Дисертації з теми "Théorie des singularités réelles"
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Brugallé, Erwan. "Courbes algébriques réelles et courbes pseudoholomorphes réelles dans les surfaces réglées." Phd thesis, Université Rennes 1, 2004. http://tel.archives-ouvertes.fr/tel-00008652.
Повний текст джерелаPopescu-Pampu, Patrick. "Arbres de contact des singularités quasi-ordinaires et graphes d'adjacence pour les 3-variétés réelles." Phd thesis, Université Paris-Diderot - Paris VII, 2001. http://tel.archives-ouvertes.fr/tel-00002800.
Повний текст джерелаOudrane, M'hammed. "Projections régulières, structure de Lipschitz des ensembles définissables et faisceaux de Sobolev." Electronic Thesis or Diss., Université Côte d'Azur, 2023. http://www.theses.fr/2023COAZ4034.
Повний текст джерелаIn this thesis we address questions around the metric structure of definable sets in o-minimal structures. In the first part we study regular projections in the sense of Mostowski, we prove that these projections exists only for polynomially bounded structures, we use regular projections to re perform Parusinski's proof of the existence of regular covers. In the second part of this thesis, we study Sobolev sheaves (in the sense of Lebeau). For Sobolev functions of positive integer regularity, we construct these sheaves on the definable site of a surface based on basic observations of definable domains in the plane
Sorea, Miruna-Ştefana. "The shapes of level curves of real polynomials near strict local minima." Thesis, Lille 1, 2018. http://www.theses.fr/2018LIL1I055/document.
Повний текст джерелаWe consider a real bivariate polynomial function vanishing at the origin and exhibiting a strict local minimum at this point. We work in a neighbourhood of the origin in which the non-zero level curves of this function are smooth Jordan curves. Whenever the origin is a Morse critical point, the sufficiently small levels become boundaries of convex disks. Otherwise, these level curves may fail to be convex, as was shown by Coste.The aim of the present thesis is twofold. Firstly, to construct examples of non-Morse strict local minima whose sufficiently small level curves are far from being convex. And secondly, to study a combinatorial object measuring this non-convexity, namely the Poincaré-Reeb tree of the restriction of the first coordinate to the region bounded by a given level curve. These planar trees are rooted and their vertices roughly speaking correspond to points on the curve with vertical tangent lines.The main objective of our study is to characterise all possible topological types of Poincaré-Reeb trees. To this end, we construct a family of examples realising a large class of such trees. As a preliminary step, we restrict our attention to the univariate case, using a tool inspired by Ghys’ work. One of our main results gives a new and constructive proof of the existence of Morse polynomials whose associated permutation (the so-called “Arnold’s snake”) is separable
Alberti, Lionel. "Propriétés Quantitatives des Singularités des Variétés Algébriques Réelles." Phd thesis, Nice, 2008. http://www.theses.fr/2008NICE4064.
Повний текст джерелаSection 2 explains a subdivision procedure triangulating an algebraic plane curve. The mathematical tools are the topological degree, alias Gauss's application, the representation of polynomials in the Bernstein basis, all of it wrapped up in a subdivision very fast and certified subdivision method. Section 3 presents a quantitative theory for measuring transversality to a semi-algebraic map (not necessarily smooth). Stem from it: A quantitative version of Thom-Mather's topological triviality theorem, A ``metrically stable'' version of the local conic structure theorem and of the existence of a ``Milnor tube'' around strata. An triangulation algorithm based on Voronoi partitions (not completely implementable because the effective estimation of transversality is not completely detailed)Section 4 presents a bound on the generic number of connected components in an affine section of a real analytic germ in terms of the multiplicity and of the dimension of the ambient space. These two parameters are not always enough to bound the number of connected components. The result is thus proved under some conditions which are shown to be minimal
Campesato, Jean-Baptiste. "Une fonction zêta motivique pour l'étude des singularités réelles." Thesis, Nice, 2015. http://www.theses.fr/2015NICE4104/document.
