992 resultados para Polynomial functions


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Molar heat capacities of ibuprofen were precisely measured with a small sample precision automated adiabatic calorimeter over the temperature range from 80 to 400 K. The polynomial functions of C-p,C-m (J K-1 mol(-1)) versus T were established on the heat capacity measurements by means of the least fitting square method. The functions are as follows: for solid ibuprofen, at the temperature range of 79.105 K less than or equal to T less than or equal to 333.297 K, C-p,C-m = 144.27 + 77.046X + 3.5171X(2) + 10.925X(3) + 11.224X(4), where X = (T - 206.201)/127.096; for liquid ibuprofen, at the temperature range of 353.406 K less than or equal to T less than or equal to 378.785 K, C-p,C-m = 325.79 + 8.9696X - 1.6073X(2) - 1.5145 X-3, where X = (T - 366.095)/12.690. A fusion transition at T = 348.02 K was found from the C-p-T curve. The molar enthalpy and entropy of the fusion transition were determined to be 26.65 kJ mol(-1) and 76.58 J mol(-1) K-1, respectively. The thermodynamic functions on the base of the reference temperature of 298.15 K, (H-T - H-298.15) and (S-T - S-298.15), were derived. Thermal characteristic of ibuprofen was studied by thermo-gravimetric analysis (TG-DTG) and differential scanning calorimeter (DSC). The temperature of fusion, the molar enthalpy and entropy of fusion obtained by DSC were well consistent with those obtained by adiabatic calorimeter. The evaporation process of ibuprofen was investigated further by TG and DTG, and the activation energy of the evaporation process was determined to be 80.3 +/- 1.4 kJ mol(-1). (C) 2003 Elsevier B.V. All rights reserved.

