Approximate Approximations and a Boundary Point Method for the Linearized Stokes System

The method of approximate approximations, introduced by Maz'ya [1], can also be used for the numerical solution of boundary integral equations. In this case, the matrix of the resulting algebraic system to compute an approximate source density depends only on the position of a finite number of boundary points and on the direction of the normal vector in these points (Boundary Point Method). We investigate this approach for the Stokes problem in the whole space and for the Stokes boundary value problem in a bounded convex domain G subset R^2, where the second part consists of three steps: In a first step the unknown potential density is replaced by a linear combination of exponentially decreasing basis functions concentrated near the boundary points. In a second step, integration over the boundary partial G is replaced by integration over the tangents at the boundary points such that even analytical expressions for the potential approximations can be obtained. In a third step, finally, the linear algebraic system is solved to determine an approximate density function and the resulting solution of the Stokes boundary value problem. Even not convergent the method leads to an efficient approximation of the form O(h^2) + epsilon, where epsilon can be chosen arbitrarily small.

The role of ligneous vegetation for livestock nutrition in the sub-Sahelian and Sudanian zones of West Africa: Potential effects of climate change

Climate change and variability in sub-Saharan West Africa is expected to have negative consequences for crop and livestock farming due to the strong dependence of these sectors on rainfall and natural resources, and the low adaptive capacity of crops farmers, agro-pastoralist and pastoralists in the region. The objective of this PhD research was to investigate the anticipated impacts of expected future climate change and variability on nutrition and grazing management of livestock in the prevailing extensive agro-pastoral and pastoral systems of the Sahelian and Sudanian zones of Burkina Faso. To achieve this, three studies were undertaken in selected village territories (100 km² each) in the southern Sahelian (Taffogo), northern Sudanian (Nobere, Safane) and southern Sudanian (Sokouraba) zone of the country during 2009 and 2010. The choice of two villages in the northern Sudanian zone was guided by the dichotomy between intense agricultural land use and high population density near Safane, and lower agricultural land use in the tampon zone between the village of Nobere and the National Park Kaboré Tambi of Pô. Using global positioning and geographical information systems tools, the spatio-temporal variation in the use of grazing areas by cattle, sheep and goats, and in their foraging behaviour in the four villages was assessed by monitoring three herds each per species during a one-year cycle (Chapter 2). Maximum itinerary lengths (km/d) were observed in the hot dry season (March-May); they were longer for sheep (18.8) and cattle (17.4) than for goats (10.5, p<0.05). Daily total grazing time spent on pasture ranged from 6 - 11 h with cattle staying longer on pasture than small ruminants (p<0.05). Feeding time accounted for 52% - 72% of daily time on pasture, irrespective of species. Herds spent longer time on pasture and walked farther distances in the southern Sahelian than the two Sudanian zones (p<0.01), while daily feeding time was longer in the southern Sudanian than in the other two zones (p>0.05). Proportional time spent resting decreased from the rainy (June - October) to the cool (November - February) and hot dry season (p<0.05), while in parallel the proportion of walking time increased. Feeding time of all species was to a significantly high proportion spent on wooded land (tree crown cover 5-10%, or shrub cover >10%) in the southern Sahelian zone, and on forest land (tree crown cover >10%) in the two Sudanian zones, irrespective of season. It is concluded that with the expansion of cropland in the whole region, remaining islands of wooded land, including also fields fallowed for three or more years with their considerable shrub cover, are particularly valuable pasturing areas for ruminant stock. Measures must be taken that counteract the shrinking of wooded land and forests across the whole region, including also active protection and (re)establishment of drought-tolerant fodder trees. Observation of the selection behaviour of the above herds of cattle and small ruminant as far as browse species were concerned, and interviews with 75 of Fulani livestock keepers on use of browse as feed by their ruminant stock and as remedies for animal disease treatment was undertaken (Chapter 3) in order to evaluate the consequence of climate change for the contribution of browse to livestock nutrition and animal health in the extensive grazing-based livestock systems. The results indicated that grazing cattle