VARIDIS - Varietats Riemannianes Discretes i Teoria del Potencial
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.
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.
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.
Col·leccions
-
Articles de revista [14]
-
Presentacions [1]
Enviaments recents
-
Ground movement control in the construction of a new metro line in Barcelona
(CRC Press, 2005)
Text en actes de congrés
Accés restringit per política de l'editorialGround movement control is of paramount importance in the construction of a new Metro line in Barcelona given the large diameter of the excavation and the need to cross heavily built areas. A variety of construction ... -
Green matrices associated with generalized linear polyominoes
(Elsevier, 2015)
Article
Accés obertA 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
(2014)
Presentació
Accés obert -
On the nucleolus of 2 × 2 assignment games
(2013)
Article
Accés obertWe 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
(2013-11)
Article
Accés restringit per política de l'editorialThe 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
(2010)
Comunicació de congrés
Accés obertEn 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
(2012)
Comunicació de congrés
Accés restringit per política de l'editorialOur 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
(Springer, 2013)
Capítol de llibre
Accés restringit per política de l'editorialIn 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
(Universidad de Almería, 2012)
Comunicació de congrés
Accés obertIn 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
(2012)
Comunicació de congrés
Accés obertThe 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
(2012)
Comunicació de congrés
Accés obertIn 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. -
Boundary value problems for Schrödinger operators on a path
(2012-05-25)
Report de recerca
Accés obertIn 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 ...