Examinando por Materia "Critical point theory (mathematical analysis)"

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    Funciones de Morse minimales en el espacio dodecaédrico de Poincaré, vía la Ecuación del Calor
    (Universidad EAFIT, 2014) Bernal Vera, Jhon Willington; Cadavid Moreno, Carlos Alberto
    Let (M,g) be a compact, connected, without boundary riemannian manifold that is homogeneous, i.e. each pair of points p, q 2M have isometric neighborhoods -- This thesis is a another step towards an understanding of the extent to which it is true that for each “generic” initial condition f0, the solution to @f/@t = gf, f (·, 0) = f0 is such that for sufficiently large t, f (·, 0) is a minimal Morse function, i.e., a Morse function whose total number of critical points is the minimal possible on M -- In this thesis we show that for the Poincaré dodecahedral space this seems to hold if one allows a generic small perturbation of the metric -- Concretely, we consider an approximation of the spherical Poincaré dodecahedral space by a suitably weighted graph, calculate the eigenvalues and eigenvectors of its laplacian oparator, and study the critical point structure of eigenvectors of some of the first nonzero eigenvalues, and observe that they have the least possible number of critical points
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    On the critical point structure of eigenfunctions belonging to the first nonzero eigenvalue of a genus two closed hyperbolic surface
    (2012-05-30) Cadavid, Carlos A.; Osorno, María C.; Ruíz, Óscar E.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
    We develop a method based on spectral graph theory to approximate the eigenvalues and eigenfunctions of the Laplace-Beltrami operator of a compact riemannian manifold -- The method is applied to a closed hyperbolic surface of genus two -- The results obtained agree with the ones obtained by other authors by different methods, and they serve as experimental evidence supporting the conjectured fact that the generic eigenfunctions belonging to the first nonzero eigenvalue of a closed hyperbolic surface of arbitrary genus are Morse functions having the least possible total number of critical points among all Morse functions admitted by such manifolds
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    Structure, stability and bonding in the 1Au10 clusters
    (Elsevier, 2012-04-19) David Caro, Jorge León; Guerra Tamayo, Doris; Restrepo Cossio, Albeiro Alonso; Universidad EAFIT. Departamento de Ciencias Básicas; Jorge León David Caro (jdavidca@eafit.edu.co); Electromagnetismo Aplicado (Gema)
    A stochastic exploration of the quantum conformational space for the 1Au10 system using a modified Metropolis acceptance test afforded 15 stable configurations in the MP2/SDDALL potential energy surface -- The global minimum is predicted to be a 3D structure with D2d symmetry -- Topological analyses of the electron densities suggest that bonding appears to be of intermediate character, with substantial contributions from both covalent and closed shell interactions and that there is a direct correlation between the topological complexity of the electron density and cluster stability -- Evidence regarding the nature of the interactions is gathered from many sources, including the total number of delocalized electrons (nde), a novel covalency index -- Localization indices and condensed Fukui functions predict higher electron populations on peripheral, lowly coordinated atoms