Author: "'Simion Stoilow' Institute of Mathematics (IMAR)" - Searchworks@Jio Institute Digital Library Search Results

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97 results on '"'Simion Stoilow' Institute of Mathematics (IMAR)"'

1. Model of two-temperature convective transfer in porous media

Author: Isabelle Gruais, Dan Poliševski, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), 'Simion Stoilow' Institute of Mathematics ( IMAR ), Romanian Academy of Sciences, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), 'Simion Stoilow' Institute of Mathematics (IMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)
Subjects: Convection, Convective heat transfer, Stokes-Boussinesq system, General Mathematics, first-order jump interface, General Physics and Astronomy, Heat transfer coefficient, two-scale convergence, Thermal diffusivity, 01 natural sciences, 35B27, 76M50, 76Rxx, 74F10, 74Q05, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], Fluid dynamics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Boussinesq approximation (water waves), Physics, Homogenization, Applied Mathematics, 010102 general mathematics, Mechanics, 010101 applied mathematics, "-caps, heat transfer coecient, Transport phenomena, Porous medium
Abstract: In this paper, we study the asymptotic behaviour of the solution of a convective heat transfer boundary problem in an $$\varepsilon $$ -periodic domain which consists of two interwoven phases, solid and fluid, separated by an interface. The fluid flow and its dependence with respect to the temperature are governed by the Boussinesq approximation of the Stokes equations. The tensors of thermal diffusion of both phases are $$\varepsilon $$ -periodic, as well as the heat transfer coefficient which is used to describe the first-order jump condition on the interface. We find by homogenization that the two-scale limits of the solutions verify the most common system used to describe local thermal non-equilibrium phenomena in porous media (see Nield and Bejan in Convection in porous media, Springer, New York, 1999; Rees and Pop in Transport phenomena in porous media III, Elsevier, Oxford, 2005). Since now, this system was justified only by volume averaging arguments.
Published: 2017
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2. Fluid flows through fractured porous media along Beavers-Joseph interfaces

Author: Dan Poliševski, Isabelle Gruais, Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), and 'Simion Stoilow' Institute of Mathematics ( IMAR )
Subjects: Homogenization, 35B27, 76M50, 76S05, 76T99, Applied Mathematics, General Mathematics, Fractured porous media, Geometry, Stokes flow, Mechanics, Homogenization (chemistry), Two-scale convergence, Physics::Fluid Dynamics, Permeability (earth sciences), [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], Fluid dynamics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Uniqueness, Beavers-Joseph interface, Porous medium, Mathematics
Abstract: We study a fluid flow traversing a porous medium and obeying the Darcy's law in the case when this medium is fractured in blocks by an e-periodic ( e > 0 ) distribution of fissures filled with a Stokes fluid. These two flows are coupled by a Beavers–Joseph type interface condition. The existence and uniqueness of this flow in our e-periodic structure are proved. As the small period of the distribution shrinks to zero, we study the asymptotic behaviour of the flow when the permeability and the entire contribution on the interface of the Beavers–Joseph transfer coefficients are of unity order. We find the homogenized problem verified by the two-scale limits of the coupled velocities and pressures. It is well-posed and provides the corresponding classical homogenized problem.
Published: 2014
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3. The effective permeability of fractured porous media subject to the Beavers-Joseph contact law

Author: Florentina-Alina Stanescu, Isabelle Gruais, Dan Poliševski, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), 'Simion Stoilow' Institute of Mathematics ( IMAR ), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)
Subjects: Homogenization, General Mathematics, 010102 general mathematics, Fractured porous media, Subject (philosophy), 01 natural sciences, Two-scale convergence, Stokes flow \sep Beavers-Joseph interface, 010101 applied mathematics, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], \MSC 35B27, 76M50, 76S05, 76T99, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Geotechnical engineering, 0101 mathematics, Porous medium, Relative permeability, Geology
Abstract: We are interested in the asymptotic behaviour of a fluid flow contained in a microscopic periodic distribution of fissures perturbating a porous medium where the Darcy law is valid, when the coupling between both systems is modeled by the Beavers-Joseph interface condition. As the small period of the distribution tends to zero, the interface condition is preserved on a microscopic scale under the additional assumption that the permeability coefficients behave like the squared period of the distribution which is also the squared size of the fissures. Moreover, the resulting pressure is purely macroscopic unlike the velocity field which also depends on the microscopic variable.
Published: 2014
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4. Asymptotic heat equation for crossing superconductive thin walls

Author: Dan Poliševski, Isabelle Gruais, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), 'Simion Stoilow' Institute of Mathematics ( IMAR ), Romanian Academy of Sciences, Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), 'Simion Stoilow' Institute of Mathematics (IMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), and Gruais, Isabelle
Subjects: Homogenization, Condensed matter physics, Box-type structure, Applied Mathematics, Fine-scale, 010102 general mathematics, Thermodynamics, Binary number, Conductivity, Thermal conduction, Microstructure, Conduction, 01 natural sciences, Homogenization (chemistry), 010101 applied mathematics, Singularity, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], 35B27, 35K57, 76R50, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Heat equation, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Electrical conductor, Analysis, Mathematics
Abstract: International audience; This work deals with the homogenization of the nonstationary heat conduction which takes place in a binary three-dimensional medium consisting of an ambiental phase having conductivity of unity order and a set of highly conductive thin walls crossing orthogonally and periodically. This situation covers in fact three types of microstructures, usually called: box-type (or honeycomb), gridwork and layered. The study is based on the energetic procedure of homogenization associated to a control-zone method, specific to the geometry of the microstructure and to the singularity of the conductivity coefficients. In the present case the main result is the system that governs the asymptotic behaviour of the temperature distribution in this binary medium. It displays a significant increase of the conductivity due to the superconductive thin walls, revealing their seemingly paradoxal behaviour of having an everlasting action on the environment, in spite of an obvious vanishing volume. Moreover, the dependence of this behaviour with respect to the relative thicknesses of the walls can be detailed.
Published: 2012

5. Homogenizing the Darcy/Stokes coupling

Author: Gruais, Isabelle, Polisevski, Dan, Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), 'Simion Stoilow' Institute of Mathematics ( IMAR ), Gruais, Isabelle, AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)
Subjects: Physics::Fluid Dynamics, Homogenization, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], 35B27, 76M50, 76S05, 76T99, Fractured porous media, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Stokes flow, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Beavers-Joseph interface, Two-scale convergence
Abstract: We study a fluid flow traversing a porous medium and obeying the Darcy's law in the case when this medium is fractured by a periodical distribution of fissures filled with a Stokes fluid. These two flows are coupled by a Beavers-Joseph type interface condition. As the small period of the distribution shrinks to zero, the resulting asymptotic behaviour is implicitely described by two underlying macroscopic quantities: the limit of the Stokes velocity and the limit of the Darcy pressure, solutions of a new coupled system obtained by homogenization. The behaviour of the macroscopic two-scale limit of the filtration velocity is given by an explicit two-scale Darcy type law, presenting coupling terms with the gradient of the limit of the Darcy pressure and with the limit of the Stokes velocity.
Published: 2011

6. Periodic structures separated by highly conductive thin layers

Author: Gruais, Isabelle, Polisevski, Dan, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), 'Simion Stoilow' Institute of Mathematics ( IMAR ), Romanian Academy of Sciences, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), 'Simion Stoilow' Institute of Mathematics (IMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), and Gruais, Isabelle
Subjects: conduction, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], genetic structures, fine-scale substructure, homogenization, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 35B27, 35K57,76R50, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]
Abstract: We derive a model for the conduction in an $\veps$-periodic structure containing highly conductive thin layers. The case of plane thin layers is first considered. It is shown that the resulting model displays an increased conductivity along the directions of the layers planes. The more involved case of tubular layers yields a similar result with an increase of the conductivity along the direction of the tubes, while the presence of highly conductive thin layers confined between spheres of $\veps$-order radii does not increase the macroscopic conductivity in any direction. It seems that the presence of $\veps$-periodic highly conductive thin layers determines an increase of the macroscopic conductivity in a certain direction only if these layers cover entirely segment lines of unity order having this direction.
Published: 2010

7. $\epsilon$-periodic structures containing highly conductive thin layers

Author: Gruais, Isabelle, Polisevski, Dan, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), 'Simion Stoilow' Institute of Mathematics ( IMAR ), Romanian Academy of Sciences, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), 'Simion Stoilow' Institute of Mathematics (IMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), and Guillemer, Marie-Annick
Subjects: [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 35B27, 35J25, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], ComputingMilieux_MISCELLANEOUS
Abstract: International audience
Published: 2010

8. Diffusion around a vanishing suspension

Author: Bentalha , Fadila, Gruais , Isabelle, Polisevski , Dan, Laboratoire de Mathématiques, Université Hadj Lakhdar Batna, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), 'Simion Stoilow' Institute of Mathematics ( IMAR ), Romanian Academy of Sciences, Université Hadj Lakhdar Batna 1, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), 'Simion Stoilow' Institute of Mathematics (IMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), and Guillemer, Marie-Annick
Subjects: [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], ComputingMilieux_MISCELLANEOUS, 35B27, 35K57, 76T20
Abstract: International audience
Published: 2008

