Laboratoire de Mathématiques de Besançon (Besançon)
Overview
Works:  48 works in 82 publications in 2 languages and 84 library holdings 

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Most widely held works by
Laboratoire de Mathématiques de Besançon (Besançon)
Algèbre et théorie des nombres : 2020 by
Université de FrancheComté(
Book
)
3 editions published in 2016 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 2016 in English and held by 4 WorldCat member libraries worldwide
Méthode nonparamétrique des noyaux associés mixtes et applications by
Francial Giscard Baudin Libengue Dobelekpoka(
Book
)
2 editions published in 2013 in French and held by 2 WorldCat member libraries worldwide
Nous présentons dans cette thèse, l'approche nonparamétrique par noyaux associés mixtes, pour les densités àsupports partiellement continus et discrets. Nous commençons par rappeler d'abord les notions essentielles d'estimationpar noyaux continus (classiques) et noyaux associés discrets. Nous donnons la définition et les caractéristiques des estimateurs à noyaux continus (classiques) puis discrets. Nous rappelons aussi les différentes techniques de choix de paramètres de lissage et nous revisitons les problèmes de supports ainsi qu'une résolution des effets de bord dans le casdiscret. Ensuite, nous détaillons la nouvelle méthode d'estimation de densités par les noyaux associés continus, lesquels englobent les noyaux continus (classiques). Nous définissons les noyaux associés continus et nous proposons la méthode modedispersion pour leur construction puis nous illustrons ceci sur les noyaux associés nonclassiques de la littérature à savoir bêta et sa version étendue, gamma et son inverse, gaussien inverse et sa réciproque le noyau de Pareto ainsi que le noyau lognormal. Nous examinons par la suite les propriétés des estimateurs qui en sont issus plusprécisément le biais, la variance et les erreurs quadratiques moyennes ponctuelles et intégrées. Puis, nous proposons un algorithme de réduction de biais que nous illustrons sur ces mêmes noyaux associés nonclassiques. Des études par simulations sont faites sur trois types d'estimateurs à noyaux lognormaux. Par ailleurs, nous étudions les comportements asymptotiques des estimateurs de densité à noyaux associés continus. Nous montrons d'abord les consistances faibles et fortes ainsi que la normalité asymptotique ponctuelle. Ensuite nous présentons les résultats des consistances faibles et fortes globales en utilisant les normes uniformes et L1. Nous illustrons ceci sur trois types d'estimateurs à noyaux lognormaux. Par la suite, nous étudions les propriétés minimax des estimateurs à noyaux associés continus. Nous décrivons d'abord le modèle puis nous donnons les hypothèses techniques avec lesquelles noustravaillons. Nous présentons ensuite nos résultats minimax tout en les appliquant sur les noyaux associés nonclassiquesbêta, gamma et lognormal. Enfin, nous combinons les noyaux associés continus et discrets pour définir les noyauxassociés mixtes. De là, les outils d'unification d'analyses discrètes et continues sont utilisés, pour montrer les différentespropriétés des estimateurs à noyaux associés mixtes. Une application sur un modèle de mélange des lois normales et de Poisson tronquées est aussi donnée. Tout au long de ce travail, nous choisissons le paramètre de lissage uniquementavec la méthode de validation croisée par les moindres carrés
2 editions published in 2013 in French and held by 2 WorldCat member libraries worldwide
Nous présentons dans cette thèse, l'approche nonparamétrique par noyaux associés mixtes, pour les densités àsupports partiellement continus et discrets. Nous commençons par rappeler d'abord les notions essentielles d'estimationpar noyaux continus (classiques) et noyaux associés discrets. Nous donnons la définition et les caractéristiques des estimateurs à noyaux continus (classiques) puis discrets. Nous rappelons aussi les différentes techniques de choix de paramètres de lissage et nous revisitons les problèmes de supports ainsi qu'une résolution des effets de bord dans le casdiscret. Ensuite, nous détaillons la nouvelle méthode d'estimation de densités par les noyaux associés continus, lesquels englobent les noyaux continus (classiques). Nous définissons les noyaux associés continus et nous proposons la méthode modedispersion pour leur construction puis nous illustrons ceci sur les noyaux associés nonclassiques de la littérature à savoir bêta et sa version étendue, gamma et son inverse, gaussien inverse et sa réciproque le noyau de Pareto ainsi que le noyau lognormal. Nous examinons par la suite les propriétés des estimateurs qui en sont issus plusprécisément le biais, la variance et les erreurs quadratiques moyennes ponctuelles et intégrées. Puis, nous proposons un algorithme de réduction de biais que nous illustrons sur ces mêmes noyaux associés nonclassiques. Des études par simulations sont faites sur trois types d'estimateurs à noyaux lognormaux. Par ailleurs, nous étudions les comportements asymptotiques des estimateurs de densité à noyaux associés continus. Nous montrons d'abord les consistances faibles et fortes ainsi que la normalité asymptotique ponctuelle. Ensuite nous présentons les résultats des consistances faibles et fortes globales en utilisant les normes uniformes et L1. Nous illustrons ceci sur trois types d'estimateurs à noyaux lognormaux. Par la suite, nous étudions les propriétés minimax des estimateurs à noyaux associés continus. Nous décrivons d'abord le modèle puis nous donnons les hypothèses techniques avec lesquelles noustravaillons. Nous présentons ensuite nos résultats minimax tout en les appliquant sur les noyaux associés nonclassiquesbêta, gamma et lognormal. Enfin, nous combinons les noyaux associés continus et discrets pour définir les noyauxassociés mixtes. De là, les outils d'unification d'analyses discrètes et continues sont utilisés, pour montrer les différentespropriétés des estimateurs à noyaux associés mixtes. Une application sur un modèle de mélange des lois normales et de Poisson tronquées est aussi donnée. Tout au long de ce travail, nous choisissons le paramètre de lissage uniquementavec la méthode de validation croisée par les moindres carrés
Calculs explicites en théorie d'Iwasawa by
Firmin Varescon(
)
2 editions published in 2014 in French and held by 2 WorldCat member libraries worldwide
In the first chapter of this thesis we explain Leopoldt's conjecture and some equivalent formulations. Then we give an algorithm that checks this conjecture for a given prime p and a number field. Next we assume that this conjecture is true, and we study the torsion part of the Galois group of the maximal abelian pramified pextension of a given number field. We present a method to compute the invariant factors of this finite group. In the third chapter we give an interpretation of our numrical result by heuristics “à la” CohenLenstra. In the fourth and last chapter, using our algorithm which computes this torsion submodule, we give new examples of numbers fields which satisfy Greenberg's conjecture
2 editions published in 2014 in French and held by 2 WorldCat member libraries worldwide
In the first chapter of this thesis we explain Leopoldt's conjecture and some equivalent formulations. Then we give an algorithm that checks this conjecture for a given prime p and a number field. Next we assume that this conjecture is true, and we study the torsion part of the Galois group of the maximal abelian pramified pextension of a given number field. We present a method to compute the invariant factors of this finite group. In the third chapter we give an interpretation of our numrical result by heuristics “à la” CohenLenstra. In the fourth and last chapter, using our algorithm which computes this torsion submodule, we give new examples of numbers fields which satisfy Greenberg's conjecture
