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.

Decomposition of and nutrient release from ruminant manure on acid sandy soils in the Sahelian zone of Niger, West Africa

In ago-pastoral systems of the semi-arid West African Sahel, targeted applications of ruminant manure to the cropland is a widespread practice to maintain soil productivity. However, studies exploring the decomposition and mineralisation processes of manure under farmers' conditions are scarce. The present research in south-west Niger was undertaken to examine the role of micro-organisms and meso-fauna on in situ release rates of nitrogen (N), phosphorus (P) and potassium (K) from cattle and sheep-goat manure collected from village corrals during the rainy season. The results show tha (1) macro-organisms played a dominant role in the initial phase of manure decomposition; (2) manure decomposition was faster on crusted than on sandy soils; (3) throughout the study N and P release rates closely followed the dry matter decomposition; (4) during the first 6 weeks after application the K concentration in the manure declined much faster than N or P. At the applied dry matter rate of 18.8 Mg ha^-1, the quantities of N, P and K released from the manure during the rainy season were up to 10-fold larger than the annual nutrient uptake of pearl millet (Pennisetum glaucum L.), the dominant crop in the traditional agro-pastoral systems. The results indicate considerable nutrient losses with the scarce but heavy rainfalls which could be alleviated by smaller rates of manure application. Those, however, would require a more labour intensive system of corralling or manure distribution.

Composition and stability of organic matter fractions in soils under different land use regimes

