Search

Your search keyword '"Mathématiques ' showing total 80,208 results
Start Over Author "Mathématiques

Refine your results

more »

more »

more »

more »

more »

more »
80,208 results on '"Mathématiques '

3. Weak solutions to Neumann discrete nonlinear system of Kirchhoff type

Author

Rodrigue Sanou, Idrissa Ibrango, Blaise Koné, and Laboratoire d’analyse Mathématiques et d’Informatique (LaMI), Institut des Sciences Exactes et Appliquées, Université Joseph KI-Zerbo, Ouagadougou, Burkina Faso.

Subjects
nonlinear difference equations, anisotropic nonlinear discrete systems, minimization methods, weak solutions, Mathematics, QA1-939
Abstract

We prove the existence of weak solutions for discrete nonlinear system of Kirchhoff type. We build some Hilbert spaces with suitable norms. We define the notion of weak solution corresponding to the problem (1.1). The proof of the main result is based on a minimization method of an energy functional J.

Published
2019
Full Text
View/download PDF

4. The Advantage of Regularizing a Specific Elliptical Problem by the Truncation and Mollification Methods

Author

YAMEOGO Pierre Claver and Dr. En Mathématiques

Abstract

The try to prove the importance and advantage of using the truncation method and the mollification method to regularize an ill-posed elliptical problem. To find appropriate solutions, we will try to calculate the difference between the original solution and the approximate solution. We give a concrete example to see how to apply the theoretical results developed in this search.

Published
2023
Full Text
View/download PDF

5. NUMERICAL BLOW-UP ON WHOLE DOMAIN FOR A QUASILINEAR PARABOLIC EQUATION WITH NONLINEAR BOUNDARY CONDITION

Author

Mathurin M. Taha, Ardjouma Ganon, Départementdemathématiquesetinformatiqueinstitutnationalpolytechniquehouphouët-Boignyumri Mathématiques Etnouvellestechnologies De L’Informationyamoussoukro, Bp , Côte D’Ivoire, and Augustin Kidjegbo Toure

Subjects
General Mathematics, Mathematical analysis, Nonlinear boundary conditions, Domain (mathematical analysis), Mathematics
Published
2020

6. Optimal shape design for navier-strokes flow

Author

Universidad de Sevilla, C.N.R.S. et Laboratorie de Mathématiques Appliquées, Bello, Juan A., Fernandez-Cara, Enrique, Simon, Jacques, Thoma, M., editor, Wyner, W., editor, Davisson, L. D., editor, MacFarlane, A. G. J., editor, Kwakernaak, H., editor, Massey, J. L., editor, Tsypkin, Ya Z., editor, Viterbi, A. J., editor, and Kall, Peter, editor

Published
1992
Full Text
View/download PDF

7. Augmentations des sous-variétés legendriennes: invariants associés et applications

Author

Chantraine, Baptiste, Mathématiques, Jean, 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), Université de Nantes - Faculté des Sciences et Techniques, and Barraud, Jean-Fraçois

Subjects
Sous-variétés legendriennes et lagrangienne, Legendrian and Lagrangian sub-manifolds, Floer theory, Augmentations, théorie de Floer, [MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG]
Published
2019

30. Calculs astronomiques byzantins dans le commentaire aux 'Tables Faciles' attribué à Stéphanos d’Alexandrie

Author

Lempire, Jean, Colloque « Pratiques algorithmiques dans les mathématiques pré-algébriques » (projet ANR \\'Algorithmic Deductive Patterns in Pre-Algebraic Mathematics\\'), and UCL - SSH/INCA - Institut des civilisations, arts et lettres

Subjects
Ptolémée, tables astronomiques, Byzance, Stéphanos d, calcul astronomique, algorithmes
Abstract

Après une brève introduction sur les "Tables Faciles" de Ptolémée et sur les commentaires grecs qui y sont consacrés (en particulier ceux de Théon d'Alexandrie), cette communication s'attache aux caractéristiques propres au calcul astronomique byzantin, c'est-à-dire à l'adaptation des procédés de calcul aux coordonnées géographiques de Constantinople. Plusieurs exemples (calculs de la longitude du soleil et de la lune, des syzygies, de l'éclipse lunaire) sont tirés du manuel astronomique attribué à Stéphanos d'Alexandrie (rédigé à Constantinople au début du VIIe siècle); on en détaille les étapes successives: sections chronologiques et conversion de calendriers, emploi des tables ptoléméennes, algorithmes respectant le modèle géométrique de Ptolémée, tableaux de calculs.

