Showing papers in "Comptes Rendus Mathematique in 2016"

TL;DR: In this paper, a Bourgain-Brezis-Mironescu-type formula for nonlocal magnetic spaces was proved, which builds a bridge between a fractional magnetic operator recently introduced and the classical theory.

TL;DR: In this article, the exact distribution of the product of two correlated normal random variables has been shown to be the same as that of the average of the mean of the two random variables.

TL;DR: In this article, the Faber polynomial expansions are used to find upper bounds for the n -th (n ≥ 3 ) coefficients of classes of bi-subordinate functions subject to a gap series condition.

TL;DR: In this article, the authors discuss algorithms that not only solve the problem on typical instances, but also provide a posteriori certificates of optimality, probably certifiably correct (PCC) algorithms.

TL;DR: In this paper, the transitivity properties of the group of morphisms generated by Vieta involutions on the solutions in congruences to the Markoff equation as well as to other Markoff type affine cubic surfaces were investigated.

TL;DR: In this article, a line bundle approach to odd-dimensional analogues of generalized complex structures is proposed, which encompasses all existing ones and elucidates the geometric meaning of the integrability condition for generalized contact structures, in light of new results on multiplicative forms and Spencer operators.

TL;DR: In this article, the affine line is shown to be a zero divisor in the Grothendieck ring of algebraic varieties over complex numbers, and the final formula is improved by removing a factor.

TL;DR: In this paper, a generalization of the quantum Bohm potential identity was proposed for the simulation of Euler-Korteweg systems with degenerate viscosities, and a numerical scheme with entropy stability property under a hyperbolic CFL condition was proposed.

TL;DR: In this paper, the Marchenko-Pastur theorem for random matrices with i.i.d. columns and a general dependence structure within the columns was proved by a simple modification of the standard Cauchy-Stieltjes resolvent method.

TL;DR: In this article, the Bergman kernel is localized around the singularities of a punctured unit disc and its local model is defined as a local model of the Poincare metric.

TL;DR: In this paper, it was shown that critical percolation on any quasi-transitive graph of exponential volume growth does not have a unique infinite cluster, and the result is new when the graph in question is either amenable or nonunimodular.

TL;DR: In this article, a sandpile model on the set of the lattice points in a large lattice polygon is studied, and the scaling limit of the deviation locus turns out to be a distinguished tropical curve passing through the perturbation points.

TL;DR: In this article, an observation estimate at one point in time for the Kolmogorov equation in the whole space is given, which implies the observability and the null controllability for the KEA with a control region which is sufficiently spread out throughout the entire space.

TL;DR: In this article, the authors describe some examples of blow-up solutions that violate this conclusion, in the sense that their mass may spread, as soon as they consider situations which mildly depart from Brezis-Merle's assumptions.

TL;DR: In this paper, a mixed variational formulation for the stationary Boussinesq problem is presented, which is augmented with Galerkin-type equations, and the resulting schemes can be rewritten as fixed-point operator equations.

TL;DR: In this article, it was shown that the sharp fractional Sobolev inequality is equivalent to either the strong fractional isocapacitary inequality (SISOI) or the sharp isoperimetric inequality.

TL;DR: In this article, the authors introduce two natural notions of Aluthge transforms (toral and spherical) for 2-variable weighted shifts and study their basic properties, and briefly discuss the relation between spherically quasinormal and isometric weighted shifts.

TL;DR: The density of the set of ordinary primes of an Abelian surface over a number field in terms of the l -adic monodromy group was studied in this article. But the density of ordinary primitives was not considered in this paper.

TL;DR: For mean field games with local coupling, the existence results are typically for weak solutions rather than strong solutions as mentioned in this paper, which places us in the case of superquadratic Hamiltonians.

TL;DR: In this article, the existence of two-dimensional solitary waves moving through a body of density stratified water lying beneath air is shown to be true for any smooth choice of upstream velocity and density distribution.

TL;DR: In this article, the authors studied the monotonicity of the convergence of the Minkowski average of a compact set A ⊂ R n towards the convex hull of A, when considering the Hausdorff distance, the volume deficit and a non-convexity index of Schneider as measures of convergence.

TL;DR: The semi-ringed topos obtained from the arithmetic site A of [3], [4], by extension of scalars from the smallest Boolean semifield B to the tropical semifield R + max was investigated in this article.

TL;DR: In this paper, it was shown that the almost automorphy of the coefficients is not necessary to obtain almost automorphic solutions for some evolution equations in Banach spaces, and this result was later improved by the authors.

TL;DR: For a given maximal mean curvature, the authors showed that the area is bounded away from zero in terms of the maximal curvature alone, and provided smooth embeddings of the ball with arbitrary small volume.

TL;DR: The strict feasibility of the primal-slack approximations leads to two significant improvements upon existing methods, and enables a full offline–online computational decomposition, in which the online cost to compute the error bound is completely independent of the dimension of the original (high-dimensional) problem.

TL;DR: In this paper, it was shown that a general condition introduced by Colombo and Gobbino to study limits of curves of maximal slope allows us to characterize also minimizing movements along a sequence of functionals as curves of the maximal slope of a limit functional.

TL;DR: In this paper, the authors present several finiteness results for algebraic groups over finitely generated fields that are more general than global fields, including the properness of the global-to-local map in the Galois cohomology of a given K-group G relative to a certain natural set V of discrete valuations of K, and the number of isomorphism classes of G having smooth reduction with respect to all places in V.

TL;DR: In this article, it was shown that M is invertible with probability at least 1−Cln3 Ωd/d for C≤d≤cn/ln2Ωn, where c,C are positive absolute constants.

TL;DR: In this paper, the restriction of semiclassical measures to every invariant torus in terms of two-microlocal measures is described, and regularity and delocalization properties for limit measures of | u h | 2 d x are shown.

TL;DR: For an isotropic reductive group G satisfying a suitable rank condition over an infinite field k, the authors showed that the sections of the A 1 -fundamental group sheaf of G over an extension field L / k can be identified with the second group homology of G (L ).