9. Homogenization of a conductive suspension in a Stokes-Boussinesq flow

Author: Bentalha , Fadila, Gruais , Isabelle, Polisevski , Dan, Laboratoire de Mathématiques, Université Hadj Lakhdar Batna 1, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Université Hadj Lakhdar Batna, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), 'Simion Stoilow' Institute of Mathematics ( IMAR ), Guillemer, Marie-Annick, Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)
Subjects: 35B27, 35Q35, 76D07, 76M50, 76S05, ComputingMilieux_MISCELLANEOUS
Abstract: International audience
Published: 2006

10. A phenomenological model for interfacial water near hydrophilic polymers

Author: A Earls, M-C Calderer, M Desroches, A Zarnescu, S Rodrigues, Mathematical, Computational and Experimental Neuroscience [Bilbao] (MCEN), Basque Center for Applied Mathematics (BCAM), University of Minnesota [MN, USA], Mathématiques pour les Neurosciences (MATHNEURO), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Basque Center for Applied Mathematics, Ikerbasque - Basque Foundation for Science, 'Simion Stoilow' Institute of Mathematics (IMAR), and Romanian Academy of Sciences
Subjects: Polymers, Surface Properties, hydrophilic polymers, [SCCO.NEUR]Cognitive science/Neuroscience, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Water, General Materials Science, interfacial water, Condensed Matter Physics, exclusion zone, Hydrophobic and Hydrophilic Interactions
Abstract: We propose a minimalist phenomenological model for the ‘interfacial water’ phenomenon that occurs near hydrophilic polymeric surfaces. We achieve this by combining a Ginzburg–Landau approach with Maxwell’s equations which leads us to a well-posed model providing a macroscopic interpretation of experimental observations. From the derived governing equations, we estimate the unknown parameters using experimental measurements from the literature. The resulting profiles of the polarization and electric potential show exponential decay near the surface, in qualitative agreement with experiments. Furthermore, the model’s quantitative prediction of the electric potential at the hydrophilic surface is in excellent agreement with experiments. The proposed model is a first step towards a more complete parsimonious macroscopic model that will, for example, help to elucidate the effects of interfacial water on cells (e.g. neuronal excitability), the effects of infrared neural stimulation or the effects of drugs mediated by interfacial water., Ikerbasque (The Basque Foundation for Science) Inria Associated Team "NeuroTransSF"
Published: 2022
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11. Sharp estimates of the solutions to B{\'e}zout's polynomial equation and a corona theorem

Author: Fricain, Emmanuel, Hartmann, Andreas, T., Ross William, Timotin, Dan, Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics and Statistics, 'Simion Stoilow' Institute of Mathematics (IMAR), and Romanian Academy of Sciences
Subjects: Mathematics::Functional Analysis, Mathematics::Complex Variables, Mathematics - Classical Analysis and ODEs, Mathematics - Complex Variables, Classical Analysis and ODEs (math.CA), FOS: Mathematics, [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV], [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Complex Variables (math.CV), Bézout's equation, de Branges--Rovnyak spaces, 30J05, 30H10, 46E22, corona theorem
Abstract: In this paper, we obtain estimates for the solutions to the classical B{\'e}zout equation that are analogous to Carleson's solution to the corona theorem for the bounded analytic functions on the open unit disk. As an application, we extend some results of Luo and obtain a corona theorem for the multipliers of a class of de Branges--Rovnyak spaces.
Published: 2022

12. Homogenization of a diffusion process in a rarefied binary structure

Author: Bentalha, Fadila, Gruais, Isabelle, Polisevski, Dan, Department of Mathematics, Université Hadj Lakhdar Batna, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), 'Simion Stoilow' Institute of Mathematics ( IMAR ), Romanian Academy of Sciences, Université Hadj Lakhdar Batna 1, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), 'Simion Stoilow' Institute of Mathematics (IMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)
Subjects: Diffusion, Mathematics - Analysis of PDEs, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], 35B27, 35K57, 76R50, fine-scale substructure, FOS: Mathematics, homogenization, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Analysis of PDEs (math.AP)
Abstract: We study the homogenization of a diffusion process which takes place in a binary structure formed by an ambiental connected phase surrounding a suspension of very small spheres distributed in an $\veps$-periodic network. The asymptotic distribution of the concentration is determined for both phases, as $\veps\to 0$, assuming that the suspension has mass of unity order and vanishing volume. Three cases are distinguished according to the values of a certain limit capacity. When it is positive and finite, the macroscopic system involves a two-concentration system, coupled through a term accounting for the non local effects. In the other two cases, where the capacity is either infinite or going to zero, although the form of the system is much simpler, some peculiar effects still account for the presence of the suspension.
Published: 2005

13. On the existence of the stabilizing solution of generalized Riccati equations arising in zero-sum stochastic difference games: the time-varying case

Author: Vasile Dragan, Samir Aberkane, Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, and The Academy of the Romanian Scientists
Subjects: Large class, Stochastic control, Algebra and Number Theory, Markov processes, Applied Mathematics, stochastic systems, 010102 general mathematics, linear systems, Zero (complex analysis), discrete time systems, 01 natural sciences, perturbation techniques, 010101 applied mathematics, random processes, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Applied mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Uniqueness, control system synthesis, 0101 mathematics, linear matrix inequalities, state feedback, Analysis, H∞ control, Mathematics
Abstract: International audience; In this paper, a large class of time-varying Riccati equations arising in stochastic dynamic games is considered. The problem of the existence and uniqueness of some globally defined solution, namely the bounded and stabilizing solution, is investigated. As an application of the obtained existence results, we address in a second step the problem of infinite-horizon zero-sum two players linear quadratic (LQ) dynamic game for a stochastic discrete-time dynamical system subject to both random switching of its coefficients and multiplicative noise. We show that in the solution of such an optimal control problem, a crucial role is played by the unique bounded and stabilizing solution of the considered class of generalized Riccati equations.
Published: 2020
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14. On the bounded and stabilizing solution of a generalized Riccati differential equation arising in connection with a zero‐sum linear quadratic stochastic differential game

Author: Vasile Dragan, Toader Morozan, S. Aberkane, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Centre de Recherche en Automatique de Nancy (CRAN), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)
Subjects: 0209 industrial biotechnology, Control and Optimization, Differential equation, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Zero (complex analysis), 02 engineering and technology, Linear quadratic, 01 natural sciences, Connection (mathematics), 020901 industrial engineering & automation, Control and Systems Engineering, Bounded function, Differential game, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Software, Mathematics
Abstract: International audience; We study a class of coupled nonlinear matrix differential equations arising in connection with the solution of a zero‐sum two‐player linear quadratic (LQ) differential game for a dynamical system modeled by an Itô differential equation subject to random switching of its coefficients. The system of differential equations under consideration contains as special cases the game‐theoretic Riccati differential equations arising in the solution of the H∞ control problem from the deterministic and stochastic cases. A set of sufficient conditions that guarantee the existence of the bounded and stabilizing solution of this kind of Riccati differential equations is provided. We show how such stabilizing solution is involved in the construction of the equilibrium strategy of a zero‐sum LQ stochastic differential game on an infinite‐time horizon and give as a byproduct the solution of such a control problem.
Published: 2019
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15. Robust Stability of Time-Varying Markov Jump Linear Systems with Respect to a Class of Structured, Stochastic, Nonlinear Parametric Uncertainties

Author: Vasile Dragan, Samir Aberkane, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Centre de Recherche en Automatique de Nancy (CRAN), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Lyapunov function, 0209 industrial biotechnology, Logic, Differential equation, robust stability, Markov jump systems, structured parametric uncertainties, stability radius, scaling, linear matrix inequalities, 02 engineering and technology, Upper and lower bounds, symbols.namesake, 020901 industrial engineering & automation, 0202 electrical engineering, electronic engineering, information engineering, QA1-939, Applied mathematics, Mathematical Physics, Parametric statistics, Mathematics, Algebra and Number Theory, Stability radius, Nonlinear system, Bounded function, symbols, 020201 artificial intelligence & image processing, Geometry and Topology, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Robust control, Analysis
Abstract: International audience; This note is devoted to a robust stability analysis, as well as to the problem of the robust stabilization of a class of continuous-time Markovian jump linear systems subject to block-diagonal stochastic parameter perturbations. The considered parametric uncertainties are of multiplicative white noise type with unknown intensity. In order to effectively address the multi-perturbations case, we use scaling techniques. These techniques allow us to obtain an estimation of the lower bound of the stability radius. A first characterization of a lower bound of the stability radius is obtained in terms of the unique bounded and positive semidefinite solutions of adequately defined parameterized backward Lyapunov differential equations. A second characterization is given in terms of the existence of positive solutions of adequately defined parameterized backward Lyapunov differential inequalities. This second result is then exploited in order to solve a robust control synthesis problem.
Published: 2021
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16. Apollonius circles and irreducibility criteria for polynomials

