http://hdl.handle.net/2117/3917 Fri, 24 May 2013 13:36:26 GMT 2013-05-24T13:36:26Z webmaster.bupc@upc.edu Universitat Politècnica de Catalunya. Servei de Biblioteques i Documentació no http://hdl.handle.net/2117/19390 Title: On periodic solutions of 2-periodic Lyness' equations Authors: Bastien, Guy; Mañosa Fernández, Víctor; Rogalski, Marc Abstract: We study the existence of periodic solutions of the nonautonomous periodic Lyness' recurrenceun+2 = (an + un+1)/un, where {an}n is a cycle with positive values a, b and with positive initial conditions. It is known that for a = b = 1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a, b) ≠ (1, 1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a ≠ b, then any odd period, except 1, appears. Fri, 24 May 2013 08:04:20 GMT http://hdl.handle.net/2117/19390 2013-05-24T08:04:20Z Bastien, Guy; Mañosa Fernández, Víctor; Rogalski, Marc no Difference equations with periodic coefficients, elliptic curves, Lyness' type equations, QRT maps, rotation number, periodic orbits. We study the existence of periodic solutions of the nonautonomous periodic Lyness' recurrenceun+2 = (an + un+1)/un, where {an}n is a cycle with positive values a, b and with positive initial conditions. It is known that for a = b = 1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a, b) ≠ (1, 1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a ≠ b, then any odd period, except 1, appears. http://hdl.handle.net/2117/19386 Title: Review on "Pairing computation on twisted Edwards form elliptic curves" Authors: Alsina Aubach, Montserrat Thu, 23 May 2013 15:32:56 GMT http://hdl.handle.net/2117/19386 2013-05-23T15:32:56Z Alsina Aubach, Montserrat no http://hdl.handle.net/2117/19298 Title: A phase-field fracture model of ferroelectric materials under electro-mechanical loading Authors: Abdollahi Hosnijeh, Amir; Arias Vicente, Irene Abstract: A phase-field model is proposed for the coupled simulation of microstructure and fracture evolution in ferroelectric materials. The model is based on energetic phase-field approaches for brittle fracture and ferroelectric domain formation and evolution. The variational nature of these approaches makes their coupling very natural. However the main challenge is to encode the electro-mechanical conditions of the sharp crack faces into the phase-field framework since the crack in this model is smeared and represented by an internal layer. We develope the model for different crack face boundary conditions. Simulations show the microstructure induced by the presence of the crack. Interactions between the microstructure and the crack are investigated under different electro-mechanical loadings. Thu, 16 May 2013 12:58:07 GMT http://hdl.handle.net/2117/19298 2013-05-16T12:58:07Z Abdollahi Hosnijeh, Amir; Arias Vicente, Irene no Coupled simulation, Crack faces, Electro-mechanical, Ferroelectric domains, Fracture model, Internal layers, Phase fields, Phase-field approaches, Phase-field models, Sharp crack A phase-field model is proposed for the coupled simulation of microstructure and fracture evolution in ferroelectric materials. The model is based on energetic phase-field approaches for brittle fracture and ferroelectric domain formation and evolution. The variational nature of these approaches makes their coupling very natural. However the main challenge is to encode the electro-mechanical conditions of the sharp crack faces into the phase-field framework since the crack in this model is smeared and represented by an internal layer. We develope the model for different crack face boundary conditions. Simulations show the microstructure induced by the presence of the crack. Interactions between the microstructure and the crack are investigated under different electro-mechanical loadings. http://hdl.handle.net/2117/19287 Title: The Manhattan product of digraphs Authors: Comellas Padró, Francesc de Paula; Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel Abstract: We study the main properties of a new product of bipartite digraphs which we call Manhattan product. This product allows us to understand the subjacent product in the Manhattan street networks and can be used to built other networks with similar good properties. It is shown