Etude des Espaces Lipschitzlibres by
Aude Dalet(
)
2 editions published in 2015 in French and held by 2 WorldCat member libraries worldwide
Godefroy and Ozawa have proved that there exists a compact space with a free space failing the approximation property. Then it is natural to ask what are the metric spaces whose freespace has the bounded approximation property. Grothendieck has proved that a separable Banach space with the approximation property has the metric approximation property. This result justifies why it is interesting to know whether a free space is a dual space. The first chapter is dedicated to duality. First we introduce a result to prove that a Banach space is a dual space, under some conditions. Then we explain how to use it in the context offree spaces and finally we apply it to countable or ultrametric proper metric spaces.In the second chapter, we study the metric approximation property of free spaces overcountable proper metric spaces.In the third chapter, ultrametric spaces are investigated. We prove first that the free spaceover a proper ultrametric space has the metric approximation property, is isomorphic to l1 andadmits a predual isomorphic to c0. Finally, in collaboration with P. Kaufmann et A. Proch`azka,we prove that the free space over a ultrametric space is never isometric to l1 and we generalizethis result to some subsets of separable Rtrees
2 editions published in 2015 in French and held by 2 WorldCat member libraries worldwide
Godefroy and Ozawa have proved that there exists a compact space with a free space failing the approximation property. Then it is natural to ask what are the metric spaces whose freespace has the bounded approximation property. Grothendieck has proved that a separable Banach space with the approximation property has the metric approximation property. This result justifies why it is interesting to know whether a free space is a dual space. The first chapter is dedicated to duality. First we introduce a result to prove that a Banach space is a dual space, under some conditions. Then we explain how to use it in the context offree spaces and finally we apply it to countable or ultrametric proper metric spaces.In the second chapter, we study the metric approximation property of free spaces overcountable proper metric spaces.In the third chapter, ultrametric spaces are investigated. We prove first that the free spaceover a proper ultrametric space has the metric approximation property, is isomorphic to l1 andadmits a predual isomorphic to c0. Finally, in collaboration with P. Kaufmann et A. Proch`azka,we prove that the free space over a ultrametric space is never isometric to l1 and we generalizethis result to some subsets of separable Rtrees
Existence non existence et multiplicité d'ondes stationnaires normalisées pour quelques équations non linéaires elliptiques by
Tingjian Luo(
Book
)
2 editions published in 2013 in English and held by 2 WorldCat member libraries worldwide
In this thesis, we study the existence, nonexistence and multiplicity of standing waves withprescribed norms for two types of nonlinear elliptic partial differential equations arisingfrom various physical models. The orbital stability of the standing waves is also discussedin some cases. The main ingredients of our proofs are variational arguments. The solutionsare found as critical points of an associated functional on a constraint.The thesis consists of seven chapters. Chapter 1 is the Introduction of the thesis.In Chapters 2 to 4, we study a class of nonlinear SchrödingerPoissonSlater equations.We establish in Chapter 2 sharp nonexistence results of least energy solutions having aprescribed L2norm. In Chapter 3 we prove an existence result for L2normalized solutions,in a situation where the associated functional is unbounded from below on the constraint.Our solutions are found as saddle points of the functional but they correspond to leastenergy solutions. We also prove that the associated standing waves are orbitally unstable.Here a key feature is that, since our suspected critical points are not global minimizers, itis not possible to use in a standard way the machinery of compactness by concentrationdeveloped by P. L. Lions. Then, in Chapter 4, we prove that under the assumptions ofChapter 3, there do exist infinitely many solutions having a prescribed L2norm. In thefollowing two chapters, we investigate a class of quasilinear Schrödinger equations. Sharpnonexistence results of least energy solutions are given in Chapter 5. In Chapter 6 weprove the existence of two positive solutions having a given norm. One of them, is relativeto the L2norm constraint, of saddle point type. The other one is a minimum, either localor global. The fact that the natural functional associated with this equation is not welldefined requires the use of a perturbation approach to obtain these two critical points.Finally, in Chapter 7 we mention some questions that this thesis has raised
2 editions published in 2013 in English and held by 2 WorldCat member libraries worldwide
In this thesis, we study the existence, nonexistence and multiplicity of standing waves withprescribed norms for two types of nonlinear elliptic partial differential equations arisingfrom various physical models. The orbital stability of the standing waves is also discussedin some cases. The main ingredients of our proofs are variational arguments. The solutionsare found as critical points of an associated functional on a constraint.The thesis consists of seven chapters. Chapter 1 is the Introduction of the thesis.In Chapters 2 to 4, we study a class of nonlinear SchrödingerPoissonSlater equations.We establish in Chapter 2 sharp nonexistence results of least energy solutions having aprescribed L2norm. In Chapter 3 we prove an existence result for L2normalized solutions,in a situation where the associated functional is unbounded from below on the constraint.Our solutions are found as saddle points of the functional but they correspond to leastenergy solutions. We also prove that the associated standing waves are orbitally unstable.Here a key feature is that, since our suspected critical points are not global minimizers, itis not possible to use in a standard way the machinery of compactness by concentrationdeveloped by P. L. Lions. Then, in Chapter 4, we prove that under the assumptions ofChapter 3, there do exist infinitely many solutions having a prescribed L2norm. In thefollowing two chapters, we investigate a class of quasilinear Schrödinger equations. Sharpnonexistence results of least energy solutions are given in Chapter 5. In Chapter 6 weprove the existence of two positive solutions having a given norm. One of them, is relativeto the L2norm constraint, of saddle point type. The other one is a minimum, either localor global. The fact that the natural functional associated with this equation is not welldefined requires the use of a perturbation approach to obtain these two critical points.Finally, in Chapter 7 we mention some questions that this thesis has raised
Aspects explicites des fonctions L et applications by
Charlotte Euvrard(
)
2 editions published in 2016 in French and held by 2 WorldCat member libraries worldwide
