El principal objectiu del grup és desenvolupar tècniques de l'anàlisi matemàtica en l'àmbit de les varietats discretes amb el propòsit d'obtenir noves eines i mètodes de resolució de problemes plantejats en aquest context. Concretament, la nostra intenció és desenvolupar un càlcul vectorial discret i utilitzar tècniques de la teoria del potencial sobre varietats discretes, tant si s'ajusten al problema físic, com si representen aproximacions del medi continu. Això ens condueix a l?estudi d'operadors i resolvents, al desenvolupament dels mètodes mimètics i a l'aplicació dels resultats obtinguts en problemes de l'enginyeria, fonamentalment d'enginyeria elèctrica.

http://futur.upc.edu/VARIDIS

The main objective of the group is to develop mathematical analysis techniques in the context of discrete manifolds in order to obtain new tools and new methods for solving problems in this field. More precisely, we aim to introduce vector calculus and potential theory techniques for discrete manifolds, whether they correspond to physical problems or to approximations in continuum mechanics. This leads on to the study of operators and resolvents, the development of mimetic methods and the application of results to engineering, mainly electrical engineering.

http://futur.upc.edu/VARIDIS

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 ...
  • Green matrices of weighted graphs with pendant vertices 

    Gago Álvarez, Silvia (2014)
    Lecture
    Open Access
  • On the nucleolus of 2 × 2 assignment games 

    Martínez De Albeniz, Javier; Rafels Pallarola, Carlos; Ybern Carballo, M. de Las Nieves (2013)
    Article
    Open Access
    We provide explicit formulas for the nucleolus of an arbitrary assignment game with two buyers and two sellers. Five different cases are analyzed depending on the entries of the assignment matrix. We extend the results to ...
  • A procedure to compute the nucleolus of the assignment game 

    Martínez De Albeniz, Javier; Rafels Pallarola, Carlos; Ybern Carballo, M. de Las Nieves (2013-11)
    Article
    Restricted access - publisher's policy
    The assignment game introduced by Shapley and Shubik (1972) [6] is a model for a two-sided market where there is an exchange of indivisible goods for money and buyers or sellers demand or supply exactly one unit of the ...
  • La función de Green y el índice de Kirchhoff de redes cluster 

    Arauz Lombardía, Cristina; Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos (2010)
    Conference lecture
    Open Access
    En este trabajo determinamos las Funciones de Green, respecto de un peso fijado sobre los vértices, en una amplia clase de redes compuestas que se engloban bajo la denominación de redes cluster. También aplicamos las ...
  • Green function on product networks 

    Arauz Lombardía, Cristina; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos (2012)
    Conference lecture
    Restricted access - publisher's policy
    Our objective is to determine the Green function of product networks in terms of the Green function of one of the factor networks and the eigenvalues and eigenfunctions of the Schr odinger operator of the other factor ...
  • Boundary value problems for Schrödinger operators on a Path Associated to Orthogonal Polynomials 

    Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gago Álvarez, Silvia (Springer, 2013)
    Part of book or chapter of book
    Restricted access - publisher's policy
    In this work, we concentrate on determining explicit expressions, via suitable orthogonal polynomials on the line, for the Green function associated with any regular boundary value problem on a weighted path, whose weights ...
  • Two-side boundary value problems in distance-regular graphs 

    Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gago Álvarez, Silvia (Universidad de Almería, 2012)
    Conference lecture
    Open Access
    In this work we analyze regular boundary value problems on a distanceregular graph associated with Schr¨odinger operators in the case that the boundary has two vertices. Moreover, we obtain the Green matrix for each ...
  • The Green function of a perturbed network 

    Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Mitjana Riera, Margarida (2012)
    Conference lecture
    Open Access
    The díscrete Green functions and their relationship whit discrete Laplace equations have deserved the interest of many researchs useing different approac. In this work we derive the Green function of a perturbed network ...
  • Generalized linear polyominoes, Green functions and Green matrices 

    Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Mitjana Riera, Margarida (2012)
    Conference lecture
    Open Access
    In this work we derive the Creen function of a generalized linear Polyomino as a suitable perturbation of the Creen function of a Hamiltonian path on it. So, our study encompasses previous work:; on polyomino-like chains.

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