Comptes Rendus de l'Académie des Sciences - Series I - Mathematics最新文献

We prove a self-normalized large deviation principle for sums of Banach space valued functions of a Markov chain. Self-normalization applies to situations for which a domination hypothesis would be necessary in order to obtain a full large deviation principle. We follow the lead of Dembo and Shao [2] who state partial large deviations principles for independent and identically distributed random sequences.

In this paper we prove that there is an infinite sequence of pairs of plane cuspidal curves, C_m,1 and C_m,2, of degree deg(C_m,1)=deg(C_m,2)→∞, such that the pairs $\text{(}\text{CP}{}^2\text{,C}{}_{\mathrm{m,1}}\text{)}$ and $\text{(}\text{CP}{}^2\text{,C}{}_{\mathrm{m,2}}\text{)}$ are diffeomorphic, but C_m,1 and C_m,2 have non-equivalent braid monodromy factorizations. These curves give rise to the negative solutions of “Dif ⇒ Def” and “Dif ⇒ Iso” problems for plane irreducible cuspidal curves. In our examples, C_m,1 and C_m,2 are complex conjugate.

We give basic results, such as restricted root systems and a model of G/H over the ring of integers, for the theory of symmetric varieties valid over fields of all characteristics.

We prove that various concrete analytic equivalence relations arising in model theory or analysis are complete, i.e., maximum in the Borel reducibility ordering. The proofs use some general results concerning the wider class of analytic quasi-orders.

We show that limits on the real axis of arguments of regularized relative determinants for differential operators on $\text{R}{}^{\mathrm{d}}$, exist in the weak sense. We call these limits generalized scattering phases. They extend, in the case of long range perturbations, the usual definition of scattering phase given by Birman–Krein theory. In Euclidean scattering, we give high energy expansions under a non-trapping assumption.

Appropriately scaled families of DiPerna–Lions renormalized solutions of the Boltzmann equation are shown to have fluctuations whose limit points (in the weak L¹ topology) are governed by a Leray solution of the limiting Navier–Stokes equations. This completes the arguments in Bardos–Golse–Levermore [Commun. on Pure and Appl. Math. 46 (5) (1993) 667–753] for the steady case, extended by Lions–Masmoudi [Arch. Ration. Mech. Anal. 158 (3) (2001) 173–193] to the time-dependent case.

The local linear estimator of the conditional cumulative distribution function is shown to be the ratio of two U-statistics. Using results from the theory of U-statistics, we show the almost sure convergence of this estimator both locally and globally. This is used to establish the almost sure convergence of conditional quantiles computed from the linear estimator.

We report on results about a study of algebraic graph invariants, based on computer exploration, and motivated by graph-isomorphism and reconstruction problems.

In this Note we establish the existence of minimizer of a nonconvex energy functional. This functional is an energy of deformation of a woven fabric subject only to his own weight and fixed on a part of its boundary. A typical example is the case of a tablecloth on a table. We make the hypothesis that the fabric is inextensible in the direction of the fibers but can undergo membrane shear and flexion deformations. We use technics introduced in [3], in the no membrane shear case. The studied energy involves tensors analog to those of [7] and [5] to which we added a regularizing term accounting for shear angle variation.

A graph multilink is a link with multiplicities in a homology 3-sphere whose exterior is a graph manifold. In this Note, we compute the Novikov homology of graph multilinks. As a corollary, we give a sharp majoration for the number of Novikov modules on a given graph link.