Topological Expansion and Exponential Asymptotics in 1D Quantum Mechanics

Borel summable semiclassical expansions in 1D quantum mechanics are considered. These are the Borel summable expansions of fundamental solutions and of quantities constructed with their help. An expansion, called topological,is constructed for the corresponding Borel functions. Its main property is to order the singularity structure of the Borel plane in a hierarchical way by an increasing complexity of this structure starting from the analytic one. This allows us to study the Borel plane singularity structure in a systematic way. Examples of such structures are considered for linear, harmonic and anharmonic potentials. Together with the best approximation provided by the semiclassical series the exponentially small contribution completing the approximation are considered. A natural method of constructing such an exponential asymptotics relied on the Borel plane singularity structures provided by the topological expansion is developed. The method is used to form the semiclassical series including exponential contributions for the energy levels of the anharmonic oscillator.Comment: 46 pages, 22 EPS figure

Measurement and comparison of individual external doses of high-school students living in Japan, France, Poland and Belarus -- the "D-shuttle" project --

Twelve high schools in Japan (of which six are in Fukushima Prefecture), four in France, eight in Poland and two in Belarus cooperated in the measurement and comparison of individual external doses in 2014. In total 216 high-school students and teachers participated in the study. Each participant wore an electronic personal dosimeter "D-shuttle" for two weeks, and kept a journal of his/her whereabouts and activities. The distributions of annual external doses estimated for each region overlap with each other, demonstrating that the personal external individual doses in locations where residence is currently allowed in Fukushima Prefecture and in Belarus are well within the range of estimated annual doses due to the background radiation level of other regions/countries

FROM DYNAMICAL SYSTEMS TO RENORMALIZATION

Abstract. We study in this paper logarithmic derivatives associated to derivations on graded complete Lie algebra, as well as the existence of inverses. These logarithmic derivatives, when invertible, generalize the exp–log correspondence between a Lie algebra and its Lie group. Such correspondences occur naturally in the study of dynamical systems when dealing with the linearization of vector fields and the non–linearizability of a resonant vector fields corresponds to the non–invertibility of a logarithmic derivative and to the existence of normal forms. These concepts, stemming from the theory of dynamical systems, can be rephrased in the abstract setting of Lie algebra and the same difficulties as in perturbative quantum field theory (pQFT) arise here. Surprisingly, one can adopt the same ideas as in pQFT with fruitful results such as new constructions of normal forms with the help of the Birkhoff decomposition. The analogy goes even further (locality of counter terms, choice of a renormalization scheme) and shall lead to more interactions between dynamical systems and quantum field theory. hal-00794157, version 1- 25 Feb 2013 1. Introduction. Since the work of A. Connes and D.K Kreimer (see [3], [4]) in perturbative quantum field theory (pQFT), it has been possible to havea purely algebraicinterpretation of some renormalizationschemes

Effet d'entraînements bi-modaux à la connaissance des lettres : approche développementale

International audienc

Effet d'une exploration "multi-sensorielle séquentielle orientée" sur le développement de la compréhension du principe alphabétique chez les enfants de 5 ans faibles connaisseurs de lettres

International audienc

Computerized comprehension training for whom and under which conditions is it efficient?

International audienceThe purpose of this study was to examine the differential impact of a computer‐based comprehension training programme according to second graders' comprehender profiles. These profiles differed in the children's abilities to process three types of textual information: literal information, text‐connecting inferences and gap‐filling inferences. The results showed that all the profiles improved significantly after the training on the question type that had caused them the greatest amount of difficulty on the pretest. In addition, factors that could a priori predict the effectiveness of the programme were investigated by comparing children who benefited from the instruction (responders) with those who did not benefit (nonresponders). Before instruction, these children differed in their lexical knowledge level and logical reasoning skills, but not in their memory or comprehension‐monitoring abilities. The results support the claim that children with comprehension difficulties form a heterogeneous group and emphasize the need to examine the differential impact of comprehension instruction according to the characteristics of poor comprehenders

Effet d'entraînements bi-modaux à la connaissance des lettres : approche développementale

International audienc

Etude de la variabilité inter- et intra-individuelle dans le développement des habiletés phonologiques : nouvelles investigations

International audienc

Évaluation de la compréhension écrite de récits chez l’enfant de 7 à 10ans : vers des profils de compreneurs

International audienceIntroductionThe aim of the study was to investigate reading comprehension skills in 7 to 10-year-old children and to present a new tool for assessing reading comprehension skills in elementary school children. Two aspects of text comprehension were assessed: literal comprehension skills and inference generation (with two subtypes of inferences, coherence inferences and knowledge-based inferences).MethodTwo narratives of varying length and complexity have been constructed and presented to 498 French-speaking children from second grade to fifth grade.ResultsThe results showed an evolution of performance with school level. Children's scores also depended on the type of comprehension skill evaluated (literal versus inferential) and difficulty of texts. Furthermore, cluster analysis yielded five profiles that clearly differ on children's ability to respond to either literal questions, coherence inferential questions, or knowledge-based inferential questions.ConclusionThe existence of different profiles of comprehenders is discussed in terms of theoretical implications. Finally, some limitations and way of improvement are presented.IntroductionCette étude vise à évaluer les habiletés de compréhension écrite de récits chez l’enfant de 7 à 10 ans en distinguant deux aspects de la compréhension d’un texte, la compréhension littérale et la compréhension inférentielle et deux types d’inférences, les inférences de cohésion et les inférences basées sur les connaissances.MéthodeDeux textes de longueur et complexité différentes ont été présentés à 498 enfants francophones (non redoublants) du CE1 au CM2. La lecture de ces textes est suivie d’une série de questions à choix multiples relavant de trois types de processus de compréhension.RésultatsLes résultats montrent un effet du niveau scolaire, du type de compréhension impliquée et du type de récits sur les performances en compréhension. D’autre part, une approche différentielle met en évidence l’existence de cinq profils de compreneurs se distinguant en fonction de leurs performances aux questions littérales, d’inférences de cohésion et d’inférences basées sur les connaissances.ConclusionLa construction de ce type d’épreuves vise à compléter l’offre des outils d’évaluation de la compréhension en lecture. D’autre part, l’analyse des profils de compreneurs apportent des éléments d’informations importants sur les processus de compréhension de récits narratifs chez l’enfant et leur développement