Classes de Hirzebruch et classes de Chern motiviques

Let X be a complex algebraic variety. We define and study new theories of characteristic classes, defined on the relative Grothendieck group of complex algebraic varieties over X as introduced and studied by Looijenga and Bittner in relation to motivic integration. One of them, $T_y$ is a homology class version of the motivic measure and generalizes the corresponding Hirzebruch characteristic. It unifies the Chern class transformation of Schwartz and MacPherson, the Todd class transformation of Baum–Fulton–MacPherson and the L-class transformation of Cappell–Shaneson. To cite this article: J.-P. Brasselet et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Algèbre de Temperley–Lieb de type B

We give a dual presentation, in the sense of the dual presentation of Artin groups, of the Temperley–Lieb algebra of type B. In particular, we obtain a basis of this algebra by considering the homomorphic images of the simple elements of the dual monoid. This algebra is the largest quotient of the Hecke algebra whose irreducible representations are parametrized by pairs of Young diagrams with at most one column in each component. To cite this article: C. Vincenti, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Ensembles de Julia quadratiques de mesure de Lebesgue strictement positive

In this Note, we prove a variant of a conjecture stated in the thesis of Chéritat. The proof is based on results announced by Inou and Shishikura, and on earlier results of McMullen and of Chéritat. According to Chéritat's thesis, this allows us to complete a plan initiated by Douady and to show that there exist quadratic polynomials having a Julia set of positive Lebesgue measure. To cite this article: X. Buff, A. Chéritat, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Algèbres de Hopf de graphes

We define graded Hopf algebras with bases labeled by various types of graphs and hypergraphs, provided with natural embeddings into an algebra of polynomials in infinitely many variables. These algebras are graded by the number of edges and can be considered as generalizations of symmetric or quasi-symmetric functions. To cite this article: J.-C. Novelli et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Minoration de rangs de courbes elliptiques

We state a quantitative result concerning the group of rational points on an elliptic curve that are defined over certain Hilbert class fields. We provide a lower bound for the rank. We present also an analytic approach based on the proof of an estimate for sums of Fourier coefficients of a modular form along values taken by a quadratic polynomial. This estimate is a non-split version of the shifted convolution problem. To cite this article: N. Templier, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Convergence de l'estimateur spline cubique de lissage dans un modèle de régression longitudinale avec erreur de type processus

This Note deals with the estimation of a smooth regression function by natural cubic splines. A convergence rate is obtained for the estimate's mean discretized and integrated squared error (MDSE and MISE) with random process noise in the data. To cite this article: D. Degras, R. Jallet, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Un choix de fenêtre optimal en estimation polynomiale locale de la fonction de répartition conditionnelle

We propose an optimal choice for the bandwidth parameter used in the local polynomial estimation of the conditional distribution function. This choice is approximated by the bandwidth which minimizes the asymptotic weighted mean integrated squared error (MISE). To cite this article: S. Ferrigno, G.R. Ducharme, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Note sur les formules de saut de Guillemin–Kalkman

The purpose of this Note is to give a jump formula in equivariant cohomology implying the jump formulas of Guillemin–Kalkman. To cite this article: P.-É. Paradan, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Irréductibilité de la première équation de Painlevé

A definition of reducibility for algebraic codimension two foliations given by closed 2-forms is proposed. Reducible foliations are characterised on theirs Galois groupoids. We apply this to the foliation given by the first Painlevé equation. Its Galois groupoid is computed and this proves its irreducibility. To cite this article: G. Casale, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Modules de cycles et motifs mixtes

For a perfect field k, we give a relation between the category of homotopy invariant sheaves with transfers defined by Voevodsky and the category of cycle modules defined by Rost. More precisely, the category of cycle modules over k is equivalent to the category obtained from the homotopy invariant sheaves with transfers by formally inverting the sheaf represented by $\text{G}{}_{\mathrm{m}}$ with its canonical structure of a presheaf with transfers. This gives a canonical monoidal structure on the category of cycle modules over k, and shows that it is Abelian. To cite this article: F. Déglise, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Cellules de Kazhdan–Lusztig et correspondance de Robinson–Schensted

