Institution
Institut Élie Cartan de Lorraine
Facility•Vandœuvre-lès-Nancy, France•
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.
Topics: Boundary value problem, Stochastic differential equation, Boundary (topology), Brownian motion, Nonlinear system
Papers published on a yearly basis
Papers
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TL;DR: In this paper, the authors consider the set of n-letters long Lyndon words on the alphabet and prove that the height of the binary tree of a random uniform element of this set satisfies the convergence condition.
Abstract: We consider the set $\mathcal{L}_n<$ of n-letters long Lyndon words on the alphabet $\mathcal{A}=\{0,1\}$. For a random uniform element ${L_n}$ of the set $\mathcal{L}_n$, the binary tree $\mathfrak{L} (L_n)$ obtained by successive standard factorization of $L_n$ and of the factors produced by these factorization is the $\textit{Lyndon tree}$ of $L_n$. We prove that the height $H_n$ of $\mathfrak{L} (L_n)$ satisfies
$\lim \limits_n \frac{H_n}{\mathsf{ln}n}=\Delta$,
in which the constant $\Delta$ is solution of an equation involving large deviation rate functions related to the asymptotics of Eulerian numbers ($\Delta ≃5.092\dots $). The convergence is the convergence in probability of random variables.
1 citations
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TL;DR: In this paper, a completely formalized definition of a general manifold is given, which is a special instance of an ordered groupoid, and the notion of natural relations between groupoids is introduced, emphasizing the close analogy with natural transformations of general category theory.
Abstract: We give a completely formalized definition of a notion of " general manifold ". It turns out that " gluing data " form an equivalence-partially ordered set (e-pos), which is a special instance of an ordered groupoid. We state and prove reconstruction theorems, allowing to reconstruct general manifolds and their mor-phisms from such gluing data. To describe morphisms between manifolds, the notion of natural relations between groupoids is introduced, which emphasizes the close analogy with natural transformations of general category theory.
1 citations
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1 citations
18 Nov 2013
TL;DR: In this paper, a short survey on the analogue of Roth's theorem in some infinite subsets of integers of zero density, such as the subset of prime numbers, is given.
Abstract: The first part of this notes is devoted to the proof of Roth's theorem on arithmetic progressions in the integers whereas a second part gives some short survey on the analogue of Roth's theorem in some infinite subsets of integers of zero density such as the subset of prime numbers.
We tried to give the reader all the details needed in the first part so that a master student can read Roth's theorem proof easily. In the second part, some proofs are only sketched and we rather tried to give an idea of the issues specific to zero density subsets than to explain precisely how all the arguments work.
1 citations
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TL;DR: In this paper, the authors investigated propagation phenomena for KPP bulk-surface systems in a cylindrical domain with general section and heterogeneous coefficients, and provided new theoretical results on several asymptotic regimes like small and high diffusion rates and sections with small and large sizes.
Abstract: In this paper, we investigate propagation phenomena for KPP bulk-surface systems in a cylindrical domain with general section and heterogeneous coefficients. As for the scalar KPP equation, we show that the asymptotic spreading speed of solutions can be computed in terms of the principal eigenvalues of a family of self-adjoint elliptic operators. Using this characterization, we analyze the dependence of the spreading speed on various parameters, including diffusion rates and the size and shape of the section of the domain. In particular, we provide new theoretical results on several asymptotic regimes like small and high diffusion rates and sections with small and large sizes. These results generalize earlier ones which were available in the radial homogeneous case. Finally, we numerically investigate the issue of shape optimization of the spreading speed. By computing its shape derivative, we observe, in the case of homogeneous coefficients, that a disk either maximizes or minimizes the speed, depending on the parameters of the problem, both with or without constraints. We also show the results of numerical shape optimization with non homogeneous coefficients, when the disk is no longer an optimizer.
1 citations
Authors
Showing all 361 results
Name | H-index | Papers | Citations |
---|---|---|---|
Ivan Nourdin | 44 | 217 | 6139 |
Marius Tucsnak | 33 | 114 | 3907 |
Victor Nistor | 31 | 158 | 3352 |
Xavier Antoine | 30 | 125 | 2992 |
Jan Sokołowski | 30 | 203 | 6056 |
Nicolas Fournier | 29 | 106 | 3044 |
Gérald Tenenbaum | 29 | 173 | 5100 |
Lionel Rosier | 29 | 126 | 3956 |
Vicente Cortés | 27 | 118 | 2356 |
Gauthier Sallet | 27 | 70 | 2007 |
Antoine Henrot | 26 | 128 | 3268 |
Samy Tindel | 26 | 168 | 2656 |
Bruno Scherrer | 25 | 69 | 1447 |
Mario Sigalotti | 25 | 180 | 2082 |
Takéo Takahashi | 24 | 87 | 1673 |