Soil organic matter (SOM) vitally impacts all soil functions and plays a key role in the global carbon (C) cycle. More than 70% of the terrestric C stocks that participate in the active C cycle are stored in the soil. Therefore, quantitative knowledge of the rates of C incorporation into SOM fractions of different residence time is crucial to understand and predict the sequestration and stabilization of soil organic carbon (SOC). Consequently, there is a need of fractionation procedures that are capable of isolating functionally SOM fractions, i.e. fractions that are defined by their stability. The literature generally refers to three main mechanisms of SOM stabilization: protection of SOM from decomposition by (i) its structural composition, i.e. recalcitrance, (ii) spatial inaccessibility and/or (iii) interaction with soil minerals and metal ions. One of the difficulties in developing fractionation procedures for the isolation of functional SOM fractions is the marked heterogeneity of the soil environment with its various stabilization mechanisms – often several mechanisms operating simultaneously – in soils and soil horizons of different texture and mineralogy. The overall objective of the present thesis was to evaluate present fractionation techniques and to get a better understanding of the factors of SOM sequestration and stabilization. The first part of this study is attended to the structural composition of SOM. Using 13C cross-polarization magic-angle spinning (CPMAS) nuclear magnetic resonance (NMR) spectroscopy, (i) the effect of land use on SOM composition was investigated and (ii) examined whether SOM composition contributes to the different stability of SOM in density and aggregate fractions. The second part of the present work deals with the mineral-associated SOM fraction. The aim was (iii) to evaluate the suitability of chemical fractionation procedures used in the literature for the isolation of stable SOM pools (stepwise hydrolysis, treatments using oxidizing agents like Na2S2O8, H2O2, and NaOCl as well as demineralization of the residue obtained by the NaOCl treatment using HF (NaOCl+HF)) by pool sizes, 13C and 14C data. Further, (iv) the isolated SOM fractions were compared to the inert organic matter (IOM) pool obtained for the investigated soils using the Rothamsted Carbon Model and isotope data in order to see whether the tested chemical fractionation methods produce SOM fractions capable to represent this pool. Besides chemical fractionation, (v) the suitability of thermal oxidation at different temperatures for obtaining stable SOC pools was evaluated. Finally, (vi) the short-term aggregate dynamics and the factors that impact macroaggregate formation and C stabilization were investigated by means of an incubation study using treatments with and without application of 15N labeled maize straw of different degradability (leaves and coarse roots). All treatments were conducted with and without the addition of fungicide. Two study sites with different soil properties and land managements were chosen for these investigations. The first one, located at Rotthalmünster, is a Stagnic Luvisol (silty loam) under different land use regimes. The Ah horizons of a spruce forest and continuous grassland and the Ap and E horizons of two plots with arable crops (continuous maize and wheat cropping) were examined. The soil of the second study site, located at Halle, is a Haplic Phaeozem (loamy sand) where the Ap horizons of two plots with arable crops (continuous maize and rye cropping) were investigated. Both study sites had a C3-/C4-vegetational change on the maize plot for the purpose of tracing the incorporation of the younger, maize-derived C into different SOM fractions and the calculation of apparent C turnover times of these. The Halle site is located near a train station and industrial areas, which caused a contamination with high amounts of fossil C. The investigation of aggregate and density fractions by 13C CPMAS NMR spectroscopy revealed that density fractionation isolated SOM fractions of different composition. The consumption of a considerable part (10–20%) of the easily available O-alkyl-C and the selective preservation of the more recalcitrant alkyl-C when passing from litter to the different particulate organic matter (POM) fractions suggest that density fractionation was able to isolate SOM fractions with different degrees of decomposition. The spectra of the aggregate fractions resembled those of the mineral-associated SOM fraction obtained by density fractionation and no considerable differences were observed between aggregate size classes. Comparison of plant litter, density and aggregate size fractions from soil under different land use showed that the type of land use markedly influenced the composition of SOM. While SOM of the acid forest soil was characterized by a large content (> 50%) of POM, which contained high amounts of spruce-litter derived alkyl-C, the organic matter in the biologically more active grassland and arable soils was dominated by mineral-associated SOM (> 95%). This SOM fraction comprised greater proportions of aryl- and carbonyl-C and is considered to contain a higher amount of microbially-derived organic substances. Land use can alter both, structure and stability of SOM fractions. All applied chemical treatments induced considerable SOC losses (> 70–95% of mineral-associated SOM) in the investigated soils. The proportion of residual C after chemical fractionation was largest in the arable Ap and E horizons and increased with decreasing C content in the initial SOC after stepwise hydrolysis as well as after the oxidative treatments with H2O2 and Na2S2O8. This can be expected for a functional stable pool of SOM, because it is assumed that the more easily available part of SOC is consumed first if C inputs decrease. All chemical treatments led to a preferential loss of the younger, maize-derived SOC, but this was most pronounced after the treatments with Na2S2O8 and H2O2. After all chemical fractionations, the mean 14C ages of SOC were higher than in the mineral-associated SOM fraction for both study sites and increased in the order: NaOCl < NaOCl+HF ≤ stepwise hydrolysis << H2O2 ≈ Na2S2O8. The results suggest that all treatments were capable of isolating a more stable SOM fraction, but the treatments with H2O2 and Na2S2O8 were the most efficient ones. However, none of the chemical fractionation methods was able to fit the IOM pool calculated using the Rothamsted Carbon Model and isotope data. In the evaluation of thermal oxidation for obtaining stable C fractions, SOC losses increased with temperature from 24–48% (200°C) to 100% (500°C). In the Halle maize Ap horizon, losses of the young, maize-derived C were considerably higher than losses of the older C3-derived C, leading to an increase in the apparent C turnover time from 220 years in mineral-associated SOC to 1158 years after thermal oxidation at 300°C. Most likely, the preferential loss of maize-derived C in the Halle soil was caused by the presence of the high amounts of fossil C mentioned above, which make up a relatively large thermally stable C3-C pool in this soil. This agrees with lower overall SOC losses for the Halle Ap horizon compared to the Rotthalmünster Ap horizon. In the Rotthalmünster soil only slightly more maize-derived than C3-derived SOC was removed by thermal oxidation. Apparent C turnover times increased slightly from 58 years in mineral-associated SOC to 77 years after thermal oxidation at 300°C in the Rotthalmünster Ap and from 151 to 247 years in the Rotthalmünster E horizon. This led to the conclusion that thermal oxidation of SOM was not capable of isolating SOM fractions of considerably higher stability. The incubation experiment showed that macroaggregates develop rapidly after the addition of easily available plant residues. Within the first four weeks of incubation, the maximum aggregation was reached in all treatments without addition of fungicide. The formation of water-stable macroaggregates was related to the size of the microbial biomass pool and its activity. Furthermore, fungi were found to be crucial for the development of soil macroaggregates as the formation of water-stable macroaggregates was significantly delayed in the fungicide treated soils. The C concentration in the obtained aggregate fractions decreased with decreasing aggregate size class, which is in line with the aggregate hierarchy postulated by several authors for soils with SOM as the major binding agent. Macroaggregation involved incorporation of large amounts maize-derived organic matter, but macroaggregates did not play the most important role in the stabilization of maize-derived SOM, because of their relatively low amount (less than 10% of the soil mass). Furthermore, the maize-derived organic matter was quickly incorporated into all aggregate size classes. The microaggregate fraction stored the largest quantities of maize-derived C and N – up to 70% of the residual maize-C and -N were stored in this fraction.