and small ruminants do make considerable use of browse species on pasture across the studied agro-ecological zones. Goats spent more time (p<0.01) feeding on browse species than sheep and cattle, which spent a low to moderate proportion of their feeding time on browsing in any of the study sites. As far as the agro-ecological zones were concerned, the contribution of browse species to livestock nutrition was more important in the southern Sahelian and northern Sudanian zone than the southern Sudanian zone, and this contribution is higher during the cold and hot dry season than during the rainy season. A total of 75 browse species were selected on pasture year around, whereby cattle strongly preferred Afzelia africana, Pterocarpus erinaceus and Piliostigma sp., while sheep and goats primarily fed on Balanites aegyptiaca, Ziziphus mauritiana and Acacia sp. Crude protein concentration (in DM) of pods or fruits of the most important browse species selected by goats, sheep and cattle ranged from 7% to 13% for pods, and from 10% to 18% for foliage. The concentration of digestible organic matter of preferred browse species mostly ranged from 40% to 60%, and the concentrations of total phenols, condensed tannins and acid detergent lignin were low. Linear regression analyses showed that browse preference on pasture is strongly related to its contents (% of DM) of CP, ADF, NDF and OM digestibility. Interviewed livestock keepers reported that browse species are increasingly use by their grazing animals, while for animal health care use of tree- and shrub-based remedies decreased over the last two decades. It is concluded that due to climate change with expected negative impact on the productivity of the herbaceous layer of communal pastures browse fodder will gain in importance for animal nutrition. Therefore re-establishment and dissemination of locally adapted browse species preferred by ruminants is needed to increase the nutritional situation of ruminant stock in the region and contribute to species diversity and soil fertility restoration in degraded pasture areas. In Chapter 4 a combination of household surveys and participatory research approaches was used in the four villages, and additionally in the village of Zogoré (southern Sahelian zone) and of Karangasso Vigué (northern Sudanian zone) to investigate pastoralists’ (n= 76) and agro-pastoralists’ (n= 83) perception of climate change, and their adaptation strategies in crop and livestock production at farm level. Across the three agro-ecological zones, the majority of the interviewees perceived an increase in maximum day temperatures and decrease of total annual rainfall over the last two decades. Perceptions of change in climate patterns were in line with meteorological data for increased temperatures while for total rainfall farmers’ views contrasted the rainfall records which showed a slight increase of precipitation. According to all interviewees climate change and variability have negative impacts on their crop and animal husbandry, and most of them already adopted some coping and adaptation strategies at farm level to secure their livelihoods and reduce negative impacts on their farming system. Although these strategies are valuable and can help crop and livestock farmers to cope with the recurrent droughts and climate variability, they are not effective against expected extreme climate events. Governmental and non-governmental organisations should develop effective policies and strategies at local, regional and national level to support farmers in their endeavours to cope with climate change phenomena; measures should be site-specific and take into account farmers’ experiences and strategies already in place.

Spatial and harvesting influence on growth, yield, quality and economic potential of Kalmegh (Andrographis paniculata Wall Ex. Nees)

Andrographis paniculata, commonly known as Kalmegh, is used both in Ayurvedic and Unani system of medicines because of its immunological, antibacterial and hepatoprotective properties. This study was carried out to investigate the influence of four harvesting times (120,135,150 days after planting and at seed maturity) and four planting distances (30×15, 30×10, 20×15 and 20×10 cm) on growth, dry herbage biomass, seed yield and quality traits of Andrographis paniculata at CCS Haryana Agricultural University, Hisar, India in the two years 2005 and 2006. The treatments were laid out in a split plot design with three replications. The maximum values for dry herbage biomass yield (5.14 t ha^(-1)), net returns (760.00 EUR ha^(-1)), B:C ratio (2.59), andrographolide content (2.63%) and total yield (135.00 kg ha^(-1)) were detected 135 days after planting with an optimum planting distance of 30×15 cm. However, the maximum iron content was estimated 120 days after planting. The highest dry herbage (4.58 t ha^(-1)) and maximum seed yield (19.7 kg ha^(-1)) were registered at plants that were lined out with a distance of 20×10 cm.