that if all the factors of such a product are (directed) cycles, then the digraph obtained is a Manhattan street network, a widely studied topology for modeling some interconnection networks. To this respect, it is proved that many properties of these networks, such as high symmetries, reduced diameter and the presence of Hamiltonian cycles, are shared by the Manhattan product of some digraphs. Moreover, we show that the Manhattan product of two Manhattan streets networks is also a Manhattan street network. Finally, some sufficient conditions for the Manhattan product of two Cayley digraphs to be also a Cayley digraph are given. Throughout our study we use some interesting recent concepts, such as the unilateral distance and related graph invariants. Thu, 16 May 2013 11:26:48 GMT http://hdl.handle.net/2117/19287 2013-05-16T11:26:48Z Comellas Padró, Francesc de Paula; Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel no We study the main properties of a new product of bipartite digraphs which we call Manhattan product. This product allows us to understand the subjacent product in the Manhattan street networks and can be used to built other networks with similar good properties. It is shown that if all the factors of such a product are (directed) cycles, then the digraph obtained is a Manhattan street network, a widely studied topology for modeling some interconnection networks. To this respect, it is proved that many properties of these networks, such as high symmetries, reduced diameter and the presence of Hamiltonian cycles, are shared by the Manhattan product of some digraphs. Moreover, we show that the Manhattan product of two Manhattan streets networks is also a Manhattan street network. Finally, some sufficient conditions for the Manhattan product of two Cayley digraphs to be also a Cayley digraph are given. Throughout our study we use some interesting recent concepts, such as the unilateral distance and related graph invariants. http://hdl.handle.net/2117/19212 Title: Statistical properties of subgroups of free groups Authors: Bassino, Frederique; Martino, Armando; Nicaud, Cyril; Ventura Capell, Enric; Weil, Pascal Abstract: The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k -tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so-called graph-based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the graph-based distribution, while they are exponentially generic in the word-based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group. Tue, 14 May 2013 13:22:38 GMT http://hdl.handle.net/2117/19212 2013-05-14T13:22:38Z Bassino, Frederique; Martino, Armando; Nicaud, Cyril; Ventura Capell, Enric; Weil, Pascal no subgroups of free groups, finite group presentations, statistical properties, Stallings graphs, partial injections, malnormality The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k -tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so-called graph-based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the graph-based distribution, while they are exponentially generic in the word-based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group. http://hdl.handle.net/2117/19182 Title: Verbalització multilingüística del llenguatge simbòlic, una eina d'aprenentatge Authors: Alsina Aubach, Montserrat; Soler Lorente, Mónica Mon, 13 May 2013 14:46:06 GMT http://hdl.handle.net/2117/19182 2013-05-13T14:46:06Z Alsina Aubach, Montserrat; Soler Lorente, Mónica no http://hdl.handle.net/2117/19168 Title: Spectral properties of the connectivity matrix and the SIS-epidemic threshold for mid-size metapopulations Authors: Juher Barrot, David; Mañosa Fernández, Víctor Abstract: We consider the spread of an infectious disease on a heterogeneous metapopulation defined by any (correlated or uncorrelated) network. The infection evolves under transmission, recovering and migration mechanisms. We study some spectral properties of a connectivity matrix arising from the continuous-time equations of the model. In particular we show that the classical sufficient condition of instability for the disease-free equilibrium, well known for the particular case of uncorrelated networks, works also for the general case. We give also an alternative condition that yields a