Articles de revista
http://hdl.handle.net/2117/79789
2019-05-22T05:37:38ZBounded solutions of self-adjoint second order linear difference equations with periodic coefficients
http://hdl.handle.net/2117/114994
Bounded solutions of self-adjoint second order linear difference equations with periodic coefficients
Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, María José
In this work we obtain easy characterizations for the boundedness of the solutions
of the discrete, self–adjoint, second order and linear unidimensional
equations with periodic coefficients, including the analysis of the so-called discrete
Mathieu equations as particular cases.
2018-03-09T11:45:32ZEncinas Bachiller, Andrés MarcosJiménez Jiménez, María JoséIn this work we obtain easy characterizations for the boundedness of the solutions
of the discrete, self–adjoint, second order and linear unidimensional
equations with periodic coefficients, including the analysis of the so-called discrete
Mathieu equations as particular cases.Second order linear difference equations
http://hdl.handle.net/2117/112719
Second order linear difference equations
Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, María José
We provide the explicit solution of a general second order linear difference equation via the computation of its associated Green function. This Green function is completely characterized and we obtain a closed expression for it using functions of two–variables, that we have called Chebyshev functions due to its intimate relation with the usual one–variable Chebyshev polynomials. In fact, we show that Chebyshev functions become Chebyshev polynomials if constant coefficients are considered.
2018-01-12T11:42:21ZEncinas Bachiller, Andrés MarcosJiménez Jiménez, María JoséWe provide the explicit solution of a general second order linear difference equation via the computation of its associated Green function. This Green function is completely characterized and we obtain a closed expression for it using functions of two–variables, that we have called Chebyshev functions due to its intimate relation with the usual one–variable Chebyshev polynomials. In fact, we show that Chebyshev functions become Chebyshev polynomials if constant coefficients are considered.Vertex-disjoint cycles in bipartite tournaments
http://hdl.handle.net/2117/111583
Vertex-disjoint cycles in bipartite tournaments
González Moreno, Diego; Balbuena Martínez, Maria Camino Teófila; Olsen, Mika
Let k=2 be an integer. Bermond and Thomassen conjectured that every digraph with minimum out-degree at least 2k-1 contains k vertex-disjoint cycles. Recently Bai, Li and Li proved this conjecture for bipartite digraphs. In this paper we prove that every bipartite tournament with minimum out-degree at least 2k-2, minimum in-degree at least 1 and partite sets of cardinality at least 2k contains k vertex-disjoint 4-cycles whenever k=3. Finally, we show that every bipartite tournament with minimum degree d=min(d+,d-) at least 1.5k-1 contains at least k vertex-disjoint 4-cycles.
2017-12-05T14:22:23ZGonzález Moreno, DiegoBalbuena Martínez, Maria Camino TeófilaOlsen, MikaLet k=2 be an integer. Bermond and Thomassen conjectured that every digraph with minimum out-degree at least 2k-1 contains k vertex-disjoint cycles. Recently Bai, Li and Li proved this conjecture for bipartite digraphs. In this paper we prove that every bipartite tournament with minimum out-degree at least 2k-2, minimum in-degree at least 1 and partite sets of cardinality at least 2k contains k vertex-disjoint 4-cycles whenever k=3. Finally, we show that every bipartite tournament with minimum degree d=min(d+,d-) at least 1.5k-1 contains at least k vertex-disjoint 4-cycles.Explicit inverse of a tridiagonal (p,r)-Toeplitz matrix
http://hdl.handle.net/2117/106362
Explicit inverse of a tridiagonal (p,r)-Toeplitz matrix
Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, María José
We have named tridiagonal (p,r)–Toeplitz matrix to those tridiagonal matrices in which each diagonal is a quasi–periodic sequence, d(p+j)=rd(j), so with period p¿N but multiplied by a real number r. We present here the necessary and sufficient conditions for the invertibility of this kind of matrices and explicitly compute their inverse. The techniques we use are related with the solution of boundary value problems associated to second order linear difference equations. These boundary value problems can be expressed throughout the discrete Schrödinger operator and their solutions can be computed using recent advances in the study of linear difference equations with quasi–periodic coefficients. The conditions that ensure the uniqueness solution of the boundary value problem lead us to the invertibility conditions for the matrix, whereas the solutions of the boundary value problems provides the entries of the inverse matrix.