Smallholder group certification in Uganda - Analysis of internal control systems in two organic export companies

The organic agricultural sector of Uganda is among the most developed in Africa in terms of its professional institutional network and high growth rates of number of certified farmers and land area. Smallholder farmers are certified organic through contract production for export companies using a group certification scheme (internal control system - ICS). The ICS is a viable and well-accepted tool to certify small-scale producers in developing countries all over the world. Difficulties in certification are still stated to be among the main constraints for Uganda’s organic sector development. Therefore, this paper reports a qualitative case study comprising 34 expert interviews in two organic fresh-produce export companies in central Uganda, aiming to explore the challenges which underlie organic certification with ICS. The study shows that farmers cannot be labelled as ‘organic by default’ but deliberately engage in organic production as a marketing strategy. The small quantities purchased by the organic companies lead to a difficult marketing situation for the farmers, causing production and infiltration risks on the farm level. These risks require increased control that challenges the companies organizationally. The risks and control needs are a reason to involve farmers in ICS procedures and innovatively adapt the ICS by means of a bypass around formal perspective restrictions. The paper discusses different perspectives on risks, risk control and certification.

Pharmaceutical consumption and residuals potentially relevant to nutrient cycling in Greater Accra, Ghana

Recycling nutrients form sanitary wastes back into agricultural ecosystems offers an option to alleviate soil depletion in regions where the use of mineral fertiliser is limited. Exemplary nutrient and water cycling approaches, including collection, treatment and use of human urine, are established at Valley View University (VVU) in Greater Accra, Ghana. Concerns have been recently raised in regard to fate and impact of pharmaceutical residues in soils and interlinked environment. To evaluate in how far emerging knowledge can be transposed onto VVU, urban and rural environments in Greater Accra, spatial disease occurrence and drug consumption patterns were studied. Malaria has been found to represent the most severe health burden in Ghana, but there is also a high prevalence of infectious diseases. Drugs consumed in great quantities and in respect to their residual loads potentially problematic in the environment belong to therapeutic groups of: antibiotics, analgesics, drugs for diabetes, antimalarials, cardiovascular drugs and anthelmintics. Drug consumption revealed to be highest in urban and lowest in rural areas. At VVU the range of consumed drugs is comparable to urban areas except for the negligible use of diabetes and cardiovascular medication as well as contraceptives.

Einfluss der Führung des Trocknungsprozesses auf den Trocknungsverlauf und die Produkteigenschaften empfindlicher biologischer Güter

Die Konvektionstrocknung ist eine der ältesten Methoden zur Konservierung von Lebensmitteln. Es ist bekannt, dass Agrarprodukte temperaturempfindlich sind. Bei Überhitzung erleiden sie chemische und physikalische Veränderungen, die ihre Qualität vermindern. In der industriellen Praxis wird die Konvektionstrocknung in der Regel auf Grundlage empirisch ermittelter Werte durchgeführt, welche die Produkttemperatur nicht berücksichtigen. Es ist deshalb nicht sichergestellt, ob der Prozess optimal oder auch nur gut betrieben wird. Inhalt dieser Arbeit ist ein Vergleich der klassischen einstufigen Konvektionstrocknung mit einer Prozessführungsstrategie bei der die Produkttemperatur als Regelgröße eingeführt wird. Anhand der Untersuchung des Trocknungsverhaltens von Äpfeln werden die beiden Verfahren analysiert, die erhaltenen Ergebnisse miteinander verglichen und daraus optimierte Trocknungsbedingungen abgeleitet. Die für dieses Projekt entwickelte Prozessanlage erlaubt die simultane Untersuchung sämtlicher wesentlicher Temperaturen, der Gewichtsveränderung und der optischen Qualitätskriterien. Gleichzeitig ist es möglich, entweder die Lufttemperatur oder die Temperatur des Produktes zur regeln, während die jeweils andere Größe als Messwert erfasst wird. Es kann weiterhin zwischen Durch- und Überströmung gewählt werden.

