Articles de revista
http://hdl.handle.net/2117/3741
2016-05-04T21:13:04ZGreen matrices associated with generalized linear polyominoes
http://hdl.handle.net/2117/84592
Green matrices associated with generalized linear polyominoes
Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Mitjana Riera, Margarida
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 Ã— 2 lattice. In this
paper, we obtain the Green function and the Kirchhoff index of a
generalized linear polyomino as a perturbation of a 2n-path by adding
weighted edges between opposite vertices. This approach deeply links
generalized linear polyomino Green functions with the inverse M-matrix
problem, and especially with the so-called Green matrices.
2016-03-17T09:28:59ZCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosMitjana Riera, MargaridaA 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 Ã— 2 lattice. In this
paper, we obtain the Green function and the Kirchhoff index of a
generalized linear polyomino as a perturbation of a 2n-path by adding
weighted edges between opposite vertices. This approach deeply links
generalized linear polyomino Green functions with the inverse M-matrix
problem, and especially with the so-called Green matrices.On the nucleolus of 2 × 2 assignment games
http://hdl.handle.net/2117/21814
On the nucleolus of 2 × 2 assignment games
Martínez De Albeniz, Javier; Rafels Pallarola, Carlos; Ybern Carballo, M. de Las Nieves
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 the case of 2 × m or m × 2 assignment games.
2014-02-28T15:22:22ZMartínez De Albeniz, JavierRafels Pallarola, CarlosYbern Carballo, M. de Las NievesWe 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 the case of 2 × m or m × 2 assignment games.A procedure to compute the nucleolus of the assignment game
http://hdl.handle.net/2117/21811
A procedure to compute the nucleolus of the assignment game
Martínez De Albeniz, Javier; Rafels Pallarola, Carlos; Ybern Carballo, M. de Las Nieves
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 goods. We give a procedure to compute the nucleolus of any assignment game, based on the distribution of equal amounts to the agents, until the game is reduced to fewer agents.
2014-02-28T15:06:04ZMartínez De Albeniz, JavierRafels Pallarola, CarlosYbern Carballo, M. de Las NievesThe 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 goods. We give a procedure to compute the nucleolus of any assignment game, based on the distribution of equal amounts to the agents, until the game is reduced to fewer agents.Kirchhoff indexes of a network
http://hdl.handle.net/2117/8290
Kirchhoff indexes of a network
Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel; Mitjana Riera, Margarida
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 network. It turns out that λ is the lowest eigenvalue of a suitable semi-definite positive Schrödinger operator and ω is the associated eigenfunction. We obtain the relation between the effective resistance, and hence between the Kirchhoff Index, with respect to λ and ω and the eigenvalues of the associated Schrödinger
operator. However, our main aim in this work is to get explicit expressions of the above parameters in terms of equilibrium measures
of the network. From these expressions, we derive a full generalization of Foster’s formulae that incorporate a positive probability of remaining in each vertex in every step of a random walk. Finally, we compute the effective resistances and the generalized Kirchhoff Index with respect to a λ and ω for some families of networks with
symmetries, specifically for weighted wagon-wheels and circular ladders.
2010-07-21T08:33:04ZBendito Pérez, EnriqueCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosGesto Beiroa, José ManuelMitjana Riera, MargaridaIn 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 network. It turns out that λ is the lowest eigenvalue of a suitable semi-definite positive Schrödinger operator and ω is the associated eigenfunction. We obtain the relation between the effective resistance, and hence between the Kirchhoff Index, with respect to λ and ω and the eigenvalues of the associated Schrödinger
operator. However, our main aim in this work is to get explicit expressions of the above parameters in terms of equilibrium measures
of the network. From these expressions, we derive a full generalization of Foster’s formulae that incorporate a positive probability of remaining in each vertex in every step of a random walk. Finally, we compute the effective resistances and the generalized Kirchhoff Index with respect to a λ and ω for some families of networks with
symmetries, specifically for weighted wagon-wheels and circular ladders.A formula for the Kirchhoff index
http://hdl.handle.net/2117/1247
A formula for the Kirchhoff index
Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel
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 considered network has some symmetries which allows us to give the corresponding formulas for the Kirchhoff index. In addition, we find the expression for the Foster's n-th Formula.
