Mean asymptotic behaviour of radix-rational sequences and dilation equations (Extended version)

The generating series of a radix-rational sequence is a rational formal power series from formal language theory viewed through a fixed radix numeration system. For each radix-rational sequence with complex values we provide an asymptotic expansion for the sequence of its Ces\`aro means. The precision of the asymptotic expansion depends on the joint spectral radius of the linear representation of the sequence; the coefficients are obtained through some dilation equations. The proofs are based on elementary linear algebra

Rational series and asymptotic expansion for linear homogeneous divide-and-conquer recurrences

Among all sequences that satisfy a divide-and-conquer recurrence, the sequences that are rational with respect to a numeration system are certainly the most immediate and most essential. Nevertheless, until recently they have not been studied from the asymptotic standpoint. We show how a mechanical process permits to compute their asymptotic expansion. It is based on linear algebra, with Jordan normal form, joint spectral radius, and dilation equations. The method is compared with the analytic number theory approach, based on Dirichlet series and residues, and new ways to compute the Fourier series of the periodic functions involved in the expansion are developed. The article comes with an extended bibliography

L' optimisme est-il le theme pour un scénario de futur de l'espace Méditerranéen?

Révoltes, crises, rébellions, insurrections, révolutions, quel que soit le nom que l’on donne aux bouleversements qui sont apparus depuis deux ans autour de la Méditerranée, ces mouvements ont donné naissance dans le monde occidental à un espoir de “printemps arabe”, avec référence plus ou moins implicite au Printemps des peuples de 1848 et au renouveau qu’a connu l’Europe centrale dans la suite des événement de 1989 (la chute du mur de Berlin étant le moment le plus spectaculaire de ce processus). Mais, après le printemps, les opinions publiques du nord comme du sud de la Méditerranée voient actuellement un automne de désillusions, sans même être passé par l’été. Comment faire renaître l’optimisme dans ces conditions? notre hypothèse est que le vocabulaire qui sous-tend notre interprétation du monde constitue un blocage à la communication entre les différents acteurs du jeu stratégique et de pouvoir et que cette absence de langage commun, ou de référentiel commun, est le ferment de l’incompréhension et du pessimisme qui peut en découler. nous nous fonderons sur plusieurs faits qui nous paraissent former des verrous sémantiques à tirer pour parvenir à une situation de communication garante de la possibilité d’échapper à la malédiction de chocs dialectiques supposés être les moteurs de l’histoire dans la lignée de hegel.The revolts, crises, mobs, rebellions, insurrections, revolutions, whatever we call the changes that have happened during the last two years around the Mediterranean have arisen in western world the hope for a “spring” of democracy, with more or less explicit reference to the renewal of Eastern Europe in 1989. After the hopes of spring, most public opinions in northern as well as southern Mediterranean foresee now an autumn of expectancies, if not a winter in certain cases. nobody has meanwhile talked of a summer. what should reasonably be our mind frame for the purpose of better knowledge and understanding of our common world, the Mediterranean? we organize our reasoning around a few selected issues, which could not be the most salient in the media, but are meaningful when put together in a non-partisan or non-politically correct perspective. The conclusion is that all those prominent issues (and some others like women, education, ecology, etc.) are the bases for discussion across the Mediterranean. Our hypothesis is that, in our century, the course of history may not be the dialectic clash set forth by hegel. On the contrary globalization and communication may also stand for a new optimism.Revoltas, crises, rebeliões, insurreições, qualquer que seja o nome que se dê às mudanças que apareceram de dez anos para cá em torno do Mediterrâneo, esses movimentos fizeram nascer no mundo ocidental uma esperança de “primavera árabe”, numa referência mais ou menos implícita à Primavera dos povos em 1848 e à renovação que a Europa Central conheceu com a sequência dos fatos de 1989 (a queda do muro de Berlim sendo o momento mais espetaculas desse processo). Mas, após a primavera, as opiniões públicas tanto do norte como do sul do Mediterrâneo veem atualmente um outono de desilusões, sem mesmo terem passado pelo verão. Como fazer renascer o otimismo nessas condições? Nossa hipótese é que o vocabulário que sustenta nossa interpretação do mundo constitui um bloqueio para a comunicação entre os diferentes atores do jogo estratégico e de poder e que esta ausência de linguagem comum, ou de referencial comum, é o fermento da incompreensão e do pessimismo que daí pode resultar. nós nos fundamentaremos em vários fatos que nos parecem formar bloqueios semânticos que devem ser eliminados para alcançar uma comunicação que garanta a oportunidade de escapar da maldição de choques dialéticos que são supostos de ser os motores da história na linha de hegel

Mondes persistants et enseignement à distance : de nouvelles perspectives ?

Intervention dans la cadre du colloque TICE Méditerranée 2007 : "L\u27humain dans la formation à distance... la problématique du changement"

Variations du poids vif et du rendement en viande de boeufs zébus de l'Adamaoua au cours de la saison sèche

Les auteurs à partir de 2 lots de 35 zébus de l'Adamaoua (Cameroun) achetés sur les marchés locaux ont essayé de chiffrer le préjudice de la saison sèche pour la production de viande bovine. Ils ont observé une diminution de poids vif de l'ordre de 18 p. 100 et noté une corrélation positive hautement significative entre le périmètre thoracique et le poids vif. Le rendement en viande (51,5 p. 100) demeure pratiquement constant au cours de la saison. (Résumé d'auteur