Recent Submissions

  • Green matrices associated with generalized linear polyominoes 

    Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Mitjana Riera, Margarida (Elsevier, 2015)
    Article
    Open Access
    A polyomino is an edge-connected union of cells in the planar square lattice. Here we consider generalized linear polyominoes; that is, the polyominoes supported by an n × 2 lattice. In this paper, we obtain the ...
  • Kirchhoff indexes of a network 

    Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel; Mitjana Riera, Margarida (Elsevier, 2010-04-15)
    Article
    Restricted access - publisher's policy
    In this work we define the effective resistance between any pair of vertices with respect to a value λ ≥ 0 and a weight ω on the vertex set. This allows us to consider a generalization of the Kirchhoff Index of a finite ...
  • A formula for the Kirchhoff index 

    Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel (2007-09-30)
    Article
    Open Access
    We show here that the Kirchhoff index of a network is the average of the Wiener capacities of its vertices. Moreover, we obtain a closed-form formula for the effective resistance between any pair of vertices when the ...
  • Application of the forces' method in dynamic systems 

    Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel (2007-10-11)
    Article
    Open Access
    We present here some applications of the Forces's method in dynamic systems. In particular, we consider the problem of the approximation of the trajectories of a conservative system of point masses by means of the minimization ...
  • Computational cost of the Fekete problem 

    Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel (2007-10-11)
    Article
    Open Access
    We present here strong numerical and statistical evidence of the fact that the Smale's 7th problem can be answered affirmatively. In particular, we show that a local minimum for the logarithmic potential energy in the ...
  • Characterization of symmetric M-matrices as resistive inverses 

    Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel (2007-01-25)
    Article
    Open Access
    We aim here at characterizing those nonnegative matrices whose inverse is an irreducible Stieltjes matrix. Specifically, we prove that any irreducible Stieltjes matrix is a resistive inverse. To do that we consider the ...
  • Potential Theory for boundary value problems on finite networks 

    Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel (2006-07)
    Article
    Open Access
    We aim here at analyzing self-adjoint boundary value problems on finite networks associated with positive semi-definite Schrödinger operators. In addition, we study the existence and uniqueness of solutions and its ...
  • Bounds on the first non-null eigenvalue for self-adjoint boundary value problems on networks 

    Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel (2006-09)
    Article
    Open Access
    We aim here at obtaining bounds on the first non-null eigenvalue for self-adjoint boundary value problems on a weighted network by means of equilibrium measures, that includes the study of Dirichlet, Neumann and Mixed ...
  • Regular boundary value problems on a path throughout Chebyshev Polynomials 

    Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel (2006-08)
    Article
    Open Access
    In this work we study the different types of regular boundary value problems on a path associated with the Schrödinger operator. In particular, we obtain the Green function for each problem and we emphasize the case of ...
  • Vector Calculus on weighted networks 

    Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos (2005-01)
    Article
    Open Access
    In this work we study the different type of regular boundary value problems on a path associated with the Schr\"odinger operator. In particular, we get the Poisson kernel and the Green function for each problem and we ...
  • Fekete points in non-smooth surfaces 

    Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel (2006-07)
    Article
    Open Access
    In this paper we present a procedure for the estimation of the Fekete points on a wide variety of non-regular objects in $R^3$. We understand the problem of the Fekete points in terms of the identification of good ...
  • Estimation of Fekete points 

    Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel (2005-05)
    Article
    Open Access
    In this paper we present a new method to estimate Fekete points on surfaces. Although our method works in a general setting, we concentrate on its application to the unit sphere because it is the prototype problem and ...

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