Повний текст джерелаThe main purpose of this thesis is to study real singularities using arguments from motivic integration as initiated by S. Koike and A. Parusiński and then continued by G. Fichou. In order to classify real singularities, T.-C. Kuo introduced the blow-analytic equivalence which is an equivalence relation on real analytic germs without moduli for isolated singularities. This notion is closely related to the notion of arc-analytic maps introduced by K. Kurdyka, thus it is natural to adapt arguments from motivic integration to the study of the relation. The difficulty lies in finding efficient ways to prove that two germs are equivalent and in constructing invariants that distinguish germs which are not in the same class. We focus on the blow-Nash equivalence, a more algebraic notion which was introduced by G. Fichou. The first part of this thesis consists in an inverse theorem for blow-Nash maps. Under certain assumptions, this ensures that the inverse of a homeomorphism which is blow-Nash is also blow-Nash. Such maps are involved in the definition of the blow-Nash equivalence. In the second part, we associate a power series to an analytic germ, called the zeta function of the germ. This construction generalizes the zeta functions of Koike-Parusiński and Fichou. Furthermore, it admits a convolution formula while being an invariant for the blow-Nash equivalence
Chevallier, Benoît. "Singularités et topologies optimales des hypersurfaces algébriques réelles de petites dimensions." Paris 7, 1996. http://www.theses.fr/1996PA077309.
Повний текст джерелаSevenheck, Christian. "Singularités lagrangiennes." Phd thesis, Ecole Polytechnique X, 2003. http://tel.archives-ouvertes.fr/tel-00003816.
Повний текст джерелаdéformation pour les singularités lagrangiennes. Pour une singularité
lagrangienne, un complexe de modules à différentielle non-linéaire,
dont la première cohomologie est isomorphe à l'espace de déformations
infinitésimales de la singularité, est défini. La cohomologie en degré deux contient des informations sur les obstructions. Ce
complexe est relié à la théorie des modules différentiels. Nous
démontrons que, sous une condition géométrique, sa cohomologie est
constituée de faisceaux constructibles. Nous décrivons une méthode
utilisant du calcul formel pour déterminer cette cohomologie pour
des surfaces quasi-homogènes.
Poutriquet, David. "K-théorie des singularités coniques isolées." Toulouse 3, 2006. http://www.theses.fr/2006TOU30091.
Повний текст джерелаIt seems natural to build an intersection K-theory for conical isolated singular varieties, and a Chern character witch takes its values in intersection cohomology groups. The intersection cohomology of the cone leads us to extend to singular setting the multiplicative K-theory groups of M. Karoubi. In general situation these groups are associated to a family of complexes of differentiable forms. Using an intersection complex chain, which depends on a non-negative integer q, we define a Chern character whose range is contained in the even intersection cohomology. But it cannot be an isomorphism even tensoring by rationnals. Thus we introduce the group of intersection K-theory of a singular variety, where the elements are classes of triples formed by a q-flat vector bundle, a subbundle, and a trivialisation of it over the boundary of the streched variety. It can be defined a Chern character between this singular K-theory and intersection cohomology, which becomes an isomorphism when tensoring by rationnals
Fichou, Goulwen. "Fonctions zêta réelles et équivalence de Nash après éclatements." Habilitation à diriger des recherches, Université Rennes 1, 2010. http://tel.archives-ouvertes.fr/tel-00554877.
Повний текст джерелаGuéré, Jérémy. "Théorie quantique des singularités, symétrie miroir et hiérarchies intégrables." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066117/document.
Повний текст джерелаIn this thesis, we provide a mirror symmetry theorem in a range of cases where the state-of-the-art techniques relying on concavity or convexity do not apply. More specifically, we work on a family of FJRW potentials named after Fan, Jarvis, Ruan, and Witten's quantum singularity theory and viewed as the counterpart of a non-convex Gromov--Witten potential via the physical LG/CY correspondence. The main result provides an explicit formula for Polishchuk and Vaintrob's virtual cycle in genus zero. In the non-concave case of the so-called chain invertible polynomials, it yields a compatibility theorem with the FJRW virtual cycle and a proof of mirror symmetry for FJRW theory. At last, we generalize our main theorem to the computation of intersection numbers between the top Chern class of the Hodge bundle and the virtual cycle in arbitrary genus. In the case of $3$-spin theory, it leads to a proof of Buryak's conjecture on the equivalence between double ramification hierarchy and $3$-KdV hierarchy
Salem, Ghada. "Homologie d'intersection géométrique pour les singularités coniques isolées." Toulouse 3, 2011. http://thesesups.ups-tlse.fr/1165/.
