http://hdl.handle.net/2117/3918 2013-05-24T20:50:32Z 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. 2013-05-24T08:04:20Z 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. 2013-05-16T11:26:48Z 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. 2013-05-14T13:22:38Z 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" 2013-04-22T11:28:54Z 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" 2013-04-22T10:46:22Z 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. 2013-04-22T10:41:17Z http://hdl.handle.net/2117/18778 Title: Alternative tests for functional and pointwise output-controllability of linear time-invariant systems Authors: García Planas, María Isabel; Domínguez García, José Luis Abstract: This paper deals with the description of a new method for calculating the functional output-controllability. It is computed by means of the rank of a certain constant matrix which can be associated to the system. Moreover, a new method for the pointwise output-controllability determination by means of constructing the output-controllability matrix associated to the system using the residues of the given linear system is developed. Finally, a simple physical example is presented 2013-04-12T10:12:39Z http://hdl.handle.net/2117/18775 Title: On the decay of solutions for the heat conduction with two temperatures Authors: Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón Abstract: This paper is devoted to the study of the asymptotic behavior of the solutions of the system of equations that models the heat conduction with two temperatures. That is, we consider a mixture of isotropic and homogeneous rigid solids. We analyze the static problem in a semi-infinite cylinder where every material point has two temperatures with nonlinear boundary conditions on the lateral side. A Phragmén–Lindelöf alternative for the solutions is obtained by means of energy arguments. Estimates for the decay and growth of the solutions are presented. We also prove that the only solution vanishing in the exterior of a bounded set is the null solution for a particular subfamily of problems. Cone-like domains are considered in the last section, and we obtain decay estimates for the solutions when the total energy is bounded. 2013-04-11T15:01:18Z http://hdl.handle.net/2117/18770 Title: On the logarithmic convexity in thermoelastiscity with microtemperatures Authors: Quintanilla de Latorre, Ramón Abstract: This article is concerned with the linear theory of thermoelasticity with microtemperatures. In a recent article we have used the logarithmic convexity method to investigate uniqueness, instability and structural stability. The results are restricted to the case when the constitutive coefficients k1 and k3 have the same signs. Here we prove that these results also hold when the coefficients k1 and k3 have opposite signs. 2013-04-11T13:01:01Z http://hdl.handle.net/2117/18733 Title: Nonsingular models of universes in teleparallel theories Authors: Haro Cases, Jaume; Amorós Torrent, Jaume Abstract: Different models of universes are considered in the context of teleparallel theories. Assuming that the universe is filled by a fluid with an equation of state P ¼ f ð Þ , for different teleparallel theories and different equation of state we study its dynamics. Two particular cases are studied in detail: in the first one we consider a function f with two zeros (two de Sitter solutions) that mimics a huge cosmological constant at early times and a pressureless fluid at late times; in the second one, in the context of loop quantum cosmology with a small cosmological constant, we consider a pressureless fluid ( P ¼ 0 , f ð Þ¼ ) which means there are de Sitter and anti–de Sitter solutions. In both cases one obtains a nonsingular universe that at early times is in an inflationary phase; after leaving this phase, it passes trough a matter dominated phase and finally at late times it expands in an accelerated way Description: PACS Numbers: 04.50.Kd, 98.80.Jk 2013-04-09T11:50:58Z http://hdl.handle.net/2117/18702 Title: A Whitehad algorithm for toral relatively hyperbolic groups Authors: Kharlampovich, Olga; Ventura Capell, Enric Abstract: The Whitehead problem is solved in the class of toral relatively hyperbolic groups G (i.e. torsion-free relatively hyperbolic groups with abelian parabolic subgroups): there is an algorithm which, given two nite tuples (u1; ... ; un) and (v1; ... ; vn) of elements of G, decides whether there is an automorphism of G taking ui to vi for all i. 2013-04-08T13:10:03Z http://hdl.handle.net/2117/18650 Title: Computation of ATR Darmon points on nongeometrically modular elliptic curves Authors: Guitart Morales, Xavier; Masdeu, Marc Abstract: ATR points were introduced by Darmon as a conjectural con- struction of algebraic points on certain elliptic curves for which the Heegner-point method is not in general available. So far, the only numerical evidence, provided by Darmon–Logan and G ̈ artner,concernedcurvesarisingasquotientsofShimuracurves. In those special cases, the ATR points can be obtained from the already existing Heegner points, thanks to results from Zhang and Darmon–Rotger–Zhao. In this paper, we compute for the first time an algebraic ATR point on a curve that is not uniformizable by any Shimura curve, thus providing the first piece of numerical evidence that Darmon’s construction works beyond geometric modularity. To this pur- pose, we improve the method proposed by Darmon and Logan by removing the requirement that the real quadratic base field be norm-Euclidean and accelerating the numerical integration of Hilbert modular forms. 2013-04-05T13:25:08Z http://hdl.handle.net/2117/18648 Title: Unravelling the linkages between water, sanitation, hygiene and rural poverty: The WASH poverty index Authors: Giné Garriga, Ricard; Pérez Foguet, Agustí Abstract: Many studies have reported the effect of water supply, sanitation and hygiene (WASH) in improving health and ultimately alleviating poverty. Current coverage estimates show however that a large proportion of people in the world still do not have access to a simple pit latrine or a source of safe drinking water, and this situation worsens in rural areas. To help end these appalling figures, much effort has gone into the development of policy instruments which support decision-making, i.e. planning, targeting and prioritization. Indices and indicators are increasingly recognised as powerful tools for such purposes. This paper details the theoretical framework and development of a multidimensional, WASH-focused, thematic indicator: the WASH Poverty Index (WASH PI). It describes the methodology in index construction and disseminates achieved results in a variety of forms to promote the utility of the tool for the integrated analysis of WASH and poverty linkages. The article uses Kenya as initial case study to illustrate the application of the index. Overall, WASH PI helps identify priority areas and guide appropriate action and policy-making towards improved service delivery. 2013-04-05T12:30:32Z http://hdl.handle.net/2117/18614 Title: Connecting Red Cells in a Bicolour Voronoi Diagram Authors: Abellanas, Manuel; Bajuelos, Antonio L.; Canales, Santiago; Claverol Aguas, Mercè; Hernández, Gregorio; Pereira de Matos, Inés Abstract: Let S be a set of n + m sites, of which n are red and have weight wR, and m are blue and weigh wB. The objective of this paper is to calculate the minimum value of the red sites’ weight such that the union of the red Voronoi cells in the weighted Voronoi diagram of S is a connected region. This problem is solved for the multiplicativelyweighted Voronoi diagram in O((n+m)2 log(nm)) time and for both the additively-weighted and power Voronoi diagram in O(nmlog(nm)) time 2013-04-04T13:14:09Z http://hdl.handle.net/2117/18603 Title: New approach to the k-independence number of a graph Authors: Caro, Yair; Hansberg Pastor, Adriana Abstract: Let G = (V,E) be a graph and k > 0 an integer. A k-independent set S V is a set of vertices such that the maximum degree in the graph induced by S is at most k. With k(G) we denote the maximum cardinality of a k-independent set of G. We prove that, for a graph G on n vertices and average degree d, k(G) > k+1 dde+k+1n, improving the hitherto best general lower bound due to Caro and Tuza [Improved lower bounds on k-independence, J. Graph Theory 15 (1991), 99–107]. 2013-04-04T10:54:16Z