Published
2014

31. Sets of range uniqueness in p-adic fields

Author

Escassut, Alain, Boussaf, Kamal, De Mathématiques Umr 6620 Université Blaise Pascal, Laboratoire, Boutabaa, Abdelbaki, Laboratoire de Mathématiques Blaise Pascal (LMBP), and Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
sets of range uniqueness, p-adic analytic functions, ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
Abstract

International audience

Published
2007

33. La fréquence des variétés de blé dans le paysage cultivé influence leur niveau de résistance observé

Author

Papaix, Julien, Du Cheyron, P., Goyeau, Henriette, Monod, Hervé, Lannou, Christian, Unité de recherche Mathématiques et Informatique Appliquées, ., ARVALIS - Institut du Végétal, ., Unité de biométrie et intelligence artificielle de jouy, Institut National de la Recherche Agronomique (INRA), ARVALIS - Institut du végétal [Paris], BIOlogie et GEstion des Risques en agriculture (BIOGER), and Institut National de la Recherche Agronomique (INRA)-AgroParisTech

Subjects
résistance quantitative, épidémiologie du paysage, [INFO]Computer Science [cs], puccinia triticina, modélisation bayesienne, [MATH]Mathematics [math], ComputingMilieux_MISCELLANEOUS
Abstract

National audience

Published
2010

34. Optimal shape design for navier-strokes flow

Author

Juan A. Bello, Enrique Fernández-Cara, Jacques Simon, and C.N.R.S. et Laboratorie de Mathématiques Appliquées

Subjects
Physics::Fluid Dynamics, Flow (mathematics), Drag, Hadamard transform, Computation, Total derivative, Mathematical analysis, Shape optimization, Vector field, Stokes flow, Mathematics
Abstract

The computation of optimal profiles, i.e. those minimizing the drag, has been investigated by several suthors. frequently, the drag has been approximated by the viscous energy which is dissipated in the fluid. For instance, O. Pironneau computes in [9,10] the “derivative” of this quantity adapting Hadamard’s normal variations techniques. F. Murat and J. Simon use in [6] formal calculus to deduce an expression for the derivative. More recently, J. Simon has considered the problem from a rigorous viewpoint in the case of a Stokes flow (cf. [13]). See als [4], for some theoretical and numerical considerations. This paper deals with optimal profiles in Navier-Stokes regime. Let us introduce an initital body Δ and assume that an admissible variation of Δ is represented by a vector field u. We prove that the mapping u→J(Δ+u), where J(Δ+u) is the energy sssociated to the body Δ+u, is Frechet-differentiable. We also apply some results from [11] to the computation of the derivative.

Published
2007

37. Modèles fondamentaux pour l'écologie

Author

Jolivet, E., Département de Mathématiques Appliquées, ., Direction scientifique sciences économiques et sociales pour l'agriculture et l'agro-alimentaire et methodes d'étude des systèmes (SESAMES), Institut National de la Recherche Agronomique (INRA), École polytechnique (X), and ProdInra, Migration

Subjects
[SDV] Life Sciences [q-bio], BIOLOGIE DES POPULATIONS, [SDV]Life Sciences [q-bio]
Abstract

Majeure d'Eco-Science*INRA, Centre de Paris Diffusion du document : INRA, Centre de Paris

Published
1997

38. Algebras and Orders

Author

Gert Sabidussi, I. G. Rosenberg, and Séminaire de mathématiques supérieures on Algebras

Subjects
Discrete mathematics, Fleischer, Clone (algebra), Completeness (order theory), Order (group theory), Arithmetic function, Affine transformation, Algebraic number, First-order logic, Mathematics
Abstract

Preface. Partial Algebras - An Introductory Survey P. Burmeister. Duality Theory on Ten Dollars a Day B.A. Davey. Algebraic Ordered Sets and their Generalizations M. Erne. A Boolean Formalization of Predicate Calculus I. Fleischer. Lectures on Free Lattices R. Freese. A Survey of Boolean Algebras with Operators B. Jonsson. Essentially Minimal Groupoids H. Machida, I.G. Rosenberg. Functional and Affine Completeness and Arithmetical Varieties A.F. Pixley. Reading, Drawing, and Order I. Rival. Hyperidentities D. Schweigert. Abstract Clone Theory W. Taylor. Now Alouette Knows It All. Index.

