952 resultados para Orthogonal polynomials on the unit circle


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The present study helped to understand the trend in rainfall patterns at smaller spatial scales and the large regional differences in the variability of rainfall. The effect of land use and orography on the diurnal variability is also understood. But a better understanding on the long term variation in rainfall is possible by using a longer dataset,which may provide insight into the rainfall variation over country during the past century. The basic mechanism behind the interannual rainfall variability would be possible with numerical studies using coupled Ocean-Atmosphere models. The regional difference in the active-break conditions points to the significance of regional studies than considering India as a single unit. The underlying dynamics of diurnal variability need to be studied by making use of a high resolution model as the present study could not simulate the local onshore circulation. Also the land use modification in this study, selected a region, which is surrounded by crop land. This implies the high possibility for the conversion of the remaining region to agricultural land. Therefore the study is useful than considering idealized conditions, but the adverse effect of irrigated crop is more than non-irrigated crop. Therefore, such studies would help to understand the climate changes occurred in the recent period. The large accumulation of rainfall between 300-600 m height of western Ghats has been found but the reason behind this need to be studied, which is possible by utilizing datasets that would better represent the orography and landuse over the region in high resolution model. Similarly a detailed analysis is needed to clearly identify the causative relations of the predictors identified with the predictant and the physical reasons behind them. New approaches that include nonlinear relationships and dynamical variables from model simulations can be included in the existing statistical models to improve the skill of the models. Also the statistical models for the forecasts of monsoon have to be continually updated.

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In the present work different new approaches for the synthesis of Vitamin A are investigated. In these synthetic schemes, all the twenty carbon atoms of the target molecule are derived either fully from components isolated from common essential oils or partially from commercially available materials. By retrosynthetic analysis, Vitamin A molecule can be disconnected into a cyclic and a linear unit. Different methods for the synthesis of the linear and the cyclic components are described. The monoterpenes, geraniol and citral, major constituents of palmarosa and lemongrass oils, have the required basic carbon framework for consideration as starting materials for the synthesis of Vitamin A. The potential of these easily available naturally occurring compounds as promising starting materials for Vitamin A synthesis is demonstrated. Organoselenium and organosulfur mediated functional group transformations for the synthesis of the functionalised conjugated C10 linear components (ie., the dimethyloctatriene derivatives) are reported. The classical approaches as well as the attempted preparation of cyclic C10 and C13 units employed in the present study as intermediates for Vitamin A synthesis are described. The utility of commercially available materials namely 2-acetylbutyrolactone and levulinic acid in -the preparation of C5 intermediates for Vitamin A synthesis is demonstrated.

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The present study aims at the investigation of the 1ysico—chemical features of a tropical tidal river viz. we Muvattupuzha river. This river is expected to receive Jderate to heavy pollution loads in years to come, from we lone industrial unit, already set up on its bank. ilike other rivers, the geographical disposition of this Lver attains unique importance as regards its dynamics for 3) availability of natural runoff water from catchment :eas, which becomes very heavy during the monsoon season 3) regular steady availability of tail race water from a /dro—electric power station throughout the yearThe study also aims at arriving at the balancing forces of inherent self~purification of the river verses pollution loads from the factory effluents. The investigation period falls ahead of actual pollution occurrence and so the ambient conditions for a period of nearly one-and-a—half years were investigated, the analyses of which providflz to formulate the inter-relations of parameters varying with seasons. Tracer experiments were carried out which revealed the dispersion and dilution characteristics of the river in the vicinity of effluent outfall. The studv covers the trial—cum-capacity production periods of the factory during which effluents of various strength and quantity were discharged into the river; a few computed values arQ’cjmpgrQdl ... with the observed values. The base data along with the profiles of Oxygen sag equation have been utilized fb develop a mathematical model of the river with regard to its water quality