This thesis focuses on Lfunctions, their explicit aspects and their applications.In the first chapter, we give a precise definition of Lfunctions and their main properties, especially about the invariants called local parameters. Then, we deal with Artin Lfunctions. For them, we have created a computer program in PARI/GP which gives the coefficients and the invariants for an Artin Lfunction above Q.In the second chapter, we make explicit a theorem of Henryk Iwaniec and Emmanuel Kowalski, which distinguishes between two Lfunctions by considering their local parameters for primes up to a theoretical bound.Actually, distinguishing between sums of local parameters of Artin Lfunctions is the same as separating the associated characters by the Frobenius automorphism. This is the subject of the third chapter, that can be related to Chebotarev Theorem. By applying the result to conjugate characters of the alternating group, we get a bound for a prime p giving the factorization modulo $p$ of a certain polynomial. This work has to be compared with a result from Joël Bellaïche (2013).Finally, we numerically illustrate our results by studying the evolution of the bound on polynomials X^n+uX+v, for n=5, 7 and 13
2 editions published in 2016 in French and held by 2 WorldCat member libraries worldwide
This thesis focuses on Lfunctions, their explicit aspects and their applications.In the first chapter, we give a precise definition of Lfunctions and their main properties, especially about the invariants called local parameters. Then, we deal with Artin Lfunctions. For them, we have created a computer program in PARI/GP which gives the coefficients and the invariants for an Artin Lfunction above Q.In the second chapter, we make explicit a theorem of Henryk Iwaniec and Emmanuel Kowalski, which distinguishes between two Lfunctions by considering their local parameters for primes up to a theoretical bound.Actually, distinguishing between sums of local parameters of Artin Lfunctions is the same as separating the associated characters by the Frobenius automorphism. This is the subject of the third chapter, that can be related to Chebotarev Theorem. By applying the result to conjugate characters of the alternating group, we get a bound for a prime p giving the factorization modulo $p$ of a certain polynomial. This work has to be compared with a result from Joël Bellaïche (2013).Finally, we numerically illustrate our results by studying the evolution of the bound on polynomials X^n+uX+v, for n=5, 7 and 13
Caractérisations des modèles multivariés de stablesTweedie multiples by
Cyrille clovis Moypemna sembona(
)
2 editions published in 2016 in French and held by 2 WorldCat member libraries worldwide
In the framework of natural exponential families, this thesis proposes differents characterizations of multivariate multiple stablesTweedie under "steepness" property. These models appeared in 2014 in the literature were first introduced and described in a restricted form of the normal stablesTweedie models before extensions to multiple cases. They are composed by a fixed univariate stableTweedie variable having a positive domain, and the remaining random variables given the fixed one are reals independent stablesTweedie variables, possibly different, with the same dispersion parameter equal to the fixed component. The corresponding normal stablesTweedie models have a fixed univariate stableTweedie and all the others are reals Gaussian variables. Through special cases such that normal, Poisson, gamma, inverse Gaussian, multiple stablesTweedie models are very common in applied probability and statistical studies. We first characterized the normal stableTweedie through their variances function or covariance matrices expressed in terms of their means vector. According to the power variance parameter values, the nature of polynomials associated with these models is deduced with the properties of the quasi orthogonal, LevySheffer systems, and polynomial recurrence relations. Then, these results allowed us to characterize by function variance the largest class of multiple stablesTweedie. Which led to a new classification, which makes more understandable the family. Finally, a extension characterization of normal stableTweedie by generalized variance function or determinant of variance function have been established via their infinite divisibility property and through the corresponding MongeAmpere equations. Expressed as product of the components of the mean vector with multiple powers parameters reals, the characterization of all multivariate multiple stable Tweedie models by generalized variance function remains an open problem
2 editions published in 2016 in French and held by 2 WorldCat member libraries worldwide
In the framework of natural exponential families, this thesis proposes differents characterizations of multivariate multiple stablesTweedie under "steepness" property. These models appeared in 2014 in the literature were first introduced and described in a restricted form of the normal stablesTweedie models before extensions to multiple cases. They are composed by a fixed univariate stableTweedie variable having a positive domain, and the remaining random variables given the fixed one are reals independent stablesTweedie variables, possibly different, with the same dispersion parameter equal to the fixed component. The corresponding normal stablesTweedie models have a fixed univariate stableTweedie and all the others are reals Gaussian variables. Through special cases such that normal, Poisson, gamma, inverse Gaussian, multiple stablesTweedie models are very common in applied probability and statistical studies. We first characterized the normal stableTweedie through their variances function or covariance matrices expressed in terms of their means vector. According to the power variance parameter values, the nature of polynomials associated with these models is deduced with the properties of the quasi orthogonal, LevySheffer systems, and polynomial recurrence relations. Then, these results allowed us to characterize by function variance the largest class of multiple stablesTweedie. Which led to a new classification, which makes more understandable the family. Finally, a extension characterization of normal stableTweedie by generalized variance function or determinant of variance function have been established via their infinite divisibility property and through the corresponding MongeAmpere equations. Expressed as product of the components of the mean vector with multiple powers parameters reals, the characterization of all multivariate multiple stable Tweedie models by generalized variance function remains an open problem
Algebraic certificates for Budan's theorem by
Daniel Bembé(
Book
)
2 editions published in 2011 in English and held by 2 WorldCat member libraries worldwide
In this work we present two algebraic certificates for Budan's theorem. Budan's theorem claims the following. Let R be an ordered field, f in R[X] of degree n and a,b in R with a<b. Then the number of sign changes in the sequence (f(b),f'(b),...,f^n(b)) is not greater than the number of sign changes in the sequence (f(a),f'(a),...,f^n(a)). This enables us to count real roots in a similar way to the real root counting by Sturm's theorem. (Budan's count of real roots is today known as ``BudanFourier count'' which, indeed, counts so called virtual roots which comprehend the real roots.) An algebraic certificate for Budan's theorem is a certain kind of proof which leads from the negation of the assumption to the contradictory algebraic identity 0>0. The algorithm for our first certificate is based on the historical proof by Budan which uses only combinatorial arguments. It has a complexity exponential in the degree of f. The algorithm for the second certificate is based on mixed Taylor series and shows a smaller complexity: The main calculation is solving a linear system; this is polynomial in the degree of f
