On periodic solutions of 2-periodic Lyness difference equations

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_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) different from (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 is not equal to b, then any odd period, except 1, appears.Comment: 27 pages; 1 figur

On the set of periods of the 2-periodic Lyness’ Equation

PreprintWe study the periodic solutions of the non–autonomous periodic Lyness’ recurrence un+2 = (an +un+1)=un, where fangn is a cycle with positive values a,b and with positive initial conditions. Among other methodological issues we give an outline of the proof of the following results: (1) If (a;b) 6= (1;1), then there exists a value p0(a;b) such that for any p > p0(a;b) there exist continua of initial conditions giving rise to 2p–periodic sequences. (2) The set of minimal periods arising when (a;b) 2 (0;¥) 2 and positive initial conditions are considered, contains all the even numbers except 4, 6, 8, 12 and 20. If a 6= b, then it does not appear any odd period, except 1.Preprin

Integrable birational maps on the plane: blending dynamics and algebraic geometry

Contingut del Pòster presentat al congrés New Trends in Dynamical SystemsPeer ReviewedPreprin

On the set of periods of the 2-periodic Lyness' equation

Publicació amb motiu de la International Conference on Difference Equations and Applications (July 22-27, 2012, Barcelona, Spain) amb el títol Difference Equations, Discrete Dynamical Systems and ApplicationsWe study the periodic solutions of the non-autonomous periodic Lyness' recurrence u = (a + u )/u, where {a} is a cycle with positive values a,b and with positive initial conditions. Among other methodological issues we give an outline of the proof of the following results: (1) If (a, b) ≠ (1, 1), then there exists a value p(a, b) such that for any p > p(a, b) there exist continua of initial conditions giving rise to 2p-periodic sequences. (2) The set of minimal periods arising when (a, b) ∈ (0,∞) and positive initial conditions are considered, contains all the even numbers except 4, 6, 8, 12 and 20. If a ≠ b, then it does not appear any odd period, except 1

Divided attention in young drivers under the influence of alcohol

Aim: The present research evaluates driving impairment linked to two crashes factors, divided attention task and alcohol, and determines whether it is higher for novice drivers than for experienced drivers. Method: Novice and experienced drivers participated in three experimental sessions in which blood alcohol concentrations (BACs) were 0.0 g/L, 0.2 g/L and 0.5 g/L. They performed a divided attention task with a main task of car-following task and an additional task of number parity identification. Driving performance, response time and accuracy on the additional task were measured. Results: ANOVA showed a driving impairment and a decrease in additional task performance from BAC of 0.5g/L, particularly for novice drivers. Indeed, the latter adopt more risky behaviour such as tailgating. In the divided attention task, driving impairment was found for all drivers and impairment on information processing accuracy was highlighted, notably in peripheral vision. Impact of research: The divided attention task used here provides a relevant method for identifying the effects of alcohol on cognitive functions and could be used in psychopharmacological research

Émergence de flaticons dans les fibres optiques

Conférence pouvant être vue sur http://youtu.be/p9OnhcHQ3MwNational audienceNous étudions expérimentalement la propagation non-linéaire d'une onde continue menant à l'émergence d'impulsions au sommet plat et sans dérive de fréquence. Ces impulsions, appelées flaticons, subissent une évolution auto-similaire de leur partie centrale et présentent des oscillations temporelles marquées dans leurs flancs

Simulation of a sodium fast core: Effect of B 1 leakage models on group constant generation

Due to their complexity, neutronic calculations are usually performed in two steps. Once the neutron transport equation has been solved over the elementary domains that compose the core (cells or assemblies with translation or reflexion boundary conditions), a set of parameters - namely macroscopic cross sections and potentially diffusion coefficients - are generated in order to model the whole core as a simplified problem which is often treated in diffusion theory. The first calculation being over a periodic lattice of cells or assemblies, leakage between different domains of the core and out of the lattice needs to be explicitly taken into account by an additional term that must be added in the neutron transport equation. For historical reasons, the leakage term is in most cases modeled by a homogeneous and isotropic probability within a "homogeneous leakage model" that is compatible with the classical collision probability method often used to solve the neutron transport equation. Driven by technological innovation in the field of computer science, "heterogeneous leakage models" have been developed and implemented in several neutron transport calculation codes. The present work discusses the effect of the leakage model used for the generation of diffusion parameters on sodium fast reactor diffusion calculations. Homogenized and condensed cross sections as well as diffusion coefficients are calculated for hexagonal sodium fast reactor assemblies using the lattice code DRAGON-3. Three different calculations are performed for each assembly: without taking neutron leakage into account, using the classical homogeneous B-1 procedure or with the heterogeneous B-1 TIBERE model. Furthermore, a homogeneous core and a simple heterogeneous core are calculated within diffusion theory using the DONJON-5 code and the results are compared with a Monte Carlo calculation. It is shown that, even if a fissile assembly can be calculated without leakage, the heterogeneous TIBERE model is best suited for "cluster calculations" (a fertile or reflector assembly surrounded by fuel assemblies). Moreover, the homogeneous B1 model should be avoided in such calculations since it is not able to handle streaming effects between the different assemblies. (C) 2016 The Authors. Published by Elsevier Ltd