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The results of the investigation of the magnetic and structural properties of the alloy system Fe0.75–xSi0.25Sbx, where x = 0, 0.05, 0.1, 0.15, 0.2, and 0.25 synthesized by mechanical alloying followed by heat treatment are described. The x-ray diffraction reveals that all samples crystallize in the DO3-type cubic phase structure. Substituting Fe by Sb led to a de-crease in the lattice constant and the unit cell volume. The magnetic properties are investigated by vibrating sample magnetometer and show that all the samples are ferromagnetically ordered at room temperature. The Curie temperature is found to decrease linearly from (850 ± 5) K for the parent alloy to (620 ± 5) K for the alloyith x = 0.25. The satura-tion magnetizations at room temperature and at 100 K are found to decrease with increasing the antimony concentration. The above results indicate that Sb dissolves in the cubic structure of this alloy system.

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This article surveys the classical orthogonal polynomial systems of the Hahn class, which are solutions of second-order differential, difference or q-difference equations. Orthogonal families satisfy three-term recurrence equations. Example applications of an algorithm to determine whether a three-term recurrence equation has solutions in the Hahn class - implemented in the computer algebra system Maple - are given. Modifications of these families, in particular associated orthogonal systems, satisfy fourth-order operator equations. A factorization of these equations leads to a solution basis.

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The method of Least Squares is due to Carl Friedrich Gauss. The Gram-Schmidt orthogonalization method is of much younger date. A method for solving Least Squares Problems is developed which automatically results in the appearance of the Gram-Schmidt orthogonalizers. Given these orthogonalizers an induction-proof is available for solving Least Squares Problems.

