5 resultados para Co-polar

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


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Physical and chemical adsorption of CO 2 on ZnO surfaces were studied by means of two different implementations of periodic density functional theory. Adsorption energies were computed and compared to values in the literature. In particular, it was found that the calculated equilibrium structure and internuclear distances are in agreement with previous work. CO 2 adsorption was analyzed by inspection of the density of states and electron localization function. Valence bands, band gap and final states of adsorbed CO 2 were investigated and the effect of atomic displacements analyzed. The partial density of states (PDOS) of chemical adsorption of CO 2 on the ZnO(0001) surface show that the p orbitals of CO 2 were mixed with the ZnO valence band state appearing at the top of the valence band and in regions of low-energy conduction band. [Figure not available: see fulltext.] © 2012 Springer-Verlag Berlin Heidelberg.

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In this article we show that for corank 1, quasi-homogeneous and finitely determined map germs f : (C-n, 0)-> (C-3, 0), n >= 3 one can obtain formulae for the polar multiplicities defined on the following stable types of f, f(Delta(f) and f(Sigma(n-2,1)(f), in terms of the weights and degrees of f. As a consequence we show how to compute the Euler obstruction of such stable types, also in terms of the weights and degrees of f.

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In this article, we investigate the geometry of quasi homogeneous corank one finitely determined map germs from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. We give a complete description, in terms of the weights and degrees, of the invariants that are associated to all stable singularities which appear in the discriminant of such map germs. The first class of invariants which we study are the isolated singularities, called 0-stable singularities because they are the 0-dimensional singularities. First, we give a formula to compute the number of An points which appear in any stable deformation of a quasi homogeneous co-rank one map germ from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. To get such a formula, we apply the Hilbert's syzygy theorem to determine the graded free resolution given by the syzygy modules of the associated iterated Jacobian ideal. Then we show how to obtain the other 0-stable singularities, these isolated singularities are formed by multiple points and here we use the relation among them and the Fitting ideals of the discriminant. For n = 2, there exists only the germ of double points set and for n = 3 there are the triple points, named points A1,1,1 and the normal crossing between a germ of a cuspidal edge and a germ of a plane, named A2,1. For n = 3, there appear also the one-dimensional singularities, which are of two types: germs of cuspidal edges or germs of double points curves. For these singularities, we show how to compute the polar multiplicities and also the local Euler obstruction at the origin in terms of the weights and degrees. © 2013 Pushpa Publishing House.