Ponències/Comunicacions de congressos
http://hdl.handle.net/2117/80522
2024-03-28T19:28:38ZTriangular matrices and combinatorial recurrences
http://hdl.handle.net/2117/109153
Triangular matrices and combinatorial recurrences
Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, María José
2017-10-25T12:18:33ZEncinas Bachiller, Andrés MarcosJiménez Jiménez, María JoséCharacterizing identifying codes through the spectrum of a graph or digraph
http://hdl.handle.net/2117/108920
Characterizing identifying codes through the spectrum of a graph or digraph
Balbuena Martínez, Maria Camino Teófila; Dalfó Simó, Cristina; Martínez Barona, Berenice
2017-10-20T12:13:09ZBalbuena Martínez, Maria Camino TeófilaDalfó Simó, CristinaMartínez Barona, BereniceFunciones de green en redes producto
http://hdl.handle.net/2117/107904
Funciones de green en redes producto
Arauz Lombardía, Cristina; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Mitjana Riera, Margarida
En esta comunicación presentaremos la versión discreta del método de separación
de variables para determinar la función de Green de redes producto en términos
de la función de Green de uno de las redes factores y los autovalores y autofunciones de un operador de Schrödinger de la otra red factor.
2017-09-22T10:02:52ZArauz Lombardía, CristinaCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosMitjana Riera, MargaridaEn esta comunicación presentaremos la versión discreta del método de separación
de variables para determinar la función de Green de redes producto en términos
de la función de Green de uno de las redes factores y los autovalores y autofunciones de un operador de Schrödinger de la otra red factor.Cálculo de la inversa de una matriz de Jacobi
http://hdl.handle.net/2117/107901
Cálculo de la inversa de una matriz de Jacobi
Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, María José
En este trabajo aportamos las condiciones necesarias y suficientes para
la invertibilidad de las matrices de Jacobi y calculamos explícitamente su inversa. Las técnicas que utilizamos están relacionadas con la soluciones de problemas de contorno que pueden calcularse gracias a avances recientes en el estudio de ecuaciones en diferencias lineales de segundo orden.
2017-09-22T09:43:02ZEncinas Bachiller, Andrés MarcosJiménez Jiménez, María JoséEn este trabajo aportamos las condiciones necesarias y suficientes para
la invertibilidad de las matrices de Jacobi y calculamos explícitamente su inversa. Las técnicas que utilizamos están relacionadas con la soluciones de problemas de contorno que pueden calcularse gracias a avances recientes en el estudio de ecuaciones en diferencias lineales de segundo orden.Resistive distances on networks
http://hdl.handle.net/2117/107459
Resistive distances on networks
Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Mitjana Riera, Margarida
2017-09-06T12:18:58ZCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosMitjana Riera, MargaridaDiscrete inverse problem on grids
http://hdl.handle.net/2117/107406
Discrete inverse problem 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 n –dimensional grid. The algorithm is based in the solution of some overdetermined partial boundary value problems defined on the grid; that is, boundary value problem where the boundary conditions are set only in a part of the boundary (partial), and moreover in a fix subset of the boundary we prescribe both the value of the function and of its normal derivative (overdetermined). Our goal is to recover the conductance of a n –dimensional grid network with boundary using only boundary measurements and global equilibrium conditions. This problem is known as inverse boundary value problem . In general, inverse problems are exponentially ill–posed, since they are highly sensitive to changes in the boundary data. However, in this work we deal with a situation where the recovery of the conductance is feasible: grid networks. The recovery of the conductances of a grid network is performed here using its Schr ¨odinger matrix and boundary value problems associated to it. Moreover, we use the Dirichlet–to–Robin matrix, also known as response matrix of the network, which contains the boundary information. It is a certain Schur complement of the Schr ¨odinger matrix. The Schur complement plays an important role in matrix analysis, statistics, numerical analysis, and many other areas of mathematics and its applications.