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Surface pollen assemblages and their relationhips with the modern vegetation and climate provide a foundation for investigating palaeo-environment conditions by fossil pollen analysis. A promising trend of palynology is to link pollen data more closely with ecology. In this study, I summarized the characteristics of surface pollen assemblages and their quantitative relation with the vegetation and climate of the typical ecological regions in northern China, based on surface pollen analysis of 205 sites and investigating of modern vegetation and climate. The primary conclusions are as follows:The differences in surface pollen assemblages for different vegetation regions are obvious. In the forest communities, the arboreal pollen percentages are more than 30%, herbs less than 50% and shrubs less than 10%; total pollen concentrations are more than 106 grains/g. In the steppe communities, arboreal pollen percentages are generally less than 5%; herb pollen percentages are more than 90%, and Artemisia and Chenopodiaceae are dominant in the pollen assemblages; total pollen concentrations range from 103 to 106 grains/g. In the desert communities, arboreal pollen percentages are less than 5%. Although Chenopodiaceae and Artemisia still dominate the pollen assemblages, Ephedra, Tamaricaceae and Nitraria are also significant important in the pollen assemblages; total pollen concentrations are mostly less than 104grains/g. In the sub-alpine or high and cold meadow communities, arboreal pollen percentages are less than 30%. and Cyperaceae is one of the most significant-taxa in the pollen assemblages. In the shrub communities, the pollen assemblages are consistent with the zonal vegetation; shrub pollen percentages are mostly less than 20%, except for Artemisia and Hippophae rhamnoides communities.There are obvious trends for the pollen percentage ratios of Artemisia to Chenopodiaceae (A/C), Pinus to Artemisia (P/A) and arbor to non-arbor (AP/NAP) in the different ecological regions. In the temperate deciduous broad-leaved forest region, the P/A ratios are generally higher than 0.1, the A/C ratios higher than 2 and the AP/NAP ratios higher than 0.3. In the temperate steppe regions, the P/A ratios are generally less than 0.1, the A/C ratios higher than 1 and the AP/NAP ratios less than 0.1. In the temperate desert regions, the P/A ratios are generally less than 0.1, the A/C ratios less than 1, and the AP/NAP ratios less than 0.1.The study on the representation and indication of pollen to vegetation shows that Pinus, Artemisia, Betula, Chenopodiaceae, Ephedra, Selaginella sinensis etc. are over-representative in the pollen assemblages and can only indicate the regional vegetation. Some pollen types, such as Quercus, Carpinus, Picea, Abies, Elaeagus, Larix, Salix, Pterocelis, Juglans, Ulmus, Gleditsia, Cotinus, Oleaceae, Spiraea, Corylus, Ostryopsis, Vites, Tetraena, Caragana, Tamaricaceae, Zygophyllum, Nitraria, Cyperaceae, Sanguisorba etc. are under-representative in the pollen assemblages, and can indicate the plant communities well. Populus, Rosaceae, Saxifranaceae, Gramineae, Leguminosae, Compositae, Caprifoliaceae etc. can not be used as significant indicators to the plants.The study on the relation of pollen percentages with plant covers shows that Pinus pollen percentages are more than 30% where pine trees exist in the surrounding region. The Picea+Abies pollen percentages are higher than 20% where the Picea+Abies trees are dominant in the communities, but less than 5% where the parent plants are sparse or absent. Larix pollen percentages vary from 5% to 20% where the Larix trees are dominant in the communities, but less than 5% where the parent plants are sparse or absent. Betula pollen percentages are higher than 40% where the Betula trees are dominant in the communities" but less than 5% where the parent plants are sparse or absent. Quercus pollen percentages are higher than 10% where the Quercus trees are dominant in the communities, but less than 1% where the parent plants sparse or absent. Carpinus pollen percentages vary from 5% to 15% where the Carpinus trees are dominant in the communities, but less than 1% where the parent plants are sparse or absent. Populus pollen percentages are about 0-5% at pure Populus communities, but cannot be recorded easily where the Populus plants mixed with other trees in the communities. Juglans pollen accounts for 25% to 35% in the forest of Juglans mandshurica, but less than 1% where the parent plants are sparse or absent. Pterocelis pollen percentages are less than 15% where the Pterocelis trees are dominant in the communities, but cannot be recorded easily where the parent plants are sparse or absent. Ulmus pollen percentages are more than 8% at Ulmus communities, but less than 1% where the Ulmus plants mixed with other trees in the communities. Vitex pollen percentages increase along with increasing of parent plant covers, but the maximum values are less than 10 %. Caragana pollen percentages are less than 20 % where the Caragana plant are dominant in the communities, and cannot be recorded easily where the parent plants are sparse or absent. Spiraea pollen percentages are less than 16 % where the Spiraea plant are dominant in the communities, and cannot be recorded easily where the parent plants are sparse or absent.The study on the relation of surface pollen assemblages with the modern climate shows that, in the axis 1 of DCA, surface samples scores have significant correlation with the average annual precipitations, and the highest determination coefficient (R2) is 0.8 for the fitting result of the third degree polynomial functions. In the axis 2 of DCA, the samples scores have significant correlation with the average annual temperatures, average July temperatures and average January temperatures, and the determination coefficient falls in 0.13-0.29 for the fitting result of the third degree polynomial functions with the highest determination coefficient for the average July temperature.The sensitivity of the different pollen taxa to climate change shows that some pollen taxa such as Pinus, Quercus, Carpinus, Juglans, Spiraea, Oleaceae, Gramineae, Tamariaceae and Ephedra are only sensitive to the change in precipitation.

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An evaluation of the change in perceived image contrast with changes in displayed image size was carried out. This was achieved using data from four psychophysical investigations, which employed techniques to match the perceived contrast of displayed images of five different sizes. A total of twenty-four S-shape polynomial functions were created and applied to every original test image to produce images with different contrast levels. The objective contrast related to each function was evaluated from the gradient of the mid-section of the curve (gamma). The manipulation technique took into account published gamma differences that produced a just-noticeable-difference (JND) in perceived contrast. The filters were designed to achieve approximately half a JND, whilst keeping the mean image luminance unaltered. The processed images were then used as test series in a contrast matching experiment. Sixty-four natural scenes, with varying scene content acquired under various illumination conditions, were selected from a larger set captured for the purpose. Results showed that the degree of change in contrast between images of different sizes varied with scene content but was not as important as equivalent perceived changes in sharpness.

