, if basic constraints have been overcome, pig farmers could turn into more commercial producers and provide pork to local markets. By that, environmentally safe meat can be offered to sensitive consumers while farmers increase their income and lower the risk of external shocks through a more diverse income generating strategy. Buffaloes have been found to be the second important livestock species on NRNNR farms. While they have been a core resource of mixed smallholderfarms in the past, the expansion of rubber tree plantations and agricultural mechanization are reasons for decreased swamp buffalo numbers today. The third study seeks to predict future utilization of buffaloes on different farm types in NRNNR by analyzing the dynamics of its buffalo population and land use changes over time and calculating labor which is required for keeping buffaloes in view of the traction power which can be utilized for field preparation. The use of buffaloes for field work and the recent development of the egional buffalo population were analyzed through interviews with 184 farmers in 2007/2008 and discussions with 62 buffalo keepers in 2009. While pig based farms (PB; n=37) have abandoned buffalo keeping, 11% of the rubber based farms (RB; n=71) and 100% of the livestock-corn based farms (LB; n=76) kept buffaloes in 2008. Herd size was 2.5 ±1.80 (n=84) buffaloes in early 2008 and 2.2 ±1.69 (n=62) in 2009. Field work on own land was the main reason forkeeping buffaloes (87.3%), but lending work buffaloes to neighbors (79.0%) was also important. Other purposes were transport of goods (16.1%), buffalo trade (11.3%) and meat consumption(6.4%). Buffalo care required 6.2 ±3.00 working hours daily, while annual working time of abuffalo was 294 ±216.6 hours. The area ploughed with buffaloes remained constant during the past 10 years despite an expansion of land cropped per farm. Further rapid replacement of buffaloes by tractors is expected in the near future. While the work economy is drastically improved by the use of tractors, buffaloes still can provide cheap work force and serve as buffer for economic shocks on poorer farms. Especially poor farms, which lack alternative assets that could quickly be liquidizedin times of urgent need for cash, should not abandon buffalo keeping. Livestock has been found to be a major part of small mixed farms in NRNNR. The general productivity was low in both analyzed species, buffaloes and pigs. Productivity of pigs can be improved through basic adjustments in feeding, reproductive and hygienic management, and with external support pig production could further be commercialized to provide pork and weaners to local markets and fattening farms. Buffalo production is relatively time intensive, and only will be of importance in the future to very poor farms and such farms that cultivate very small terraces on steep slopes. These should be encouraged to further keep buffaloes. With such measures, livestock production in NRNNR has good chances to stay competitive in the future.

Time Discretization of the SST-generalized Navier-Stokes Equations: Positive and Negative Results

In the theory of the Navier-Stokes equations, the proofs of some basic known results, like for example the uniqueness of solutions to the stationary Navier-Stokes equations under smallness assumptions on the data or the stability of certain time discretization schemes, actually only use a small range of properties and are therefore valid in a more general context. This observation leads us to introduce the concept of SST spaces, a generalization of the functional setting for the Navier-Stokes equations. It allows us to prove (by means of counterexamples) that several uniqueness and stability conjectures that are still open in the case of the Navier-Stokes equations have a negative answer in the larger class of SST spaces, thereby showing that proof strategies used for a number of classical results are not sufficient to affirmatively answer these open questions. More precisely, in the larger class of SST spaces, non-uniqueness phenomena can be observed for the implicit Euler scheme, for two nonlinear versions of the Crank-Nicolson scheme, for the fractional step theta scheme, and for the SST-generalized stationary Navier-Stokes equations. As far as stability is concerned, a linear version of the Euler scheme, a nonlinear version of the Crank-Nicolson scheme, and the fractional step theta scheme turn out to be non-stable in the class of SST spaces. The positive results established in this thesis include the generalization of classical uniqueness and stability results to SST spaces, the uniqueness of solutions (under smallness assumptions) to two nonlinear versions of the Euler scheme, two nonlinear versions of the Crank-Nicolson scheme, and the fractional step theta scheme for general SST spaces, the second order convergence of a version of the Crank-Nicolson scheme, and a new proof of the first order convergence of the implicit Euler scheme for the Navier-Stokes equations. For each convergence result, we provide conditions on the data that guarantee the existence of nonstationary solutions satisfying the regularity assumptions needed for the corresponding convergence theorem. In the case of the Crank-Nicolson scheme, this involves a compatibility condition at the corner of the space-time cylinder, which can be satisfied via a suitable prescription of the initial acceleration.

