Zobrazeno 1 - 10
of 214
pro vyhledávání: '"Bernard Etienne"'
Large Language Models (LLMs) have shown impressive abilities in data annotation, opening the way for new approaches to solve classic NLP problems. In this paper, we show how to use LLMs to create NuNER, a compact language representation model special
Externí odkaz:
http://arxiv.org/abs/2402.15343
Autor:
Bernard, Etienne
The Generalized Relative Entropy inequality is a ubiquitous property in mathematical models applied in physics or biology. In spite of its importance, it is currently proved on a case-by-case basis in the literature. Here, we show that GRE is actuall
Externí odkaz:
http://arxiv.org/abs/2206.12249
Autor:
Bernard, Étienne, Salvarani, Francesco
Publikováno v:
In Applied Mathematics Letters September 2023 143
Autor:
Bernard, Etienne, Gabriel, Pierre
Publikováno v:
Journal of Evolution Equations, 2020, 20 (2), pp.375-401
The objective is to prove the asynchronous exponential growth of the growth-fragmentation equation in large weighted $L^1$ spaces and under general assumptions on the coefficients. The key argument is the creation of moments for the solutions to the
Externí odkaz:
http://arxiv.org/abs/1809.10974
Publikováno v:
Kinetic and Related Models, 2019, 12 (3), pp.551-571
We study the asymptotic behaviour of the following linear growth-fragmentation equation$$\dfrac{\partial}{\partial t} u(t,x) + \dfrac{\partial}{\partial x} \big(x u(t,x)\big) + B(x) u(t,x) =4 B(2x)u(t,2x),$$ and prove that under fairly general assump
Externí odkaz:
http://arxiv.org/abs/1609.03846
Publikováno v:
Kinetic and Related Models \textbf{11} (2018), 43--69
In this short paper, we formally derive the thin spray equation for a steady Stokes gas, i.e. the equation consists in a coupling between a kinetic (Vlasov type) equation for the dispersed phase and a (steady) Stokes equation for the gas. Our startin
Externí odkaz:
http://arxiv.org/abs/1609.02504
Publikováno v:
Commun. Math. Sci. 15 (2017), 1703-1741
This article proposes a derivation of the Vlasov-Navier-Stokes system for spray/aerosol flows. The distribution function of the dispersed phase is governed by a Vlasov-equation, while the velocity field of the propellant satisfies the Navier-Stokes e
Externí odkaz:
http://arxiv.org/abs/1608.00422
Autor:
Bernard, Etienne, Gabriel, Pierre
Publikováno v:
Journal of Functional Analysis, 2017, 272 (8), pp.3455-3485
We are interested in the large time behavior of the solutions to the growth-fragmentation equation. We work in the space of integrable functions weighted with the principal dual eigenfunction of the growth-fragmentation operator. This space is the la
Externí odkaz:
http://arxiv.org/abs/1605.03030
Publikováno v:
Communication in Mathematical Sciences, vol. 13, no. 3, (2015), 641-671
The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer in a compos
Externí odkaz:
http://arxiv.org/abs/1309.1774