Theoretical study of magnetism, structure and chemical order in transition-metal alloy clusters

Research on transition-metal nanoalloy clusters composed of a few atoms is fascinating by their unusual properties due to the interplay among the structure, chemical order and magnetism. Such nanoalloy clusters, can be used to construct nanometer devices for technological applications by manipulating their remarkable magnetic, chemical and optical properties. Determining the nanoscopic features exhibited by the magnetic alloy clusters signifies the need for a systematic global and local exploration of their potential-energy surface in order to identify all the relevant energetically low-lying magnetic isomers. In this thesis the sampling of the potential-energy surface has been performed by employing the state-of-the-art spin-polarized density-functional theory in combination with graph theory and the basin-hopping global optimization techniques. This combination is vital for a quantitative analysis of the quantum mechanical energetics. The first approach, i.e., spin-polarized density-functional theory together with the graph theory method, is applied to study the Fe$_m$Rh$_n$ and Co$_m$Pd$_n$ clusters having $N = m+n \leq 8$ atoms. We carried out a thorough and systematic sampling of the potential-energy surface by taking into account all possible initial cluster topologies, all different distributions of the two kinds of atoms within the cluster, the entire concentration range between the pure limits, and different initial magnetic configurations such as ferro- and anti-ferromagnetic coupling. The remarkable magnetic properties shown by FeRh and CoPd nanoclusters are attributed to the extremely reduced coordination number together with the charge transfer from 3$d$ to 4$d$ elements. The second approach, i.e., spin-polarized density-functional theory together with the basin-hopping method is applied to study the small Fe$_6$, Fe$_3$Rh$_3$ and Rh$_6$ and the larger Fe$_{13}$, Fe$_6$Rh$_7$ and Rh$_{13}$ clusters as illustrative benchmark systems. This method is able to identify the true ground-state structures of Fe$_6$ and Fe$_3$Rh$_3$ which were not obtained by using the first approach. However, both approaches predict a similar cluster for the ground-state of Rh$_6$. Moreover, the computational time taken by this approach is found to be significantly lower than the first approach. The ground-state structure of Fe$_{13}$ cluster is found to be an icosahedral structure, whereas Rh$_{13}$ and Fe$_6$Rh$_7$ isomers relax into cage-like and layered-like structures, respectively. All the clusters display a remarkable variety of structural and magnetic behaviors. It is observed that the isomers having similar shape with small distortion with respect to each other can exhibit quite different magnetic moments. This has been interpreted as a probable artifact of spin-rotational symmetry breaking introduced by the spin-polarized GGA. The possibility of combining the spin-polarized density-functional theory with some other global optimization techniques such as minima-hopping method could be the next step in this direction. This combination is expected to be an ideal sampling approach having the advantage of avoiding efficiently the search over irrelevant regions of the potential energy surface.

Matter fluxes in mountain oases of Al Jabal Al Akhdar, Oman

Since 1970 when Sultan Qaboos bin Said Al Said took over power from this father, agriculture in Oman has undergone major transformations as a consequence of rapid population and economic growth. In this process groundwater extraction has dramatically increased to meet domestic and agricultural needs. Recently, the agro-ecosystem of ancient mountain oases of Oman have received greater attention as interest has grown to understand the causes of their often millennia old sustainable productivity. Particularly little is known about the carbon (C) and nutrient turnover in these intensive landuse systems. This is partly due to the difficulties to measure such processes in the often remote fields. To fill the existing gap of knowledge, field studies were conducted in five oases at different altitudes of Al Jabal Al Akhdar, the highest agricultural area in Oman, to determine C and nutrient fluxes as well as nutrient use efficiencies for two different cropping systems as affected by temperature, irrigation, and manure quality. The results of this study indicated that water scarcity as a result of low precipitation and an increase in urban water consumption is a major threat to the sustainability of agriculture in these oases. Optimizing the use of irrigation water is a major challenge for agriculture in these oases, particularly given ever increasing competition for this most limiting resource. Traditionally, farmers of these oases adapt to variation of irrigation water supply by minimizing the growing area of annual crops, leaving these areas uncultivated through drought seasons (Luedeling and Buerkert 2008). In this study, a remarkable reduction in annual crop area was observed in 2009 for all oases. Our results suggested that water scarcity as a result of low precipitation and the increase in urban water consumption cause such changes in land use. The data also underline the intensive C and nutrient turnover in the man-made irrigated agroecosystems and confirmed the importance of the large manure quantities applied continuously to the terraces as a key factor responsible for sustainable soil productivity. To trace the fate of C and plant nutrients that are released from the large amount of manure applied by oasis farmers, more detailed studies under controlled conditions, using isotope signatures, would be needed.

