http://hdl.handle.net/2117/3740 Sat, 25 May 2013 18:00:06 GMT 2013-05-25T18:00:06Z webmaster.bupc@upc.edu Universitat Politècnica de Catalunya. Servei de Biblioteques i Documentació no http://hdl.handle.net/2117/17276 Title: Two-side boundary value problems in distance-regular graphs Authors: Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gago Álvarez, Silvia Abstract: 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 regular problem. In each case, the Green matrix is given in terms of two families of orthogonal polynomials, one of them corresponding with the distance polynomials of the distance-regular graph. Fri, 11 Jan 2013 12:28:45 GMT http://hdl.handle.net/2117/17276 2013-01-11T12:28:45Z Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gago Álvarez, Silvia no 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 regular problem. In each case, the Green matrix is given in terms of two families of orthogonal polynomials, one of them corresponding with the distance polynomials of the distance-regular graph. http://hdl.handle.net/2117/16454 Title: The Green function of a perturbed network Authors: Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Mitjana Riera, Margarida Abstract: 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 in terms of the Green function of its base network. Fri, 07 Sep 2012 10:39:29 GMT http://hdl.handle.net/2117/16454 2012-09-07T10:39:29Z Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Mitjana Riera, Margarida no 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 in terms of the Green function of its base network. http://hdl.handle.net/2117/16453 Title: Generalized linear polyominoes, Green functions and Green matrices Authors: Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Mitjana Riera, Margarida Abstract: 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. Fri, 07 Sep 2012 10:28:56 GMT http://hdl.handle.net/2117/16453 2012-09-07T10:28:56Z Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Mitjana Riera, Margarida no 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. http://hdl.handle.net/2117/16111 Title: Boundary value problems for Schrödinger operators on a path Authors: Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gago Álvarez, Silvia Abstract: 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 are determined by the coefficients of the three terms recurrence relation defining the polynomials. Our study is similar to what is known for boundary value problems associated with ordinary differential equations. Thu, 21 Jun 2012 08:55:34 GMT http://hdl.handle.net/2117/16111 2012-06-21T08:55:34Z Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gago Álvarez, Silvia no 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 are determined by the coefficients of the three terms recurrence relation defining the polynomials. Our study is similar to what is known for boundary value problems associated with ordinary differential equations. http://hdl.handle.net/2117/15768 Title: Betweenness-selfcentric graphs Authors: Gago Álvarez, Silvia; Hurajová, Jana; Madaras, Tomas Abstract: The betweenness centrality of a vertex of a graph is the portion of shortest paths between all pairs of vertices passing through that vertex. In this paper, we study properties and constructions of graphs whose vertices have the same value of betweenness centrality. Wed, 02 May 2012 08:54:06 GMT http://hdl.handle.net/2117/15768 2012-05-02T08:54:06Z Gago Álvarez, Silvia; Hurajová, Jana; Madaras, Tomas no The betweenness centrality of a vertex of a graph is the portion of shortest paths between all pairs of vertices passing through that vertex. In this paper, we study properties and constructions of graphs whose vertices have the same value of betweenness centrality. http://hdl.handle.net/2117/14935 Title: Smoothing of yield surfaces and a reformulation of multi-surface plasticity Authors: Gesto Beiroa, José Manuel; Gens Solé, Antonio; Vaunat, Jean Abstract: In this work we describe a procedure for the smoothing of non-regular yield surfaces and plastic potential functions. We also present several application examples corresponding to different well-known cases. Moreover, we show that a multi-surface plasticity model can be reduced to a model with a single yield surface by using the same smoothing procedure. Fri, 03 Feb 2012 18:49:51 GMT http://hdl.handle.net/2117/14935 2012-02-03T18:49:51Z Gesto Beiroa, José Manuel; Gens Solé, Antonio; Vaunat, Jean no Corners, Yield Surface, Plastic Potential, Multi-Surface Plasticity In this work we describe a procedure for the smoothing of non-regular yield surfaces and plastic potential functions. We also present several application examples corresponding to different well-known cases. Moreover, we show that a multi-surface plasticity model can be reduced to a model with a single yield surface by using the same smoothing procedure. http://hdl.handle.net/2117/14821 Title: Jacobi matrices and