2 editions published in 2011 in English and held by 2 WorldCat member libraries worldwide
In this work we present two algebraic certificates for Budan's theorem. Budan's theorem claims the following. Let R be an ordered field, f in R[X] of degree n and a,b in R with a<b. Then the number of sign changes in the sequence (f(b),f'(b),...,f^n(b)) is not greater than the number of sign changes in the sequence (f(a),f'(a),...,f^n(a)). This enables us to count real roots in a similar way to the real root counting by Sturm's theorem. (Budan's count of real roots is today known as ``BudanFourier count'' which, indeed, counts so called virtual roots which comprehend the real roots.) An algebraic certificate for Budan's theorem is a certain kind of proof which leads from the negation of the assumption to the contradictory algebraic identity 0>0. The algorithm for our first certificate is based on the historical proof by Budan which uses only combinatorial arguments. It has a complexity exponential in the degree of f. The algorithm for the second certificate is based on mixed Taylor series and shows a smaller complexity: The main calculation is solving a linear system; this is polynomial in the degree of f
Sur la théorie des représentations et les algèbres d'opérateurs des produits en couronnes libres by
Francois Lemeux(
Book
)
2 editions published in 2014 in French and held by 2 WorldCat member libraries worldwide
In this thesis, we study the combinatorial and operator algebraic properties of certain free compact quantum groups. We prove in chapter 2 that the duals of the quantum reflexion groups have, in most cases, the Haagerup property. In chapter 3, we describe the fusion rules of the free wreath product of a discrete group by the quantum permutation group. To do this, we describe the interrwinner spaces berween certain “basic” corepresentations of these free wreath products in terms of noncrossing partitions decorated by the elements of the group . This provides a whole new class of compact quantum groups whose fusions rules are explicitly computed. We give several applications of this result.We prove that, in most cases, the reduced C*algebras associates with these free wreath products are simple with unique trace. We also prove that the associated II 1 factors are full. To conclude, we extend the result of chapter 2 to the free wreath products of finite groups by the quantum permutation group
2 editions published in 2014 in French and held by 2 WorldCat member libraries worldwide
In this thesis, we study the combinatorial and operator algebraic properties of certain free compact quantum groups. We prove in chapter 2 that the duals of the quantum reflexion groups have, in most cases, the Haagerup property. In chapter 3, we describe the fusion rules of the free wreath product of a discrete group by the quantum permutation group. To do this, we describe the interrwinner spaces berween certain “basic” corepresentations of these free wreath products in terms of noncrossing partitions decorated by the elements of the group . This provides a whole new class of compact quantum groups whose fusions rules are explicitly computed. We give several applications of this result.We prove that, in most cases, the reduced C*algebras associates with these free wreath products are simple with unique trace. We also prove that the associated II 1 factors are full. To conclude, we extend the result of chapter 2 to the free wreath products of finite groups by the quantum permutation group
Détection des changements de points multiples et inférence du modèle autorégressif à seuil by
Mohamed Abdillahi Elmi(
Book
)
2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide
Cette thèse est composée de deux parties: une première partie traite le problème de changement de régime et une deuxième partie concerne le processusautorégressif à seuil dont les innovations ne sont pas indépendantes. Toutefois, ces deux domaines de la statistique et des probabilités se rejoignent dans la littérature et donc dans mon projet de recherche. Dans la première partie, nous étudions le problème de changements derégime. Il existe plusieurs méthodes pour la détection de ruptures mais les principales méthodes sont : la méthode de moindres carrés pénalisés (PLS)et la méthode de derivée filtrée (FD) introduit par Basseville et Nikirov. D'autres méthodes existent telles que la méthode Bayésienne de changementde points. Nous avons validé la nouvelle méthode de dérivée filtrée et taux de fausses découvertes (FDqV) sur des données réelles (des données du vent sur des éoliennes et des données du battement du coeur). Bien naturellement, nous avons donné une extension de la méthode FDqV sur le cas des variables aléatoires faiblement dépendantes.Dans la deuxième partie, nous étudions le modèle autorégressif à seuil (en anglais Threshold Autoregessive Model (TAR)). Le TAR est étudié dans la littérature par plusieurs auteurs tels que Tong(1983), Petrucelli(1984, 1986), Chan(1993). Les applications du modèle TAR sont nombreuses par exemple en économie, en biologie, l'environnement, etc. Jusqu'à présent, le modèle TAR étudié concerne le cas où les innovations sont indépendantes. Dans ce projet, nous avons étudié le cas où les innovations sont non corrélées. Nous avons établi les comportements asymptotiques des estimateurs du modèle. Ces résultats concernent la convergence presque sûre, la convergence en loi et la convergence uniforme des paramètres
2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide
Cette thèse est composée de deux parties: une première partie traite le problème de changement de régime et une deuxième partie concerne le processusautorégressif à seuil dont les innovations ne sont pas indépendantes. Toutefois, ces deux domaines de la statistique et des probabilités se rejoignent dans la littérature et donc dans mon projet de recherche. Dans la première partie, nous étudions le problème de changements derégime. Il existe plusieurs méthodes pour la détection de ruptures mais les principales méthodes sont : la méthode de moindres carrés pénalisés (PLS)et la méthode de derivée filtrée (FD) introduit par Basseville et Nikirov. D'autres méthodes existent telles que la méthode Bayésienne de changementde points. Nous avons validé la nouvelle méthode de dérivée filtrée et taux de fausses découvertes (FDqV) sur des données réelles (des données du vent sur des éoliennes et des données du battement du coeur). Bien naturellement, nous avons donné une extension de la méthode FDqV sur le cas des variables aléatoires faiblement dépendantes.Dans la deuxième partie, nous étudions le modèle autorégressif à seuil (en anglais Threshold Autoregessive Model (TAR)). Le TAR est étudié dans la littérature par plusieurs auteurs tels que Tong(1983), Petrucelli(1984, 1986), Chan(1993). Les applications du modèle TAR sont nombreuses par exemple en économie, en biologie, l'environnement, etc. Jusqu'à présent, le modèle TAR étudié concerne le cas où les innovations sont indépendantes. Dans ce projet, nous avons étudié le cas où les innovations sont non corrélées. Nous avons établi les comportements asymptotiques des estimateurs du modèle. Ces résultats concernent la convergence presque sûre, la convergence en loi et la convergence uniforme des paramètres
Théorie spectrale d'opérateurs symétrisables non compacts et modèles cinétiques partiellement élastiques by
Yahya Mohamed(
)
2 editions published in 2015 in French and held by 2 WorldCat member libraries worldwide