2007-10-17T14:55:49ZBendito Pérez, EnriqueCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosGesto Beiroa, José ManuelWe 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 considered network has some symmetries which allows us to give the corresponding formulas for the Kirchhoff index. In addition, we find the expression for the Foster's n-th Formula.Application of the forces' method in dynamic systems
http://hdl.handle.net/2117/1246
Application of the forces' method in dynamic systems
Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel
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 of the action integral and the computation of planar central configurations.
2007-10-17T14:33:10ZBendito Pérez, EnriqueCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosGesto Beiroa, José ManuelWe 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 of the action integral and the computation of planar central configurations.Computational cost of the Fekete problem
http://hdl.handle.net/2117/1241
Computational cost of the Fekete problem
Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel
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 2-sphere satisfying the Smale's conditions can be identified with a computational cost of approximately O(N^10})
2007-10-11T16:42:31ZBendito Pérez, EnriqueCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosGesto Beiroa, José ManuelWe 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 2-sphere satisfying the Smale's conditions can be identified with a computational cost of approximately O(N^10})Characterization of symmetric M-matrices as resistive inverses
http://hdl.handle.net/2117/1168
Characterization of symmetric M-matrices as resistive inverses
Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel
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 network defined by the off-diagonal entries of the matrix and we identify the matrix with a positive definite
Schrödinger operator which ground state is determined by the its lowest eigenvalue and the corresponding positive eigenvector. We also analyze the case in which the operator is positive semidefinite which corresponds to the study of singular irreducible symmetric M-matrices. The key tool is the definition of the effective resistance with respect to a nonnegative value and a weight. We prove that these effective resistances verify similar properties to those satisfied by the standard effective resistances which leads us to carry out an exhaustive analysis of the generalized inverses of singular irreducible symmetric M-matrices. Moreover we pay special attention on those generalized inverses identified with Green operators, which in particular
includes the analysis of the Moore-Penrose inverse.
2007-08-01T19:30:23ZBendito Pérez, EnriqueCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosGesto Beiroa, José ManuelWe 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 network defined by the off-diagonal entries of the matrix and we identify the matrix with a positive definite
Schrödinger operator which ground state is determined by the its lowest eigenvalue and the corresponding positive eigenvector. We also analyze the case in which the operator is positive semidefinite which corresponds to the study of singular irreducible symmetric M-matrices. The key tool is the definition of the effective resistance with respect to a nonnegative value and a weight. We prove that these effective resistances verify similar properties to those satisfied by the standard effective resistances which leads us to carry out an exhaustive analysis of the generalized inverses of singular irreducible symmetric M-matrices. Moreover we pay special attention on those generalized inverses identified with Green operators, which in particular
includes the analysis of the Moore-Penrose inverse.Potential Theory for boundary value problems on finite networks
http://hdl.handle.net/2117/589
Potential Theory for boundary value problems on finite networks
Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel
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 variational formulation.
Moreover, we will tackle a well-known problem in the framework
of Potential Theory, the so-called condenser principle. Then,
we generalize of the concept of effective resistance between
two vertices of the network and we characterize the Green
function of some BVP in terms of effective resistances.
2006-12-01T17:44:29ZBendito Pérez, EnriqueCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosGesto Beiroa, José ManuelWe 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 variational formulation.
Moreover, we will tackle a well-known problem in the framework
of Potential Theory, the so-called condenser principle. Then,
we generalize of the concept of effective resistance between
two vertices of the network and we characterize the Green
function of some BVP in terms of effective resistances.Bounds on the first non-null eigenvalue for self-adjoint boundary value problems on networks
http://hdl.handle.net/2117/588
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
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 problems. We also show the sharpness of these bounds throughout the analysis of some known examples. In particular, we emphasize the case of
distance-regular graphs, and we show that the bounds obtained are better than the known until now.
2006-12-01T17:29:22ZBendito Pérez, EnriqueCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosGesto Beiroa, José ManuelWe 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 problems. We also show the sharpness of these bounds throughout the analysis of some known examples. In particular, we emphasize the case of
distance-regular graphs, and we show that the bounds obtained are better than the known until now.