more accurate estimation of the epidemic threshold for correlated (either assortative or dissortative) networks Description: Preprint version of the paper Mon, 13 May 2013 08:19:06 GMT http://hdl.handle.net/2117/19168 2013-05-13T08:19:06Z Juher Barrot, David; Mañosa Fernández, Víctor no SIS epidemics, Complex networks, Spectral properties, Connectivity matrix, Disease-free equilibrium. We consider the spread of an infectious disease on a heterogeneous metapopulation defined by any (correlated or uncorrelated) network. The infection evolves under transmission, recovering and migration mechanisms. We study some spectral properties of a connectivity matrix arising from the continuous-time equations of the model. In particular we show that the classical sufficient condition of instability for the disease-free equilibrium, well known for the particular case of uncorrelated networks, works also for the general case. We give also an alternative condition that yields a more accurate estimation of the epidemic threshold for correlated (either assortative or dissortative) networks http://hdl.handle.net/2117/19152 Title: Los niveles de determinación como herramienta para analizar tareas de modelización matemática Authors: Gómez Urgellés, Joan Vicenç Abstract: Este trabajo se enmarca en las nuevas necesidades y expectativas de la educación matemática en el sistema educativo español: "preparar al alumno para su incorporación a estudios superiores y para su inserción laboral, y formado para el ejercicio de sus derechos y obligaciones en la vida como ciudadanas y ciudadanos" Thu, 09 May 2013 14:08:10 GMT http://hdl.handle.net/2117/19152 2013-05-09T14:08:10Z Gómez Urgellés, Joan Vicenç no Este trabajo se enmarca en las nuevas necesidades y expectativas de la educación matemática en el sistema educativo español: "preparar al alumno para su incorporación a estudios superiores y para su inserción laboral, y formado para el ejercicio de sus derechos y obligaciones en la vida como ciudadanas y ciudadanos" http://hdl.handle.net/2117/19118 Title: Random test examples with known minimum for convex semi-infinite programming problems Authors: Ferrer Biosca, Alberto; Miranda Galcerán, Eva Abstract: A signi cant research activity has occurred in the area of convex semi- in nite optimization in the recent years. Many new theoretical, algorithm and computational contribution has been obtained . Despite these numerous con- tributions, there still exits a lack of representative convex semi-in nite test problems. Test problems are of major importance for researchers interested in the algorithmic development. This article is motivated by the scarcity of con- vex semi-in nite test problems and describes a procedure for generating convex semi-in nite families of test problems with optimal solution and optimal value known. Tue, 07 May 2013 11:19:15 GMT http://hdl.handle.net/2117/19118 2013-05-07T11:19:15Z Ferrer Biosca, Alberto; Miranda Galcerán, Eva no A signi cant research activity has occurred in the area of convex semi- in nite optimization in the recent years. Many new theoretical, algorithm and computational contribution has been obtained . Despite these numerous con- tributions, there still exits a lack of representative convex semi-in nite test problems. Test problems are of major importance for researchers interested in the algorithmic development. This article is motivated by the scarcity of con- vex semi-in nite test problems and describes a procedure for generating convex semi-in nite families of test problems with optimal solution and optimal value known. http://hdl.handle.net/2117/19014 Title: Aula virtual de soporte a la docencia y al autoaprendizaje del cálculo para estudiantes universitarios con material docente y aplicaciones basadas en software libre Authors: Jarauta Bragulat, Eusebio; Pelayo Melero, Ignacio Manuel Fri, 26 Apr 2013 12:40:48 GMT http://hdl.handle.net/2117/19014 2013-04-26T12:40:48Z Jarauta Bragulat, Eusebio; Pelayo Melero, Ignacio Manuel no http://hdl.handle.net/2117/19012 Title: Aula virtual de apoyo a la docencia y al autoaprendizaje de cálculo para estudiantes universitarios con material docente y aplicaciones basadas en software libre Authors: Jarauta Bragulat, Eusebio; Pelayo