8 resultados para APPROXIMATE SOLUTIONS

em Repositório Institucional UNESP - Universidade Estadual Paulista "Julio de Mesquita Filho"


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Pós-graduação em Matemática Universitária - IGCE

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Pós-graduação em Matemática Universitária - IGCE

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Despite the great importance of ion transport, most of the widely accepted models and theories are valid only in the not very practical limit of low concentrations. Aiming to extend the range of applicability to moderate concentrations, a number of modified models and equations (some approximate, some fundamented on different assumptions, and some just empirical) have been reported. In this work, a general treatment for the electrical conductivity of ionic solutions has been developed, considering the electrical conductivity as a transport phenomenon governed by dissipation and feedback. A general expression for the dependence of the specific conductivity on the solution viscosity (and indirectly on concentration), from which the whole conductivity curve can be obtained, has been derived. The validity of this general approach is demonstrated with experimental results taken from the literature for aqueous and nonaqueous solutions of electrolytes.

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An approximate expression is constructed for the energy of an anharmonic potential with centrifugal barrier. In order to obtain such an analytical expression, the quasi-exact solvability is used and then a fitting of these exact solutions is done.

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The simultaneous formation of nanometer sized zinc oxide (ZnO), and acetate zinc hydroxide double salt (Zn-HDS) is described. These phases, obtained using the sol-gel synthesis route based on zinc acetate salt in alcoholic media, were identified by direct characterization of the reaction products in solution using complementary techniques: nephelometry, in situ Small-Angle X-ray Scattering (SAXS), UV-Vis spectroscopy and Extended X-ray Absorption Fine Structures (EXAFS). In particular, the hydrolytic pathway of ethanolic zinc acetate precursor solutions promoted by addition of water with the molar ratio N = [H2O]/[Zn2+] = 0.05 was investigated in this paper. The aim was to understand the formation mechanism of ZnO colloidal suspension and to reveal the factors responsible for the formation of Zn-HDS in the final precipitates. The growth mechanism of ZnO nanoparticles is based on primary particle (radius approximate to 1.5 nm) rotation inside the primary aggregate (radius < 3.5 nm) giving rise to an epitaxial attachment of particles and then subsequent coalescence. The growth of second ZnO aggregates is not associated with the Otswald ripening, and could be associated with changes in equilibrium between solute species induced by the superficial etching of Zn-HDS particles at the advanced stage of kinetic.

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The electrochemical behaviour of potentiodynamically formed thin anodic films of polycrystalline tin in aqueous sodium bicarbonate solutions (pH approximate to 8.3) were studied using cyclic voltammetry and electrochemical impedance spectroscopy. Different equivalent circuits corresponding to various potential regions were employed to account for the electrochemical processes taking place under each condition. (C) 2004 Elsevier Ltd. All rights reserved.

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An approximate analytic expression for the eigenenergies of the anharmonic oscillator V(x)=Ax6+Bx2 is introduced, starting from particular analytic solutions which are valid when certain relations between the parameters A and B are held. © 1995 The American Physical Society.