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The content of this paper is a generalization of a theorem by Joseph Rabinoff: if P is a finite family of pointed and rational polyhedra in Nℝ such that there exists a fan in Nℝ that contains all the recession cones of the polyhedra of P, if k is a complete non-archimedean field, if S is a connected and regular k-analytic space (in the sense of Berkovich) and Y is a closed k-analytic subset of U P × k S which is relative complete intersection and contained in the relative interior of U P × k S over S, then the quasifiniteness of π : Y → S implies its flatness and finiteness; moreover, all the finite fibers of π have the same length. This namely gives a analytic justification to the concept of stable intersection used in the theory of tropical intersection. [ABSTRACT FROM AUTHOR]

In this paper, we show that there are solutions of degree r of the equation of Pell–Abel on some real hyperelliptic curve of genus g if and only if r > g . This result, which is known to the experts, has consequences, which seem to be unknown to the experts. First, we deduce the existence of a primitive kdifferential on an hyperelliptic curve of genus g with a unique zero of order k(2g −2) for every (k, g ) 6= (2, 2). Moreover, we show that there exists a non Weierstrass point of order n modulo a Weierstrass point on a hyperelliptic curve of genus g if and only if n > 2g . [ABSTRACT FROM AUTHOR]

A major problem in knot theory is to decide whether the Jones polynomial detects the unknot. In this paper we study a weaker related problem, namely whether the Jones polynomial reduced modulo an integer m detects the unknot. The answer is known to be negative for m = 2r with r ≥ 1 and m = 3. Here we show that if the answer is negative for some m, then it is negative for mr with any r ≥ 1. In particular, for any r ≥ 1, we construct nontrivial knots whose Jones polynomial is trivial modulo 3r. [ABSTRACT FROM AUTHOR]

We present in this paper a consistent nonparametric test for heteroscedasticity when data are of functional kind. The latter is constructed by evaluating the difference between the conditional and unconditional variances. We show the asymptotic normality of the statistical test under the null hypothesis. In addition, we prove that this test is consistent against all deviations from homoscedasticity condition. [ABSTRACT FROM AUTHOR]

Résumé Dans cet article, nous établissons une identité pour des polynômes d'Appell généralisant des formules explicites pour les nombres et polynômes de Bernoulli généralisés. In this paper, we establish an identity for some Appell polynomials generalizing explicit formulas for generalized Bernoulli numbers and polynomials. [ABSTRACT FROM AUTHOR]

Statistical physics and stochastic modelling in economic sciences share the same mathematical bases given by the Gibbs distribution, but system characteristics are different. For instance, an economic system can be described by a Bose–Einstein statistics with few non-degenerate states and an infinitesimal “temperature”; under such conditions, the approximation of the most probable configuration is invalid. Therefore, the calculus of the exact solution needs using a Metropolis algorithm, which estimates a Gibbs distribution. This paper presents a much more efficient algorithm. For small systems, the exact distribution on the canonical set can be computed, and then this distribution is compared to the solutions of the old and new algorithms. [ABSTRACT FROM AUTHOR]

In the framework of semiclassical resonances, we make more precise the link between the polynomial estimates of the extension of the resolvent and the propagation of the singularities through the trapped set. This approach makes it possible to eliminate infinity and to concentrate the study near the trapped set. It has allowed us in previous papers to obtain the asymptotic of resonances in various geometric situations. [ABSTRACT FROM AUTHOR]

This paper introduces the notion of a metric for a simplex. Such a metric is a key ingredient when solving a PDE system by means of a Finite Element Method. Both mesh generation methods and error estimates (as far as interpolation error is considered) are concerned. Moreover, this metric gives information about the geometry of the corresponding element, typically about its shape quality in any Euclidean space. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new nonparametric estimation of the regression function when both the response and the explanatory variables are of the functional kind. First, we construct a local linear estimator of this regression operator, then we state its rate for the uniform almost complete convergence. This latter is expressed as a function of the small ball probability of the predictor and as a function of the entropy of the set on which the uniformity is obtained. [ABSTRACT FROM AUTHOR]

Let d ( n ) and d ⁎ ( n ) be the numbers of divisors and the numbers of unitary divisors of the integer n , and let S ( x ) = ∑ n ≤ x D ( n ) = ∑ n ≤ x d ( n ) d ⁎ ( n ) ( x ≥ 1 ) . A divisor d of a integer n is called unitary if it is prime with n d . In this paper, we prove that S ( x ) ∼ A x ( x → + ∞ ) , where A = π 2 6 ∏ p ( 1 − 1 2 p 2 + 1 2 p 3 ) = 1.4276565 ⋯ , and for all x ≥ 1 , S ( x ) = A x + R ( x ) such that | R ( x ) | ≤ 3 2 ζ ( 3 2 ) x 1 2 + 5 4 ζ ( 2 3 ) x 1 3 + O ( x 1 5 ) . [ABSTRACT FROM AUTHOR]

We define an explicit framework, involving sums of series, for p -adic multiple polylogarithms twisted by Frobenius, and for p -adic multiple zeta values. This framework is made of two types of combinatorial tools: operations related to the fundamental group of P 1 \ { 0 , 1 , ∞ } , which enable us reduce ourselves to the computation of “elementary” regularized iterated integrals, and the p -adic computation of each such elementary iterated integral. The explicit formulae that are obtained imply non-optimal bounds on the valuation of p -adic multiple zeta values. This is a summary of the paper [6] . [ABSTRACT FROM AUTHOR]

For a root system in R d furnished with its Weyl–Coxeter group W and a multiplicity function k ≥ 0 , we consider the associated commuting system of Dunkl operators D 1 , … , D d and the Dunkl Laplacian Δ k = D 1 2 + … + D d 2 . This paper studies the properties of the functions u of class C 2 m on an open W -invariant set Ω ⊂ R d and satisfying Δ k m u = 0 on Ω ( D -polyharmonicity if m > 1 and D -harmonicity if m = 1 ). In particular, we introduce a new operator, which is a generalization of the classical volume mean value operator and which characterizes D -harmonicity (resp. D -polyharmonicity) and we give some applications. [ABSTRACT FROM AUTHOR]