Melero, Ignacio Manuel Fri, 26 Apr 2013 12:30:02 GMT http://hdl.handle.net/2117/19012 2013-04-26T12:30:02Z Jarauta Bragulat, Eusebio; Pelayo Melero, Ignacio Manuel no http://hdl.handle.net/2117/18915 Title: On the restricted connectivity and superconnectivity in graphs with given girth Authors: Balbuena Martínez, Maria Camino Teófila; Cera, M; Diánez, A; García-Vázquez, P; Marcote Ordax, Francisco Javier Abstract: The restricted connectivity κ′(G)κ′(G) of a connected graph G is defined as the minimum cardinality of a vertex-cut over all vertex-cuts X such that no vertex uu has all its neighbors in X; the superconnectivity κ1(G)κ1(G) is defined similarly, this time considering only vertices uu in G-XG-X, hence κ1(G)⩽κ′(G)κ1(G)⩽κ′(G). The minimum edge-degree of G is ξ(G)=min{d(u)+d(v)-2:uv∈E(G)}ξ(G)=min{d(u)+d(v)-2:uv∈E(G)}, d(u)d(u) standing for the degree of a vertex uu. In this paper, several sufficient conditions yielding κ1(G)⩾ξ(G)κ1(G)⩾ξ(G) are given, improving a previous related result by Fiol et al. [Short paths and connectivity in graphs and digraphs, Ars Combin. 29B (1990) 17–31] and guaranteeing κ1(G)=κ′(G)=ξ(G)κ1(G)=κ′(G)=ξ(G) under some additional constraints. Description: "Discrete Mathemetics Top Cited Article 2005-2010" Mon, 22 Apr 2013 11:28:54 GMT http://hdl.handle.net/2117/18915 2013-04-22T11:28:54Z Balbuena Martínez, Maria Camino Teófila; Cera, M; Diánez, A; García-Vázquez, P; Marcote Ordax, Francisco Javier no The restricted connectivity κ′(G)κ′(G) of a connected graph G is defined as the minimum cardinality of a vertex-cut over all vertex-cuts X such that no vertex uu has all its neighbors in X; the superconnectivity κ1(G)κ1(G) is defined similarly, this time considering only vertices uu in G-XG-X, hence κ1(G)⩽κ′(G)κ1(G)⩽κ′(G). The minimum edge-degree of G is ξ(G)=min{d(u)+d(v)-2:uv∈E(G)}ξ(G)=min{d(u)+d(v)-2:uv∈E(G)}, d(u)d(u) standing for the degree of a vertex uu. In this paper, several sufficient conditions yielding κ1(G)⩾ξ(G)κ1(G)⩾ξ(G) are given, improving a previous related result by Fiol et al. [Short paths and connectivity in graphs and digraphs, Ars Combin. 29B (1990) 17–31] and guaranteeing κ1(G)=κ′(G)=ξ(G)κ1(G)=κ′(G)=ξ(G) under some additional constraints. http://hdl.handle.net/2117/18913 Title: An improvement of Ostrowski root-finding method Authors: Grau Sánchez, Miguel; Díaz Barrero, José Luis Abstract: An improvement to the iterative method based on the Ostrowski one to compute nonlinear equation solutions, which increases the local order of convergence is suggested. The adaptation of a strategy presented here gives a new iteration function with an additional evaluation of the function. It also shows a smaller cost if we use adaptive multi-precision arithmetic. The numerical results computed using this system with a floating point system representing 200 decimal digits support this theory. Description: "Applied Mathematics and Computation Top Cited Article 2005-2010" Mon, 22 Apr 2013 10:46:22 GMT http://hdl.handle.net/2117/18913 2013-04-22T10:46:22Z Grau Sánchez, Miguel; Díaz Barrero, José Luis no An improvement to the iterative method based on the Ostrowski one to compute nonlinear equation solutions, which increases the local order of convergence is suggested. The adaptation of a strategy presented here gives a new iteration function with an additional evaluation of the function. It also shows a smaller cost if we use adaptive multi-precision arithmetic. The numerical results computed using this system with a floating point system representing 200 decimal digits support this theory. http://hdl.handle.net/2117/18912 Title: Moments in graphs Authors: Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest Abstract: Let G be a connected graph with vertex set V and a weight function that assigns a nonnegative number to each of its vertices. Then, the -moment of G at vertex u is de ned to be M G(u) = P v2V (v) dist(u; v), where dist( ; ) stands for the distance function. Adding up all these numbers, we obtain the -moment of G: This parameter generalizes, or it is closely related to, some well-known graph invari- ants, such as the Wiener index W(G), when (u) = 1=2 for every u 2 V , and the degree distance D0(G), obtained when (u) = (u), the