2017-09-05T13:00:41ZArauz Lombardía, CristinaCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosIn this work, we present an algorithm to the recovery of the conductance of a n –dimensional grid. The algorithm is based in the solution of some overdetermined partial boundary value problems defined on the grid; that is, boundary value problem where the boundary conditions are set only in a part of the boundary (partial), and moreover in a fix subset of the boundary we prescribe both the value of the function and of its normal derivative (overdetermined). Our goal is to recover the conductance of a n –dimensional grid network with boundary using only boundary measurements and global equilibrium conditions. This problem is known as inverse boundary value problem . In general, inverse problems are exponentially ill–posed, since they are highly sensitive to changes in the boundary data. However, in this work we deal with a situation where the recovery of the conductance is feasible: grid networks. The recovery of the conductances of a grid network is performed here using its Schr ¨odinger matrix and boundary value problems associated to it. Moreover, we use the Dirichlet–to–Robin matrix, also known as response matrix of the network, which contains the boundary information. It is a certain Schur complement of the Schr ¨odinger matrix. The Schur complement plays an important role in matrix analysis, statistics, numerical analysis, and many other areas of mathematics and its applications.Green’s kernel for subdivision networks
http://hdl.handle.net/2117/107370
Green’s kernel for subdivision networks
Carmona Mejías, Ángeles; Mitjana Riera, Margarida; Monsó Burgués, Enrique P.J.
2017-09-04T13:20:25ZCarmona Mejías, ÁngelesMitjana Riera, MargaridaMonsó Burgués, Enrique P.J.Effective resistances and Kirchhoff index in subdivision networks
http://hdl.handle.net/2117/107170
Effective resistances and Kirchhoff index in subdivision networks
Carmona Mejías, Ángeles; Monsó Burgués, Enrique P.J.; Mitjana Riera, Margarida
In this work we compute the effective resistances and the Kirchhoff Index of subdivision networks in terms of the corresponding parameters of the original network. Our techniques are based on the study of discrete operators using discrete Potential Theory. Starting from a given network G = ( V, E, c ), we add a new vertex v xy at every edge { x, y } ¿ E and define new conductances c ( x, v xy ) so as to satisfy the electrical compatibility condition 1 c ( x, y ) = 1 c ( x, v xy ) + 1 c ( y, v xy ) , in order to obtain a subdivision network G S = ( V S , E S , c ) . In this setting we prove how the solution to a compatible Poisson problem on the subdivision network G S can be related with the solution of a suitable Poisson problem on the inicial network G . We use contraction and extension of functions from C ( V S ) to C ( V ) and viceversa, respectively to achieve our result. As effective resistances are computed with the aid of a solution (no matter what) to a particular Poisson problem, we can stablish an affine relationship between effective resistances defined for vertices in G S and the effective resistances defined for vertices in G . Here the coefficients are simply weighted averages of the conductances previously stated. Finally we relate the Kirchhoff index of the subdivision network K (G S ) with the Kirchhoff index of the initial network K (G) by using the so called Green‘s kernel function because the desired parameter can be computed as the trace of the kernel.
2017-08-28T07:37:06ZCarmona Mejías, ÁngelesMonsó Burgués, Enrique P.J.Mitjana Riera, MargaridaIn this work we compute the effective resistances and the Kirchhoff Index of subdivision networks in terms of the corresponding parameters of the original network. Our techniques are based on the study of discrete operators using discrete Potential Theory. Starting from a given network G = ( V, E, c ), we add a new vertex v xy at every edge { x, y } ¿ E and define new conductances c ( x, v xy ) so as to satisfy the electrical compatibility condition 1 c ( x, y ) = 1 c ( x, v xy ) + 1 c ( y, v xy ) , in order to obtain a subdivision network G S = ( V S , E S , c ) . In this setting we prove how the solution to a compatible Poisson problem on the subdivision network G S can be related with the solution of a suitable Poisson problem on the inicial network G . We use contraction and extension of functions from C ( V S ) to C ( V ) and viceversa, respectively to achieve our result. As effective resistances are computed with the aid of a solution (no matter what) to a particular Poisson problem, we can stablish an affine relationship between effective resistances defined for vertices in G S and the effective resistances defined for vertices in G . Here the coefficients are simply weighted averages of the conductances previously stated. Finally we relate the Kirchhoff index of the subdivision network K (G S ) with the Kirchhoff index of the initial network K (G) by using the so called Green‘s kernel function because the desired parameter can be computed as the trace of the kernel.Green's function of a weighted $n$-cycle
http://hdl.handle.net/2117/106599
Green's function of a weighted $n$-cycle
Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gago Álvarez, Silvia; Jiménez Jiménez, María José; Mitjana Riera, Margarida
2017-07-19T08:53:18ZCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosGago Álvarez, SilviaJiménez Jiménez, María JoséMitjana Riera, MargaridaExplicit inverse of a tridiagonal (p,r)-Toeplitz matrix
http://hdl.handle.net/2117/106597
Explicit inverse of a tridiagonal (p,r)-Toeplitz matrix
Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, María José
2017-07-19T08:46:53ZEncinas Bachiller, Andrés MarcosJiménez Jiménez, María José