Kazhdan and Lusztig have introduced (left, right and two-sided) cells in an arbitrary Coxeter group. For the symmetric group, they showed that these cells are given by the Robinson–Schensted correspondence. Here, we describe a Robinson–Schensted correspondence for the complex reflection groups G(e,1,n). In a recent joint work with C. Bonnafé, we have shown that, in the case e=2 (where G(2,1,n) is the Coxeter group of type B_n), this correspondence determines the Kazhdan–Lusztig cells with respect to certain unequal parameters. To cite this article: L. Iancu, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Consistance d'un estimateur de minimum de variance étendue

We consider a generalization of the criterion minimized by the K-means algorithm, where a neighborhood structure is used in the calculus of the variance. Such a tool is used, for example with Kohonen maps, to measure the quality of the quantification preserving the neighborhood relationships. If we assume that the parameter vector is in a compact Euclidean space and all its components are separated by a minimal distance, we show the strong consistency of the set of parameters almost realizing the minimum of the empirical extended variance. To cite this article: J. Rynkiewicz, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Factorialité de l'anneau des séries de Dirichlet analytiques

We study arithmetical properties of the ring of analytic Dirichlet series. In particular, we prove a theorem of division by several series and we deduce from it that the ring is factorial. To cite this article: F. Bayart, A. Mouze, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Groupes vectoriels et schéma de Picard

This Note contains slight variations on a well known theme: linear sub-groups of the Picard functor of a proper scheme over a field k. In particular, we give exemples of a field k, with positive characteristic, and a projective k-scheme X, normal, but not geometrically reduced, such that the neutral component of its Picard functor is representable by a nonzero vectorial group scheme. To cite this article: M. Raynaud, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Principes de grandes déviations pour des processus de « coarse graining »

We improve the Large Deviations Principle satisfied by a Coarse Grained process already analyzed by Boucher, Ellis and Turkington [Ann. Probab. 27 (1999) 297–324]. To cite this article: J. Trashorras, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Moyennes empiriques pour les mosaïques de Voronoi du disque de Poincaré

Let Φ be a stationary ergodic point process with finite intensity of the Poincaré disk. After defining the typical cell associated to the Voronoi tessellation of Φ, we study the convergence of empirical means of this tessellation. Contrary to the Euclidean case, several natural choices of means exist, leading to different behavior. The case where Φ is a Poisson process is more specifically characterized. To cite this article: F. Lips, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

N-complexes et algèbres de Hopf

We show that the category of N-complexes is monoidally equivalent to the category of comodules over a well chosen Hopf algebra. This generalizes Pareigis' previous result for N=2. To cite this article: J. Bichon, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Effondrement de quotients aléatoires de groupes hyperboliques avec torsion

We show that random quotients of hyperbolic groups with ‘harmful’ torsion collapse at densities smaller than expected. To cite this article: Y. Ollivier, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Propriété de Liouville et équation de Poisson pour le laplacien généralisé de Dunkl

Let Δ_k be the Dunkl generalized Laplacian associated to a root system R of $\text{R}{}^{\mathrm{N}}$ and a non-negative function k defined on R and invariant by the Weyl group. In this Note, we show that this differential-difference operator on $\text{R}{}^{\mathrm{N}}$ satisfies the Liouville property, then we solve the Poisson equation Δ_ku=?f by using a generalized Fourier analysis method. To cite this article: L. Gallardo, L. Godefroy, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Estimation de la fonction de survie sous biais de longueur pour des risques concurrents et proportionnels

Consider a population of individuals who experience two causes of death. We observe the ones alive at time t₀ and follow them until death. Given this length bias sample, we propose an estimator of the survival function of ‘initial survival times’ (i.e., for the entire population) under the assumption of proportional hazards for the two causes of death. The large sample behaviour of our estimator is also studied. To cite this article: J.-Y. Dauxois et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).