Published
1993

39. Shape Optimization and Free Boundaries

Author

Optimization Séminaire de mathématiques supérieures on Shape, Free Boundaries, Michel C. Delfour, and Gert Sabidussi

Subjects
Mathematical theory, Variational inequality, Attractor, Mathematical analysis, Boundary (topology), Shape optimization, Aerodynamics, Differentiable function, Diffusion (business), Mathematics
Abstract

Boundary problems in geochemistry, J. Chadam shape derivatives and differentiability of min max, M.C. Delfour some free boundary problems with industrial applications, A. Fasano problemes de surfaces libres en mecanique des fluides, M. Fortin numerical structural optimization via a relaxed formulation, R.V. Kohn optimal shape design with applications to aerodynamics, O. Pironneau approximation and localization of attractors, K. Promislow and R. Temam shape sensitivity analysis of variational inequalities, J. Sokolowski diffusion with strong absorption, I. Stakgold an introduction to the mathematical theory of the porous medium equation, J.L. Vazquez asymptotic behaviour near extinction points for a semilinear equation with strong absorption, J.J.L. Velazquez introduction to shape optimization problems and free boundary problems, J. -P. Zolesio.

Published
1992

40. Quantum field theory in the large <f>N</f> limit: a review

Author

Moshe, Moshe and Zinn-Justin, 2</f>CEA/Saclay F-91191 Gif-sur-Yvette Cédex, France##Institut de Mathématiques de Jussieu–Chevaleret, Université de Paris VII, France

Subjects
*QUANTUM field theory, *QUANTUM theory, *DYNAMICS, *FIELD theory (Physics)
Abstract

We review the solutions of O(N) and U(N) quantum field theories in the large N limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large N, the method relies on constructing effective field theories for composite fields after integration over the original degrees of freedom. We first solve a general scalar U(φ2) field theory for N large and discuss various non-perturbative physical issues such as critical behaviour. We show how large N results can also be obtained from variational calculations. We illustrate these ideas by showing that the large N expansion allows to relate the (φ2)2 theory and the non-linear σ-model, models which are renormalizable in different dimensions. Similarly, a relation between CP(N−1) and abelian Higgs models is exhibited. Large N techniques also allow solving self-interacting fermion models. A relation between the Gross–Neveu, a theory with a four-fermi self-interaction, and a Yukawa-type theory renormalizable in four dimensions then follows. We discuss dissipative dynamics, which is relevant to the approach to equilibrium, and which in some formulation exhibits quantum mechanics supersymmetry. This also serves as an introduction to the study of the 3D supersymmetric quantum field theory. Large N methods are useful in problems that involve a crossover between different dimensions. We thus briefly discuss finite size effects, finite temperature scalar and supersymmetric field theories. We also use large N methods to investigate the weakly interacting Bose gas. The solution of the general scalar U(φ2) field theory is then applied to other issues like tricritical behaviour and double scaling limit. [Copyright &y& Elsevier]

Published
2003
Full Text
View/download PDF

41. Normal forms of hyperbolic logarithmic transseries

Author

D. Peran, M. Resman, J.P. Rolin, T. Servi, Department of Mathematics [Zagreb], Faculty of Science [Zagreb], University of Zagreb-University of Zagreb, Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), and Servi, Tamara

Subjects
Applied Mathematics, Mathematics::History and Overview, FOS: Mathematics, fixed point theory, formal normal forms, hyperbolic fixed point, Koenigs sequence, linearization, logarithmic transseries, [MATH] Mathematics [math], Dynamical Systems (math.DS), Mathematics - Dynamical Systems, [MATH]Mathematics [math], 34C20, 37C25, 47H10, 39B12, 46A19, 26A12, 12J15, Analysis
Abstract

We find the normal forms of hyperbolic logarithmic transseries with respect to parabolic logarithmic normalizing changes of variables. We provide a necessary and sufficient condition on such transseries for the normal form to be linear. The normalizing transformations are obtained via fixed point theorems, and are given algorithmically, as limits of Picard sequences in appropriate topologies., Comment: 33 pages, 0 figures

Published
2023

42. Non-identifiability visualisation algorithms

Author

Munier, Nathanaël, Soubies, Emmanuel, Weiss, Pierre, Institut de Mathématiques de Toulouse UMR5219 (IMT), 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), Centre de Biologie Intégrative (CBI), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Groupe de Recherche et d'Etudes de Traitement du Signal et des Images, ANR-21-CE48-0008,MICROBLIND,Problèmes inverses aveugles et microscopie optique(2021), and ANR-11-LABX-0040,CIMI,Centre International de Mathématiques et d'Informatique (de Toulouse)(2011)