Повний текст джерелаIn the first part, we construct a Poincaré duality for pseudo-manifolds with isolated conical singularities. The Poincaré duality is not true in the singular case. In 1980, Goresky and Mac Pherson, introduce the intersection homology for which the rational Poincaré duality remains true for conical singularities. We modifie their cohomology by constructing a non free complex, quasi-isomorphic to the intersection complex but whose cohomology verifies the Poincaré duality. In the second part, we define a geometrical theory of the intersection homology. It results that any intersection cycle can be represented by the cap product of the fundamental class of a manifold with boundary by a class of J-cohomology of this manifold. To end we show that J-cohomology verifies an isomorphism of Thom
Akriche, Mouadh. "Nombres de Betti des surfaces elliptiques réelles." Chambéry, 2005. http://www.theses.fr/2005CHAMS054.
Повний текст джерелаReal surfaces of Kodaira dimension 1, or more precisely the slightly larger class of real elliptic surfaces, form the only class of real algebraic surfaces of special type whose topological classification is not achieved. We give a complete answer to the question of possible values of Betti numbers of the real part of real regular elliptic surfaces with real section, for each complex family. In particular, we find again well-known answers for this question, in the case of rational elliptic or elliptic K3 surfaces
Poizat, Didier. "Singularités infrarouges et singularités de masse dans les théories quantiques des champs relativistes à température finie." Nice, 1990. http://www.theses.fr/1990NICE4419.
Повний текст джерелаde, Felipe Paramio Ana Belén. "Topologie des espaces de valuations et géométrie des singularités." Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCC136.
Повний текст джерелаWe study the fiber of the Riemann-Zariski space above a closed point x of an algebraic variety X defined over an algebraically closed field. We characterize its homeomorphism type for regular points and normal surface singularities. This is done by studying the relation between this space and the normalized non-Archimedean link of x in X. We prove that their behavior is the same
Ilahi, Abderrazak. "Validation du calcul sur ordinateur : application de la théorie des singularités." Toulouse 1, 1998. http://www.theses.fr/1998TOU10045.
Повний текст джерелаThe computation of spectra of matrices plays an important role in scientific computing. However, the finite precision arithmetic of the computers induces unavoidable perturbations. In this document, we develop theoretical notions for analysing the errors resulting on the eigen values when the matrix is perturbed. These theoretical notions are also useful for the assessment of the qualitative computation approach used in the toolbox precise. We study in depth the behaviour of the eigen values of a family of homotopic perturbations, thanks to new notions such as the Puiseux value, the distance to the stratum and the influent Jordan structure. In this theoretical study, we demonstrate the link between the distance to the stratum and the reliability of the asymptotic analysis. If the size of the perturbation of the matrix a cannot be neglected with respect to the distance to the stratum, the Jordan structure of a will be pessimistic or even misleading. The influent Jordan structure in the vicinity of a can be determined with homotopic perturbations. This influent Jordan structure allows us to estimate, in a reliable and accurate way, the errors on the eigen values of a when they are computed in finite precision
Molnar, Ioana. "Contributions à la théorie des espaces de fonctions : singularités et relèvements." Thesis, Lyon 1, 2014. http://www.theses.fr/2014LYO10092/document.
