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.

Covariant bi-differential operators on matrix space

Abstract: A family of bi-differential operators from C ∞ Mat(m, R)×Mat(m, R) into C ∞ Mat(m, R) which are covariant for the projective action of the group SL(2m, R) on Mat(m, R) is constructed, generalizing both the transvectants and the Rankin-Cohen brackets (case m = 1). Resume On construit une famille d' operateurs bi-differentiels de C ∞ Mat(m, R) × Mat(m, R) dans C ∞ Mat(m, R) qui sont covari-ants pour l'action projective du groupe SL(2m, R) sur Mat(m, R). Dans le cas m = 1, cette construction fournit une nouvelle approche des transvectants et des crochets de Rankin-Cohen.

A Method to Deal With the Critical Case in Stochastic Population Dynamics

Abstract: In numerous papers, the behaviour of stochastic population models is investigated through the sign of a real quantity which is the growth rate of the population near the extinction set In many cases, it is proven that when this growth rate is positive, the process is persistent in the long run, while if it is negative, the process converges to extinction However, the critical case when the growth rate is null is rarely treated The aim of this paper is to provide a method that can be applied in many situations to prove that in the critical case, the process con-gerves in temporal average to extinction A number of applications are given, for Stochastic Dierential Equations and Piecewise Deterministic Markov Processes modelling prey-predator, epidemilogical or structured population dynamics

An infinite family of multiplicatively independent bases of number systems in cyclotomic number fields

Abstract: Let $\zeta_k$ be a $k$-th primitive root of unity, $m\geq\phi(k)+1$ an integer and $\Phi_k(X)\in\mathbb Z [X]$ the $k$-th cyclotomic polynomial. In this paper we show that the pair $(-m+\zeta_k,\mathcal N)$ is a canonical number system, with $\mathcal N=\{0,1,\dots,|\Phi_k(m)|\}$. Moreover we also discuss whether the two bases $-m+\zeta_k$ and $-n+\zeta_k$ are multiplicatively independent for positive integers $m$ and $n$ and $k$ fixed.

Déformation de variétés kählériennes compactes : invariance de la G-dimension et extension de sections pluricanoniques

Abstract: L'objectif de cette these consiste en l'etude du revetement universel des varietes kahleriennes compactes, de leurs systemes pluricanoniques et des liens qui les unissent. Dans un premier temps, nous etudions la $\Gamma$-reduction d'une variete kahlerienne compacte vue comme quotient de Remmert bimeromorphe de son revetement universel. La dimension de l'espace quotient est par definition la $\Gamma$-dimension d'une telle variete. Les grandes lignes de l'etude de cet invariant sont les suivantes : lien avec l'existence de formes holomorphes $L^2$ sur le revetement universel, comportement de la $\Gamma$-dimension dans les fibrations, place de la $\Gamma$-reduction dans la theorie de la classification, structure des varietes de type $\pi_1$-general (au moins en petite dimension). La fin de cette premiere partie est consacree a l'etude de l'invariance par deformation de la $\Gamma$-dimension en dimension 3. Cette propriete est etablie dans diverses situations, par exemple dans les cas des familles de varietes kahleriennes qui ne sont pas de type general. La deuxieme partie porte sur la methode One-Tower d'extension de formes pluricanoniques. Nous mettons en effet cette partie a profit pour montrer comment adapter cette methode dans differentes situations. Ainsi, apres quelques rappels sur les differentes notions de positivite des fibres en droites et sur les ideaux multiplicateurs, nous etablissons des resultats d'extension de sections pluricanoniques dans les contextes suivants : famille projective de varietes (avec fibre canonique tordu par un fibre en droites pseudo-effectif), hypersurface d'une variete projective, fibre generale de la $\Gamma$-reduction pour les varietes de type general et famille des revetements universels.

Moments of the frequency spectrum of a splitting tree with neutral Poissonian mutations

Abstract: We consider a branching population where individuals live and reproduce independently. Their lifetimes are i.i.d. and they give birth at a constant rate b. The genealogical tree spanned by this process is called a splitting tree, and the population counting process is a homogeneous, binary Crump-Mode-Jagers process. We suppose that mutations affect individuals independently at a constant rate $\\theta$ during their lifetimes, under the infinite-alleles assumption: each new mutation gives a new type, called allele, to his carrier. We study the allele frequency spectrum which is the numbers A(k, t) of types represented by k alive individuals in the population at time t. Thanks to a new construction of the coalescent point process describing the genealogy of individuals in the splitting tree, we are able to compute recursively all joint factorial moments of (A(k, t)) k$\ge$1. These moments allow us to give an elementary proof of the almost sure convergence of the frequency spectrum in a supercritical splitting tree.