Subjects
Problème inverse, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], Identifiabilité, [INFO]Computer Science [cs], [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Abstract

International audience; The identification of a set of parameters x from observed data y is often reduced to the resolution of a problem of the type f(x) = y, where f is a continuous application. This equation appears in domains such as (blind) inverse problems, data assimilation, or optimal control. When the solution is not unique, it may be important to inform the user about the set of plausible solutions. We propose here an algorithm to locally describe a set of solutions of this equation. It is essentially based on automatic differentiation and on a local parameterization of the solution manifold. We illustrate the interest of this approach on two toy examples.; L'identification d'un ensemble de paramètres x à partir de données observées y est souvent réduite à la résolution d'un problème du type f(x) = y, où f est une application continue. Cette équation apparaît dans des domaines tels que les problèmes inverses (aveugles), l'assimilation de données ou encore le contrôle optimal. Lorsque la solution n'est pas unique, il peut être important d'en informer l'utilisateur et de le renseigner sur l'ensemble des solutions plausibles. Nous proposons ici un algorithme permettant de décrire localement un ensemble de solutions de cette équation. Il repose essentiellement sur la différentiation automatique et sur une paramétrisation locale de la variété des solutions. Nous illustrons l'intérêt de cette approche sur deux exemples jouets.

Published
2023

43. One-Shot Federated Conformal Prediction

Author

Humbert, Pierre, Bars, Batiste Le, Bellet, Aurélien, Arlot, Sylvain, Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Statistique mathématique et apprentissage (CELESTE), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Machine Learning in Information Networks (MAGNET), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), ANR-20-CE23-0015,PRIDE,Apprentissage automatique décentralisé et préservant la vie privée(2020), Laboratoire de Mathématiques d'Orsay [LMO], Statistique mathématique et apprentissage [CELESTE], Machine Learning in Information Networks [MAGNET], and Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]

Subjects
FOS: Computer and information sciences, [STAT]Statistics [stat], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, Machine Learning (stat.ML)
Abstract

International audience; In this paper, we introduce a conformal prediction method to construct prediction sets in a oneshot federated learning setting. More specifically, we define a quantile-of-quantiles estimator and prove that for any distribution, it is possible to output prediction sets with desired coverage in only one round of communication. To mitigate privacy issues, we also describe a locally differentially private version of our estimator. Finally, over a wide range of experiments, we show that our method returns prediction sets with coverage and length very similar to those obtained in a centralized setting. Overall, these results demonstrate that our method is particularly well-suited to perform conformal predictions in a one-shot federated learning setting.

Published
2023

44. A Quasi Time-Reversible scheme based on density matrix extrapolation on the Grassmann manifold for Born-Oppenheimer Molecular Dynamics

Author

Pes, Federica, Mazzeo, Patrizia, Lipparini, Filippo, Polack, Etienne, Dusson, Geneviève, Stamm, Benjamin, Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC), Simons Targeted Grant Award No. 89663, Italian Ministry of University and Research, grant 2020HT-SXMA 002 (PSI-MOVIE), DFG, under Germany’s Excellence Strategy – EXC 2075 – 390740016, ANR-15-IDEX-0003,BFC,ISITE ' BFC(2015), and European Project: 810367,EMC2(2019)

Subjects
Chemical Physics (physics.chem-ph), Physics - Chemical Physics, Soft Condensed Matter (cond-mat.soft), FOS: Physical sciences, [PHYS.PHYS.PHYS-CHEM-PH]Physics [physics]/Physics [physics]/Chemical Physics [physics.chem-ph], Condensed Matter - Soft Condensed Matter
Abstract

This article proposes a so-called Quasi Time-Reversible (QTR G-Ext) scheme based on Grassmann extrapolation of density matrices for an accurate calculation of initial guesses in Born-Oppenheimer Molecular Dynamics simulations. The method shows excellent results on four large molecular systems, ranging from 21 to 94 atoms simulated with Kohn-Sham density functional theory surrounded with a classical environment with 6k to 16k atoms. Namely, it clearly reduces the number of self-consistent field iterations, while keeping a similar energy drift as in the extended Lagrangian Born-Oppenheimer method.