Nitrogen requirements of cassava in selected soils of Thailand

Cassava (Manihot esculenta) is one of the most important export crops in Thailand, yet the nitrogen requirement is unknown and not considered by growers and producers. Cassava requirements for N were determined in field experiments during a period of four years and four sites on the Satuk (Suk), Don Chedi (Dc), Pak Chong (Pc),and Ban Beung (BBg) soil series in Lopburi, Supanburi, Nakhon Ratchasima, and Chonburi sites, respectively. The fertilizer treatment structure comprised 0, 62.5, 125, 187.5, 250 and 312.5 kg N ha^(-1) as urea. At each site cassava was harvested at nine months and yield parameters and the minimum datasets were taken. The fertilizer rate which resulted in maximum yield ranged from 187.5 kg N ha^(-1) in Supanburi and Chonburi (fresh weight yield of 47,500 and 30,000 kg ha^(-1) respectively) to 250 kg N ha^(-1) in Lopburi and Nakhon Ratchasima (fresh weight yield of 64,100 and 46,700 kg ha^(-1) respectively). Yield appeared to decrease at the higher, 312 kg ha^(-1), at Supanburi and Lopburi, and 250 kg ha^(-1) (Chonburi) fertilizer N rates. Net revenue was 70.4 and 72.9 % higher than where no N was appliedLopburi and Nakhon Ratchasima sites. Net revenue at the Supanburi and Chonburi sites were 53.8 and 211.0 % higher than that where no N was applied. This study suggests that at all sites improved cassava production and net revenue could be obtained with the judicious application of higher quantities of N. The results provide needed guidance to nitrogen fertilization of the important industrial crop cassava in Thailand.

Socio-economic characterization of integrated cropping systems in urban and peri-urban agriculture of Faisalabad, Pakistan

Faisalabad city is surrounded by agricultural lands, where farmers are growing vegetables, grain crops, and fodder for auto-consumption and local marketing. To study the socioeconomic impact and resource use in these urban and peri-urban agricultural production (UPA) systems, a baseline survey was conducted during 2009–2010. A total of 140 households were selected using a stratified sampling method and interviewed with a structured questionnaire. The results revealed that 96 % of the households rely on agriculture as their main occupation. Thirty percent of the households were owners of the land and the rest cultivated either rented or sharecropped land. Most of the families (70 %) were headed by a member with primary education, and only 10 % of the household head had a secondary school certificate. Irrigationwater was obtained from waste water (37 %), canals (27 %), and mixed alternative sources (36 %). A total of 35 species were cultivated in the UPA systems of which were 65% vegetables, 15% grain and fodder crops, and 5% medicinal plants. Fifty-nine percent of the households cultivated wheat, mostly for auto-consumption. The 51 % of the respondents grew cauliflower (Brassica oleracea L.) and gourds (Cucurbitaceae) in the winter and summer seasons, respectively. Group marketing was uncommon and most of the farmers sold their produce at the farm gate (45 %) and on local markets (43 %). Seeds and fertilizers were available from commission agents and dealers on a credit basis with the obligation to pay by harvested produce. A major problem reported by the UPA farmers of Faisalabad was the scarcity of high quality irrigation water, especially during the hot dry summer months, in addition to lacking adequate quantities of mineral fertilizers and other inputs during sowing time. Half of the respondents estimated their daily income to be less than 1.25 US$ and spent almost half of it on food. Monthly average household income and expenses were 334 and 237 US$, respectively.

Home gardens and Dioscorea species – A case study from the climatic zones of Sri Lanka

Home gardens are considered as vital units for enhancing food security particularly in developing nations of South Asia, such as Sri Lanka. Although the yam crop Dioscorea spp. constitute a popular but still minor component in Sri Lankan home gardens, they have the potential of producing large quantities of edible material with minimal inputs. However, their real value in South Asian home gardens is not yet reported. Hence, this study was carried out to get insights into home garden characteristics, gardener demography as well as current management practices within 300 Sri Lankan home garden systems that are located along a climatic gradient. By using interviews and field observations, gardeners, who cultivated in particular Dioscorea species, were studied within 10 of the 25 administrative districts distributed in the wet, intermediate and dry climatic zone of Sri Lanka. Furthermore, current management practices of yams cultivation were analyzed on local scale and compared afterwards with management recommendations published in the year 2006 by the Department of Agriculture. Dioscorea species were found in a majority of home gardens, especially in wet and intermediate zones of Sri Lanka. D. alata was the most prominent species and was managed at a subsistence level and not as per recommendations developed by the Department of Agriculture. Our results revealed that Dioscorea alata is an essential component of Sri Lankan home gardens in rural areas and can yield substantial quantities of edible tubers with low input, especially during times of food scarcities, and has therefore the potential to enhance food security and rural development.