Articles de revista
http://hdl.handle.net/2117/3918
Mon, 21 Aug 2017 17:51:55 GMT2017-08-21T17:51:55ZA note on a family of non-gravitational central force potentials in dimension one
http://hdl.handle.net/2117/106571
A note on a family of non-gravitational central force potentials in dimension one
Alvarez-Ramírez, M.; Corbera Subirana, Montserrat; Cors Iglesias, Josep Maria; García, A.
In this work, we study a one-parameter family of differential equations and the different scenarios that arise with the change of parameter. We remark that these are not bifurcations in the usual sense but a wider phenomenon related with changes of continuity or differentiability. We offer an alternative point of view for the study for the motion of a system of two particles which will always move in some fixed line, we take R for the position space. If we fix the center of mass at the origin, the system reduces to that of a single particle of unit mass in a central force field. We take the potential energy function U(x)=|x|ß, where x is the position of the single particle and ß is some positive real number.
Tue, 18 Jul 2017 10:41:26 GMThttp://hdl.handle.net/2117/1065712017-07-18T10:41:26ZAlvarez-Ramírez, M.Corbera Subirana, MontserratCors Iglesias, Josep MariaGarcía, A.In this work, we study a one-parameter family of differential equations and the different scenarios that arise with the change of parameter. We remark that these are not bifurcations in the usual sense but a wider phenomenon related with changes of continuity or differentiability. We offer an alternative point of view for the study for the motion of a system of two particles which will always move in some fixed line, we take R for the position space. If we fix the center of mass at the origin, the system reduces to that of a single particle of unit mass in a central force field. We take the potential energy function U(x)=|x|ß, where x is the position of the single particle and ß is some positive real number.Non-commutative integrable systems on bsymplectic manifolds
http://hdl.handle.net/2117/106379
Non-commutative integrable systems on bsymplectic manifolds
Miranda Galcerán, Eva; Kiesenhoferb, Anna
In this paper we study noncommutative integrable systems on b-Poisson manifolds. One important source of examples (and motivation) of such systems comes from considering noncommutative systems on manifolds with boundary having the right asymptotics on the boundary. In this paper we describe this and other examples and prove an action-angle theorem for noncommutative integrable systems on a b-symplectic manifold in a neighborhood of a Liouville torus inside the critical set of the Poisson structure associated to the b-symplectic structure.
Thu, 13 Jul 2017 12:03:41 GMThttp://hdl.handle.net/2117/1063792017-07-13T12:03:41ZMiranda Galcerán, EvaKiesenhoferb, AnnaIn this paper we study noncommutative integrable systems on b-Poisson manifolds. One important source of examples (and motivation) of such systems comes from considering noncommutative systems on manifolds with boundary having the right asymptotics on the boundary. In this paper we describe this and other examples and prove an action-angle theorem for noncommutative integrable systems on a b-symplectic manifold in a neighborhood of a Liouville torus inside the critical set of the Poisson structure associated to the b-symplectic structure.On the phase-lag with equation with spatial dependent lags
http://hdl.handle.net/2117/106377
On the phase-lag with equation with spatial dependent lags
Liu, Zhuangyi; Quintanilla de Latorre, Ramón; Wang, Yang
In this paper we investigate several qualitative properties of the solutions of the dual-phase-lag heat equation and the three-phase-lag heat equation. In the first case we assume that the parameter tTtT depends on the spatial position. We prove that when 2tT-tq2tT-tq is strictly positive the solutions are exponentially stable. When this property is satisfied in a proper sub-domain, but 2tT-tq=02tT-tq=0 for all the points in the case of the one-dimensional problem we also prove the exponential stability of solutions. A critical case corresponds to the situation when 2tT-tq=02tT-tq=0 in the whole domain. It is known that the solutions are not exponentially stable. We here obtain the polynomial stability for this case. Last section of the paper is devoted to the three-phase-lag case when tTtT and t¿¿ depend on the spatial variable. We here consider the case when t¿¿=¿¿tq and tTtT is a positive constant, and obtain the analyticity of the semigroup of solutions. Exponential stability and impossibility of localization are consequences of the analyticity of the semigroup.