Author: Yann Bugeaud, Mihai Cipu, Nicolae Ciprian Bonciocat, Anca Iuliana Bonciocat, Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), 'Simion Stoilow' Institute of Mathematics (IMAR), and Romanian Academy of Sciences
Subjects: Canonical decomposition, Polynomial, Mathematics - Number Theory, 11R09 (Primary), 11C08 (Secondary), General Mathematics, 010102 general mathematics, 0402 animal and dairy science, Multivariate polynomials, 04 agricultural and veterinary sciences, 040201 dairy & animal science, 01 natural sciences, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], Combinatorics, symbols.namesake, Integer, Prime factor, FOS: Mathematics, symbols, Irreducibility, Number Theory (math.NT), 0101 mathematics, Circles of Apollonius, Complex plane, Mathematics
Abstract: We prove the irreducibility of integer polynomials $f(X)$ whose roots lie inside an Apollonius circle associated to two points on the real axis with integer abscisae $a$ and $b$, with ratio of the distances to these points depending on the canonical decomposition of $f(a)$ and $f(b)$. In particular, we obtain irreducibility criteria for the case where $f(a)$ and $f(b)$ have few prime factors, and $f$ is either an Enestr\"om-Kakeya polynomial, or has a large leading coefficient. Analogous results are also provided for multivariate polynomials over arbitrary fields, in a non-Archimedean setting., Comment: 21 pages, 1 figure
Published: 2021
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17. Exact detectability: application to generalized Lyapunov and Riccati equations

Author: Vasile Dragan, Ioan-Lucian Popa, Eduardo F. Costa, Samir Aberkane, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Instituto de Ciencias Matematicas e de Computacao, Universidade de Sao Paulo, Brazil, Department of Mathematics '1 Decembrie 1918', University of Alba Iulia, Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)
Subjects: Lyapunov function, Mean square, Large class, 0209 industrial biotechnology, Class (set theory), General Computer Science, 02 engineering and technology, Linear quadratic, 01 natural sciences, symbols.namesake, 020901 industrial engineering & automation, Exponential stability, Exact detectability, Exponential stability in mean square, Riccati equation, Applied mathematics, 0101 mathematics, Electrical and Electronic Engineering, Mathematics, Mechanical Engineering, 010102 general mathematics, Popov–Belevitch–Hautus test, Connection (mathematics), ESTABILIDADE DE LIAPUNOV, Control and Systems Engineering, symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract: International audience; This paper is devoted to the application of the recently developed results about exact detectability of a large class of time-varying hybrid stochastic systems (Drăgan et al., 2020). More specifically, we will show from one side the connection between this new detectability notion and the derivation of a criterion for exponential stability in mean square for this class of systems. In the second part, we will show the central role played by exact detectability in Riccati equations arising in linear quadratic (LQ) regulator problems for such stochastic systems: it is a necessary and sufficient condition for the Riccati equation to have a unique positive semi-definite and stabilizing solution.
Published: 2021
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18. Population balance approach for predicting polymer particles morphology

Author: Rusconi, Simone, Dutykh, Denys, Zarnescu, Arghir, Sokolovski, Dmitri, Akhmatskaya, Elena, Basque Center for Applied Mathematics (BCAM), Basque Center for Applied Mathematics, Laboratoire de Mathématiques (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Basque Foundation for Science (Ikerbasque), and DUTYKH, Denys
Subjects: [PHYS.PHYS.PHYS-FLU-DYN]Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], [PHYS.PHYS.PHYS-CLASS-PH]Physics [physics]/Physics [physics]/Classical Physics [physics.class-ph], [PHYS.PHYS.PHYS-COMP-PH] Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph], [PHYS.PHYS.PHYS-FLU-DYN] Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA], [PHYS.PHYS.PHYS-CHEM-PH] Physics [physics]/Physics [physics]/Chemical Physics [physics.chem-ph], [PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph], [INFO.INFO-NA] Computer Science [cs]/Numerical Analysis [cs.NA], [PHYS.MECA.MEFL] Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [PHYS.PHYS.PHYS-CLASS-PH] Physics [physics]/Physics [physics]/Classical Physics [physics.class-ph], [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [PHYS.PHYS.PHYS-CHEM-PH]Physics [physics]/Physics [physics]/Chemical Physics [physics.chem-ph], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: 2 pages, 8 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/; International audience; Polymer particles morphology can be defined as a pattern of phase-separated domains comprising a multi-phase polymer particle [1]. Properties of a polymer particle strongly depend on its morphology, and thus the control of particle morphology is a key factor for success in producing high-quality polymers materials, such as coatings, adhesives and additives [2]. Currently, an accurate prediction of particles morphology is still a challenge due to its complexity. Several modelling approaches, describing the dynamics of the morphology of a single particle, have been suggested in the last few years [3, 4, 5]. However, the single-particle approaches only provide a partial view of realistic systems, containing millions of particles. Furthermore, such models are computationally demanding even with the use of High-Performance Computers.
Published: 2020

19. Exact detectability and exact observability of discrete-time linear stochastic systems with periodic coefficients

Author: Vasile Dragan, Samir Aberkane, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, The Academy of the Romanian Scientists, Centre de Recherche en Automatique de Nancy (CRAN), and Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)
Subjects: 0209 industrial biotechnology, Class (set theory), Exact observability, 020208 electrical & electronic engineering, Mean square sense, Order (ring theory), 02 engineering and technology, Sense (electronics), PBH type criterion, Characteristic multipliers, 020901 industrial engineering & automation, Exponential stability, Discrete time and continuous time, Control and Systems Engineering, Exact detectability, Periodic coefficients, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, Observability, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Electrical and Electronic Engineering, Discrete-time stochastic systems, Mathematics
Abstract: International audience; This paper is devoted to the problem of detectability and observability of a class of time-varying stochastic systems. The main contribution of this note is to propose a PBH-type test which is equivalent to the detectability of the considered stochastic systems in the sense that all unstable modes produce some non-zero output. Then, we apply the obtained results in order to derive a criterion of exponential stability in mean square sense as well as existence conditions for the stabilizing solution of a class of discrete-time time-varying Riccati equations.
Published: 2020
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20. Hodge decomposition for Cousin groups and Oeljeklaus-Toma manifolds

Author: Alexandra Otiman, Matei Toma, Otiman, ALEXANDRA IULIA, Toma, Matei, Department of Mathematics and Physics, Roma TRE University, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Faculty of Mathematics and Computer Science [Bucuresti], University of Bucharest (UniBuc), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), The authors acknowledge the support of the Max Planck Institute for Mathematics in Bonn where part of this research was carried out, and A. O. is partially supported by a grant of Ministry of Research and Innovation, CNCS - UEFISCDI, project number PNIII-P4-ID-PCE-2016-0065, within PNCDI III.
Subjects: Mathematics - Differential Geometry, Pure mathematics, Cousin, 01 natural sciences, Mathematics::Algebraic Topology, Theoretical Computer Science, 010104 statistics & probability, Mathematics (miscellaneous), Mathematics::K-Theory and Homology, FOS: Mathematics, 0101 mathematics, [MATH]Mathematics [math], Complex Variables (math.CV), Mathematics::Symplectic Geometry, 32J18, 32M17, Hodge decomposition, Mathematics, Mathematics - Complex Variables, Mathematics::Complex Variables, 010102 general mathematics, Regular polygon, 2010 Mathematics Subject Classification : 32J18, 32M17, Dolbeault cohomology, 16. Peace & justice, Cohomology, Differential geometry, Differential Geometry (math.DG), Complex variables, Cousin groups, Oeljeklaus-Toma manifolds, Mathematics::Differential Geometry
Abstract: We compute the Dolbeault cohomology of geodesically convex domains contained in Cousin groups which satisfy a strong dispersiveness condition. As a consequence we obtain a description of the Dolbeault cohomology of Oeljeklaus-Toma manifolds and in particular the fact that the Hodge decomposition holds for their cohomology., Comment: To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
Published: 2020
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21. Scaling property for fragmentation processes related to avalanches

Author: Oana Lupaşcu-Stamate, Madalina Deaconu, Lucian Beznea, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, University of Bucharest (UniBuc), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Processus aléatoires spatio-temporels et leurs applications (PASTA), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Simuler et calibrer des modèles stochastiques (TOSCA-NGE-POST), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Romanian Academy
Subjects: Physics, Stochastic modelling, fragmentation stochastic differential equation, 010102 general mathematics, Monte Carlo method, scaling, jump process, 01 natural sciences, Market fragmentation, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, Stochastic differential equation, Fractal, Statistical physics, 0101 mathematics, Mathematics Subject Classification39A13, 65C30, 60J45, 65C05, 60J35, Nuclear Experiment, Jump process, Scaling
Abstract: International audience; We emphasize a scaling property for the continuous time fragmentation processes related to a stochastic model for the fragmentation phase of an avalanche. We present numerical results that confirm the validity of the scaling property for our model, based on the appropriate stochastic differential equation of fragmentation and on a fractal property of the solution.
Published: 2020
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22. A Generic View on the Unified Zero-Knowledge Protocol and Its Applications