2017-07-12T11:43:11ZEncinas Bachiller, Andrés MarcosJiménez Jiménez, María JoséWe have named tridiagonal (p,r)–Toeplitz matrix to those tridiagonal matrices in which each diagonal is a quasi–periodic sequence, d(p+j)=rd(j), so with period p¿N but multiplied by a real number r. We present here the necessary and sufficient conditions for the invertibility of this kind of matrices and explicitly compute their inverse. The techniques we use are related with the solution of boundary value problems associated to second order linear difference equations. These boundary value problems can be expressed throughout the discrete Schrödinger operator and their solutions can be computed using recent advances in the study of linear difference equations with quasi–periodic coefficients. The conditions that ensure the uniqueness solution of the boundary value problem lead us to the invertibility conditions for the matrix, whereas the solutions of the boundary value problems provides the entries of the inverse matrix.Equilibrium measures on finite networks. Effective resistance and hitting time
http://hdl.handle.net/2117/106041
Equilibrium measures on finite networks. Effective resistance and hitting time
Carmona Mejías, Ángeles; Bendito Pérez, Enrique; Encinas Bachiller, Andrés Marcos
We aim here at showing how the equilibrium measures for a finite network can be used to obtain simple expressions for both Green and Poisson kernels and hence we can deduce nice expressions of the hitting time and the effective resistance. Also, we will give a new and simple proof, using equilibrium measures, of the algorithm that compute the resistive inverse of a effective resistance matrix.
2017-06-30T12:42:33ZCarmona Mejías, ÁngelesBendito Pérez, EnriqueEncinas Bachiller, Andrés MarcosWe aim here at showing how the equilibrium measures for a finite network can be used to obtain simple expressions for both Green and Poisson kernels and hence we can deduce nice expressions of the hitting time and the effective resistance. Also, we will give a new and simple proof, using equilibrium measures, of the algorithm that compute the resistive inverse of a effective resistance matrix.Dirichlet-to-Robin matrix on networks
http://hdl.handle.net/2117/106039
Dirichlet-to-Robin matrix on networks
Arauz Lombardía, Cristina; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos
In this work, we de ne the Dirichlet{to{Robin matrix associated with a Schr odinger
type matrix on general networks, and we prove that it satis es the alternating
property which is essential to characterize those matrices that can be the response
matrices of a network. We end with some examples of the sign pattern behavior of
the alternating paths.
2017-06-30T11:45:43ZArauz Lombardía, CristinaCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosIn this work, we de ne the Dirichlet{to{Robin matrix associated with a Schr odinger
type matrix on general networks, and we prove that it satis es the alternating
property which is essential to characterize those matrices that can be the response
matrices of a network. We end with some examples of the sign pattern behavior of
the alternating paths.Recovering the conductances on grids
http://hdl.handle.net/2117/106034
Recovering the conductances on grids
Arauz Lombardía, Cristina; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos
In this work, we present an algorithm to the recovery of the conductance of a 2–
dimensional grid. The algorithm is based in the solution of some overdetermined
partial boundary value problems defined on the grid.