Thu, 13 Jul 2017 11:42:19 GMThttp://hdl.handle.net/2117/1063772017-07-13T11:42:19ZLiu, ZhuangyiQuintanilla de Latorre, RamónWang, YangIn this paper we investigate several qualitative properties of the solutions of the dual-phase-lag heat equation and the three-phase-lag heat equation. In the first case we assume that the parameter tTtT depends on the spatial position. We prove that when 2tT-tq2tT-tq is strictly positive the solutions are exponentially stable. When this property is satisfied in a proper sub-domain, but 2tT-tq=02tT-tq=0 for all the points in the case of the one-dimensional problem we also prove the exponential stability of solutions. A critical case corresponds to the situation when 2tT-tq=02tT-tq=0 in the whole domain. It is known that the solutions are not exponentially stable. We here obtain the polynomial stability for this case. Last section of the paper is devoted to the three-phase-lag case when tTtT and t¿¿ depend on the spatial variable. We here consider the case when t¿¿=¿¿tq and tTtT is a positive constant, and obtain the analyticity of the semigroup of solutions. Exponential stability and impossibility of localization are consequences of the analyticity of the semigroup.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, M. Jose
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.
Wed, 12 Jul 2017 11:43:11 GMThttp://hdl.handle.net/2117/1063622017-07-12T11:43:11ZEncinas Bachiller, Andrés MarcosJiménez Jiménez, M. JoseWe 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.
Fri, 30 Jun 2017 12:42:33 GMThttp://hdl.handle.net/2117/1060412017-06-30T12:42:33ZCarmona 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 Lombardia, 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.
Fri, 30 Jun 2017 11:45:43 GMThttp://hdl.handle.net/2117/1060392017-06-30T11:45:43ZArauz Lombardia, 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 Lombardia, 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.
Fri, 30 Jun 2017 11:22:37 GMThttp://hdl.handle.net/2117/1060342017-06-30T11:22:37ZArauz Lombardia, 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.On the optimization of bipartite secret sharing schemes
http://hdl.handle.net/2117/105969
On the optimization of bipartite secret sharing schemes
Farràs Ventura, Oriol; Metcalf-Burton, Jessica Ruth; Padró Laimon, Carles; Vázquez González, Leonor
Optimizing the ratio between the maximum length of the shares and the length of the secret value in secret sharing schemes for general access structures is an extremely difficult and long-standing open problem. In this paper, we study it for bipartite access structures, in which the set of participants is divided in two parts, and all participants in each part play an equivalent role. We focus on the search of lower bounds by using a special class of polymatroids that is introduced here, the tripartite ones. We present a method based on linear programming to compute, for every given bipartite access structure, the best lower bound that can be obtained by this combinatorial method. In addition, we obtain some general lower bounds that improve the previously known ones, and we construct optimal secret sharing schemes for a family of bipartite access structures.
Thu, 29 Jun 2017 08:25:56 GMThttp://hdl.handle.net/2117/1059692017-06-29T08:25:56ZFarràs Ventura, OriolMetcalf-Burton, Jessica RuthPadró Laimon, CarlesVázquez González, LeonorOptimizing the ratio between the maximum length of the shares and the length of the secret value in secret sharing schemes for general access structures is an extremely difficult and long-standing open problem. In this paper, we study it for bipartite access structures, in which the set of participants is divided in two parts, and all participants in each part play an equivalent role. We focus on the search of lower bounds by using a special class of polymatroids that is introduced here, the tripartite ones. We present a method based on linear programming to compute, for every given bipartite access structure, the best lower bound that can be obtained by this combinatorial method. In addition, we obtain some general lower bounds that improve the previously known ones, and we construct optimal secret sharing schemes for a family of bipartite access structures.Ideal hierarchical secret sharing schemes
http://hdl.handle.net/2117/105968
Ideal hierarchical secret sharing schemes
Farràs Ventura, Oriol; Padró Laimon, Carles
Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention since the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed, but it was not known what access structures admit such a scheme. We solve this problem by providing a natural definition for the family of the hierarchical access structures and, more importantly, by presenting a complete characterization of the ideal hierarchical access structures, that is, the ones admitting an ideal secret sharing scheme. Our characterization is based on the well known connection between ideal secret sharing schemes and matroids and, more specifically, on the connection between ideal multipartite secret sharing schemes and integer polymatroids. In particular, we prove that every hierarchical matroid port admits an ideal linear secret sharing scheme over every large enough finite field. Finally, we use our results to present a new proof for the existing characterization of the ideal weighted threshold access structures.