Author: Diana Maimuţ, George Teseleanu, Advanced Technology Institute [Bucarest], 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Maryline Laurent, Thanassis Giannetsos, TC 11, and WG 11.2
Subjects: Security analysis, business.industry, Computer science, Generalization, Hash function, Authentication scheme, 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, 010201 computation theory & mathematics, Authentication protocol, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, [INFO]Computer Science [cs], Zero-knowledge proof, business, Wireless sensor network, Protocol (object-oriented programming), Computer network
Abstract: Part 2: Authentication; International audience; We present a generalization of Maurer’s unified zero-knowledge (UZK) protocol, namely a unified generic zero-knowledge (UGZK) construction. We prove the security of our UGZK protocol and discuss special cases. Compared to UZK, the new protocol allows to prove knowledge of a vector of secrets instead of only one secret. We also provide the reader with a hash variant of UGZK and the corresponding security analysis. Last but not least, we extend Cogliani et al.’s lightweight authentication protocol by describing a new distributed unified authentication scheme suitable for wireless sensor networks and, more generally, the Internet of Things.
Published: 2019
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23. Effects of vorticity on the travelling waves of some shallow water two-component systems

Author: Delia Ionescu-Kruse, Denys Dutykh, Laboratoire de Mathématiques (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), 'Simion Stoilow' Institute of Mathematics (IMAR), and Romanian Academy of Sciences
Subjects: [PHYS.PHYS.PHYS-FLU-DYN]Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], Integrable system, Zakharov-Ito system, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], FOS: Physical sciences, Near and far field, Physics - Classical Physics, Pattern Formation and Solitons (nlin.PS), [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], phase-plane analysis, MSC: 74J30 (primary), 76F10, 35C07, 76B25, 70K05, 35Q35 (secondary)PACS: 47.35.Bb (primary), 47.11.Kb, 47.10.Df (secondary), 01 natural sciences, Camassa-Holm equations, [NLIN.NLIN-PS]Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS], [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Traveling wave, Discrete Mathematics and Combinatorics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI], [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], 0101 mathematics, Nonlinear Sciences::Pattern Formation and Solitons, Kaup-Boussinesq equations, Physics, [PHYS.PHYS.PHYS-AO-PH]Physics [physics]/Physics [physics]/Atmospheric and Oceanic Physics [physics.ao-ph], Nonlinear Sciences - Exactly Solvable and Integrable Systems, Applied Mathematics, Mathematical analysis, Fluid Dynamics (physics.flu-dyn), Classical Physics (physics.class-ph), Physics - Fluid Dynamics, Vorticity, Nonlinear Sciences - Pattern Formation and Solitons, waves on shear flow, 010101 applied mathematics, analytical solutions, Physics - Atmospheric and Oceanic Physics, Waves and shallow water, Nonlinear Sciences::Exactly Solvable and Integrable Systems, Phase space, multi-pulsed solutions, solitary waves, Atmospheric and Oceanic Physics (physics.ao-ph), cnoidal waves, Phase plane analysis, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Exactly Solvable and Integrable Systems (nlin.SI), Analysis
Abstract: In the present study we consider three two-component (integrable and non-integrable) systems which describe the propagation of shallow water waves on a constant shear current. Namely, we consider the two-component Camassa-Holm equations, the Zakharov-Ito system and the Kaup--Boussinesq equations all including constant vorticity effects. We analyze both solitary and periodic-type travelling waves using the simple and geometrically intuitive phase space analysis. We get the pulse-type solitary wave solutions and the front solitary wave solutions. For the Zakharov-Ito system we underline the occurrence of the pulse and anti-pulse solutions. The front wave solutions decay algebraically in the far field. For the Kaup-Boussinesq system, interesting analytical multi-pulsed travelling wave solutions are found., Comment: 27 pages, 14 figures, 45 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/
Published: 2019
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24. Numerical approach for stochastic differential equations of fragmentation; application to avalanches

Author: Oana Lupaşcu-Stamate, Madalina Deaconu, Lucian Beznea, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, University of Bucharest (UniBuc), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), TO Simulate and CAlibrate stochastic models (TOSCA), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Gheorghe Mihoc -Caius Iacob, and Institute of Mathematical Statistics and Applied Mathematics, Bucharest
Subjects: General Computer Science, Computer science, Stochastic modelling, Phase (waves), 010103 numerical & computational mathematics, 02 engineering and technology, Space (mathematics), stochastic equation of fragmentation, 01 natural sciences, Theoretical Computer Science, measure-valued process, Stochastic differential equation, Fractal, numerical methods, 0202 electrical engineering, electronic engineering, information engineering, Statistical physics, 0101 mathematics, Nuclear Experiment, Numerical Analysis, Applied Mathematics, Numerical analysis, Fragmentation (computing), Process (computing), branching process and kernel, Fragmentation equation and kernel, space of fragmentation sizes, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], avalanche, Modeling and Simulation, 020201 artificial intelligence & image processing
Abstract: International audience; This paper builds and develops an unifying method for the construction of a continuous time fragmentation-branching processes on the space of all fragmentation sizes, induced either by continuous fragmentation kernels or by discontinuous ones. This construction leads to a stochastic model for the fragmentation phase of an avalanche. We introduce also an approximation scheme for the process which solves the corresponding stochastic differential equations of fragmentation. A new achievement of the paper is to compute the distributions of the branching processes approximating the forthcoming branching-fragmentation process. This numerical approach of the associated branching-fragmentation process, is, to our knowledge, one of the first in this direction. We present also numerical results that confirm the validity of the fractal property which was emphasized by our model for an avalanche.
Published: 2019
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25. REMARKS ON ARTIN APPROXIMATION WITH CONSTRAINTS

Author: Popescu, Dorin, Rond, Guillaume, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), and Rond, Guillaume
Subjects: [MATH.MATH-AC] Mathematics [math]/Commutative Algebra [math.AC], [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC], FOS: Mathematics, MSC: Primary: 13B40, Secondary: 03C20, 12L10, 13J05, 14B12, 12L10, 13B40, Mathematics - Commutative Algebra, 13J05, Commutative Algebra (math.AC), 14B12, 03C20
Abstract: We study various approximation results of solutions of equations $f(x,Y)=0$ where $f(x,Y)\in\mathbb K[[x]][Y]^r$ and $x$ and $Y$ are two sets of variables, and where some components of the solutions $y(x)\in\mathbb K[[x]]^m$ do not depend on all the variables $x_j$. These problems have been highlighted by M. Artin., Comment: 9 pages. To appear in Osaka J. Math
Published: 2019

26. Peierls' substitution for low lying spectral energy windows

Author: Radu Purice, Horia D. Cornean, Bernard Helffer, Department of Mathematical Sciences [Aalborg], Aalborg University [Denmark] (AAU), Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN), 'Simion Stoilow' Institute of Mathematics (IMAR), and Romanian Academy of Sciences
Subjects: Wannier functions, Spectral gaps, FOS: Physical sciences, 01 natural sciences, 010305 fluids & plasmas, Mathematics - Spectral Theory, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Quantum mechanics, 0103 physical sciences, FOS: Mathematics, 0101 mathematics, [MATH]Mathematics [math], Spectral Theory (math.SP), Eigenvalues and eigenvectors, Mathematical Physics, Physics, Wannier function, Magnetic pseudo-differential operators, spectral gaps, Wannier functions, Chern class, Magnetic pseudo-differential operators, Operator (physics), 010102 general mathematics, Spectrum (functional analysis), Spectral density, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), Mathematics::Spectral Theory, Magnetic field, Brillouin zone, Geometry and Topology
Abstract: We consider a $2d$ magnetic Schr\"odinger operator perturbed by a weak magnetic field which slowly varies around a positive mean. In a previous paper we proved the appearance of a `Landau type' structure of spectral islands at the bottom of the spectrum, under the hypothesis that the lowest Bloch eigenvalue of the unperturbed operator remained simple on the whole Brillouin zone, even though its range may overlap with the range of the second eigenvalue. We also assumed that the first Bloch spectral projection was smooth and had a zero Chern number. In this paper we extend our previous results to the only two remaining possibilities: either the first Bloch eigenvalue remains isolated while its corresponding spectral projection has a non-zero Chern number, or the first two Bloch eigenvalues cross each other., Comment: 27 pages
Published: 2019
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27. THE RENORMALIZED VOLUME AND UNIFORMISATION OF CONFORMAL STRUCTURES

