Superefficient drift estimation on the Wiener space

In the framework of a nonparametric functional estimation for the drift of a Brownian motion $X_t$ we construct Stein type estimators of the form $X_t+D_t\log F$ which are superefficient when $\sqrt{F}$ is a superharmonic functional on the Wiener space for the Malliavin derivative D. To cite this article: N. Privault, A. Réveillac, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

A class of nonpositively curved Kähler manifolds biholomorphic to the unit ball in Cn

Let $(M,g)$ be a simply connected complete Kähler manifold with nonpositive sectional curvature. Assume that g has constant negative holomorphic sectional curvature outside a compact set. We prove that M is then biholomorphic to the unit ball in ${\mathbb{C}}^n$, where ${\dim }_{\mathbb{C}}M=n$. To cite this article: H. Seshadri, K. Verma, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

On a Hölder covariant version of mean dimension

Let Γ be a infinite countable group which acts naturally on ${?}^p(\Gamma )$. We introduce a modification of mean dimension which is an obstruction for ${?}^p(\Gamma )$ and ${?}^q(\Gamma )$ to be Hölder conjugates. To cite this article: A. Gournay, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Piatetski-Shapiro phenomenon in the uniqueness problem

We extend the phenomenon discovered by Piatetski-Shapiro (1954) to $l^q$ spaces. To be precise, for any $q>2$ we construct a compact K on the circle, which supports a distribution S with Fourier transform $\stackrel{?}{S}\in l^q$, but does not support such a measure. To cite this article: N. Lev, A. Olevskii, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

The harmonic measure and a Reuter-type result for a process with Bessel components

Let $B_{p\text{,}q}$ be the $R^2$-valued process $(B_p\text{,}{B}_q)$ with independent Bessel components $B_p$ and $B_q$ with indices p and q strictly positive. In this paper we compute explicitly the law of the hitting time and place of a circle, centered at the origin, when $B_{p\text{,}q}$ starts from the center and deduce a Reuter-type independence result. We use mainly analytical tools from PDE theory. To cite this article: A. Ziadi, A. Bencherif-Madani, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

On the proportion of rank 0 twists of elliptic curves

Let E be an elliptic curve defined over Q, let $E_d$ denote its dth quadratic twist, and $r_{E_d}:=\mathrm{rank}{E}_d(\mathbf{Q})$. We prove, that, for any positive integer k there are pairwise non-isogenous elliptic curves $E^1,\dots ,E^k$ such that $r_{{E^1}_p}=\cdots =r_{{E^k}_p}=0$ for a positive proportion of primes p. To cite this article: A. Dąbrowski, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Recovery of sparsest signals via ℓq-minimization

In this paper, it is proved that every s-sparse vector $\mathbf{x}\in {\mathbb{R}}^n$ can be exactly recovered from the measurement vector $\mathbf{z}=\mathbf{Ax}\in {\mathbb{R}}^m$ via some ${?}^q$-minimization with $0<q?1$, as soon as each s-sparse vector $\mathbf{x}\in {\mathbb{R}}^n$ is uniquely determined by the measurement z. Moreover it is shown that the exponent q in the ${?}^q$-minimization can be so chosen to be about $0.6796\times (1?{\delta }_{2s}(\mathbf{A}))$, where ${\delta }_{2s}(\mathbf{A})$ is the restricted isometry constant of order 2s for the measurement matrix A.     

Normal,unipotent subgroup schemes of reductive groups

Let G be a reductive group over a field k of characteristic p. Let $k^{\mathrm{sep}}$ be a separable closure of k. If $p\ne 2$, there exists a linear representation of G that is faithful and semisimple; moreover, any unipotent, normal subgroup scheme of G is trivial. For $p=2$, these two properties hold if and only if $G_{k^{\mathrm{sep}}}$ has no direct factor that is isomorphic to ${\mathbf{SO}}_{2n+1}$ for some $n?1$. To cite this article: A. Vasiu, C. R. Acad. Sci. Paris, Ser. I 341 (2005).