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The regional population growth in West Africa, and especially its urban centers, will bring about new and critical challenges for urban development policy, especially in terms of ensuring food security and providing employment for the growing population. (Peri-) urban livestock and vegetable production systems, which can contribute significantly to these endeavours, are limited by various constraints, amongst them limited access to expensive production factors and their (in)efficient use. To achieve sustainable production systems with low consumer health risks, that can meet the urban increased demand, this doctoral thesis determined nutrient use efficiencies in representative (peri-) urban livestock production systems in three West African cities, and investigated potential health risks for consumers ensuing from there. The field study, which was conducted during July 2007 to December 2009, undertook a comparative analysis of (peri-) urban livestock production strategies across 210 livestock keeping households (HH) in the three West African cities of Kano/Nigeria (84 HH), Bobo Dioulasso/Burkina Faso (63 HH) and Sikasso/Mali (63 HH). These livestock enterprises were belonging to the following three farm types: commercial gardening plus field crops and livestock (cGCL; 88 HH), commercial livestock plus subsistence field cropping (cLsC; 109 HH) and commercial gardening plus semi-commercial livestock (cGscL; 13 HH) which had been classified in a preceding study; they represented the diversity of (peri-) urban livestock production systems in West Africa. In the study on the efficiency of ruminant livestock production, lactating cowsand sheep herd units were differentiated based on whether feed supplements were offered to the animals at the homestead (Go: grazing only; Gsf: mainly grazing plus some supplement feeding). Inflows and outflows of nutrients were quantified in these herds during 18 months, and the effects of seasonal variations in nutrient availability on animals’ productivity and reproductive performance was determined in Sikasso. To assess the safety of animal products and vegetables, contamination sources of irrigated lettuce and milk with microbiological contaminants, and of tomato and cabbage with pesticide residues in (peri-) urban agriculture systems of Bobo Dioulasso and Sikasso were characterized at three occasions in 2009. Samples of irrigation water, organic fertilizer and ix lettuce were collected in 6 gardens, and samples of cabbage and tomato in 12 gardens; raw and curdled milk were sampled in 6 dairy herds. Information on health risks for consumers of such foodstuffs was obtained from 11 health centers in Sikasso. In (peri-) urban livestock production systems, sheep and goats dominated (P<0.001) in Kano compared to Bobo Dioulasso and Sikasso, while cattle and poultry were more frequent (P<0.001) in Bobo Dioulasso and Sikasso than in Kano. Across cities, ruminant feeding relied on grazing and homestead supplementation with fresh grasses, crop residues, cereal brans and cotton seed cake; cereal grains and brans were the major ingredients of poultry feeds. There was little association of gardens and livestock; likewise field cropping and livestock were rarely integrated. No relation existed between the education of the HH head and the adoption of improved management practices (P>0.05), but the proportion of HH heads with a long-term experience in (peri-) urban agriculture was higher in Kano and in Bobo Dioulasso than in Sikasso (P<0.001). Cattle and sheep fetched highest market prices in Kano; unit prices for goats and chicken were highest in Sikasso. Animal inflow, outflow and dairy herd growth rates were significantly higher (P<0.05) in the Gsf than in the Go cattle herds. Maize bran and cottonseed expeller were the main feeds offered to Gsf cows as dry-season supplement, while Gsf sheep received maize bran, fresh grasses and cowpea pods. The short periodic transhumance of Go dairy cows help them maintaining their live weight, whereas Gsf cows lost weight during the dry season despite supplement feeding at a rate of 1506 g dry matter per cow and day, resulting in low productivity and reproductive performance. The daily live weight gains of calves and lambs, respectively, were low and not significantly different between the Go and the Gsf system. However, the average live weight gains of lambs were significantly higher in the dry season (P<0.05) than in the rainy season because of the high pressure of gastrointestinal parasites and of Trypanosoma sp. In consequence, 47% of the sheep leaving the Go and Gsf herds died due to diseases during the study period. Thermo-tolerant coliforms and Escherichia coli contamination levels of irrigation water significantly exceeded WHO recommendations for the unrestricted irrigation of vegetables consumed raw. Microbial contamination levels of lettuce at the farm gate and the market place in Bobo Dioulasso and at the farm gate in Sikasso were higher than at the market place in Sikasso (P<0.05). Pesticide residues were detected in only one cabbage and one tomato sample and were below the maximum residue limit for consumption. Counts of thermo-tolerant coliforms and Escherichia coli were higher in curdled than in raw milk (P<0.05). From 2006 to x 2009, cases of diarrhea/vomiting and typhoid fever had increased by 11% and 48%, respectively, in Sikasso. For ensuring economically successful and ecologically viable (peri-) urban livestock husbandry and food safety of (peri-) urban foodstuffs of animal and plant origin, the dissemination and adoption of improved feeding practices, livestock healthcare and dung management are key. In addition, measures fostering the safety of animal products and vegetables including the appropriate use of wastewater in (peri-) urban agriculture, restriction to approve vegetable pesticides and the respect of their latency periods, and passing and enforcement of safety laws is required. Finally, the incorporation of environmentally sound (peri-) urban agriculture in urban planning by policy makers, public and private extension agencies and the urban farmers themselves is of utmost importance. To enable an efficient (peri-) urban livestock production in the future, research should concentrate on cost-effective feeding systems that allow meeting the animals’ requirement for production and reproduction. Thereby focus should be laid on the use of crop-residues and leguminous forages. The improvement of the milk production potential through crossbreeding of local cattle breeds with exotic breeds known for their high milk yield might be an accompanying option, but it needs careful supervision to prevent the loss of the local trypanotolerant purebreds.

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The aim of this work is to find simple formulas for the moments mu_n for all families of classical orthogonal polynomials listed in the book by Koekoek, Lesky and Swarttouw. The generating functions or exponential generating functions for those moments are given.

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Optimum experimental designs depend on the design criterion, the model and the design region. The talk will consider the design of experiments for regression models in which there is a single response with the explanatory variables lying in a simplex. One example is experiments on various compositions of glass such as those considered by Martin, Bursnall, and Stillman (2001). Because of the highly symmetric nature of the simplex, the class of models that are of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather different from those of standard regression analysis. The optimum designs are also rather different, inheriting a high degree of symmetry from the models. In the talk I will hope to discuss a variety of modes for such experiments. Then I will discuss constrained mixture experiments, when not all the simplex is available for experimentation. Other important aspects include mixture experiments with extra non-mixture factors and the blocking of mixture experiments. Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007). If time and my research allows, I would hope to finish with a few comments on design when the responses, rather than the explanatory variables, lie in a simplex. References Atkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum Experimental Designs, with SAS. Oxford: Oxford University Press. Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results on optimal and efficient designs for constrained mixture experiments. In A. C. Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000, pp. 225–239. Dordrecht: Kluwer. Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal Statistical Society, Ser. B 20, 344–360. 1