The prediction of seasonal and inter-annual climate variations and their impacts on the water resources in the eastern seaboard of Thailand

The research of this thesis dissertation covers developments and applications of short-and long-term climate predictions. The short-term prediction emphasizes monthly and seasonal climate, i.e. forecasting from up to the next month over a season to up to a year or so. The long-term predictions pertain to the analysis of inter-annual- and decadal climate variations over the whole 21st century. These two climate prediction methods are validated and applied in the study area, namely, Khlong Yai (KY) water basin located in the eastern seaboard of Thailand which is a major industrial zone of the country and which has been suffering from severe drought and water shortage in recent years. Since water resources are essential for the further industrial development in this region, a thorough analysis of the potential climate change with its subsequent impact on the water supply in the area is at the heart of this thesis research. The short-term forecast of the next-season climate, such as temperatures and rainfall, offers a potential general guideline for water management and reservoir operation. To that avail, statistical models based on autoregressive techniques, i.e., AR-, ARIMA- and ARIMAex-, which includes additional external regressors, and multiple linear regression- (MLR) models, are developed and applied in the study region. Teleconnections between ocean states and the local climate are investigated and used as extra external predictors in the ARIMAex- and the MLR-model and shown to enhance the accuracy of the short-term predictions significantly. However, as the ocean state – local climate teleconnective relationships provide only a one- to four-month ahead lead time, the ocean state indices can support only a one-season-ahead forecast. Hence, GCM- climate predictors are also suggested as an additional predictor-set for a more reliable and somewhat longer short-term forecast. For the preparation of “pre-warning” information for up-coming possible future climate change with potential adverse hydrological impacts in the study region, the long-term climate prediction methodology is applied. The latter is based on the downscaling of climate predictions from several single- and multi-domain GCMs, using the two well-known downscaling methods SDSM and LARS-WG and a newly developed MLR-downscaling technique that allows the incorporation of a multitude of monthly or daily climate predictors from one- or several (multi-domain) parent GCMs. The numerous downscaling experiments indicate that the MLR- method is more accurate than SDSM and LARS-WG in predicting the recent past 20th-century (1971-2000) long-term monthly climate in the region. The MLR-model is, consequently, then employed to downscale 21st-century GCM- climate predictions under SRES-scenarios A1B, A2 and B1. However, since the hydrological watershed model requires daily-scale climate input data, a new stochastic daily climate generator is developed to rescale monthly observed or predicted climate series to daily series, while adhering to the statistical and geospatial distributional attributes of observed (past) daily climate series in the calibration phase. Employing this daily climate generator, 30 realizations of future daily climate series from downscaled monthly GCM-climate predictor sets are produced and used as input in the SWAT- distributed watershed model, to simulate future streamflow and other hydrological water budget components in the study region in a multi-realization manner. In addition to a general examination of the future changes of the hydrological regime in the KY-basin, potential future changes of the water budgets of three main reservoirs in the basin are analysed, as these are a major source of water supply in the study region. The results of the long-term 21st-century downscaled climate predictions provide evidence that, compared with the past 20th-reference period, the future climate in the study area will be more extreme, particularly, for SRES A1B. Thus, the temperatures will be higher and exhibit larger fluctuations. Although the future intensity of the rainfall is nearly constant, its spatial distribution across the region is partially changing. There is further evidence that the sequential rainfall occurrence will be decreased, so that short periods of high intensities will be followed by longer dry spells. This change in the sequential rainfall pattern will also lead to seasonal reductions of the streamflow and seasonal changes (decreases) of the water storage in the reservoirs. In any case, these predicted future climate changes with their hydrological impacts should encourage water planner and policy makers to develop adaptation strategies to properly handle the future water supply in this area, following the guidelines suggested in this study.