Published
2023

45. The Coble Quadric

Author

Benedetti, Vladimiro, Faenzi, Daniele, Bolognesi, Michele, Manivel, L, Institut de Mathématiques de Bourgogne [Dijon] (IMB), Université de Bourgogne (UB)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 (IMT), 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), Feder Bourgogne, Région Bourgogne-Franche-Comté, ANR-20-CE40-0023,FanoHK,Des variétés de Fano aux hyperkählériennes : géométrie et catégories dérivées(2020), ANR-21-CE40-0017,BRIDGES,Interactions Brésil-France en théorie de jauge, structures extrémales et stabilité(2021), ANR-17-EURE-0002,EIPHI,Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité(2017), Benedetti, Vladimiro, Des variétés de Fano aux hyperkählériennes : géométrie et catégories dérivées - - FanoHK2020 - ANR-20-CE40-0023 - AAPG2020 - VALID, Interactions Brésil-France en théorie de jauge, structures extrémales et stabilité - - BRIDGES2021 - ANR-21-CE40-0017 - AAPG2021 - VALID, and Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité - - EIPHI2017 - ANR-17-EURE-0002 - EURE - VALID

Subjects
Coble hypersurfaces, Mathematics - Algebraic Geometry, degeneracy loci, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], FOS: Mathematics, 14h60, 22E46, Moduli spaces of stable bundles, subvarieties of Grassmannians, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Hecke lines, self-dual hypersurfaces, Algebraic Geometry (math.AG)
Abstract

Given a smooth genus three curve $C$, the moduli space of rank two stable vector bundles on C with trivial determinant embeds in $\mathbb{P}^8$ as a hypersurface whose singular locus is the Kummer threefold of $C$; this hypersurface is the Coble quartic. Gruson, Sam and Weyman realized that this quartic could be constructed from a general skew-symmetric fourform in eight variables. Using the lines contained in the quartic, we prove that a similar construction allows to recover SU$_C(2, L)$, the moduli space of rank two stable vector bundles on C with fixed determinant of odd degree L, as a subvariety of $G(2, 8)$. In fact, each point $p \in C$ defines a natural embedding of SU$_C(2, \mathcal{O}(p))$ in $G(2, 8)$. We show that, for the generic such embedding, there exists a unique quadratic section of the Grassmannian which is singular exactly along the image of SU$_C(2, \mathcal{O}(p))$, and thus deserves to be coined the Coble quadric of the pointed curve $(C, p)$.

Published
2023

46. Construction and analysis of a HDG+ method for the diffusive-flux formulation of the convected Helmholtz equation

Author

Barucq, Hélène, Rouxelin, Nathan, Tordeux, Sébastien, Modélisation et simulation de la propagation des ondes fondées sur des mesures expérimentales pour caractériser des milieux géophysiques et héliophysiques et concevoir des objets complexes (MAKUTU), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Polytechnique de Bordeaux (Bordeaux INP), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), and Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)

Subjects
harmonic regime, Hybridizable Discontinuous Galerkin Method (HDG), aeroacoustics, error analysis, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], convected Helmholtz equation
Abstract

We construct HDG methods based on the diffusive flux formulation of the convected acoustic wave equation.We mostly describe the HDG+ method which involves different polynomial degrees for approximating the unknowns, hence leading to a more efficient method with a super-convergencelike behaviour. A detailed analysis of the methods including local and global well-posedness, as well as convergence estimates is carried out. The HDG+ method is also compared with a more conventional HDG method to demonstrate its effectiveness.

Published
2023

47. Transport-entropy forms of direct and Converseblaschke-Santal{\'o} inequalities

Author

Fradelizi, Matthieu, Gozlan, Nathael, Sadovsky, Shay, Zugmeyer, Simon, Laboratoire Analyse et Mathématiques Appliquées (LAMA), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), School of Mathematical Sciences [Tel Aviv] (TAU), Raymond and Beverly Sackler Faculty of Exact Sciences [Tel Aviv] (TAU), Tel Aviv University (TAU)-Tel Aviv University (TAU), Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), and The first and second named author are supported by a grant of the Simone and Cino Del Duca foundation.