2017-06-30T11:22:37ZArauz Lombardía, CristinaCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosIn this work, we present an algorithm to the recovery of the conductance of a 2–
dimensional grid. The algorithm is based in the solution of some overdetermined
partial boundary value problems defined on the grid.Resistance distances on networks
http://hdl.handle.net/2117/105199
Resistance distances on networks
Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Mitjana Riera, Margarida
This paper aims to study a family of distances in networks associated witheffective resistances. Speci cally, we consider the e ective resistance distance with respect to a positive parameter and a weight on the vertex set; that is, the effective resistance distance associated with an irreducible and symmetric M-matrix whose lowest eigenvalue is the parameter and the weight function is the associated eigenfunction. The main idea is to consider the network embedded in a host network with additional edges whose conductances are given in terms of the mentioned parameter. The novelty of these distances is that they take into account not only the influence of shortest and longest weighted paths but also the importance of the vertices. Finally, we prove that the adjusted forest metric introduced by P. Chebotarev and E. Shamis is nothing else but a distance associated with a Schr odinger operator with
constant weight
2017-06-07T08:53:45ZCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosMitjana Riera, MargaridaThis paper aims to study a family of distances in networks associated witheffective resistances. Speci cally, we consider the e ective resistance distance with respect to a positive parameter and a weight on the vertex set; that is, the effective resistance distance associated with an irreducible and symmetric M-matrix whose lowest eigenvalue is the parameter and the weight function is the associated eigenfunction. The main idea is to consider the network embedded in a host network with additional edges whose conductances are given in terms of the mentioned parameter. The novelty of these distances is that they take into account not only the influence of shortest and longest weighted paths but also the importance of the vertices. Finally, we prove that the adjusted forest metric introduced by P. Chebotarev and E. Shamis is nothing else but a distance associated with a Schr odinger operator with
constant weightThe group inverse of subdivision networks
http://hdl.handle.net/2117/101529
The group inverse of subdivision networks
Carmona Mejías, Ángeles; Mitjana Riera, Margarida; Monsó Burgués, Enrique P.J.
In this paper, given a network and a subdivision of it, we show how the Group Inverse of the subdivision network can be related to the Group Inverse of initial given network. Our approach establishes a relationship between solutions of related Poisson problems on both networks and takes advantatge on the definition of the Group Inverse matrix.
2017-02-24T11:50:56ZCarmona Mejías, ÁngelesMitjana Riera, MargaridaMonsó Burgués, Enrique P.J.In this paper, given a network and a subdivision of it, we show how the Group Inverse of the subdivision network can be related to the Group Inverse of initial given network. Our approach establishes a relationship between solutions of related Poisson problems on both networks and takes advantatge on the definition of the Group Inverse matrix.A family of mixed graphs with large order and diameter 2
http://hdl.handle.net/2117/101356
A family of mixed graphs with large order and diameter 2
Araujo Pardo, Gabriela; Balbuena Martínez, Maria Camino Teófila; Miller, Mirka; Zdimalova, Maria
A mixed regular graph is a connected simple graph in which each vertex has both a fixed outdegree (the same indegree) and a fixed undirected degree. A mixed regular graphs is said to be optimal if there is not a mixed regular graph with the same parameters and bigger order.
We present a construction that provides mixed graphs of undirected degree qq, directed degree View the MathML sourceq-12 and order 2q22q2, for qq being an odd prime power. Since the Moore bound for a mixed graph with these parameters is equal to View the MathML source9q2-4q+34 the defect of these mixed graphs is View the MathML source(q-22)2-14.
In particular we obtain a known mixed Moore graph of order 1818, undirected degree 33 and directed degree 11 called Bosák’s graph and a new mixed graph of order 5050, undirected degree 55 and directed degree 22, which is proved to be optimal.
2017-02-21T19:33:17ZAraujo Pardo, GabrielaBalbuena Martínez, Maria Camino TeófilaMiller, MirkaZdimalova, MariaA mixed regular graph is a connected simple graph in which each vertex has both a fixed outdegree (the same indegree) and a fixed undirected degree. A mixed regular graphs is said to be optimal if there is not a mixed regular graph with the same parameters and bigger order.
We present a construction that provides mixed graphs of undirected degree qq, directed degree View the MathML sourceq-12 and order 2q22q2, for qq being an odd prime power. Since the Moore bound for a mixed graph with these parameters is equal to View the MathML source9q2-4q+34 the defect of these mixed graphs is View the MathML source(q-22)2-14.
In particular we obtain a known mixed Moore graph of order 1818, undirected degree 33 and directed degree 11 called Bosák’s graph and a new mixed graph of order 5050, undirected degree 55 and directed degree 22, which is proved to be optimal.