Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences

Periodic orbits of integrable birational maps on the plane: blending dynamics and algebraic geometry, the Lyness' case

Contingut del Pòster presentat al congrés New Trends in Dynamical Systems

On the approximation of the subgrid scale for systems of equations

Postprint (published version)

Rational periodic sequences for the Lyness recurrence

Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods $1,2,3,5,6,7,8,9,10$ or $12$ and that these are the only periods that rational sequences $\{x_n\}_n$ can have. It is known that if we restrict our attention to positive rational values of $a$ and positive rational initial conditions the only possible periods are $1,5$ and $9$. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien \& Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order $n, n\ge5,$ including $n$ infinity. This fact implies that the Lyness map is a universal normal form for most birrational maps on elliptic curves.

Integrability and non-integrability of periodic non-autonomous Lyness recurrences

This paper studies non-autonomous Lyness type recurrences of the form x_{n+2}=(a_n+x_n)/x_{n+1}, where a_n is a k-periodic sequence of positive numbers with prime period k. We show that for the cases k in {1,2,3,6} the behavior of the sequence x_n is simple(integrable) while for the remaining cases satisfying k not a multiple of 5 this behavior can be much more complicated(chaotic). The cases k multiple of 5 are studied separately.

Integrability and non-integrability of periodic non-autonomous Lyness recurrences (revised and enlarged version)

This paper studies non-autonomous Lyness type recurrences of the form xn+2 = (an+xn+1)=xn, where fang is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k 2 f1; 2; 3; 6g the behavior of the sequence fxng is simple (integrable) while for the remaining cases satisfying this behavior can be much more complicated (chaotic). We also show that the cases where k is a multiple of 5 present some di erent features.

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.

Leonhard Euler: quatre lIiçons escollides

L'FME dedica el curs acadèmic 2006-2007 a la figura del matemàtic suís Leonhard Euler, una de les ments més importants de la història, comparable a Gauss o Arquímedes. La lliçó inaugural va anar a càrrec d'Enric Fossas, catedràtic i director de l'Institut d'Organització i Control de Sistemes Industrials de la UPC

Study of the robustness of the European air routes network

working paper

Gestión del conocimiento y del capital intelectual en una PYME del sector textil

Se presenta una propuesta para la Gestión del Conocimiento en una empresa del sector textilque desarrolla las actividades de ennoblecimiento del producto. El objetivo ha sido diseñar unsistema de soporte para la toma de decisiones, que considere la perspectiva de la medición delCapital Intelectual, y que incorpore elementos del Cuadro de Mando Integral. La realizaciónde la propuesta se basa en una amplia documentación sobre modelos y casos, tanto de Gestióndel Conocimiento como de la Medición del Capital Intelectual.

Work Organization Practices for Lean Production: A Study in Spanish and Brazilian Manufacturers

This work aims to discuss particular work organization practices in human resources reported as successful by companies adopting lean production principles, and investigate them through real examples observed on manufacturing plants in Spain and Brazil. A set of work organization practices was previously established by one of the authors, through interviews with practitioners of lean production and review of the literature. A series of visits and informal interviews at Spanish and Brazilian automotive parts manufacturers that follow lean production were conducted to verify that the set of policies are indeed practiced.

Using MILP to plan holidays and working hours under an annualised hours agreement

Annualising work hours (AH) is a means of achievement flexibility in the use of human resources to face the seasonal nature of demand. In Corominas et al. (1) two MILP models are used to solve the problem of planning staff working hours with annual horizon. The costs due to overtime and to the employment of temporary workers are minimised, and the distribution of working time over the course of the year for each worker and the distribution of working time provided by temporary workers are regularised.In the aforementioned paper, the following is assumed: (i) the holiday weeks are fixed a priori and (ii) the workers are from different categories who are able to perform specific type of task have se same efficiency; moreover, the values of the binary variables (and others) in the second model are fixed to those in the first model (thus, in the second model these will intervene as constants and not as variables, resulting in an LP model).In the present paper, these assumptions are relaxed and a more general problem is solved. The computational experiment leads to the conclusion that MILP is a technique suited to dealing with the problem.

Genetic algorithm for sequencing in midex model non-permutation flowshops using constrained buffers

Este trabajo presenta un Algoritmo Genético (GA) del problema de secuenciar unidades en una línea de producción. Se tiene en cuenta la posibilidad de cambiar la secuencia de piezas mediante estaciones con acceso a un almacén intermedio o centralizado. El acceso al almacén además está restringido, debido al tamaño de las piezas.AbstractThis paper presents a Genetic Algorithm (GA) for the problem of sequencing in a mixed model non-permutation flowshop. Resequencingis permitted where stations have access to intermittent or centralized resequencing buffers. The access to a buffer is restricted by the number of available buffer places and the physical size of the products.

Heuristic procedures for solving the General Assembly Line Balancing Problem with Setups (GALBPS)

The General Assembly Line Balancing Problem with Setups (GALBPS) was recently defined in the literature. It adds sequence-dependent setup time considerations to the classical Simple Assembly Line Balancing Problem (SALBP) as follows: whenever a task is assigned next to another at the same workstation, a setup time must be added to compute the global workstation time, thereby providing the task sequence inside each workstation. This paper proposes over 50 priority-rule-based heuristic procedures to solve GALBPS, many of which are an improvement upon heuristic procedures published to date.

What is the meaning of ‘talent’ in the world of work?

The ongoing confusion about the meaning of ‘talent’ within the world of work is hindering the establishment of widely accepted talent management theories and practices. The aim of this paper is to contribute to the literature on talent management by offering an in-depth review of the talent concept within the specific context of the world of work, and proposing a framework for its conceptualization. We group different theoretical approaches to talent into ‘object’ (i.e., talent as natural ability; talent as mastery; talent as commitment; talent as fit) versus ‘subject’ approaches (i.e., talent as all people; talent as some people) and identify dynamics existing within and between them, as well as implications for talent management theory and practice. Finally, we discuss different avenues for further research aimed at developing the talent—and consequently, the talent management—construct further.