Author: Colin Guillarmou, Sergiu Moroianu, Jean-Marc Schlenker, Département de Mathématiques et Applications - ENS Paris (DMA), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), ANR-10-BLAN-0105,ACG,Aspects Conformes de la Géométrie(2010), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), and École normale supérieure - Paris (ENS Paris)
Subjects: Mathematics - Differential Geometry, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], FOS: Mathematics, Mathematics [G03] [Physical, chemical, mathematical & earth Sciences], FOS: Physical sciences, Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre], Mathematical Physics (math-ph), Mathematical Physics
Abstract: We study the renormalized volume of asymptotically hyperbolic Einstein (AHE in short) manifolds $(M,g)$ when the conformal boundary $\pl M$ has dimension $n$ even. Its definition depends on the choice of metric $h_0$ on $\partial M$ in the conformal class at infinity determined by $g$, we denote it by ${\rm Vol}_R(M,g;h_0)$. We show that ${\rm Vol}_R(M,g;\cdot)$ is a functional admitting a "Polyakov type" formula in the conformal class $[h_0]$ and we describe the critical points as solutions of some non-linear equation $v_n(h_0)={\rm const}$, satisfied in particular by Einstein metrics. In dimension $n=2$, choosing extremizers in the conformal class amounts to uniformizing the surface, while in dimension $n=4$ this amounts to solving the $\sigma_2$-Yamabe problem. Next, we consider the variation of ${\rm Vol}_R(M,\cdot;\cdot)$ along a curve of AHE metrics $g^t$ with boundary metric $h_0^t$ and we use this to show that, provided conformal classes can be (locally) parametrized by metrics $h$ solving $v_n(h)=\int_{\pl M}v_n(h){\rm dvol}_{h}$, the set of ends of AHE manifolds (up to diffeomorphisms isotopic to Identity) can be viewed as a Lagrangian submanifold in the cotangent space to the space $\mc{T}(\pl M)$ of conformal structures on $\pl M$. We obtain as a consequence a higher-dimensional version of McMullen's quasifuchsian reciprocity. We finally show that conformal classes admitting negatively curved Einstein metrics are local minima for the renormalized volume for a warped product type filling., Comment: 58 pages, 2 figures
Published: 2018

28. On a Class of Parametric (p, 2)-equations

Author: Vicenţiu D. Rădulescu, Dušan Repovš, Nikolaos S. Papageorgiou, National Technical University of Athens [Athens] (NTUA), 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, University of Ljubljana, and Slovenian Research Agency through Grants P1-0292, J1-7025 and J1-6721 (D. Repovs) and the Romanian Research Council through the grant UEFISCDI-PCCA-23/2014 (V. Radulescu)
Subjects: Control and Optimization, nonlinear maximum principle, Multiplicity results, 35J20, 35J60, 58E05, Lambda, 01 natural sciences, Omega, Combinatorics, Mathematics - Analysis of PDEs, near resonance, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], constant sign and nodal solutions, 0101 mathematics, Parametric equation, Eigenvalues and eigenvectors, Parametric statistics, Physics, Applied Mathematics, 010102 general mathematics, udc:517.956.2, Multiplicity (mathematics), local minimizer, 35J20, 35J60, 58E05, 010101 applied mathematics, critical group, Laplace operator, Analysis of PDEs (math.AP)
Abstract: We consider parametric equations driven by the sum of a ▫$p$▫-Laplacian and a Laplace operator (the so-called ▫$(p, 2)$▫-equations). We study the existence and multiplicity of solutions when the parameter ▫$lambda > 0$▫ is near the principal eigenvalue ▫$hat{lambda}_1(p) > 0$▫ of ▫$(-Delta_p,W^{1-p}_0(Omega))$▫. We prove multiplicity results with precise sign information when the near resonance occurs from above and from below of ▫$hat{lambda}_1(p) > 0$▫.
Published: 2016
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29. Inverse Scattering for the 1-D Helmholtz Equation

Author: Ingrid Beltiţă, Renata Bunoiu, Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), 'Simion Stoilow' Institute of Mathematics (IMAR), and Romanian Academy of Sciences
Subjects: Inverse scattering transform, Helmholtz equation, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Operator theory, 34A55, 34L25, 01 natural sciences, 010101 applied mathematics, Computational Mathematics, Computational Theory and Mathematics, Mathematics - Classical Analysis and ODEs, Elementary proof, Line (geometry), Inverse scattering problem, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Uniqueness, [MATH]Mathematics [math], 0101 mathematics, Mathematics
Abstract: We prove a uniqueness result for Nevanlinna functions. and this result is then used to give an elementary proof of the uniqueness in the inverse scattering problem for the equation $ u" + \frac{k^2}{c^2}u=0 $ on $\mathbb R$. Here $c$ is a real positive measurable function that is bounded from below by a positive constant, and is close to $1$ at $\pm \infty$., 22 pages
Published: 2015
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30. A BEALS CRITERION FOR MAGNETIC PSEUDODIFFERENTIAL OPERATORS PROVED WITH MAGNETIC GABOR FRAMES

Author: Horia D. Cornean, Bernard Helffer, Radu Purice, Department of Mathematical Sciences [Aalborg], Aalborg University [Denmark] (AAU), Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN), 'Simion Stoilow' Institute of Mathematics (IMAR), and Romanian Academy of Sciences
Subjects: Pure mathematics, magnetic pseudo-differential calculus, Applied Mathematics, 010102 general mathematics, Mathematics::Analysis of PDEs, Commutator (electric), FOS: Physical sciences, Mathematical Physics (math-ph), Differential operator, 01 natural sciences, law.invention, 010101 applied mathematics, Mathematics - Analysis of PDEs, law, Tight frame, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], FOS: Mathematics, Beals criterion, 0101 mathematics, [MATH]Mathematics [math], Gabor frames, Mathematical Physics, Analysis, Mathematics, Analysis of PDEs (math.AP)
Abstract: First, we give a new proof for the Beals commutator criterion for non-magnetic Weyl pseudo-differential operators based on classical Gabor tight frames. Second, by introducing a modified 'magnetic' Gabor tight frame, we naturally derive the magnetic analogue of the Beals criterion originally considered by Iftimie-M\u{a}ntoiu-Purice., Comment: 8 pages, to appear in Commun. P.D.E
Published: 2018
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31. On the asymptotic structure of the stabilizing solution of a class of singularly perturbed Ricatti equation of stochastic control

Author: Dragan, Vasile, Popa, Ioan-Lucian, Aberkane, Samir, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, The Academy of the Romanian Scientists, University of Alba Iulia, Université 1 Decembrie 1918 [Alba Iulia], Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), and Aberkane, Samir
Subjects: Riccati equations of stochastic control, singularly perturbed linear stochastic systems, optimal control problem, Markovian jumping parameters, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract: International audience; An optimal control problem for a system of linear Itˆo differential equations withtwo fast time scales and Markovian jumping is considered. The asymptoticstructure for the stabilizing solution satisfying a sign condition for the coupledstochastic algebraic Riccati equations is derived. Furthermore, a near optimalcontrol whose gain matrices do not depend upon small parameters is discussed.
Published: 2018

32. Foundational (Co)datatypes and (Co)recursion for Higher-Order Logic

Author: Fabian Meier, Andrei Popescu, Mathias Fleury, René Thiemann, Christian Sternagel, Aymeric Bouzy, Julian Biendarra, Johannes Hölzl, Dmitriy Traytel, Jasmin Christian Blanchette, Lorenz Panny, Andreas Lochbihler, Ondřej Kunčar, Martin Desharnais, Technische Universität Munchen - Université Technique de Munich [Munich, Allemagne] (TUM), Max-Planck-Institut für Informatik (MPII), Max-Planck-Gesellschaft, Modeling and Verification of Distributed Algorithms and Systems (VERIDIS), Max-Planck-Gesellschaft-Max-Planck-Gesellschaft-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Formal Methods (LORIA - FM), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Vrije Universiteit Amsterdam [Amsterdam] (VU), InstantJob, Ludwig Maximilian University [Munich] (LMU), Computer Science Department - Carnegie Mellon University, University of Pittsburgh (PITT), Pennsylvania Commonwealth System of Higher Education (PCSHE)-Pennsylvania Commonwealth System of Higher Education (PCSHE), Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich), Google Switzerland, Research at Google, Technische Universiteit Eindhoven (TU/e), 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Middlesex University [London], Department of Computer Science [Innsbruck], Leopold Franzens Universität Innsbruck - University of Innsbruck, Clare Dixon and Marcelo Finger, Discrete Mathematics, Coding Theory and Cryptology, Department of Formal Methods (LORIA - FM), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Max-Planck-Institut für Informatik (MPII), Max-Planck-Gesellschaft-Max-Planck-Gesellschaft, University of Innsbruck, Dixon, Clare, Finger, Marcelo, Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), Theoretical Computer Science, and Network Institute
Subjects: Recursion, Programming language, Coinduction, HOL, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], 020207 software engineering, 0102 computer and information sciences, 02 engineering and technology, computer.software_genre, 01 natural sciences, Higher-order logic, TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES, 010201 computation theory & mathematics, TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS, Line (geometry), 0202 electrical engineering, electronic engineering, information engineering, Recursive functions, computer, Axiom, Mathematics
Abstract: International audience; We describe a line of work that started in 2011 towards enriching Isabelle/HOL's language with coinductive datatypes, which allow infinite values, and with a more expressive notion of inductive datatype than previously supported by any system based on higher-order logic. These (co)datatypes are complemented by definitional principles for (co)recursive functions and reasoning principles for (co)induction. In contrast with other systems offering codatatypes, no additional axioms or logic extensions are necessary with our approach.
Published: 2017
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33. Low lying spectral gaps induced by slowly varying magnetic fields

