We introduce a new class of higher order numerical schemes for parabolic partial differential equations that are more robust than the well-known Rannacher schemes. The new family of algorithms utilizes diagonal Padé schemes combined with positivity-preserving Padé schemes instead of first subdiagonal Padé schemes. We utilize a partial fraction decomposition to address problems with accuracy and computational efficiency in solving the higher order methods and to implement the algorithms in parallel. Optimal order convergence for nonsmooth data is proved for the case of a self-adjoint operator in Hilbert space as well as in Banach space for the general case. Numerical experiments support the theorems, including examples in pricing options with nonsmooth payoff in financial mathematics.
The effect of cinnamon doses on blood serum glucose was studied in type 2 diabetic individuals for 60 days. Sixty type 2 diabetic individuals of both sexes and of age 48±6.5 years were divided into 6 groups; each group was having 10 individuals. Groups 1, 2 and 3 were assigned for 1g, 3g and 6g cinnamon doses/day respectively. Groups 4, 5 and 6 were assigned for 1g, 3g and 6g placebo doses/day respectively. The doses were equally distributed over the day. Cinnamon and placebo were given in the form of capsules with breakfast, lunch and dinner. The doses were given for 40 days and after 40 days; there was a 20 days blank period. Fasting blood samples were taken on days 0 (starting day of the experiment) 20, 40 and 60 and blood serums were separated. The blood serum glucose of both the cinnamon and placebo groups were determined. The mean fasting serum glucose levels for cinnamon doses on days 0, 20, 40 and 60 were 208.7, 189.1, 156.5 and 176.6 mg/dl for 1 g cinnamon dose/day; 206.2, 178.4, 170.3 and 177.8 mg/dl for 3 g cinnamon dose/day and 233.9, 183.2, 166.4 and 205.7 mg/dl for 6 g cinnamon dose/day respectively. The cinnamon doses significantly (P<0.05) reduced the mean fasting serum glucose levels while the placebo doses did not affect the serum glucose levels. In the light of this research, it is recommended that Type 2 diabetic individuals should use 1-3g cinnamon in their food preparations on regular basis. They can use cinnamon shakers for sprinkling of cinnamon powder on the curry in the plate. They can prepare cinnamon tea without sugar and can use it after meals. Also they can chew cinnamon bark after meals. This will keep their sugar level near to normal values.
22H . M . R AW S O N et al. was only 1.5 million t and decreasing. The situation was creating serious concerns for food security and diminishing foreign currency reserves.There are two standard approaches to increasing production: first to look for unused or under-utilized land that might be adapted to wheat cultivation and second to explore ways to increase yield per unit area in current wheat cropping areas. In the second approach yield is increased by reducing perceived environmental and genetic limitations.The paper presents the research activities designed to address the two approaches and meet the original request for assistance. At the outset basic requirements had to be fulfilled. Local crops researchers, agricultural extension workers and farmers had to commit to the project and be actively involved throughout. This would ensure that the project would build on best regional and local agricultural knowledge and avoid naïve suggestions that might have been tested previously and failed, or might otherwise be inappropriate. Researchers from the Wheat Research Centre (WRC) of the Bangladesh Agricultural Research Institute (BARI) in association with the Department of Agricultural Extension (DAE), together with individuals of CIMMYT Bangladesh provided this network of expertise. Agricultural experts from other countries acted as consultants.Of interest to the study was land in southern Bangladesh that normally remains fallow during the dry season, so is potentially available to wheat. Constraints of high temperatures, salinity and available season length of less than 100 days had been commonly thought to preclude economic returns for wheat in that region. Further, water for irrigation is very limited thus making alternative crops like dry-season rice impractical. Could wheat be grown by working around the constraints in some way? Fallow land is estimated at more than 400 000 ha in southern Bangladesh. This land grows rice during the several months of the wet season during which time it remains largely submerged by monsoon waters.The primary requirement was to identify the main constraints to high yield in both the southern and traditional wheat lands, and then to ask farmers to test a range of methods on their farms to minimize those constraints. CIMMYT Bangladesh and WRC researchers had already concluded from many field trials in the traditional wheat growing areas of Bangladesh that the success of a rice-wheat rotation depended on meeting the optimum planting and harvesting dates for both the rice and the wheat (rice was usually transplanted aman, T. aman, grown during the wet season). The optimum planting date for wheat in the region had been estimated as the end of November (Ortiz-Monasterio et al., 1994). Despite this knowledge, wheat was commonly planted too late, so constraining vegetative growth and pushing the grain-filling phase into the very high temperatures of late March; because of the consequent short season and rapid maturity of the crop, yields were low and uneconomic. Sometimes wheat could ...
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