Papers by Jean-marc Sac-Épée
Results in Mathematics, 2017
This article is concerned with the asymptotic behaviour of the Mahler measure (defined for the oc... more This article is concerned with the asymptotic behaviour of the Mahler measure (defined for the occasion) of functions of the form $$z^n + f(z)$$zn+f(z), where f(z) is a holomorphic function on an open subset of $${\mathbb {C}}$$C such that $$f(0) \ne 0$$f(0)≠0.
HAL (Le Centre pour la Communication Scientifique Directe), 2021
It is well known that the set of Mahler measures of single variable polynomial has limit points o... more It is well known that the set of Mahler measures of single variable polynomial has limit points of which a list established by D. Boyd and M. Mossinghoff has been extended through approaches based on genetic algorithms. In this paper, we wish to further extend the list of known limit points by adapting a method of missing data restoration.
Le Centre pour la Communication Scientifique Directe - HAL - Université de Nantes, Feb 21, 2022
The chronic obstructive pulmonary disease (COPD) is a highly prevalent lung disease, in which unu... more The chronic obstructive pulmonary disease (COPD) is a highly prevalent lung disease, in which unusual interactions between brocytes and CD8+ T lymphocytes in the peribronchial area could induce chronic inammation and tissue remodeling. We considered a probabilistic cellular automata type model where the two types of cells follow simple local interaction rules taking into account cell death, proliferation, migration and inltration. A rigorous mathematical analysis carried out within the framework of a streamlined model makes it possible to estimate with precision the parameters of the model using multiscale experimental data obtained in control and disease conditions. The simulation of the model is simple to be implemented. In simulations, two distinct patterns emerged, which can be analyzed quantitatively. In particular, we show that the change in brocyte density in the COPD condition is mainly the consequence of their inltration into the lung during exacerbations, suggesting possible explanations for experimental observations in normal and COPD tissue. Our integrated approach combining probabilistic cellular automata type model and experimental ndings will provide further insights into COPD in future studies.
ZAMM, 2006
We consider a general formulation for optimization problems involving the eigenvalues of the Lapl... more We consider a general formulation for optimization problems involving the eigenvalues of the Laplace operator. Both the cases of Dirichlet and Neumann conditions on the free boundary are studied. We list several results concerning the existence of optimal domains, together with some conjectures and open problems. The last section contains some numerical computations.
Journal of Number Theory, 2021
In this work, we are dealing with some properties relating the zeros of a polynomial and its Mahl... more In this work, we are dealing with some properties relating the zeros of a polynomial and its Mahler measure. We provide estimates on the number of real zeros of a polynomial, lower bounds on the distance between the zeros of a polynomial and non-zeros located on the unit circle and a lower bound on the number of zeros of a polynomial in the disk {|x− 1| < 1}.
In this work, we propose new candidates expected to be limit points of Mahler measures of polynom... more In this work, we propose new candidates expected to be limit points of Mahler measures of polynomials. The tool we use for determining these candidates is the Expectation-Maximization algorithm, whose goal is to optimize the likelihood for the given data points, i.e. the known Mahler measures up to degree 44, to be generated by a specific mixture of Gaussians. We will give the mean (which is a candidate to be a new limit point) and the relative amplitude of each component of the more likely gaussian mixture.
Experimental Mathematics
ABSTRACT In this article, by the mean of genetic algorithms, we enlarge the list of known limit p... more ABSTRACT In this article, by the mean of genetic algorithms, we enlarge the list of known limit points of Mahler measures.
Journal of Mathematics Research, 2016
Applied Mathematics Research eXpress
In this work, we deal with the flow of two immiscible and incompressible fluids. Both fluids are ... more In this work, we deal with the flow of two immiscible and incompressible fluids. Both fluids are supposed to satisfy Stokes equations. The kinematic viscosity of one of the fluids is supposed to be very small compared with the one of the other fluid. We study the behaviour of the resulting diphasic flow when the ratio of the two viscosities tends to zero. We first establish a priori estimates involving this ratio. Then, we use a singular perturbations method which consists in looking for the velocities and the pressures as asymptotic expansions. We rigorously prove the existence and uniqueness of the terms of these expansions and establish convergence results by giving error estimates. We find, as a first approximation, that the connected parts of the fluid whose kinematic viscosity is very high behave like hard suspensions carried away by the small-viscosity fluid. Moreover, we give precisely couples and forces acting on these as hard suspensions.
Comptes Rendus Mathematique
Control and cybernetics
In this work, we propose new candidates expected to be limit points of Mahler measures of polynom... more In this work, we propose new candidates expected to be limit points of Mahler measures of polynomials. The tool we use for determining these candidates is the Expectation-Maximization algorithm, whose goal is to optimize the likelihood for the given data points, i.e. the known Mahler measures up to degree 44, to be generated by a specific mixture of Gaussians. We will give the mean (which is a candidate to be a new limit point) and the relative amplitude of each component of the more likely gaussian mixture.
Journal of Applied Mathematics, 2015
Mathematics of Computation, 2006
SIAM Journal on Numerical Analysis, 2005
ABSTRACT The discretization by finite element methods of a new variational formulation of crack p... more ABSTRACT The discretization by finite element methods of a new variational formulation of crack problems is considered. The new formulation, called the smooth domain method, is derived for crack problems in the case of an elastic membrane. Inequality type boundary conditions are prescribed at the crack faces. The resulting model takes the form of a unilateral contact problem on the crack. We study and implement various mixed finite element methods for the numerical approximation of the model. A priori error estimates are derived, and results of computations are provided. The convergence rates obtained from the numerical simulations are in agreement with the theoretical estimates.
Semigroup Forum, 2014
The first aim of this paper is to illustrate numerically that the Dirichlet-to-Neumann semigroup ... more The first aim of this paper is to illustrate numerically that the Dirichlet-to-Neumann semigroup represented by P. Lax acts as a magnifying glass. In this perspective, we used the finite element method for the discretization of the correspondent boundary dynamical system using the implicit and explicit Euler schemes. We prove by using the Chernoff's Theorem that the implicit and explicit Euler methods converge to the exact solution and we use the (P1)-finite elements to illustrate this convergence through a FreeFem++ implementation which provides a movie available online. In the Dirichlet-to-Neumann semigroup represented by P. Lax the conductivity γ is the identity matrix I n , but for an other conductivity γ, the authors of [3] supplied an estimation of the operator norm of the difference between the Dirichlet-to-Neumann operator Λ γ and Λ 1 , when γ = βI n and β = 1 near the boundary ∂Ω (see Lemma 2.1). We will use this result to estimate the accuracy between the correspondent Dirichlet-to-Neumann semigroup and the Lax semigroup, for f ∈ H 1/2 (∂Ω).
Mathematical Modelling of Natural Phenomena, 2009
ABSTRACT We consider mixed and hybrid variational formulations to the linearized elasticity syste... more ABSTRACT We consider mixed and hybrid variational formulations to the linearized elasticity system in domains with cracks. Inequality type conditions are prescribed at the crack faces which results in unilateral contact problems. The variational formulations are extended to the whole domain including the cracks which yields, for each problem, a smooth domain formulation. Mixed finite element methods such as PEERS or BDM methods are designed to avoid locking for nearly incompressible materials in plane elasticity. We study and implement discretizations based on such mixed finite element methods for the smooth domain formulations to the unilateral crack problems. We obtain convergence rates and optimal error estimates and we present some numerical experiments in agreement with the theoretical results.
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Papers by Jean-marc Sac-Épée