Author: Bernard Helffer, Horia D. Cornean, Radu Purice, Department of Mathematical Sciences [Aalborg], Aalborg University [Denmark] (AAU), Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN), 'Simion Stoilow' Institute of Mathematics (IMAR), and Romanian Academy of Sciences
Subjects: Structure (category theory), FOS: Physical sciences, 01 natural sciences, Mathematics - Spectral Theory, Matrix (mathematics), symbols.namesake, Quantum mechanics, 0103 physical sciences, FOS: Mathematics, [MATH]Mathematics [math], 0101 mathematics, Spectral Theory (math.SP), Eigenvalues and eigenvectors, Mathematical Physics, Mathematics, Operator (physics), 010102 general mathematics, Mathematical analysis, Spectrum (functional analysis), Mathematical Physics (math-ph), Magnetic field, symbols, 010307 mathematical physics, Analysis, Intensity (heat transfer), Schrödinger's cat
Abstract: We consider a periodic Schr\"odinger operator in two dimensions perturbed by a weak magnetic field whose intensity slowly varies around a positive mean. We show in great generality that the bottom of the spectrum of the corresponding magnetic Schr\"odinger operator develops spectral islands separated by gaps, reminding of a Landau-level structure. First, we construct an effective Hofstadter-like magnetic matrix which accurately describes the low lying spectrum of the full operator. The construction of this effective magnetic matrix does not require a gap in the spectrum of the non-magnetic operator, only that the first and the second Bloch eigenvalues do not cross but their ranges might overlap. The crossing case is more difficult and will be considered elsewhere. Second, we perform a detailed spectral analysis of the effective matrix using a gauge-covariant magnetic pseudo-differential calculus adapted to slowly varying magnetic fields. As an application, we prove in the overlapping case the appearance of spectral islands separated by gaps., Comment: 55 pages, to appear in J. Funct. Anal
Published: 2017
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34. A classification of torsors over Laurent polynomial rings

Author: Philippe Gille, Arturo Pianzola, Vladimir Chernousov, University of Alberta, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Algèbre, géométrie, logique (AGL), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), and V. Chernousov was partially supported by the Canada Research Chairs Program and an NSERC research grant.P. Gille was supported by the Romanian IDEI project PCE$_{-}$2012-4-364 of the Ministry of National EducationCNCS-UEFISCIDI. A. Pianzola wishes to thank NSERC and CONICET for their continuous support
Subjects: Matemáticas, General Mathematics, TORSOR, Field (mathematics), 01 natural sciences, Matemática Pura, Combinatorics, MULTILOOP ALGEBRA, FOS: Mathematics, Fraction (mathematics), 0101 mathematics, Algebraic number, Mathematics, Ring (mathematics), Laurent polynomial, 010102 general mathematics, [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA], Zero (complex analysis), Mathematics - Rings and Algebras, MSC: 14F20, 20G15, 17B67, 11E72, 16. Peace & justice, 010101 applied mathematics, multiloop algebra, torsor, REDUCTIVE GROUP SCHEME, Rings and Algebras (math.RA), Torsor, CIENCIAS NATURALES Y EXACTAS, Reductive group scheme
Abstract: Let R\_n be the ring of Laurent polynomials in n variables over a field k of characteristic zero and let K\_n be its fraction field.Given a linear algebraic k-group $G$, we show that a K\_n-torsor under G which is unramified with respect to X=Spec(R\_n)extends to a unique toral R\_n-torsor under G. This result, in turn, allows us to classify all G-torsors over R\_n., 18 pages
Published: 2017

35. Schwarz method for dual contact problems

Author: Frédéric Lebon, Lori Badea, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Laboratoire de Mécanique et d'Acoustique [Marseille] (LMA ), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)
Subjects: 0211 other engineering and technologies, 010103 numerical & computational mathematics, 02 engineering and technology, Schwarz method, Space (mathematics), 01 natural sciences, Omega, Domain (mathematical analysis), Domain decomposition methods, Convergence (routing), [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], Applied mathematics, 0101 mathematics, 021106 design practice & management, Mathematics, Variable (mathematics), Subspace correction methods, Applied Mathematics, Mathematical analysis, Variational inequalities, Contact problems, Computational Mathematics, Variational inequality, Dual formulation, Subspace topology
Abstract: International audience; In this paper, we analyze the convergence of the Schwarz method for contact problems with Tresca friction formulated in stress variables. In this dual variable, the problem is written as a variational inequality in the space $H_\text{div}(\Omega)$, $\Omega$ being the domain of the problem. The method is introduced as a subspace correction algorithm. In this case, the global convergence and the error estimation of the method are already proved in the literature under some assumptions. However, the checking of these hypotheses in the space $H_\text{div}(\Omega)$ cannot be proved easily, as for the space $H^1(\Omega)$. The main result of this paper is to prove that these hypotheses are verified for this particular variational inequality. As in the case of the classical problems formulated in primal variables, the error estimate we obtain depends on the overlapping parameter of the domain decomposition.
Published: 2017
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36. Irreducibility criteria for compositions of polynomials with integer coefficients

Author: Nicolae Ciprian Bonciocat, Mihai Cipu, Maurice Mignotte, Yann Bugeaud, Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), 'Simion Stoilow' Institute of Mathematics (IMAR), and Romanian Academy of Sciences
Subjects: Polynomial, Degree (graph theory), Irreducible polynomial, General Mathematics, 010102 general mathematics, Prime number, Of the form, 01 natural sciences, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], 010101 applied mathematics, Combinatorics, Quadratic equation, Integer, Irreducibility, 0101 mathematics, Mathematics::Representation Theory, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract: We provide irreducibility criteria for some classes of compositions of polynomials with integer coefficients of the form $$F\circ G$$ , with F being a quadratic irreducible polynomial and G a polynomial of arbitrary degree.
Published: 2017
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37. Fourier Transforms of C *-Algebras of Nilpotent Lie Groups

Author: Ingrid Beltiţă, Jean Ludwig, Daniel Beltiţă, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), and This research has been partially supported by the Grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0131.
Subjects: Pure mathematics, General Mathematics, 010102 general mathematics, Lie group, 010103 numerical & computational mathematics, 01 natural sciences, symbols.namesake, Nilpotent, Fourier transform, symbols, 0101 mathematics, [MATH]Mathematics [math], Mathematics::Representation Theory, Mathematics
Abstract: International audience; For any nilpotent Lie group G we provide a description of the image of its C*-algebra C∗(G) through its operator-valued Fourier transform. Specifically, we show that C∗(G) admits a finite composition series such that that the spectra of the corresponding quotients are Hausdorff sets in the relative topology, defined in terms of the fine stratification of the space of coadjoint orbits of G, and the canonical fields of elementary C*-algebras defined by the successive subquotients are trivial. We give a description of the image of the Fourier transform as a C*-algebra of piecewise continuous operator fields on the spectrum, determined by the boundary behavior of the restrictions of operator fields to the spectra of the subquotients in the composition series. For uncountable families of three-step nilpotent Lie groups and also for a sequence of nilpotent Lie groups of arbitrarily high nilpotency step, we prove that every continuous trace subquotient of their C*-algebras has its Dixmier–Douady invariant equal to zero.
Published: 2017
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38. Octonion Algebras over Rings Are Not Determined by their Norms

Author: Philippe Gille, Département de Mathématiques et Applications - ENS Paris (DMA), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Class (set theory), Ring (mathematics), Pure mathematics, Algèbres d'octonions, 14L24, 20G41, Mathematics::Number Theory, General Mathematics, [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA], 010102 general mathematics, descente, Mathematics - Rings and Algebras, 010103 numerical & computational mathematics, 01 natural sciences, Octonion, torseurs, Rings and Algebras (math.RA), FOS: Mathematics, Mathematics::Differential Geometry, 0101 mathematics, Descent (mathematics), Mathematics
Abstract: Answering a question of H. Petersson, we provide a class of examples of pair of octonion algebras over a ring having isometric norms., Comment: 8 pages
Published: 2014
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39. A Szegö type theorem for truncated Toeplitz operators

