1,720,986 research outputs found
Calibrations and isoperimetric profiles
Full text linkWe equip many noncompact nonsimply connected surfaces with smooth Riemannian metrics whose isoperimetric profile is smooth, a highly nongeneric property. The computation of the profile is based on a calibration argument, a rearrangement argument, the Bol-Fiala curvature dependent inequality, together with new results on the profile of surfaces of revolution and some hardware know-how
L1-Poincaré inequalities for differential forms on Euclidean spaces and Heisenberg groups
Full text linkIn this paper, we prove interior Poincaré and Sobolev inequalities in Euclidean spaces and in Heisenberg groups, in the limiting case where the exterior (resp. Rumin) differential of a differential form is measured in L1 norm. Unlike for Lp, p>1, the estimates are doomed to fail in top degree. The singular integral estimates are replaced with inequalities which go back to Bourgain-Brezis in Euclidean spaces, and to Chanillo-Van Schaftingen in Heisenberg groups
Poincaré and sobolev inequalities for differential forms in heisenberg groups and contact manifolds
Full text linkIn this paper, we prove contact Poincaré and Sobolev inequalities in Heisenberg groups, where the word 'contact' is meant to stress that de Rham's exterior differential is replaced by the exterior differential of the so-called Rumin complex, which recovers the scale invariance under the group dilations associated with the stratification of the Lie algebra of. In addition, we construct smoothing operators for differential forms on sub-Riemannian contact manifolds with bounded geometry, which act trivially on cohomology. For instance, this allows us to replace a closed form, up to adding a controlled exact form, with a much more regular differential form
Bounded Geometry, Growth and Topology
No full textAbstractWe characterize functions which are growth types of Riemannian manifolds of bounded geometry
Apprendre la menace du stéréotype pour améliorer les performances des filles en mathématiques
No full textNombre d’études ont montré que la menace du stéréotype réduit la performance des apprenants. Fort de ce constat,
plusieurs études ont été conduites pour réduire les interférences suscitées par la peur de confirmer le stéréotype dans des situations
évaluatives. Parmi les stratégies évoquées dans la littérature, Johns et al. (2005) ont montré qu’on pouvait améliorer les performances
d’étudiantes en mathématiques en les alertant des effets de la menace du stéréotype. Cette étude visait à tester cette hypothèse dans le
contexte scolaire. 360 élèves (dont 185 filles), âgés de 14 à 16 ans, scolarisés en France et en Italie ont participé à l’étude. Elle s’est
déroulée en deux phases. Une première visait à recueillir des informations sur les perceptions des élèves (e.g., adhésion au stéréotype
de genre) et leur score à une tâche logico-mathématique (matrice de Raven). Une seconde, menée quelques semaines plus tard, visait
à assigner les élèves dans une des trois conditions expérimentales et à leur demander de réaliser une série de calculs en 3 minutes.
Dans une condition (menace), la tâche de calcul était présentée comme une épreuve logico-mathématique reportant des écarts de
performances selon le genre des élèves. Dans une seconde condition, aucune information comparative n’était énoncée (contrôle). Dans
une troisième condition (remédiation), l'épreuve était décrite comme une épreuve logico-mathématique reportant des écarts de
performances mais les sujets étaient informés que la menace du stéréotype pouvait perturber la performance des filles en
mathématiques. La performance correspondait au nombre d’exercices corrects rapportés sur le nombre d’exercices tentés. L’adhésion
au stéréotype et le score aux matrices de Raven ont été intégrés comme covariables dans l’analyse. Les résultats révèlent un effet
d’interaction entre le genre et la condition expérimentale sur le score de performance (F (2, 352) = 3,40 ; p <. 04). Ils vont dans le sens
des conclusions de Johns et al. (2005) : dans la condition menace, les filles performent moins bien que les garçons ; aucune différence
n’étant observée dans la condition remédiation et le groupe contrôle. En conclusion, les performances des filles en mathématiques
peuvent être améliorées en les alertant des effets de la menace du stéréotype. Nous discuterons aussi la mesure de performance au
regard d’autres alternatives considérées
Cohomology of annuli, duality and L^∞-differential forms on Heisenberg groups
Full text linkIn the last few years the authors proved Poincare and Sobolev type inequalities in Heisenberg groups H-n for differential forms in the Rumin's complex. The need to substitute the usual de Rham complex of differential forms for Euclidean spaces with the Rumin's complex is due to the different stratification of the Lie algebra of Heisenberg groups. The crucial feature of Rumin's complex is that d(c) is a differential operator of order 1 or 2 according to the degree of the form. Roughly speaking, Poincare and Sobolev type inequalities are quantitative formulations of the well known topological problem whether a closed form is exact. More precisely, for suitable p and q, we mean that every exact differential form omega in L-p admits a primitive phi in Lq such that ||phi||L-q <= C ||omega||L-p . The cases of the norm L-p, p >= 1 and q < infinity have been already studied in a series of papers by the authors. In the present paper we deal with the limiting case where q = infinity: it is remarkable that, unlike in the scalar case, when the degree of the forms omega is at least 2, we can take q = oo in the left-hand side of the inequality. The corresponding inequality in the Euclidean setting R-N (p = N and q = infinity) was proven by Bourgain & Brezis. (c) 2023 Elsevier Inc. All rights reserved
Semianalyticity of isoperimetric profiles.
No full textIt is shown that, in dimensions <8, isoperimetric profiles of compact real analytic Riemannian manifolds are semianalytic
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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