Institut Élie Cartan de Lorraine

About: Institut Élie Cartan de Lorraine is a facility organization based out in Vandœuvre-lès-Nancy, France. It is known for research contribution in the topics: Boundary value problem & Stochastic differential equation. The organization has 345 authors who have published 1084 publications receiving 15512 citations. The organization is also known as: Institut Élie-Cartan de Nancy.

Moyennes de certaines fonctions multiplicatives sur les entiers friables

Abstract: An integer n is called friable when its prime number factorization consists exclusively of (relatively) small factors. Let P(n) be the largest prime factor occurring in this factorization, and let S(x,y) denote the set {n? x,P(n)? y}. This work investigates the asymptotic behaviour of the summatory function Psi_f(x, y):=\sum_{n\in S(x,y)}f(n) when f is a multiplicative arithmetical function satisfying some simple and general conditions concerning its mean behaviour on primes and on powers of primes. One such condition is |\sum_{p? z}f(p)\log p-\kappa z|? Cz/R(z) (z>1), where C is a constant and \kappa>0; requirements on R are technical conditions too long to state here, but satisfied by any "reasonable" positive increasing function. By setting R(z)=(\log z)^\delta in the very general Theoreme 2.1, the authors obtain a more general as well as more precise estimate on \Psi_f(x, y) (Corollaire 2.2) than that recently obtained by J. M. Song [Acta Arith. 102 (2002), no. 2, 105--129; MR1889623 (2003a:11123)]. Their next result (Corollaire 2.3) offers a general estimate in the case where f(p) is on average very close to a constant, and contains without loss of precision estimates of the literature for particular functions f, such as the so-called Piltz functions \tau_k, or the function µ^2 where µ is the Mobius function. Then, as a further application of their first result, they establish an Erdos-Wintner theorem on friable integers (Theoreme 2.4). They finally mention an application to the case where f(n) is the characteristic function of the integers that can be represented as a sum of two squares of integers (Theoreme 2.5); their estimate is uniformly valid for x ? 3, exp((\log x)^{2/5+\epsilon})? y? x. The paper begins with an historical introduction, and is followed by an extensive bibliography on the subject.

On a particular class of self-decomposable random variables: the durations of Bessel excursions straddling independent exponential times

Abstract: The distributional properties of the duration of a recurrent Bessel process straddling an independent exponential time are studied in detail. Althrough our study may be considered as a particular case of M. Winkel's in [Wink], the infinite divisibility structure of these Bessel durations is particularly rich and we develop algebraic properties for a family of random variables arising from the Levy measures of these durations.

On probability laws of solutions to differential systems driven by a fractional Brownian motion

Abstract: This article investigates several properties related to densities of solutions (Xt)t∈[0,1](Xt)t∈[0,1] to differential equations driven by a fractional Brownian motion with Hurst parameter H>1/4H>1/4. We first determine conditions for strict positivity of the density of XtXt. Then we obtain some exponential bounds for this density when the diffusion coefficient satisfies an elliptic type condition. Finally, still in the elliptic case, we derive some bounds on the hitting probabilities of sets by fractional differential systems in terms of Newtonian capacities.

Adult Diffuse Low-Grade Gliomas: 35-Year Experience at the Nancy France Neurooncology Unit.

Abstract: Background: To report survival, spontaneous prognostic factors, and treatment efficacy in a French monocentric cohort of diffuse low-grade glioma (DLGG) patients over 35 years of follow-up. Methods: A monocentric retrospective study of 339 patients diagnosed with a new DLGG between 01/01/1982 and 01/01/2017 was created. Inclusion criteria were patient age ≥18 years at diagnosis and histological diagnosis of WHO grade II glioma (according to 1993, 2007, and 2016 WHO classifications). The survival parameters were estimated using the Kaplan-Meier method with a 95% confidence interval. Differences in survival were tested for statistical significance by the log-rank test. Factors were considered significant when p ≤ 0.1 and p ≤ 0.05 in the univariate and multivariate analyses, respectively. Results: A total of 339 patients were included with a median follow-up of 8.7 years. The Kaplan-Meier median overall survival was 15.7 years. At the time of radiological diagnosis, Karnofsky Performance Status score and initial tumor volume were significant independent prognostic factors. Oncological prognostic factors were the extent of resection for patients who underwent surgery and the timing of radiotherapy for those concerned. In this study, patients who had delayed radiotherapy (provided remaining low grade) did not have worse survival compared with patients who had early radiotherapy. The functional capabilities of the patients were preserved enough so that they could remain independent during at least three quarters of the follow-up. Conclusion: This large monocentric series spread over a long time clarifies the effects of different therapeutic strategies and their combination in the management of DLGG.

Solving Inverse Source Problems Using Observability. Applications to the Euler-Bernoulli Plate Equation

Abstract: The aim of this paper is to provide a general framework for solving a class of inverse source problems by using exact observability of infinite dimensional systems. More precisely, we show that if a system is exactly observable, then a source term in this system can be identified by knowing its intensity and appropriate observations which often correspond to measurements of some boundary traces. This abstract theory is then applied to obtain new identifiability results for a system governed by the Euler-Bernoulli plate equation. Using a different methodology, we show that exact observability can be used to identify both the locations and the intensities of combinations of point sources in the plate equation.