Author: Dan Timotin, Elizabeth Strouse, Mohamed Zarrabi, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), 'Simion Stoilow' Institute of Mathematics (IMAR), and Romanian Academy of Sciences
Subjects: Discrete mathematics, Numerical Analysis, Pure mathematics, Applied Mathematics, General Mathematics, 010102 general mathematics, Spectral theorem, Type (model theory), Operator theory, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, Linear subspace, Toeplitz matrix, truncated Toeplitz operators, Chain (algebraic topology), 0103 physical sciences, Szegö Theorem, Multiplication, MSC: 47B35, 30J10, 47A45, 010307 mathematical physics, 0101 mathematics, Invariant (mathematics), Model spaces, Analysis, Mathematics
Abstract: International audience; Truncated Toeplitz operators are compressions of multiplication operators on L 2 to model spaces (that is, subspaces of H 2 which are invariant with respect to the backward shift). For this class of operators we prove certain Szegö type theorems concerning the asymptotics of their compressions to an increasing chain of finite dimensional model spaces. The Toeplitz operators are compressions of multiplication operators on the space L 2 (T) to the Hardy space H 2 ; the multiplier is called the symbol of the operator. With respect to the standard exponential basis, their matrices are constant along diagonals; if we truncate such a matrix considering only its upper left finite corner, we obtain classical Toeplitz matrices. It does not come as a surprise that there are connections between the asymptotics of these Toeplitz matrices and the whole Toeplitz operator, or its symbol. A central result is Szegö's strong limit theorem and its variants (see, for instance, [4] and the references within), which deal with the asymptotics of the eigenvalues of the Toeplitz matrix. On the other hand, certain generalizations of Toeplitz matrices have attracted a great deal of attention in the last decade, namely compressions of multiplication operators to subspaces of the Hardy space which are invariant under the backward shift. These " model spaces " are of the form H 2 ⊖uH 2 with u an inner function, and the compressions are called truncated Toeplitz operators. They have been formally introduced in [11]; see [8] for a more recent survey. Although classical Toeplitz matrices have often been a starting point for investigating truncated Toeplitz operators , the latter may exhibit surprising properties. It thus seems natural to see whether an analogue of Szegö's strong limit theorem can be obtained in this more general context. Viewed as truncated Toeplitz operators, the Toeplitz matrices act on model spaces corresponding to the inner functions u(z) = z n , and Szegö's theorem is about the asymptotical situation when n → ∞. The natural generalization is then to consider a sequence of zeros (λ j) in D, and to let the truncations act on the model space corresponding to the finite Blaschke product associated to λ j , 1 ≤ j ≤ n.
Published: 2017

40. Travelling wave solutions for some two-component shallow water models

Author: Denys Dutykh, Delia Ionescu-Kruse, Laboratoire de Mathématiques (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), 'Simion Stoilow' Institute of Mathematics (IMAR), and Romanian Academy of Sciences
Subjects: [PHYS.PHYS.PHYS-FLU-DYN]Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], Integrable system, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Type (model theory), phase-plane analysis, 01 natural sciences, Camassa-Holm equations, 010305 fluids & plasmas, [NLIN.NLIN-PS]Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS], Component (UML), 0103 physical sciences, Traveling wave, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI], [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], 0101 mathematics, Mathematics, [PHYS.PHYS.PHYS-AO-PH]Physics [physics]/Physics [physics]/Atmospheric and Oceanic Physics [physics.ao-ph], 74J30 (primary), 76B15, 76B25, 70K05 (secondary)47.35.Bb (primary), 47.11.Kb, 47.10.Df (secondary), Applied Mathematics, 010102 general mathematics, Mathematical analysis, Green-Naghdi model, Waves and shallow water, Classical mechanics, solitary waves, cnoidal waves, Phase plane analysis, Serre equations, travelling waves, Analysis
Abstract: 21 pages, 13 figures, 37 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/; International audience; In the present study we perform a unified analysis of travelling wave solutions to three different two-component systems which appear in shallow water theory. Namely, we analyse the celebrated Green-Naghdi equations, the integrable two-component Camassa-Holm equations and a new two-component system of Green-Naghdi type. In particular, we are interested in solitary and cnoidal-type solutions, as two most important classes of travelling waves that we encounter in applications. We provide a complete phase-plane analysis of all possible travelling wave solutions which may arise in these models.In particular, we show the existence of new type of solutions.
Published: 2016
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41. Three-point Lie algebras and Grothendieck's dessins d'enfants

Author: Chernousov, V., Gille, Philippe, Pianzola, Arturo, University of Alberta, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Algèbre, géométrie, logique (AGL), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), and V. Chernousov was partially supported by the Canada Research Chairs Program and an NSERC research grant. P. Gille was supported by the IDEI Romanian project PN-II-ID-PCE-2012-4. A. Pianzola wishes to thank NSERC and CONICET for their continuous support
Subjects: [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA], Mathematics - Rings and Algebras, dessins d'enfants, affine and three pointed affine Lie algebras, torsor, Rings and Algebras (math.RA), Mathematics::Quantum Algebra, MSC 2000: 17B67, 11E72, 14L30, 14E20, FOS: Mathematics, Cartan subalgebra, multiloop algebra, Mathematics::Representation Theory, Reductive group scheme
Abstract: We define and classify the analogues of the affine Kac-Moody Lie algebras for the ring corresponding to the complex projective line minus three points. The classification is given in terms of Grothendieck's dessins d'enfants. We also study the question of conjugacy of Cartan subalgebras for these algebras., Comment: 16 pages
Published: 2016

42. Sur la classification des schémas en groupes semi-simples

Author: Gille, Philippe, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Algèbre, géométrie, logique (AGL), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Projet IDEI PCE_2012-4-364 du Ministère de l'Education Nationale de Roumanie CNCS-UEFISCIDI, and Gille, Philippe
Subjects: réductibilité, sous-groupes paraboliques, données radicielles, [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA], [MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA], [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], isotropie, Schémas en groupes, 14L15, 14L30
Abstract: 81 pages; International audience; We deal with the classification of semisimple group schemes via the Bruhat-Tits' presentation of non-abelian cohomology. The goal is to generalize Galois techniques to more general rings. It leads us to investigate the concept of reducibility for reductive group schemes with special attention to one parameter subgroups. It requires also the study of parabolic subgroups and their normalizers of a non-necessarily connected affine smooth group scheme G whose neutral component is reductive. The text discusses in an appendix also certain analogies for Weyl group schemes and twisted root data.
Published: 2016

43. Asymptotic analysis of a thin rigid stratified elastic plate – viscous fluid interaction problem

Author: Ruxandra Stavre, Grigory Panasenko, Irina Malakhova-Ziablova, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), 'Simion Stoilow' Institute of Mathematics (IMAR), and Romanian Academy of Sciences
Subjects: dimension reduction, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], homogenization, Modulus, Viscous liquid, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, Homogenization (chemistry), Physics::Fluid Dynamics, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Uniqueness, Boundary value problem, 0101 mathematics, Variational analysis, Linear elasticity, Mathematics, asymptotic expansion, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Stokes equations, 010101 applied mathematics, interface, Asymptotic expansion, Analysis, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; A three-dimensional model for the interaction of a thin stratified rigid plate and a viscous fluid layer is considered. This problem depends on a small parameter $\varepsilon$ which is the ratio of the thickness of the plate and that of the fluid layer. The right-hand side functions are 1-periodic with respect to the tangential variables of the plate. The plate’s Young’s modulus is of order $\varepsilon^{-3}$, i.e. it is great, while its density is of order 1. At the solid–fluid interface, the velocity and the normal stress are continuous. The variational analysis of this model (including the existence, uniqueness of the solution and its regularity) is provided. An asymptotic expansion of the solution is constructed and justified. The error estimate is proved for the partial sums of the asymptotic expansion. The limit problem contains a non-standard boundary condition for the Stokes equations. The existence, uniqueness, and regularity of its solution are proved. The asymptotic analysis is applied to the partial asymptotic dimension reduction of the solid phase and the derivation of the asymptotically exact junction conditions between two-dimensional and three-dimensional models of the plate.
Published: 2016
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44. Positivity, decay, and extinction for a singular diffusion equation with gradient absorption

Author: Razvan Gabriel Iagar, Philippe Laurençot, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Diffusion equation, viscosity solutions, Diffusion, gradient estimates, 01 natural sciences, Singular diffusion, gradient absorption, Mathematics - Analysis of PDEs, FOS: Mathematics, Initial value problem, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Absorption (logic), 0101 mathematics, Mathematics, Mathematical physics, extinction, 010102 general mathematics, Mathematical analysis, p-Laplacian, 35B40, 35K67, 35K92, 35K10, 35B33, 49L25, 010101 applied mathematics, Extinction (optical mineralogy), Finite time, Analysis, Analysis of PDEs (math.AP)
Abstract: We study qualitative properties of non-negative solutions to the Cauchy problem for the fast diffusion equation with gradient absorption ∂ t u − Δ p u + | ∇ u | q = 0 in ( 0 , ∞ ) × R N , where N ⩾ 1 , p ∈ ( 1 , 2 ) , and q > 0 . Based on gradient estimates for the solutions, we classify the behavior of the solutions for large times, obtaining either positivity as t → ∞ for q > p − N / ( N + 1 ) , optimal decay estimates as t → ∞ for p / 2 ⩽ q ⩽ p − N / ( N + 1 ) , or extinction in finite time for 0 q p / 2 . In addition, we show how the diffusion prevents extinction in finite time in some ranges of exponents where extinction occurs for the non-diffusive Hamilton–Jacobi equation.
Published: 2012
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45. Bounded symbols and Reproducing Kernel Thesis for truncated Toeplitz operators