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Many shorebirds are long-distance migrants and depend on the energy gained at stopover sites to complete migration. Competing hypotheses have described strategies used by migrating birds; the energy-selection hypothesis predicts that shorebirds attempt to maximize energy gained at stopover sites, whereas the time-selection hypothesis predicts that shorebirds attempt to minimize time spent at stopover sites. The energy- and time-selection hypotheses both predict that birds in better condition will depart sites sooner. However, numerous studies of stopover duration have found little support for this prediction, leading to the suggestion that migrating birds operate under energy and time constraints for only a small portion of the migratory season. During fall migration 2002, we tested the prediction that birds in better condition depart stopover sites sooner by examining the relationship between stopover duration and body condition for migrating Least Sandpipers (Calidris minutilla) at three stopover sites in the Lower Mississippi Alluvial Valley. We also tested the assumption made by the Lower Mississippi Alluvial Valley Migratory Bird Science Team that shorebirds stay in the Mississippi Valley for 10 d. The assumption of 10 d was used to estimate the amount of habitat required by shorebirds in the Mississippi Valley during fall migration; a period longer than 10 d would increase the estimate of the amount habitat required. We used multiple-day constancy models of apparent survival and program MARK to estimate stopover duration for 293 individually color-marked and resighted Least Sandpipers. We found that a four-day constancy interval and a site x quadratic time trend interaction term best modeled apparent survival. We found only weak support for body condition as a factor explaining length of stopover duration, which is consistent with findings from similar work. Stopover duration estimates were 4.1 d (95% CI = 2.8–6.1) for adult Least Sandpipers at Bald Knob National Wildlife Refuge, Arkansas, 6.5 d (95% CI = 4.9–8.7) for adult and 6.1 d (95% CI =4.2–9.1) for juvenile Least Sandpipers at Yazoo National Wildlife Refuge, Mississippi, and 6.9 d (95% CI = 5.5–8.7) for juvenile Least Sandpipers at Morgan Brake National Wildlife Refuge, Mississippi. Based on our estimates of stopover duration and the assumption made by the Lower Mississippi Alluvial Valley Migratory Bird Science Team, there is sufficient habitat in the lower Mississippi Valley to support shorebirds during fall migration.

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Using a simple stochastic model, the authors illustrate that the occurrence of a meridional dipole in the first empirical orthogonal function (EOF) of a time-dependent zonal jet is a simple consequence of the north–south excursion of the jet center, and this geometrical fact can be understood without appealing to fluid dynamical principles. From this it follows that one ought not, perhaps, be surprised at the fact that such dipoles, commonly referred to as the Arctic Oscillation (AO) or the Northern Annular Mode (NAM), have robustly been identified in many observational studies and appear to be ubiquitous in atmospheric models across a wide range of complexity.

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We need a new definition for the kilogram! The present definition was sanctioned by the first General Conference on Weights and Measures (CGPM, Conférence Général des Poids et Mesures) in 1889, with a minor revision to the words in 1901, and remains unchanged after 116 years. It is the only base unit of the International System of Units (the SI) that is still defined in terms of a prototype artifact, the International Prototype of the Kilogram (IPK), which is kept in a safe at the International Bureau of Weights and Measures (the BIPM, Bureau International des Poids et Mesures) in Sèvres, near Paris.

