Desamparados Fernández-Ternero
University of Seville
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Publication
Featured researches published by Desamparados Fernández-Ternero.
Pattern Recognition Letters | 2012
R. Ayala; Desamparados Fernández-Ternero; José Antonio Vilches
Highlights? We get conditions under which a 2-complex admits a perfect discrete Morse function. ? We study the topology of comlpexes admitting such kind of functions. ? These results are a first step in the study of these functions on 3-manifolds. This paper is focused on the study of perfect discrete Morse functions on a 2-simplicial complex. These are those discrete Morse functions such that the number of critical i-simplices coincides with the ith Betti number of the complex. In particular, we establish conditions under which a 2-complex admits a perfect discrete Morse function and conversely, we get topological properties necessary for a 2-complex admitting such kind of functions. This approach is more general than the known results in the literature (Lewiner et al., 2003), since our study is not restricted to surfaces. These results can be considered as a first step in the study of perfect discrete Morse functions on 3-manifolds.
computational topology in image context | 2012
R. Ayala; Desamparados Fernández-Ternero; José Antonio Vilches
This work is focused on characterizing the existence of a perfect discrete Morse function on a triangulated 3-manifold M, that is, a discrete Morse function satisfying that the numbers of critical simplices coincide with the corresponding Betti numbers. We reduce this problem to the existence of such kind of function on a spine L of M, that is, a 2-subcomplex L such that M−Δ collapses to L, where Δ is a tetrahedron of M. Also, considering the decomposition of every 3-manifold into prime factors, we prove that if every prime factor of M admits a perfect discrete Morse function, then M admits such kind of function.
Communications in Algebra | 2001
Desamparados Fernández-Ternero; J. Núñez-Valdés
Let be the Kac-Moody algebra associated to the affine Cartan matrix F 4 (1). Each nilpotent Lie algebra of type F 4 (1) is isomorphic to a quotient of the positive part of . We determine the isomorphism classes of nilpotent Lie algebras of type F 4 (1).
Electronic Notes in Discrete Mathematics | 2011
R. Ayala; Desamparados Fernández-Ternero; José Antonio Vilches
Abstract This work is focused on the links between Formanʼs discrete Morse theory and graph theory. More precisely, we are interested on putting the optimization of a discrete Morse function in terms of matching theory. It can be done by describing the process of cancellation of pairs of critical simplices by means of obtaining Morse matchings on the corresponding Hasse diagram with a greater number of edges using the combinatorial notion of transference.
International Journal of Open Problems in Computer Science and Mathematics | 2012
Desamparados Fernández-Ternero; Juan Núñez; Ángel F. Tenorio
This paper is devoted to study and compare two algebraic algorithms related to the computation of Lie algebras by using statistical techniques. These techniques allow us to decide which of them is more suitable and less costly depending on several variables, like the dimension of the considered algebra.
Revista Matematica Iberoamericana | 2003
Eduardo Díaz; Rafael Fernández-Mateos; Desamparados Fernández-Ternero; Juan Núñez
In this paper, we use the graphs as a tool to study nilpotent Lie algebras. It implies to set up a link between graph theory and Lie theory. To do this, it is already known that every nilpotent Lie algebra of maximal rank is associated with a generalized Cartan matrix
Journal of Algebra | 2002
Desamparados Fernández-Ternero; J. Núñez-Valdés
A
Topology and its Applications | 2015
Desamparados Fernández-Ternero; Enrique Macías-Virgós; José Antonio Vilches
and it is isomorphic to a quotient of the positive part
Topology and its Applications | 2009
R. Ayala; Luis M. Fernández; Desamparados Fernández-Ternero; José Antonio Vilches
\mathfrak{n}_+
arXiv: Algebraic Topology | 2016
Desamparados Fernández-Ternero; Enrique Macías-Virgós; Erika Minuz; José Antonio Vilches
of the Kac-Moody algebra