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mathematics - Functional Analysis, Mahler conjecture, Optimal Transport, Probability (math.PR), FOS: Mathematics, 52A20, 52A40, 60E15, Talagrand’s transport inequality, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], Mathematics - Probability, Blaschke-Santaló inequality, Functional Analysis (math.FA)
Abstract

We explore alternative functional or transport-entropy formulations of the Blaschke-Santal{\'o} inequality and of its conjectured counterpart due to Mahler. In particular, we obtain new direct and reverse Blaschke-Santal{\'o} inequalities for s-concave functions. We also obtain new sharp symmetrized transport-entropy inequalities for a large class of spherically invariant probability measures, including the uniform measure on the unit Euclidean sphere and generalized Cauchy and Barenblatt distributions. Finally, we show that the Mahler's conjecture is equivalent to some reinforced log-Sobolev type inequality on the sphere.

Published
2023

48. Reduced basis method for non-symmetric eigenvalue problems: application to the multigroup neutron diffusion equations

Author

Conjungo Taumhas, Yonah, Dusson, Geneviève, Ehrlacher, Virginie, Lelièvre, Tony, Madiot, François, Service d’Études des Réacteurs et de Mathématiques Appliquées (SERMA), Département de Modélisation des Systèmes et Structures (DM2S), CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC), MATHematics for MatERIALS (MATHERIALS), École des Ponts ParisTech (ENPC)-École des Ponts ParisTech (ENPC)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), ANR-15-IDEX-0003,BFC,ISITE ' BFC(2015), and European Project: 810367,EMC2(2019)

Subjects
FOS: Mathematics, Numerical Analysis (math.NA), Mathematics - Numerical Analysis, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

In this article, we propose a reduced basis method for parametrized non-symmetric eigenvalue problems arising in the loading pattern optimization of a nuclear core in neutronics. To this end, we derive a posteriori error estimates for the eigenvalue and left and right eigenvectors. The practical computation of these estimators requires the estimation of a constant called prefactor, which we can express as the spectral norm of some operator. We provide some elements of theoretical analysis which illustrate the link between the expression of the prefactor we obtain here and its well-known expression in the case of symmetric eigenvalue problems, either using the notion of numerical range of the operator, or via a perturbative analysis. Lastly, we propose a practical method in order to estimate this prefactor which yields interesting numerical results on actual test cases. We provide detailed numerical simulations on two-dimensional examples including a multigroup neutron diffusion equation.

Published
2023

49. Convergence rate of entropy-regularized multi-marginal optimal transport costs

Author

Nenna, Luca, Pegon, Paul, Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales (MOKAPLAN), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and ANR-11-LABX-0056,LMH,LabEx Mathématique Hadamard(2011)

Subjects
Primary: 49Q22, Secondary: 49N15, 94A17, 49K40, Entropic regularization, Schrödinger problem, Multi-marginal optimal transport, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], Functional Analysis (math.FA), Convex analysis, Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, Optimization and Control (math.OC), Optimal transport, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Optimization and Control, 49Q22, 49N15, 94A17, 49K40, Analysis of PDEs (math.AP)
Abstract

We investigate the convergence rate of multi-marginal optimal transport costs that are regularized with the Boltzmann-Shannon entropy, as the noise parameter $\varepsilon$ tends to $0$. We establish lower and upper bounds on the difference with the unregularized cost of the form $C\varepsilon\log(1/\varepsilon)+O(\varepsilon)$ for some explicit dimensional constants $C$ depending on the marginals and on the ground cost, but not on the optimal transport plans themselves. Upper bounds are obtained for Lipschitz costs or locally semi-concave costs for a finer estimate, and lower bounds for $\mathcal{C}^2$ costs satisfying some signature condition on the mixed second derivatives that may include degenerate costs, thus generalizing results previously in the two marginals case and for non-degenerate costs. We obtain in particular matching bounds in some typical situations where the optimal plan is deterministic.

Published
2023

50. On Markov intertwining relations and primal conditioning

Author

Arnaudon, Marc, Coulibaly-Pasquier, Koléhè, Miclo, Laurent, 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), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 (IMT), 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 AFOSR-22IOE016

Subjects
Algebraic and probabilistic Markov intertwining relations, MSC2020: primary: 60J10, secondary: 15B51, Doob transform, discrete Pitman intertwining, top-to-random shuffle, subset conditioning, [MATH]Mathematics [math], birth-and-death Markov chains, strong stationary times
Abstract

Given an intertwining relation between two finite Markov chains, we investigate how it can be transformed by conditioning the primal Markov chain to stay in a proper subset. A natural assumption on the underlying link kernel is put forward. The three classical examples of discrete Pitman, top-torandom shuffle and absorbed birth-and-death chain intertwinings serve as illustrations.

Published
2023

Catalog

Books, media, physical & digital resources
See catalog results