This thesis is devoted to spectral theory of party elastic neutron transport equations introduced in 1974 by physicists E. LARSEN W and PF ZWEIFEL. The collision operator is then the sum of an inelastic part (corresponding to classical neutron transport models) and an elastic part that induces new spectral phenomena to be studied. The objective of this thesis is the analysis of their asymptotic spectrum (the part of the discrete spectrum that determines the time asymptotic behavior of the associated Cauchy problems). The spectral study of these partly elastic models involves spectral properties of bounded noncompact and symmetrizable operators. Thus the first part of the thesis deals with spectral theory of non compact symmetrizable operators on Hilbert spaces. We give a series of functional analytic results on these operators. In particular we give a method which provides us with all the real eigenvalues located outside the essential spectral disc and provide variational characterizations of these eigenvalues. The second part of the thesis focuses on spectral analysis of partly elastic isotropic and space homogeneous kinetic models (i.e. the cross sections depend only on speed modulus). Among other things, we show that the asymptotic spectrum consists at most of isolated eigenvalues with finite algebraic multiplicity. We also show that this point spectrum is real. Further we show that the number of real eigenvalues of the partly elastic transport operator increases indefinitely with the size of the spatial domain. We show also that all these eigenvalues tend to the spectral bound of the space homogeneous partly elastic operator when the size of domain tends to infinity. Most of these results are also extended to anisotropic models
2 editions published in 2015 in French and held by 2 WorldCat member libraries worldwide
This thesis is devoted to spectral theory of party elastic neutron transport equations introduced in 1974 by physicists E. LARSEN W and PF ZWEIFEL. The collision operator is then the sum of an inelastic part (corresponding to classical neutron transport models) and an elastic part that induces new spectral phenomena to be studied. The objective of this thesis is the analysis of their asymptotic spectrum (the part of the discrete spectrum that determines the time asymptotic behavior of the associated Cauchy problems). The spectral study of these partly elastic models involves spectral properties of bounded noncompact and symmetrizable operators. Thus the first part of the thesis deals with spectral theory of non compact symmetrizable operators on Hilbert spaces. We give a series of functional analytic results on these operators. In particular we give a method which provides us with all the real eigenvalues located outside the essential spectral disc and provide variational characterizations of these eigenvalues. The second part of the thesis focuses on spectral analysis of partly elastic isotropic and space homogeneous kinetic models (i.e. the cross sections depend only on speed modulus). Among other things, we show that the asymptotic spectrum consists at most of isolated eigenvalues with finite algebraic multiplicity. We also show that this point spectrum is real. Further we show that the number of real eigenvalues of the partly elastic transport operator increases indefinitely with the size of the spatial domain. We show also that all these eigenvalues tend to the spectral bound of the space homogeneous partly elastic operator when the size of domain tends to infinity. Most of these results are also extended to anisotropic models
Some aspects of the geometry of Lipschitz free spaces by
Colin Petitjean(
)
2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide
Some aspects of the geometry of Lipschitz free spaces.First and foremost, we give the fundamental properties of Lipschitz free spaces. Then, we prove that the canonical image of a metric space M is weakly closed in the associated free space F(M). We prove a similar result for the set of molecules.In the second chapter, we study the circumstances in which F(M) is isometric to a dual space. In particular, we generalize a result due to Kalton on this topic. Subsequently, we focus on uniformly discrete metric spaces and on metric spaces originating from pBanach spaces.In the next chapter, we focus on l1like properties. Among other things, we prove that F(M) has the Schur property provided the space of little Lipschitz functions is 1norming for F(M). Under additional assumptions, we manage to embed F(M) into an l1sum of finite dimensional spaces.In the fourth chapter, we study the extremal structure of F(M). In particular, we show that any preserved extreme point in the unit ball of a free space is a denting point. Moreover, if F(M) admits a predual, we obtain a precise description of its extremal structure.The fifth chapter deals with vectorvalued Lipschitz functions.We generalize some results obtained in the first three chapters.We finish with some considerations of norm attainment. For instance, we obtain a density result for vectorvalued Lipschitz maps which attain their norm
2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide
Some aspects of the geometry of Lipschitz free spaces.First and foremost, we give the fundamental properties of Lipschitz free spaces. Then, we prove that the canonical image of a metric space M is weakly closed in the associated free space F(M). We prove a similar result for the set of molecules.In the second chapter, we study the circumstances in which F(M) is isometric to a dual space. In particular, we generalize a result due to Kalton on this topic. Subsequently, we focus on uniformly discrete metric spaces and on metric spaces originating from pBanach spaces.In the next chapter, we focus on l1like properties. Among other things, we prove that F(M) has the Schur property provided the space of little Lipschitz functions is 1norming for F(M). Under additional assumptions, we manage to embed F(M) into an l1sum of finite dimensional spaces.In the fourth chapter, we study the extremal structure of F(M). In particular, we show that any preserved extreme point in the unit ball of a free space is a denting point. Moreover, if F(M) admits a predual, we obtain a precise description of its extremal structure.The fifth chapter deals with vectorvalued Lipschitz functions.We generalize some results obtained in the first three chapters.We finish with some considerations of norm attainment. For instance, we obtain a density result for vectorvalued Lipschitz maps which attain their norm
Etudes mathématiques et numériques des problèmes paraboliques avec des conditions aux limites by
Mohamed Karimou Gazibo(
Book
)
2 editions published in 2013 in French and held by 2 WorldCat member libraries worldwide