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The modelling of a nonlinear stochastic dynamical processes from data involves solving the problems of data gathering, preprocessing, model architecture selection, learning or adaptation, parametric evaluation and model validation. For a given model architecture such as associative memory networks, a common problem in non-linear modelling is the problem of "the curse of dimensionality". A series of complementary data based constructive identification schemes, mainly based on but not limited to an operating point dependent fuzzy models, are introduced in this paper with the aim to overcome the curse of dimensionality. These include (i) a mixture of experts algorithm based on a forward constrained regression algorithm; (ii) an inherent parsimonious delaunay input space partition based piecewise local lineal modelling concept; (iii) a neurofuzzy model constructive approach based on forward orthogonal least squares and optimal experimental design and finally (iv) the neurofuzzy model construction algorithm based on basis functions that are Bézier Bernstein polynomial functions and the additive decomposition. Illustrative examples demonstrate their applicability, showing that the final major hurdle in data based modelling has almost been removed.

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In this paper we present results for the systematic study of reversible-equivariant vector fields - namely, in the simultaneous presence of symmetries and reversing symmetries - by employing algebraic techniques from invariant theory for compact Lie groups. The Hilbert-Poincare series and their associated Molien formulae are introduced,and we prove the character formulae for the computation of dimensions of spaces of homogeneous anti-invariant polynomial functions and reversible-equivariant polynomial mappings. A symbolic algorithm is obtained for the computation of generators for the module of reversible-equivariant polynomial mappings over the ring of invariant polynomials. We show that this computation can be obtained directly from a well-known situation, namely from the generators of the ring of invariants and the module of the equivariants. (C) 2008 Elsevier B.V, All rights reserved.

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One may construct, for any function on the integers, an irreducible module of level zero for affine sl(2) using the values of the function as structure constants. The modules constructed using exponential-polynomial functions realize the irreducible modules with finite-dimensional weight spaces in the category (O) over tilde of Chari. In this work, an expression for the formal character of such a module is derived using the highest weight theory of truncations of the loop algebra.

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he aetiology of osteoporotic vertebral fractures is multi-factorial, and cannot be explained solely by low bone mass. After sustaining an initial vertebral fracture, the risk of subsequent fracture increases greatly. Examination of physiologic loads imposed on vertebral bodies may help to explain a mechanism underlying this fracture cascade. This study tested the hypothesis that model-derived segmental vertebral loading is greater in individuals who have sustained an osteoporotic vertebral fracture compared to those with osteoporosis and no history of fracture. Flexion moments, and compression and shear loads were calculated from T2 to L5 in 12 participants with fractures (66.4 ± 6.4 years, 162.2 ± 5.1 cm, 69.1 ± 11.2 kg) and 19 without fractures (62.9 ± 7.9 years, 158.3 ± 4.4 cm, 59.3 ± 8.9 kg) while standing. Static analysis was used to solve gravitational loads while muscle-derived forces were calculated using a detailed trunk muscle model driven by optimization with a cost function set to minimise muscle fatigue. Least squares regression was used to derive polynomial functions to describe normalised load profiles. Regression co-efficients were compared between groups to examine differences in loading profiles. Loading at the fractured level, and at one level above and below, were also compared between groups. The fracture group had significantly greater normalised compression (p = 0.0008) and shear force (p < 0.0001) profiles and a trend for a greater flexion moment profile. At the level of fracture, a significantly greater flexion moment (p = 0.001) and shear force (p < 0.001) was observed in the fracture group. A greater flexion moment (p = 0.003) and compression force (p = 0.007) one level below the fracture, and a greater flexion moment (p = 0.002) and shear force (p = 0.002) one level above the fracture was observed in the fracture group. The differences observed in multi-level spinal loading between the groups may explain a mechanism for increased risk of subsequent vertebral fractures. Interventions aimed at restoring vertebral morphology or reduce thoracic curvature may assist in normalising spine load profiles.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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A Sigatoka-negra (Mycosphaerella fijiensis) ameaça os bananais comerciais em todas as áreas produtoras do mundo e provoca danos quantitativos e qualitativos na produção, acarretando sérios prejuízos financeiros. Faz-se necessário o estudo da vulnerabilidade das plantas em diversos estádios de desenvolvimento e das condições climáticas favoráveis à ocorrência da doença. Objetivou-se com este trabalho desenvolver um modelo probabilístico baseado em funções polinomiais que represente o risco de ocorrência da Sigatokanegra em função da vulnerabilidade decorrente de fatores intrínsecos à planta e ao ambiente. Realizou-se um estudo de caso, em bananal comercial localizado em Jacupiranga, Vale do Ribeira, SP, considerando o monitoramento semanal do estado da evolução da doença, séries temporais de dados meteorológicos e dados de sensoriamento remoto. Foram gerados mapas georreferenciados do risco da Sigatoka-negra em diferentes épocas do ano. Um modelo para estimar a evolução da doença a partir de imagens de satélite foi obtido com coeficiente de determinação R² igual a 0,9. A metodologia foi desenvolvida para a detecção de épocas e locais que reúnem condições favoráveis à ocorrência da Sigatoka-negra e pode ser aplicada, com os devidos ajustes, em diferentes localidades, para avaliar o risco da ocorrência da doença em polos produtores de banana.