Повний текст джерелаIn this thesis we study some aspects of certain functional spaces. On the one hand we focus on the singularities of maps W^{1, n} with values in the unit sphere S^n, and secondly, on liftings of maps W^{s, p} with values in the circle S^1.The first part concerns the minimization problem of a weighted Dirichlet energy. Admissible maps are functions which are continuous functions outside a given singular set prescribed by the boundary of a rectifiable current. We obtain the exact formula, which improves the result of Alberto, Baldi and Orlando (2003). In the same time, we generalize some results previously obtained by Brezis, Coron, Lieb (1986), Almgren, Browder, Lieb (1988).The second part focuses on the best control of unimodular maps and it is based on the work of Bourgain, Brezis, Mironescu (2000, 2002). Using some known methods and some new ones, we study optimal estimates of seminorms W^{s, p} of liftings, for different values of s and p. We also obtain a new characterization of the space W^{s, p} for s<1 in terms of dyadic seminorm
Trivedi, Saurabh. "Sur les stratifications réelles et analytiques complexes (a) - régulières de Whitney et Thom." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4719.
Повний текст джерелаTrotman in 1979 proved that real smooth stratifications which satisfy the condition of $(a)$-regularity are precisely those stratifications for which transversality to the strata of smooth mappings is a stable condition in the strong topology. This was a surprising result since $(t)$-regularity seemed to be more appropriate for stability of transversality, a mistake that was made in several articles before this result of Trotman. Our first result is an analogue of this result of Trotman for the weak topology.Trotman asked more than ten years ago whether a similar result holds for complex analytic stratifications. We will give an analogue of Trotman's result in the complex setting using Forstneriv c's notion of Oka manifolds and show that the result is not true in general by giving counterexamples.In his Ph.D. thesis Trotman conjectured a generalization of his result for Thom $(a_f)$-regular stratifications. In an attempt to prove this conjecture we noticed that while transversality to a foliation is a stable condition, it is not generic in general. Thus, mimicking the proof of the result of Trotman would not suffice to obtain this generalization. Nevertheless, we will present a proof of this conjecture in this work. This result can be summarized by saying that Thom $(a_f)$-faults in a stratification can be detected by perturbation of maps transverse to the foliation induced by $f$. Some other techniques of detecting $(a_f)$-faults are also given towards the end
Priziac, Fabien. "Filtration par le poids équivariante pour les variétés algébriques réelles avec action." Phd thesis, Université Rennes 1, 2012. http://tel.archives-ouvertes.fr/tel-00787619.
Повний текст джерелаRiffaud, Oana. "Réversibilité du stockage géologique des déchets radioactifs : la théorie des options réelles dans l'aide à la décision." Thesis, Nancy 2, 2011. http://www.theses.fr/2011NAN20009.
Повний текст джерелаIn France, the Act n° 2006-739 of 28 June 2006 establishes the reversible geological disposal for intermediate and high-level waste (ILWand HLW). The reversibility is mainly justified by the need to preserve some ability to adapt over the long term (at least one hundred years) in a context of multiple uncertainties. The proposed thesis examines how the real options approach can be effectively applied to the French project of reversible geological disposal for the radioactive waste, developed by the National Agency for Radioactive Waste (ANDRA). Different aspects of decision making process are addressed through three real options models. Each model emphasizes a certain type of real option : the switching option, the extension option and the learning option. The first model focuses on the uncertainty about the value of a radioactive waste package and its influence on the switching options between different stages of retrievability. The results show that the reversible project of geological disposal involves a series of compound options (options on options) which may create follow-up opportunities and interactions. For example, realizing an earlier real option (such as closing the galleries of access) can change the value of future options for the retrieval of waste packages. Given these interactions between options, their value must be simultaneously determined. In the second model, the focus is moved to the construction of the geological repository. The result of the second model shows that there may be a value associated with the progressive development of the operating capacity due to the uncertainty on the demand for radioactive waste disposal. This is precisely the value of the extension option which must be calculated to determine whether it is economically advantageous to increase the capacity. The third model, more conceptual, is an attempt to open new avenues of research on the value of the learning option in the presence of endogenous information. The option value is analyzed by integrating two sources of learning (Learning by doing and R & D)
Béchet, Fabien. "Étude théorique et numérique des singularités en théorie des coques minces élastiques." Lille 1, 2007. https://pepite-depot.univ-lille.fr/LIBRE/Th_Num/2007/50376-2007-B_chet.pdf.