This thesis focuses on the theoretical study and numerical analysis of parabolic equations with boundary conditions.The first part is devoted to degenerate parabolic equation which combines features of a hyperbolic conservation law with those of a porous medium equation. We define suitable notions of entropy solutions foreach of the boundary conditions (zeroflux, Robin, Dirichlet). The main difficulty in these studies residesin the formulation of the adequate notion of entropy solution and in the proof of uniqueness. There isa technical difficulty due to the lack of regularity required to treat the boundaries terms. We take advantage of the fact that boundary regularity results are easier to obtain for the stationary problem, inparticular in one space dimension. Thus, using strongweak uniqueness approach we get the uniquenesswith the choice of a nonsymmetric test function and using the nonlinear semigroup theory. The existence of solution is proved in two steps, combining the method of parabolic regularization and Galerkinapproximations. Next, we develop a direct approach to construct approximate solutions by an implicitfinite volume scheme. In both cases, the estimates in the appropriately chosen functional spaces are combined with arguments of weak or strong compactness and various tricks to pass to the limit in nonlinearterms. In the appendix, we propose a result of existence of strong trace of a solution for the degenerateparabolic problem. In another appendix of independent interest, we introduce a new concept of solutioncalled integral process solution. We exploit it to overcome the difficulty of proving the convergence ofour finite volume scheme to an entropy solution for the zeroflux boundary problem.The second part of this thesis deals with a free boundary problem describing the propagation of a combustion front and the evolution of the temperature in a heterogeneous medium. So we have a coupledproblem consisting of the heat equation of bidimensional space and a HamiltonJacobi equation. The objective is to construct a numerical scheme and to verify that the numerical solution converges to a wavesolution for a long time. Recall that an existence of wave solution for this problem was already proven inan analytical framework. At first, we focus on the study of a onedimensional problem. Here, we face aproblem of stability of the scheme. This is due to a difficulty of taking into account the Neumann boundary condition. Through a technique of change of unknown, we can propose a monotone scheme. Wealso adapt this technique for solving twodimensional problem. Using a change of variables, we obtaina fixed domain where the discretization becomes easy. The monotony of the scheme is proved under anadditional assumption of monotone propagation that requires the free boundary moves in the directionsof a cone given beforehand
2 editions published in 2013 in French and held by 2 WorldCat member libraries worldwide
This thesis focuses on the theoretical study and numerical analysis of parabolic equations with boundary conditions.The first part is devoted to degenerate parabolic equation which combines features of a hyperbolic conservation law with those of a porous medium equation. We define suitable notions of entropy solutions foreach of the boundary conditions (zeroflux, Robin, Dirichlet). The main difficulty in these studies residesin the formulation of the adequate notion of entropy solution and in the proof of uniqueness. There isa technical difficulty due to the lack of regularity required to treat the boundaries terms. We take advantage of the fact that boundary regularity results are easier to obtain for the stationary problem, inparticular in one space dimension. Thus, using strongweak uniqueness approach we get the uniquenesswith the choice of a nonsymmetric test function and using the nonlinear semigroup theory. The existence of solution is proved in two steps, combining the method of parabolic regularization and Galerkinapproximations. Next, we develop a direct approach to construct approximate solutions by an implicitfinite volume scheme. In both cases, the estimates in the appropriately chosen functional spaces are combined with arguments of weak or strong compactness and various tricks to pass to the limit in nonlinearterms. In the appendix, we propose a result of existence of strong trace of a solution for the degenerateparabolic problem. In another appendix of independent interest, we introduce a new concept of solutioncalled integral process solution. We exploit it to overcome the difficulty of proving the convergence ofour finite volume scheme to an entropy solution for the zeroflux boundary problem.The second part of this thesis deals with a free boundary problem describing the propagation of a combustion front and the evolution of the temperature in a heterogeneous medium. So we have a coupledproblem consisting of the heat equation of bidimensional space and a HamiltonJacobi equation. The objective is to construct a numerical scheme and to verify that the numerical solution converges to a wavesolution for a long time. Recall that an existence of wave solution for this problem was already proven inan analytical framework. At first, we focus on the study of a onedimensional problem. Here, we face aproblem of stability of the scheme. This is due to a difficulty of taking into account the Neumann boundary condition. Through a technique of change of unknown, we can propose a monotone scheme. Wealso adapt this technique for solving twodimensional problem. Using a change of variables, we obtaina fixed domain where the discretization becomes easy. The monotony of the scheme is proved under anadditional assumption of monotone propagation that requires the free boundary moves in the directionsof a cone given beforehand
Functional and harmonic analysis of noncommutative Lp spaces associated to compact quantum groups by
Xumin Wang(
)
2 editions published in 2019 in English and held by 2 WorldCat member libraries worldwide
This thesis is devoted to studying the analysis on compact quantum groups. It consists of two parts. First part presents the classification of invariant quantum Markov semigroups on these quantum homogeneous spaces. The generators of these semigroups are viewed as Laplace operators on these spaces.The classical sphere, the free sphere, and the halfliberated sphere are considered as examples and the generators of Markov semigroups on these spheres are classified. We compute spectral dimensions for the three families of spheres based on the asymptotic behavior of the eigenvalues of their Laplace operator.In the second part, we study of convergence of Fourier series for nonabelian groups and quantum groups. It is wellknown that a number of approximation properties of groups can be interpreted as some summation methods and mean convergence of associated noncommutative Fourier series. We establish a general criterion of maximal inequalities for approximative identities of noncommutative Fourier multipliers. As a result, we prove that for any countable discrete amenable group, there exists a sequence of finitely supported positive definite functions, so that the associated Fourier multipliers on noncommutative Lpspaces satisfy the pointwise convergence. Our results also apply to the almost everywhere convergence of Fourier series of Lpfunctions on nonabelian compact groups. On the other hand, we obtain the dimension free bounds of noncommutative HardyLittlewood maximal inequalities in the operatorvalued Lp space associated with convex bodies
2 editions published in 2019 in English and held by 2 WorldCat member libraries worldwide
This thesis is devoted to studying the analysis on compact quantum groups. It consists of two parts. First part presents the classification of invariant quantum Markov semigroups on these quantum homogeneous spaces. The generators of these semigroups are viewed as Laplace operators on these spaces.The classical sphere, the free sphere, and the halfliberated sphere are considered as examples and the generators of Markov semigroups on these spheres are classified. We compute spectral dimensions for the three families of spheres based on the asymptotic behavior of the eigenvalues of their Laplace operator.In the second part, we study of convergence of Fourier series for nonabelian groups and quantum groups. It is wellknown that a number of approximation properties of groups can be interpreted as some summation methods and mean convergence of associated noncommutative Fourier series. We establish a general criterion of maximal inequalities for approximative identities of noncommutative Fourier multipliers. As a result, we prove that for any countable discrete amenable group, there exists a sequence of finitely supported positive definite functions, so that the associated Fourier multipliers on noncommutative Lpspaces satisfy the pointwise convergence. Our results also apply to the almost everywhere convergence of Fourier series of Lpfunctions on nonabelian compact groups. On the other hand, we obtain the dimension free bounds of noncommutative HardyLittlewood maximal inequalities in the operatorvalued Lp space associated with convex bodies
