956 resultados para Simultaneous Diophantine approximations


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The abundance and distribution of collapsed objects such as galaxy clusters will become an important tool to investigate the nature of dark energy and dark matter. Number counts of very massive objects are sensitive not only to the equation of state of dark energy, which parametrizes the smooth component of its pressure, but also to the sound speed of dark energy, which determines the amount of pressure in inhomogeneous and collapsed structures. Since the evolution of these structures must be followed well into the nonlinear regime, and a fully relativistic framework for this regime does not exist yet, we compare two approximate schemes: the widely used spherical collapse model and the pseudo-Newtonian approach. We show that both approximation schemes convey identical equations for the density contrast, when the pressure perturbation of dark energy is parametrized in terms of an effective sound speed. We also make a comparison of these approximate approaches to general relativity in the linearized regime, which lends some support to the approximations.

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In this work we show that the smooth classification of divergent diagrams of folds (f(1),..., f(s)) : (R-n, 0) -> (R-n x(...)xR(n), 0) can be reduced to the classification of the s-tuples (p(1)., W) of associated involutions. We apply the result to obtain normal forms when s <= n and {p(1),...,p(s)} is a transversal set of linear involutions. A complete description is given when s = 2 and n >= 2. We also present a brief discussion on applications of our results to the study of discontinuous vector fields and discrete reversible dynamical systems.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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

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The production of chlorine was investigated in the photoelectrocatalytic oxidation of a chloride-containing solution using a TiO(2) thin-film electrode biased at current density from 5 to 50 mA cm(-2) and illuminated by UV light. Such parameters as chloride concentrations from 0.001 to 0.10 mol L(-1), pH 2-12, and interfering salts were varied in this study in order to determine their effect on this oxidation process. At an optimum condition this photoelectrocatalytic method can produce active chlorine at levels compatible to water disinfections processes using a chloride concentration higher than 0.010 mol L(-1) at a pH of 4 and a current density of 30 mA cm(-2). The method was successfully applied to treat surface water collected from a Brazilian river. After 150 min of photoelectrocatalytic oxidation, we obtained a 90% reduction in total organic carbon removal, a 100% removal of turbidity, a 93% decrease in colour and a chemical oxygen demand (COD) removal of around 96% (N=3). The proposed technology based on photoelectrocatalytic oxidation was also tested in treating 250 mL of a solution containing 0.05 mol L(-1) NaCl and 50 mu g L(-1) of Microcystin aeruginosa. The bacteria is completely removed after 5 min of photoelectrocatalysis following an initial rate constant removal of -0.260 min(-1), suggesting that the present method could be considered as a promising alternative to chlorine-based disinfections. (C) 2008 Elsevier Ltd. All rights reserved.

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

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The generalized temperature integral I(m, x) appears in non-isothermal kinetic analysis when the frequency factor depends on the temperature. A procedure based on Gaussian quadrature to obtain analytical approximations for the integral I(m, x) was proposed. The results showed good agreement between the obtained approximation values and those obtained by numerical integration. Unless other approximations found in literature, the methodology presented in this paper can be easily generalized in order to obtain approximations with the maximum of accurate.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)