Author: Isabelle Chalendar, Emmanuel Fricain, Dan Timotin, Anton Baranov, Javad Mashreghi, Department of Mathematics and Mechanics, St Peterburg State University, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université LAVAL, Département de Mathématiques et de Statistiques, Université Laval [Québec] (ULaval), 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Mathematics and Mechanics Faculty [St Petersbourg], St Petersburg State University (SPbU), Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), and Département de Mathématiques et de Statistiques
Subjects: 010102 general mathematics, Operator theory, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 47B35, 47B32, 01 natural sciences, Linear subspace, Toeplitz matrix, Functional Analysis (math.FA), Algebra, Mathematics - Functional Analysis, Kernel (algebra), Operator (computer programming), model spaces, Symbol (programming), Bounded function, 0103 physical sciences, FOS: Mathematics, 010307 mathematical physics, 0101 mathematics, Reproducing Kernel Thesis, Model spaces, ComputingMilieux_MISCELLANEOUS, Toeplitz operators, Analysis, Mathematics
Abstract: Compressions of Toeplitz operators to coinvariant subspaces of $H^2$ are called truncated Toeplitz operators. We study two questions related to these operators. The first, raised by Sarason, is whether boundedness of the operator implies the existence of a bounded symbol; the second is the reproducing kernel thesis. We show that in general the answer to the first question is negative, and we exhibit some classes of spaces for which the answers to both questions are positive., Version 2 (33 pages)
Published: 2010
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46. Mass transportation proofs of free functional inequalities, and free Poincaré inequalities

Author: Ionel Popescu, Michel Ledoux, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Georgia Institute of Technology [Atlanta], Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Mass transport, Pure mathematics, Spectral gap, Distribution (number theory), Context (language use), Mathematical proof, 01 natural sciences, 010104 statistics & probability, symbols.namesake, FOS: Mathematics, 0101 mathematics, ComputingMilieux_MISCELLANEOUS, Mathematics, Probability (math.PR), 010102 general mathematics, Functional inequalities, Free probability, Functional Analysis (math.FA), Mathematics - Functional Analysis, Poincaré conjecture, symbols, Random matrices, Convex function, Random matrix, Mathematics - Probability, Analysis
Abstract: This work is devoted to direct mass transportation proofs of families of functional inequalities in the context of one-dimensional free probability, avoiding random matrix approximation. The inequalities include the free form of the transportation, Log-Sobolev, HWI interpolation and Brunn-Minkowski inequalities for strictly convex potentials. Sharp constants and some extended versions are put forward. The paper also addresses two versions of free Poincar\'e inequalities and their interpretation in terms of spectral properties of Jacobi operators. The last part establishes the corresponding inequalities for measures on $\R_{+}$ with the reference example of the Marcenko-Pastur distribution., Comment: This paper will apear in Journal of Fucntional Analysis
Published: 2009
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47. Finitely strictly singular operators between James spaces

Author: Emmanuel Fricain, Dan Timotin, Alexey I. Popov, Isabelle Chalendar, Vladimir G. Troitsky, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), University of Alberta, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), and Laboratoire Paul Painlevé (LPP)
Subjects: Discrete mathematics, Zigzag vector, 010102 general mathematics, Invariant subspace, Banach space, Strictly singular operator, 010103 numerical & computational mathematics, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, Linear subspace, Combinatorics, James space, Operator (computer programming), James' space, 0101 mathematics, Invariant (mathematics), ComputingMilieux_MISCELLANEOUS, Analysis, Subspace topology, Mathematics
Abstract: An operator T : X → Y between Banach spaces is said to be finitely strictly singular if for every e > 0 there exists n such that every subspace E ⊆ X with dim E ⩾ n contains a vector x such that ‖ T x ‖ e ‖ x ‖ . We show that, for 1 ⩽ p q ∞ , the formal inclusion operator from J p to J q is finitely strictly singular. As a consequence, we obtain that the strictly singular operator with no invariant subspaces constructed by C. Read is actually finitely strictly singular. These results are deduced from the following fact: if k ⩽ n then every k-dimensional subspace of R n contains a vector x with ‖ x ‖ l ∞ = 1 such that x m i = ( − 1 ) i for some m 1 ⋯ m k .
Published: 2009
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48. On a conjecture on exponential Diophantine equations

Author: Maurice Mignotte, Mihai Cipu, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Institut de Recherche Mathématique Avancée (IRMA), Université Louis Pasteur - Strasbourg I-Centre National de la Recherche Scientifique (CNRS), The first author has been partially supported by the CEEX Program of the Romanian Ministry of Education, Research and Youth, Grant 2-CEx06-11-20/2006, The Simion Stoilow Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania, Université Louis Pasteur, U. F. R. de Math\' ematiques, Rue Ren\' e Descartes, 67084 Strasbourg, and France
Subjects: Algebra and Number Theory, Conjecture, Mathematics - Number Theory, exponential equations, Diophantine equation, Of the form, 11D09, 11D45, 11J20, 11J86, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], Exponential function, Combinatorics, FOS: Mathematics, Number Theory (math.NT), Uniqueness, linear forms in logarithms, Terai's conjecture, Prime power, MSC 11D09, 11D45, 11J20, 11J86, Mathematics
Abstract: We study the solutions of a Diophantine equation of the form $a^x+b^y=c^z$, where $a\equiv 2 \pmod 4$, $b\equiv 3 \pmod 4$ and $\gcd (a,b,c)=1$. The main result is that if there exists a solution $(x,y,z)=(2,2,r)$ with $r>1$ odd then this is the only solution in integers greater than 1, with the possible exception of finitely many values $(c,r)$. We also prove the uniqueness of such a solution if any of $a$, $b$, $c$ is a prime power. In a different vein, we obtain various inequalities that must be satisfied by the components of a putative second solution.
Published: 2009
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49. Allophonie et position dans la syllabe : Indices acoustiques des consonnes latérales

Author: Chitoran, Ioana, Popescu, Andrei, Centre de Linguistique Inter-langues, de Lexicologie, de Linguistique Anglaise et de Corpus (CLILLAC-ARP (EA_3967)), Université Paris Diderot - Paris 7 (UPD7), 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, and Ce travail a bénéficié / bénéficié partiellement d'une aide de l’Etat gérée par l'Agence Nationale de la Recherche au titre du programme 'Investissements d’Avenir' portant la référence ANR-10-LABX-0083
Subjects: [SHS.LANGUE]Humanities and Social Sciences/Linguistics, ComputingMilieux_MISCELLANEOUS
Abstract: International audience
Published: 2016

50. Hilbert series and Lefschetz properties of dimension one almost complete intersections

Author: Alexandru Dimca, Dorin Popescu, Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), 'Simion Stoilow' Institute of Mathematics (IMAR), and Romanian Academy of Sciences
Subjects: Pure mathematics, [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC], Dimension (graph theory), Complete intersection, Commutative Algebra (math.AC), 01 natural sciences, symbols.namesake, Mathematics - Algebraic Geometry, Mathematics::Algebraic Geometry, 0103 physical sciences, FOS: Mathematics, Ideal (ring theory), 0101 mathematics, [MATH]Mathematics [math], Algebraic Geometry (math.AG), Quotient, ComputingMilieux_MISCELLANEOUS, Mathematics, Hilbert–Poincaré series, Algebra and Number Theory, Mathematics::Commutative Algebra, 010102 general mathematics, Mathematics - Commutative Algebra, Jacobian matrix and determinant, symbols, Gravitational singularity, 010307 mathematical physics, Counterexample
Abstract: We generalize some properties related to Hilbert series and Lefschetz properties of Milnor algebras of projective hypersurfaces with isolated singularities to the more general case of an almost complete intersection ideal $J$ of dimension one. When the saturation $I$ of $J$ is a complete intersection, we get explicit formulas for a number of related invariants. New examples of hypersurfaces $V:f=0$ in $P^n$ whose Jacobian ideal $J_f$ satisfies this property and with explicit nontrivial Alexander polynomials are given in any dimension. A Lefschetz type property for the graded quotient $I/J$ is proved for $n=2$ and a counterexample due to A. Conca is given for such a property when $n=3$. Two conjectures are also stated in the paper., v. 2: the major addition is a section on Lefschetz properties in 3 variables
Published: 2016
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