Analyse mathématique et numérique de modèles gyrocinétiques by
Céline CaldiniQueiros(
Book
)
2 editions published in 2013 in French and held by 2 WorldCat member libraries worldwide
The main subject of this thesis is the gyrokinetic equation. We present a rigourous developpement of the Vlasov equation limits with different collision operator in a strong magnetic field and numerical methods.We start with a study of the gyroaverage operator. The average operator has been introduced by M. Bostan in the case of an equation where part of the transport is highly penalised. Then weapply our results at the two approximation we study : the finite Larmor radius approximation and the guidingcenter approximation.We first focus on the precise and explicit computation of the FokkerPlanckLandau operator average in the finite Larmor radius approximation. The FokkerPlanckLandau operator containsconvolution and diffusion terms, it is then reasonable to first compute the average of the Boltzmann relaxation operator.We then focus on the guidingcenter approximation and present a numerical scheme based on amicromacro decomposition of the particles distribution fonction which comes from a joint workwith N. Crouseilles and M. Lemou. We obtain a scheme which is uniformly consistant with the continuous model for any order of the magnetic field. Numerical simulation based on this approach are presented. The last chapter of this thesis presents a project which was realised during the Cemracs 2012concerning the modelisation of blood flow in cerebral veins
2 editions published in 2013 in French and held by 2 WorldCat member libraries worldwide
The main subject of this thesis is the gyrokinetic equation. We present a rigourous developpement of the Vlasov equation limits with different collision operator in a strong magnetic field and numerical methods.We start with a study of the gyroaverage operator. The average operator has been introduced by M. Bostan in the case of an equation where part of the transport is highly penalised. Then weapply our results at the two approximation we study : the finite Larmor radius approximation and the guidingcenter approximation.We first focus on the precise and explicit computation of the FokkerPlanckLandau operator average in the finite Larmor radius approximation. The FokkerPlanckLandau operator containsconvolution and diffusion terms, it is then reasonable to first compute the average of the Boltzmann relaxation operator.We then focus on the guidingcenter approximation and present a numerical scheme based on amicromacro decomposition of the particles distribution fonction which comes from a joint workwith N. Crouseilles and M. Lemou. We obtain a scheme which is uniformly consistant with the continuous model for any order of the magnetic field. Numerical simulation based on this approach are presented. The last chapter of this thesis presents a project which was realised during the Cemracs 2012concerning the modelisation of blood flow in cerebral veins
Sur les modèles Tweedie multivariés by
Johann Cuenin(
)
2 editions published in 2016 in French and held by 2 WorldCat member libraries worldwide
Après avoir fait un rappel sur les généralités concernant les familles exponentielles naturelles et les lois Tweedie univariées qui en sont un exemple particulier, nous montrerons comment étendre ces lois au cas multivarié. Une première construction permettra de définir des vecteurs aléatoires Tweedie paramétrés pas un vecteur de moyenne et une matrice de dispersion. Nous montrerons que les corrélations entre les lois marginales peuvent être contrôlées et varient entre 1 et 1. Nous verrons aussi que ces vecteurs ont quelques propriétés communes avec les vecteurs gaussiens. Nous en donnerons une représentation matricielle qui permettra d'en simuler des observations. La seconde construction permettra d'introduire les modèles Tweedie multiples constitués d'une variable Tweedie dont l'observation sera la dispersion des autres marges, toutes de lois Tweedie elles aussi. Nous donnerons la variance généralisée de ces lois et montrerons que cette dernière peutêtre estimée efficacement. Enfin, nous verrons que, modulo certaines restrictions, nous pourrons donner une caractérisation par la fonction de variance généralisée des familles exponentielles naturelles générées par ces lois
2 editions published in 2016 in French and held by 2 WorldCat member libraries worldwide
Après avoir fait un rappel sur les généralités concernant les familles exponentielles naturelles et les lois Tweedie univariées qui en sont un exemple particulier, nous montrerons comment étendre ces lois au cas multivarié. Une première construction permettra de définir des vecteurs aléatoires Tweedie paramétrés pas un vecteur de moyenne et une matrice de dispersion. Nous montrerons que les corrélations entre les lois marginales peuvent être contrôlées et varient entre 1 et 1. Nous verrons aussi que ces vecteurs ont quelques propriétés communes avec les vecteurs gaussiens. Nous en donnerons une représentation matricielle qui permettra d'en simuler des observations. La seconde construction permettra d'introduire les modèles Tweedie multiples constitués d'une variable Tweedie dont l'observation sera la dispersion des autres marges, toutes de lois Tweedie elles aussi. Nous donnerons la variance généralisée de ces lois et montrerons que cette dernière peutêtre estimée efficacement. Enfin, nous verrons que, modulo certaines restrictions, nous pourrons donner une caractérisation par la fonction de variance généralisée des familles exponentielles naturelles générées par ces lois
Plongements grossièrement Lipschitz et presque Lipschitz dans les espaces de Banach by
François Netillard(
Book
)
2 editions published in 2019 in French and held by 2 WorldCat member libraries worldwide
The central theme of this thesis is the study of embeddings of metric spaces into Banach spaces.The first study focuses on the coarse Lipschitz embeddings between James Spaces Jp for p≻1 and p finite. We obtain that, for p,q different, Jq does not coarse Lipschitz embed into Jp. We also obtain, in the case where q≺p, that the compression exponent of Jq in Jp is lower or equal to q/p. Another natural question is to know whether we have similar results for the dual spaces of James spaces. We obtain that, for p,q different, Jp* does not coarse Lipschitz embed into Jq*. Further to this work, we establish a more general result about the coarse Lipschitz embeddability of a Banach space which has a qAUS norm into a Banach space which has a pAMUC norm for p≺q. With the help of a renorming theorem, we deduce also a result about the Szlenk index. Moreover, after defining the quasiLipschitz embeddability, which is slightly different to the almost Lipschitz embeddability, we obtain the following result: For two Banach spaces X, if X is crudely finitely representable with constant C (where C≻1) in any subspace of Y of finite codimension, then every proper subset M of X quasiLipschitz embeds into Y. To conclude, we obtain the following corollary: Let X be a locally minimal Banach space, and Y be a Banach space which is crudely finitely representable in X. Then, for M a proper subspace of Y, M quasiLipschitz embeds into X
