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A classification of asymptotic behaviors of Green functions of random walks in the quadrant
International audienceThis paper investigates the asymptotic behavior of Green functions associated to partially homogeneous random walks in the quadrant Z2+. There are four possible distributions for the jumps of these processes, depending on the location of the starting point: in the interior, on the two positive axes of the boundary, and at the origin (0, 0).With mild conditions on the positive jumps of the random walk, which can be unbounded, a complete analysis of the asymptotic behavior of the Green function of the random walk killed at (0, 0) is achieved. The main result is that eight regions of the set of parameters determine completely the possible limiting behaviors of Green functions of these Markov chains. These regions are defined by a set of relations for several characteristics of the distributions of the jumps.In the transient case, a description of the Martin boundary is obtained and in the positive recurrent case, our results give the exact limiting behavior of the invariant distribution of a state whose norm goes to infinity along some asymptotic direction in the quadrant. These limit theorems extend results of the literature obtained, up to now, essentially for random walks whose jump sizes are either 0 or 1 on each coordinate.Our approach relies on a combination of several methods: probabilistic representations of solutions of analytical equations, Lyapounov functions, convex analysis, methods of homogeneous random walks, and complex analysis arguments
Introduction of Structural Diversity at the C2 Position of Unsaturated Iminosugars through Palladium‐Catalyzed Cross‐Coupling Reactions
International audienceTo vary the functionality of iminosugars at the C2 position, protected 2‐iodoiminoglycals in the D‐gluco, D‐galacto, and D‐xylo series are efficiently synthesized from sugar lactams. Their mild palladium‐catalyzed aminocarbonylation, arylation, and phosphonylation are successful and provide a range of C2‐functionalized iminoglycals in good yields. Two of these compounds are O ‐deprotected to afford 1,2‐unsaturated iminosugars that prove to be modest inhibitors of glycosidases
Le placement en famille d'accueil : rappels procéduraux et reconnaissance de l'« aliénation » de l'enfant
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Transmission of the AtmosPhere for AStronomical data: TAPAS upgrade
International audienceContext: Current molecular databases and realistic global atmospheric models allow us to predict accurate atmospheric transmittance spectra. Observers with ground-based spectrographs may use this information to identify the telluric absorption lines, to correct their astronomical spectra for these lines fully or partially, or take them into account in forward models.Aims: The TAPAS online service provides atmospheric transmittance spectra of the most important species, as well as Rayleigh extinction, adapted to any observing location, date, and direction. We describe recent updates, improvements, and additional tools.Methods: TAPAS interpolates the location in the atmospheric profiles of temperature, pressure, H2O, O2 and O3 that are extracted from the meteorological field of the European Centre for Medium Term Weather Forecast (ECMWF) for the date and time of the observation. The composite profiles are produced by a Data Terra/AERIS/ESPRI product called Arletty, and they are supplemented by auxiliary climatological models for additional species. The transmittance spectra are computed with the code LBLRTM. The default width of the spectral pixels is chosen to ensure that the shapes of all the absorption lines are reproduced for each species. Major improvements with respect to the previous TAPAS are the extension of the wavelength range in the near-UV down to 300 nm and the extension in the near-IR up to 3500 nm; the use of the recent version of the HITRAN database (HITRAN2020); the addition of NO2 transmittance to complement H2O, O2, O3, N2O, CO2, and CH4; an increased accessibility and a reduced time to obtain the results; and the possibility to force the total H2O column to match the column measured at the observatory at the time of record.Results: We show O3 absorption in the near-UV and near-IR and NO2 absorption in the visible. We illustrate the quality of TAPAS by means of comparisons between models and ESO/VLT/CRIRES recorded spectra of a hot star with a spectral resolution of ~130 000 in two intervals in the near-IR with strong H2O, N2O, CO2, and CH4 absorption. We describe the measurement of an instrumental line spread function based on TAPAS O2 lines and a method using the singular value decomposition technique that can be made entirely automated.Conclusions: The new TAPAS tool provides realistic simulations of the telluric lines. It gives access to the weakest H2O or O2 lines, and to the very weak highly irregular NO2 lines. It can be used to improve the wavelength assignment when calibration lamps provide only a few emission lines, and to accurately measure the line spread function in most regions in which telluric features are present. The extended wavelength range will be particularly useful for future or recent spectrographs in the near-UV and in the near-IR