degree of vertex u. In this paper we derive some exact formulas for computing the -moment of a graph obtained by a general operation called graft product, which can be seen as a generalization of the hierarchical product, in terms of the corresponding -moments of its factors. As a consequence, we provide a method for obtaining nonisomorphic graphs with the same -moment for every (and hence with equal mean distance, Wiener index, degree distance, etc.). In the case when the factors are trees and/or cycles, techniques from linear algebra allow us to give formulas for the degree distance of their product. Mon, 22 Apr 2013 10:41:17 GMT http://hdl.handle.net/2117/18912 2013-04-22T10:41:17Z Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest no Let G be a connected graph with vertex set V and a weight function that assigns a nonnegative number to each of its vertices. Then, the -moment of G at vertex u is de ned to be M G(u) = P v2V (v) dist(u; v), where dist( ; ) stands for the distance function. Adding up all these numbers, we obtain the -moment of G: This parameter generalizes, or it is closely related to, some well-known graph invari- ants, such as the Wiener index W(G), when (u) = 1=2 for every u 2 V , and the degree distance D0(G), obtained when (u) = (u), the degree of vertex u. In this paper we derive some exact formulas for computing the -moment of a graph obtained by a general operation called graft product, which can be seen as a generalization of the hierarchical product, in terms of the corresponding -moments of its factors. As a consequence, we provide a method for obtaining nonisomorphic graphs with the same -moment for every (and hence with equal mean distance, Wiener index, degree distance, etc.). In the case when the factors are trees and/or cycles, techniques from linear algebra allow us to give formulas for the degree distance of their product. http://hdl.handle.net/2117/18908 Title: Polynomials in finite geometries Authors: Ball, Simeon Michael Abstract: A method of using polynomials to describe objects in finite geometries is outlined and the problems where this method has led to a solution are surveyed. These problems concern nuclei, affine blocking sets, maximal arcs and unitals. In the case of nuclei these methods give lower bounds on the number of nuclei to a set of points in PG(n, q), usually dependent on some binomial coefficient not vanishing modulo the characteristic of the field. These lower bounds on nuclei lead directly to lower bounds on affine blocking sets with respect to lines. A short description of how linear polynomials can be used to construct maximal arcs in certain translation planes is included. A proof of the non-existence of maximal arcs in PG(2, q) when q is odd is outlined and some bounds are given as to when a (k, n)-arc can be extended to a maximal arc in PG(2, q). These methods can also be applied to unitals embedded in PG(2, q). One implication of this is that when q is the square of a prime a non-classical unital has a limited amount of Baer sublines amongst its secants. Mon, 22 Apr 2013 08:26:51 GMT http://hdl.handle.net/2117/18908 2013-04-22T08:26:51Z Ball, Simeon Michael no A method of using polynomials to describe objects in finite geometries is outlined and the problems where this method has led to a solution are surveyed. These problems concern nuclei, affine blocking sets, maximal arcs and unitals. In the case of nuclei these methods give lower bounds on the number of nuclei to a set of points in PG(n, q), usually dependent on some binomial coefficient not vanishing modulo the characteristic of the field. These lower bounds on nuclei lead directly to lower bounds on affine blocking sets with respect to lines. A short description of how linear polynomials can be used to construct maximal arcs in certain translation planes is included. A proof of the non-existence of maximal arcs in PG(2, q) when q is odd is outlined and some bounds are given as to when a (k, n)-arc can be extended to a maximal arc in PG(2, q). These methods can also be applied to unitals embedded in PG(2, q). One implication of this is that when q is the square of a prime a non-classical unital has a limited amount of Baer sublines amongst its secants.