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.

Safety Evaluation of Critical Applications Distributed on TDMA-Based Networks

Abstract: Critical embedded systems have to provide a high level of dependability. In automotive domain, for example, TDMA protocols are largely recommended because of their deterministic behavior. Nevertheless, under the transient environmental perturbations, the loss of communication cycles may occur with a certain probability and, consequently, the system may fail. This presentation analyzes the impact of the transient perturbations (especially due to Electromagnetic Interferences) on the dependability of systems distributed on TDMA-based networks. The dependability of such system is modeled as that of “consecutive-k-out-of-n:F” systems and we provide a efficient way for its evaluation.

The logistic S.D.E.

Abstract: We consider the logistic SDE which is obtained by addition of a diffusion coefficient of the type β√x to the usual and deterministic Verhust-Volterra differential equation We show that this SDE is the limit of a sequence of birth and death Markov chains This permits to interpret the solution Vt as the size at time t of a self-controlled tumor which is submitted to a radiotherapy treatment We mainly focus on the family of stopping times Te, where Te is the first hitting of level e > 0 by (Vt) We calculate their Laplace transforms and also the first moment of Te Finally we determine the asymptotic behavior of Te, as e → 0

Une nouvelle minoration pour la trace absolue des entiers algébriques totalement positifs

Abstract: Nous donnons dans cette note une nouvelle minoration de la trace absolue des entiers algebriques totalement positifs. La methode utilisee est celle des fonctions auxiliaires explicites. Une legere variante dans l'utilisation de l'algorithme recursif nous a permis d'ameliorer les resultats anterieurs. Nous en deduisons une nouvelle minoration pour la trace absolue des entiers algebriques totalement positifs et reciproques.

Tube estimates for diffusions under a local strong Hörmander condition

Abstract: On etudie des bornes inferieures et superieures pour la probabilite qu’un processus de diffusion dans $R^{n}$ reste dans un petit tube autour d’un squelette deterministe jusqu’a un temps fixe. Les coefficients de diffusion $\sigma_{1},\dots,\sigma_{d}$ peuvent degenerer, mais on suppose qu’ils satisfont a une condition d’Hormander forte sur les coefficients et leurs crochets de Lie de premier ordre autour du squelette d’interet. Le tube est ecrit en termes d’une norme qui prend en compte la structure non isotrope du probleme: en temps $\delta$ petit, le processus de diffusion se propage avec vitesse $\sqrt{\delta}$ dans la direction des vecteurs de diffusion $\sigma_{j}$ et avec vitesse $\delta$ dans la direction de $[\sigma_{i},\sigma_{j}]$. On prouve d’abord des bornes inferieures et superieures en temps court (non asymptotiques) pour la densite de la diffusion. Ensuite, on prouve l’estimee de tube en utilisant une concatenation de ces estimees de densite en temps court.

Special Varieties and classification Theory

Abstract: A new class of compact Kahler manifolds, called special, is defined, which are the ones having no surjective meromorphic map to an orbifold of general type. The special manifolds are in many respect higher-dimensional generalisations of rational and elliptic curves. For example, we show that being rationally connected or having vanishing Kodaira dimension implies being special. Moreover, for any compact Kahler $X$ we define a fibration $c_X:X\to C(X)$, which we call its core, such that the general fibres of $c_X$ are special, and every special subvariety of $X$ containing a general point of $X$ is contained in the corresponding fibre of $c_X$. We then conjecture and prove in low dimensions and some cases that: 1) Special manifolds have an almost abelian fundamental group. 2) Special manifolds are exactly the ones having a vanishing Kobayashi pseudometric. 3) The core is a fibration of general type, which means that so is its base $C(X)$,when equipped with its orbifold structure coming from the multiple fibres of $c_X$. 4) The Kobayashi pseudometric of $X$ is obtained as the pull-back of the orbifold Kobayashi pseudo-metric on $C(X)$, which is a metric outside some proper algebraic subset. 5) If $X$ is projective,defined over some finitely generated (over $\Bbb Q$) subfield $K$ of the complex number field, the set of $K$-rational points of $X$ is mapped by the core into a proper algebraic subset of $C(X)$. These two last conjectures are the natural generalisations to arbitrary $X$ of Lang's conjectures formulated when $X$ is of general type.