boundary value problems in distance-regular graphs Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gago Álvarez, Silvia Abstract: In this work we analyze regular boundary value problems on a distance-regular graph associated with SchrÄodinger operators. These problems include the cases in which the boundary has two or one vertices. Moreover, we obtain the Green matrix for each regular problem. In each case, the Green matrices are given in terms of two families of orthogonal polynomials one of them corresponding with the distance polynomials of the distance-regular graphs. Thu, 26 Jan 2012 10:21:55 GMT http://hdl.handle.net/2117/14821 2012-01-26T10:21:55Z Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gago Álvarez, Silvia no In this work we analyze regular boundary value problems on a distance-regular graph associated with SchrÄodinger operators. These problems include the cases in which the boundary has two or one vertices. Moreover, we obtain the Green matrix for each regular problem. In each case, the Green matrices are given in terms of two families of orthogonal polynomials one of them corresponding with the distance polynomials of the distance-regular graphs. http://hdl.handle.net/2117/8331 Title: M-Matrix Inverse problem for distance-regular graphs Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Mitjana Riera, Margarida Thu, 22 Jul 2010 07:31:15 GMT http://hdl.handle.net/2117/8331 2010-07-22T07:31:15Z Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Mitjana Riera, Margarida no http://hdl.handle.net/2117/8290 Title: Kirchhoff indexes of a network Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel; Mitjana Riera, Margarida Abstract: 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. Wed, 21 Jul 2010 08:33:04 GMT http://hdl.handle.net/2117/8290 2010-07-21T08:33:04Z Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel; Mitjana Riera, Margarida no 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. http://hdl.handle.net/2117/1247 Title: A formula for the Kirchhoff index Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel Abstract: 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. Wed, 17 Oct 2007 14:55:49 GMT http://hdl.handle.net/2117/1247 2007-10-17T14:55:49Z Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel no Kirchhoff index, effective resistance, equilibrium measure 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. http://hdl.handle.net/2117/1246 Title: Application of the forces' method in dynamic systems Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel Abstract: 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. Wed, 17 Oct 2007 14:33:10 GMT http://hdl.handle.net/2117/1246 2007-10-17T14:33:10Z Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel no dynamic systems, forces' method, choreographies 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. http://hdl.handle.net/2117/1241 Title: Computational cost of the Fekete problem Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel Abstract: 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}) Thu, 11 Oct 2007 16:42:31 GMT http://hdl.handle.net/2117/1241 2007-10-11T16:42:31Z Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel no Fekete points, Smale's 7th problem 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}) http://hdl.handle.net/2117/1168 Title: Characterization of symmetric M-matrices as resistive inverses Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel Abstract: 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. Wed, 01 Aug 2007 19:30:23 GMT http://hdl.handle.net/2117/1168 2007-08-01T19:30:23Z Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel no Schrödinger operator, M-matrices, generalized inverses, Green kernels, Moore-Penrose inverse, effective resistance, Kirchhoff index 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. http://hdl.handle.net/2117/589 Title: Potential Theory for boundary value problems on finite networks Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel Abstract: 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. Fri, 01 Dec 2006 17:44:29 GMT http://hdl.handle.net/2117/589 2006-12-01T17:44:29Z Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel no Discrete Potential Theory, Combinatorial Laplacian, Schrödinger operator, Boundary value problems, Effective resistance, Green function 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. http://hdl.handle.net/2117/588 Title: Bounds on the first non-null eigenvalue for self-adjoint boundary value problems on networks Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel Abstract: 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. Fri, 01 Dec 2006 17:29:22 GMT http://hdl.handle.net/2117/588 2006-12-01T17:29:22Z Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel no Networks, Self-adjoint eigenvalue problems, Discrete laplacian, Equilibrium measures, Distance-regular graphs 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.