2 editions published in 2019 in French and held by 2 WorldCat member libraries worldwide
The central theme of this thesis is the study of embeddings of metric spaces into Banach spaces.The first study focuses on the coarse Lipschitz embeddings between James Spaces Jp for p≻1 and p finite. We obtain that, for p,q different, Jq does not coarse Lipschitz embed into Jp. We also obtain, in the case where q≺p, that the compression exponent of Jq in Jp is lower or equal to q/p. Another natural question is to know whether we have similar results for the dual spaces of James spaces. We obtain that, for p,q different, Jp* does not coarse Lipschitz embed into Jq*. Further to this work, we establish a more general result about the coarse Lipschitz embeddability of a Banach space which has a qAUS norm into a Banach space which has a pAMUC norm for p≺q. With the help of a renorming theorem, we deduce also a result about the Szlenk index. Moreover, after defining the quasiLipschitz embeddability, which is slightly different to the almost Lipschitz embeddability, we obtain the following result: For two Banach spaces X, if X is crudely finitely representable with constant C (where C≻1) in any subspace of Y of finite codimension, then every proper subset M of X quasiLipschitz embeds into Y. To conclude, we obtain the following corollary: Let X be a locally minimal Banach space, and Y be a Banach space which is crudely finitely representable in X. Then, for M a proper subspace of Y, M quasiLipschitz embeds into X
Analyse d'image hyperspectrale by
Adrien Faivre(
)
2 editions published in 2017 in French and held by 2 WorldCat member libraries worldwide
This dissertation addresses hyperspectral image analysis, a set of techniques enabling exploitation of microspectroscopy images. Images produced by these sensors constitute cubic arrays, meaning that every pixel in the image is actually a spectrum.The size of these images, which is often quite large, calls for an upgrade for classical image analysis algorithms.We start out our investigation with clustering techniques. The main idea is to regroup every spectrum contained in a hyperspectralimage into homogeneous clusters. Spectrums taken across the image can indeed be generated by similar materials, and hence display spectral signatures resembling each other. Clustering is a commonly used method in data analysis. It belongs nonetheless to a class of particularly hard problems to solve, named NPhard problems. The efficiency of a few heuristics used in practicewere poorly understood until recently. We give theoretical arguments guaranteeing success when the groups studied displaysome statistical property.We then study unmixing techniques. The objective is no longer to decide to which class a pixel belongs, but to understandeach pixel as a mix of basic signatures supposed to arise from pure materials. The mathematical underlying problem is again NPhard.After studying its complexity, and suggesting two lengthy relaxations, we describe a more practical way to constrain the problemas to obtain regularized solutions.We finally give an overview of other hyperspectral image analysis methods encountered during this thesis, amongst whomare independent component analysis, nonlinear dimension reduction, and regression against a spectrum library
2 editions published in 2017 in French and held by 2 WorldCat member libraries worldwide
This dissertation addresses hyperspectral image analysis, a set of techniques enabling exploitation of microspectroscopy images. Images produced by these sensors constitute cubic arrays, meaning that every pixel in the image is actually a spectrum.The size of these images, which is often quite large, calls for an upgrade for classical image analysis algorithms.We start out our investigation with clustering techniques. The main idea is to regroup every spectrum contained in a hyperspectralimage into homogeneous clusters. Spectrums taken across the image can indeed be generated by similar materials, and hence display spectral signatures resembling each other. Clustering is a commonly used method in data analysis. It belongs nonetheless to a class of particularly hard problems to solve, named NPhard problems. The efficiency of a few heuristics used in practicewere poorly understood until recently. We give theoretical arguments guaranteeing success when the groups studied displaysome statistical property.We then study unmixing techniques. The objective is no longer to decide to which class a pixel belongs, but to understandeach pixel as a mix of basic signatures supposed to arise from pure materials. The mathematical underlying problem is again NPhard.After studying its complexity, and suggesting two lengthy relaxations, we describe a more practical way to constrain the problemas to obtain regularized solutions.We finally give an overview of other hyperspectral image analysis methods encountered during this thesis, amongst whomare independent component analysis, nonlinear dimension reduction, and regression against a spectrum library
Clearing vectors in financial networks by
Khalil El bitar(
)
2 editions published in 2016 in English and held by 2 WorldCat member libraries worldwide
Systemic risk threatening the financial system is a major concern for regulators. Adequate indicators of systemic risk would help them perform appropriate regulatory laws.The thesis proposes a dynamic model of banking system to calculate a systemic risk indicator of two components : The probability of a triggering event originated from external asset price decline, and the corresponding losses through the financial system. The thesis also proves the existence and uniqueness of two clearing equilibrium: the first deals with a model of différent debt seniorities, the second with a model of several illiquid asset following a proportional liquidation strategy
2 editions published in 2016 in English and held by 2 WorldCat member libraries worldwide
Systemic risk threatening the financial system is a major concern for regulators. Adequate indicators of systemic risk would help them perform appropriate regulatory laws.The thesis proposes a dynamic model of banking system to calculate a systemic risk indicator of two components : The probability of a triggering event originated from external asset price decline, and the corresponding losses through the financial system. The thesis also proves the existence and uniqueness of two clearing equilibrium: the first deals with a model of différent debt seniorities, the second with a model of several illiquid asset following a proportional liquidation strategy
Publications mathématiques de l'Université de FrancheComté Besançon by Laboratoire de mathématiques (Besançon)(
)
in French and held by 2 WorldCat member libraries worldwide
in French and held by 2 WorldCat member libraries worldwide
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 Université de FrancheComté Other Degree grantor Editor
 École doctorale CarnotPasteur (Besançon / Dijon) (2012....). Other Degree grantor
 Université Bourgogne FrancheComté Degree grantor
 Xu, Quanhua (1961....). Other Opponent Thesis advisor
 Dombry, Clément Other Opponent Thesis advisor
 École doctorale Louis Pasteur (Besançon / ....2012) Other Degree grantor
 Franz, Uwe (1966....). Other Opponent Thesis advisor
 Le Merdy, Christian Other Opponent Thesis advisor
 Kokonendji, Célestin Clotaire Opponent Thesis advisor
 Saussereau, Bruno Opponent Thesis advisor
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