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Three experiments conducted over two years (2002-04) at the Crops Research Unit, University of Reading, investigated competition between autumn sown oilseed rape cultivars (Brassica napus L. ssp. oleifera var. biennis (DC.) Metzg.) and Lolium multiflorum Lam., L. x boucheanum Kunth and Alopecurus myosuroides Huds., sown as indicative grass weeds. Rape cultivar (cv.) had a substantial effect on grass weed seed return. Over the six cultivars tested, L. multiflorum spikelet production ranged from just under 400 spikelets/m(2) in the presence of cv. Winner to nearly 5800 in competition with cv. Lutin. Cultivar competitiveness was associated with high biomass, large dense floral layers and early stem extension. There was some evidence of differential competitive tolerance between rape cultivars. The results suggested that rape cultivars could be screened for competitiveness by measuring floral layer interception of photosynthetic active radiation. L. x boucheanum cultivars varied in ability to compete with rape. In the absence of inter-specific competition, spikelet density was similar for Aberecho and Polly (circa 31000 spikelets/m(2)) but when grown with rape Polly outyielded Aberecho (i.e. 12 090 and 7990 spikelets/m(2) respectively).

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Four experiments conducted over three seasons (2002–05) at the Crops Research Unit, University of Reading, investigated effects of canopy management of autumn sown oilseed rape (Brassica napus L. ssp. oleifera var. biennis (DC.) Metzg.) on competition with grass weeds. Emphasis was placed on the effect of the crop on the weeds. Rape canopy size was manipulated using sowing date, seed rate and the application of autumn fertilizer. Lolium multiflorum Lam., L.rboucheanum Kunth and Alopecurus myosuroides Huds. were sown as indicative grass weeds. The effects of sowing date, seed rate and autumn nitrogen on crop competitive ability were correlated with rape biomass and fractional interception of photosynthetically active radiation (PAR) by the rape floral layer, to the extent that by spring there was good evidence of crop: weed replacement. An increase in seed rate up to the highest plant densities tested increased both rape biomass and competitiveness, e.g. in 2002/3, L. multiflorum head density was reduced from 539 to 245 heads/m2 and spikelet density from 13 170 to 5960 spikelets/m2 when rape plant density was increased from 16 to 81 plants/m2. Spikelets/head of Lolium spp. was little affected by rape seed rate, but the length of heads of A. myosuroides was reduced by 9%when plant density was increased from 29–51 plants/m2. Autumn nitrogen increased rape biomass and reduced L. multiflorum head density (415 and 336 heads/m2 without and with autumn nitrogen, respectively) and spikelet density (9990 and 8220 spikelets/m2 without and with autumn nitrogen, respectively). The number of spikelets/head was not significantly affected by autumn nitrogen. Early sowing could increase biomass and competitiveness, but poor crop establishment sometimes overrode the effect. Where crop and weed establishment was similar for both sowing dates, a 2-week delay (i.e. early September to mid-September) increased L. multiflorum head density from 226 to 633 heads/m2 and spikelet density from 5780 to 15 060 spikelets/m2.

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Three experiments conducted over two years (2002-04) at the Crops Research Unit, University of Reading, investigated competition between autumn sown oilseed rape cultivars (Brassica napus L. ssp. oleifera var. biennis (DC.) Metzg.) and Lolium multiflorum Lam., L. x boucheanum Kunth and Alopecurus myosuroides Huds., sown as indicative grass weeds. Rape cultivar (cv.) had a substantial effect on grass weed seed return. Over the six cultivars tested, L. multiflorum spikelet production ranged from just under 400 spikelets/m(2) in the presence of cv. Winner to nearly 5800 in competition with cv. Lutin. Cultivar competitiveness was associated with high biomass, large dense floral layers and early stem extension. There was some evidence of differential competitive tolerance between rape cultivars. The results suggested that rape cultivars could be screened for competitiveness by measuring floral layer interception of photosynthetic active radiation. L. x boucheanum cultivars varied in ability to compete with rape. In the absence of inter-specific competition, spikelet density was similar for Aberecho and Polly (circa 31000 spikelets/m(2)) but when grown with rape Polly outyielded Aberecho (i.e. 12 090 and 7990 spikelets/m(2) respectively).