Повний текст джерелаGmira, Abdelilah. "Comportements asymptotiques et singularités des solutions de problèmes quasi-linéaires." Tours, 1989. http://www.theses.fr/1989TOUR4005.
Повний текст джерелаMérindol, Jean-Yves. "Singularités, périodes des structures de Hodge mixtes et géométrie." Paris 11, 1985. http://www.theses.fr/1985PA112097.
Повний текст джерелаWe prove here a Torelli theorem for some affine varieties U: the polarized mixed Hodge structure on H*(U) determines u. For example it is true for an affine cubic surface or an intersection of two quadrics. The study of the period map of the MHS gives some results on the deformations of the cone over U/U. Then we can obtain a geometric interpretation of the polarization of the MHS by the mean of the theory of roots systems and theta divisor
Borghol, Rouba. "Singularités au bord de solutions d'équations quasilinéaires." Tours, 2005. http://www.theses.fr/2005TOUR4022.
Повний текст джерелаThis thesis divided into five chapters, is devoted to the study of two types of equations: p-harmonic equation and p-harmonic equation with absorption. The first chapter is devoted to the study of the boundary singularities of p-harmonic functions into a half-space. In order to characterize the boundary singularities in any smooth domain, we derive a series of boundary Harnack inequalities for positive solutions of some quasilinear equations, this is imposed into the second chapter. In the third chapter, we study the existence and the classification of positive singular solutions of p-harmonic equation with absorption in a spherical cone. In some cases we prove that the isolated singularities are removable, and in another case we show the existence of two distinct types of singularities. In the last two chapters, we extend these results to a general domain, but in the case p = N. We also give a device to construct by induction separable p-harmonic functions
Sacchelli, Ludovic. "Singularités en géométrie sous-riemannienne." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLX050/document.
Повний текст джерелаWe investigate the relationship between features of of sub-Riemannian geometry and an array of singularities that typically arise in this context.With sub-Riemannian Whitney theorems, we ensure the existence of global extensions of horizontal curves defined on closed set by requiring a non-singularity hypothesis on the endpoint-map of the nilpotent approximation of the manifold to be satisfied.We apply perturbative methods to obtain asymptotics on the length of short locally-length-minimizing curves losing optimality in contact sub-Riemannian manifolds of arbitrary dimension. We describe the geometry of the singular set and prove its stability in the case of manifolds of dimension 5.We propose a construction to define line fields using pairs of vector fields. This provides a natural topology to study the stability of singularities of line fields on surfaces
Silhol, Robert. "Etude et classification des surfaces algébriques réelles." Tours, 1986. http://www.theses.fr/1986TOUR4006.
Повний текст джерелаPinson, Franck. "Ajustement de primitives d'objets de forme libre sur un ensemble de données réelles." Compiègne, 1989. http://www.theses.fr/1989COMPD179.
Повний текст джерелаPoulet, Marina. "Equations de Mahler : groupes de Galois et singularités régulières." Thesis, Lyon, 2021. https://tel.archives-ouvertes.fr/tel-03789627.
Повний текст джерелаThis thesis is devoted to the study of Mahler equations and the solutions of these equations, called Mahler functions. Classic examples of Mahler functions are the generating series of automatic sequences. The first part of this thesis deals with the Galoisian aspects of Mahler equations. Our main result is an analog for Mahler equations of the Schlesinger’s density theorem according to which the monodromy of a regular singular differential equation is Zariski-dense in its differential Galois group. To this end, we start by attaching a pair of connection matrices to each regular singular Mahler equation. These matrices enable us to construct a subgroup of the Galois group of the Mahler equation and we prove that this subgroup is Zariski-dense in the Galois group. The only assumption of this density theorem is the regular singular condition on the considered Mahler equation. The second part of this thesis is devoted to the construction of an algorithm which recognizes whether or not a Mahler equation is regular singular
Tomasini, Arnaud. "Intersections maximales de quadriques réelles." Thesis, Strasbourg, 2014. http://www.theses.fr/2014STRAD035/document.