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Data comprising 1,719 milk yield records from 357 females (predominantly Murrah breed), daughters of 110 sires, with births from 1974 to 2004, obtained from the Programa de Melhoramento Genetic de Bubalinos (PROMEBUL) and from records of EMBRAPA Amazonia Oriental - EAO herd, located in Belem, Para, Brazil, were used to compare random regression models for estimating variance components and predicting breeding values of the sires. The data were analyzed by different models using the Legendre's polynomial functions from second to fourth orders. The random regression models included the effects of herd-year, month of parity date of the control; regression coefficients for age of females (in order to describe the fixed part of the lactation curve) and random regression coefficients related to the direct genetic and permanent environment effects. The comparisons among the models were based on the Akaike Infromation Criterion. The random effects regression model using third order Legendre's polynomials with four classes of the environmental effect were the one that best described the additive genetic variation in milk yield. The heritability estimates varied from 0.08 to 0.40. The genetic correlation between milk yields in younger ages was close to the unit, but in older ages it was low.

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Heat capacity, thermal conductivity, and density of whole milk, skimmed milk, and partially skimmed milk were determined at concentrations varying from (72.0 to 92.0) mass % water content and from (0.1 to 7.8) mass % fat content, at temperatures ranging from (275.15 to 344.15) K. Heat capacity and thermal conductivity varied from (3.4 to 4.1) J(.)g(-) K-1.(-1) and from (0.5 to 0.6) W(.)m(-1) K-1.(-1), respectively. Density varied from (1011.8 to 1049.5) kg(.)m(-3). Polynomial functions were used to model the dependence of the properties upon the studied variables. A linear relationship was obtained for all the properties. In the tested range, water content exhibited a greater influence on the properties, while fat content showed a smaller influence.

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The study of algorithms for active vibration control in flexible structures became an area of enormous interest for some researchers due to the innumerable requirements for better performance in mechanical systems, as for instance, aircrafts and aerospace structures. Intelligent systems, constituted for a base structure with sensors and actuators connected, are capable to guarantee the demanded conditions, through the application of diverse types of controllers. For the project of active controllers it is necessary, in general, to know a mathematical model that enable the representation in the space of states, preferential in modal coordinates to permit the truncation of the system and reduction in the order of the controllers. For practical applications of engineering, some mathematical models based in discrete-time systems cannot represent the physical problem, therefore, techniques of identification of system parameters must be used. The techniques of identification of parameters determine the unknown values through the manipulation of the input (disturbance) and output (response) signals of the system. Recently, some methods have been proposed to solve identification problems although, none of them can be considered as being universally appropriate to all the situations. This paper is addressed to an application of linear quadratic regulator controller in a structure where the damping, stiffness and mass matrices were identified through Chebyshev's polynomial functions.