Examinando por Materia "Interpolation spaces"

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    Hessian Eigenfunctions for Triangular Mesh Parameterization
    (SCITEPRESS, 2016) Mejía, Daniel; Ruíz, Oscar; Cadavid, Carlos A.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
    Hessian Locally Linear Embedding (HLLE) is an algorithm that computes the nullspace of a Hessian functional H for Dimensionality Reduction (DR) of a sampled manifold M -- This article presents a variation of classic HLLE for parameterization of 3D triangular meses -- Contrary to classic HLLE which estimates local Hessian nullspaces, the proposed approach follows intuitive ideas from Differential Geometry where the local Hessian is estimated by quadratic interpolation and a partition of unity is used to join all neighborhoods -- In addition, local average triangle normals are used to estimate the tangent plane TxM at x ∈ M instead of PCA, resulting in local parameterizations which reflect better the geometry of the surface and perform better when the mesh presents sharp features -- A high frequency dataset (Brain) is used to test our algorithm resulting in a higher rate of success (96.63%) compared to classic HLLE (76.4%)
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    On the Maximal Operator Ideal Associated with a Tensor Norm Defined by Interpolation Spaces
    (CANADIAN MATHEMATICAL SOC, 2010-12-01) Puerta, M. E.; Loaiza, G.; Puerta, M. E.; Loaiza, G.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
    The classical approach to studying operator ideals using tensor norms mainly focuses on those tensor norms and operator ideals defined by means of `p spaces. In a previous paper, an interpolation space, defined via the real method and using `p spaces, was used to define a tensor norm, and the associated minimal operator ideals were characterized. In this paper, the next natural step is taken, that is, the corresponding maximal operator ideals are characterized. As an application, necessary and sufficient conditions for the coincidence of the maximal and minimal ideals are given. Finally, the previous results are used in order to find some new metric properties of the mentioned tensor norm. © Canadian Mathematical Society 2010.
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    Ultraproducts of real interpolation spaces between L p -spaces
    (SPRINGER, 2006-06-01) López Molina, J.A.; Puerta, M.E.; Rivera, M.J.; López Molina, J.A.; Puerta, M.E.; Rivera, M.J.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
    Let {(L p0 (Od, µd), L p1 (Od, µd)) , d e D}, 1 = p0 < p1 < 8, be a family of compatible couples of L p -spaces. We show that, given a countably incomplete ultrafilter U in D, the ultraproduct (L p0 (Od, µd), L p1 (Od, µd))? q)U , 0< ? < 1,1 = q < 8 of interpolation spaces defined by the real method is isomorphic to the direct sum of an interpolation space of type (L p0 (O1, ? 1 L p1 (O1, ? 1)) ?, q , an intermediate Köthe space between l p0 (O2, ? 2) and l p1 (O2, ? 2), (O2, ? 2)being a purely atomic measure space, and a Köthe function space K(O3) defined on some purely non atomic measure space (O3, ? 3) in such a way that O2 O3 ? ?. © Springer-Verlag Berlin Heidelberg 2006.