Повний текст джерелаReal algebraic geometry is in its simplest definition, the study of sets of solutions of a system of polynomial equations with real coefficients. In this theme, we focus on the intersections of quadrics where already the case of three quadrics remains wide open. Our subject can be summarized as the topological study of real algebraic varieties and interaction between their topology on the one hand and their deformations and degenerations on the other hand, a problem coming from the 16th Hilbert problem and enriched by recent developments. In this thesis, we will focus on maximum intersections of real quadrics and particularly prove the existence of such intersections using research developments made since the late 80. In the case of intersections of three quadrics, we will point the very close link between the intersections on the one hand and on the other plane curves, and show that the study of M-curves (one of the problems of the 16th Hilbert problem) may be done through the study of maximum intersections. Next, we will use the study on nodal plane curves to determine in some cases deformation classes of intersections of three real quadrics
Caradot, Antoine. "Singularité et théorie de Lie." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1086/document.
Повний текст джерелаLet Γ be a finite subgroup of SU2(ℂ). Then the quotient ℂ2/Γ can be embedded in ℂ3 as a surface with an isolated singularity. The quotient ℂ2/Γ is called a Kleinian singularity, after F. Klein who studied them first in 1884. Through their minimal resolutions, these singularities have a deep connection with simply-laced Dynkin diagrams of types Ar, Dr and Er. In the 1970's E. Brieskorn and P. Slodowy took advantage of this connection to describe the resolutions and deformations of these singularities in terms of Lie theory. In 1998 P. Slodowy and H. Cassens constructed the semiuniversal deformations of the Kleinian singularities using quiver theory and work from 1989 by P.B. Kronheimer on symplectic geometry. In Lie theory, the classification of simple Lie algebras allows for a separation in two classes: those simply-laced of types Ar, Dr and Er, and those of types Br, Cr, F4 and G2 called inhomogeneous. With the use of a second finite subgroup Γ’ of SU2(ℂ) such that Γ ⊲ Γ’, P. Slodowy extended in 1978 the definition of a Kleinian singularity to the inhomogeneous types by adding to ℂ2/Γ the group of automorphisms Ω= Γ’/Γ of the Dynkin diagram associated to the singularity. The purpose of this thesis is to generalize H. Cassens' and P. Slodowy's construction to the singularities of types Br, Cr, F4 and G2. It will lead to explicit semiuniversal deformations of inhomogeneous types on the fibers of which the group Ω acts. By quotienting such a map we obtain a deformation of a singularity ℂ2/Γ’
Baldé, Moussa. "Deux problèmes liés à la théorie du contrôle et à la théorie des singularités : métriques sous-riemanniennes et observabilité non linéaire." Rouen, 1999. http://www.theses.fr/1999ROUES070.
Повний текст джерелаAstier, Raphaël. "L'uniformisation locale des surfaces d'Artin-Schreier en caractéristique positive." Versailles-St Quentin en Yvelines, 2002. http://www.theses.fr/2002VERS015V.
Повний текст джерелаThis thesis deals with uniformization, in characteristic p>0, of a rational valuation, in special cases where this valuation is centered on a singularity locally defined by the following equations :- either zp̂+f(x,y)=0, with f not a p-th power, and ordf >p,- or zp̂+e(x,y)z+f(x,y)=0, with ord (ez+f)>p (Artin-Schreier's case). Historically, it was in such cases that all difficulty of resolving surfaces in positive characteristic was concentrated. The novelty bringed in this work consists first in giving a bound to theminimum number of closed point's blowing-ups needed to uniformize, and second in anticipating (from the first ring) the Newton polygon's evolution and the parameter's choice for the successive blowing-ups along the valuation. In a first part, we come back on the Giraud's normal form of f in O_X(X)where X is a two dimensional regular scheme of characteristic p. The startingpoint is an polynomial expansion of f with a generating sequence for the valuation. We can then study and anticipate the behavior of this expansion and the associated Newton polygon modulo a p-th power. We then give a bound on the maximum number of blowing-ups needed for this polygon to become minimal, with only one vertex, and of maximal height one. This case correspond to the normal form of f. In a second part, using this results for the two above-mentionned cases, wegive an algorithm witch anticipate, in the first ring, the translations on zneeded to keep a minimal Newton polygon during the blowing-ups sequence (alongthe valuation), and we quantify the maximal size of such a sequence with last ring corresponding to a quasi-ordinary singularity
Moncet, Arnaud. "Géométrie et dynamique sur les surfaces algébriques réelles." Phd thesis, Université Rennes 1, 2012. http://tel.archives-ouvertes.fr/tel-00724509.