Thu, 29 Jun 2017 08:18:46 GMThttp://hdl.handle.net/2117/1059682017-06-29T08:18:46ZFarràs Ventura, OriolPadró Laimon, CarlesHierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention since the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed, but it was not known what access structures admit such a scheme. We solve this problem by providing a natural definition for the family of the hierarchical access structures and, more importantly, by presenting a complete characterization of the ideal hierarchical access structures, that is, the ones admitting an ideal secret sharing scheme. Our characterization is based on the well known connection between ideal secret sharing schemes and matroids and, more specifically, on the connection between ideal multipartite secret sharing schemes and integer polymatroids. In particular, we prove that every hierarchical matroid port admits an ideal linear secret sharing scheme over every large enough finite field. Finally, we use our results to present a new proof for the existing characterization of the ideal weighted threshold access structures.Finding lower bounds on the complexity of secret sharing schemes by linear programming
http://hdl.handle.net/2117/105967
Finding lower bounds on the complexity of secret sharing schemes by linear programming
Padró Laimon, Carles; Vázquez González, Leonor; Yang, An
Optimizing the maximum, or average, length of the shares in relation to the length of the secret for every given access structure is a difficult and long-standing open problem in cryptology. Most of the known lower bounds on these parameters have been obtained by implicitly or explicitly using that every secret sharing scheme defines a polymatroid related to the access structure. The best bounds that can be obtained by this combinatorial method can be determined by using linear programming, and this can be effectively done for access structures on a small number of participants.
By applying this linear programming approach, we improve some of the known lower bounds for the access structures on five participants and the graph access structures on six participants for which these parameters were still undetermined. Nevertheless, the lower bounds that are obtained by this combinatorial method are not tight in general. For some access structures, they can be improved by adding to the linear program non-Shannon information inequalities as new constraints. We obtain in this way new separation results for some graph access structures on eight participants and for some ports of non-representable matroids. Finally, we prove that, for two access structures on five participants, the combinatorial lower bound cannot be attained by any linear secret sharing scheme
Thu, 29 Jun 2017 07:37:30 GMThttp://hdl.handle.net/2117/1059672017-06-29T07:37:30ZPadró Laimon, CarlesVázquez González, LeonorYang, AnOptimizing the maximum, or average, length of the shares in relation to the length of the secret for every given access structure is a difficult and long-standing open problem in cryptology. Most of the known lower bounds on these parameters have been obtained by implicitly or explicitly using that every secret sharing scheme defines a polymatroid related to the access structure. The best bounds that can be obtained by this combinatorial method can be determined by using linear programming, and this can be effectively done for access structures on a small number of participants.
By applying this linear programming approach, we improve some of the known lower bounds for the access structures on five participants and the graph access structures on six participants for which these parameters were still undetermined. Nevertheless, the lower bounds that are obtained by this combinatorial method are not tight in general. For some access structures, they can be improved by adding to the linear program non-Shannon information inequalities as new constraints. We obtain in this way new separation results for some graph access structures on eight participants and for some ports of non-representable matroids. Finally, we prove that, for two access structures on five participants, the combinatorial lower bound cannot be attained by any linear secret sharing scheme