La preuve en mathématiques : difficultés d'étudiants et apports potentiels des assistants de preuve
International audienceThe transition between secondary and tertiary education is characterized, in particular, by different requirements and a change in the relationship to concepts and proving processes, which are more complex and more formal. International research on technology in mathematics education calls for an analysis of the uses and the potentialities of proof assistants to proof learning. We present the first results of an exploratory study in which the proof’s conceptions of 153 first-year university students and their evolution after 10 hours of sessions with proof assistants.La rupture entre le secondaire et le supérieur est notamment marquée par un changement d'exigences et de rapport aux objets et processus de preuve, plus complexes et plus formels. Les recherches internationales sur les technologies dans les apprentissages en mathématiques en appellent à une analyse des usages et apports des assistants de preuve dans l'apprentissage de la preuve. Nous présentons les premiers résultats d'une étude exploratoire sur les conceptions sur la preuve de 153 étudiants de première année d'université, et leur évolution après 10h de séances mobilisant des assistants de preuve
Access to N -Fluorinated Azapeptides and Azapeptoids as Peptidomimetic Scaffolds
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L’épaississement du texte par la réécriture : enjeux et pratiques dans l’enseignement de la production écrite au cycle 3
This dissertation, entitled ‘Thickening up a text through rewriting: issues and practices in the teaching of written production in cycle 3’, is part of a reflection on the teaching of writing in primary school.The first part of the paper summarises research into writing. In particular, we draw on the work of Dominique Bucheton, who sees writing as a complex problem-solving process. We show that producing a text is not just a matter of writing, but involves multiple skills: mastering spelling, using punctuation, respecting the codes of different types of texts and adapting one's style to the context. We also refer to Hayes and Flower's research, which highlights the cognitive dimension of writing, involving reflection on the subject and the reader's expectations. As a new teacher in a CM2 class, I set up a teaching system centred on thickening the text through rewriting. My aim was to understand how to support pupils in their writing process in order to thicken their initial text. Based on my results, I analysed the rewriting operations carried out by the pupils, the origin of the changes made to the texts and the pupils' feedback on this experience.This research shows that providing support for rewriting can indeed help to thicken written work, while developing a sense of authorship in pupils. In conclusion, the study stresses the importance of thoughtful teaching of written production, incorporating time for rewriting and peer assessment, to encourage pupils' commitment and autonomy. Some points of caution are also mentioned, to be taken into account when setting up such a sequence.Ce mémoire intitulé « l'épaississement du texte par la réécriture : enjeux et pratiques dans l'enseignement de la production écrite au cycle 3 », s'inscrit dans une réflexion sur l'enseignement de l'écriture à l'école primaire.Dans la première partie, une synthèse des recherches autour de la production écrite est effectuée. Nous nous appuyons notamment sur les travaux de Dominique Bucheton, qui considère l'écriture comme un processus complexe de résolution de problèmes. Nous montrons que produire un texte ne se limite pas seulement à écrire, mais implique de multiples compétences : maîtriser l'orthographe, utiliser la ponctuation, respecter les codes des différents types de textes et adapter son style selon le contexte. Nous nous référons également aux recherches de Hayes et Flower, qui mettent en lumière la dimension cognitive de l'écriture, impliquant une réflexion sur le sujet et les attentes du lecteur. En tant que jeune enseignante dans une classe de CM2, j’ai mis en place un dispositif pédagogique centré sur l'épaississement du texte par la réécriture. Mon objectif était de comprendre comment accompagner les élèves dans leur processus d'écriture afin d’épaissir leur texte initial. À partir de mes résultats, j’ai analysé les opérations de réécriture mises en œuvre par les élèves, l'origine des modifications apportées aux textes et le retour des élèves sur cette expérience.Cette recherche montre que l'accompagnement de la réécriture peut effectivement contribuer à l'épaississement des productions écrites, tout en développant une posture d'auteur chez les élèves. En conclusion, l’étude souligne l'importance d'un enseignement réfléchi de la production écrite, intégrant des temps de réécriture et d'évaluation entre pairs, pour favoriser l'engagement et l'autonomie des élèves. Des points de vigilances sont également mentionnés, et à prendre en compte lors d’une mise en place d’une telle séquence