Повний текст джерелаMoutoussamy, Isabelle. "Symétries et singularités de solutions d'équations paraboliques semi-linéaires." Tours, 1987. http://www.theses.fr/1987TOUR4009.
Повний текст джерелаKhechichine, Fatima-Zohra. "Familles génériques à quatre paramètres de champs de vecteurs quadratiques dans le plan : singularité à partie linéaire nulle." Dijon, 1991. http://www.theses.fr/1991DIJOS020.
Повний текст джерелаPol, Delphine. "Singularités libres, formes et résidus logarithmiques." Thesis, Angers, 2016. http://www.theses.fr/2016ANGE0021/document.
Повний текст джерелаThe theory of logarithmic vector fields and logarithmic differential forms along a reduced singular hypersurface is developed by K. Saito. These notions appear in the study of the Gauss-Manin connection of some families of singularities and their semi-universal unfolding. If the module of logarithmic vector fields is free, the hypersurface is called a free divisor. A.G. Aleksandrov and A. Tsikh generalize the notions of logarithmic differential forms and logarithmic residues to reduced complete intersections and Cohen-Macaulay spaces. In this work, we study the logarithmic differential forms of a reduced singular space of any codimension embedded in a smooth manifold, and we develop a notion of free singularity which extend the notion of free divisor. The residues of logarithmic differential forms as well as theirgeneralization to higher codimension spaces are crucial in this thesis. Our first purpose is to give characterizations of freeness for complete intersections and Cohen-Macaulay spaces which generalize the case of hypersurfaces. We then give a particular attention to a family of free singularities, namely the curves, for which we describe the module of logarithmic residues thanks to their set of values
Ly, Vath Vathana. "Quelques applications du controle stochastique aux options réelles et au risque de liquidité." Paris 7, 2006. http://www.theses.fr/2006PA077016.
Повний текст джерелаWe study stochastic control applications to real options and to liquidity risk model. More precisely, we investigate, in the first part, a model of optimal portfolio selection under liquidity risk and price impact, then, in the second part, two real option problems: an optimal switching problem and a mixed singular/switching control problem for a dividend policy with reversible investment, and finally, in the third part, a competitive market equilibrium problem under asymmetric information. In the resolution of these problems, stochastic control techniques will be intensively used. The typical approach consists in expressing the dynamic programming principle related to each case, in order to obtain a PDE characterization of the value functions. Based on this approach, we show, in the liquidity risk problem and both real options, that the corresponding value functions are unique solution to the associated system of HJB variational inequalities. In each problem of the first two parts, we obtain the solutions, in particular the optimal control, either explicitly or via an iterative method
Kanyinda, Kasanda Alois. "La gestion de risque de l'eau : application de la théorie des options réelles à l'industrie de l' eau." Paris 9, 2004. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=2004PA090060.
Повний текст джерелаIn this thesis, we analyse the problem of water shortage which concerns many countries in the world. This problem has many dimensions: social, economic and political in particular. In this work, we are interested by the economic dimension. Our objective is to give some solutions to this problem with the framework of real options. The methodology proposed in this thesis takes into count the implicit flexibility of investment projects. Multiple evaluating methods of modern finance are used to determine the exact price of real options related to water shortage problems. The Black & Scholes model and its extensions are used (Exchange option, American option, etc. ), in the special case of the option of importing water. The comparison of all result helps to give some conclusions about which technique must be used
Pichereau, Anne. "(Co)homologie de Poisson et singularités isolées en petites dimensions, avec une application en théorie des déformations." Poitiers, 2006. http://www.theses.fr/2006POIT2354.
Повний текст джерелаThe main purpose of this work is to compute Poisson cohomology and homology, in low dimensions, for two types of affine Poisson varieties: smooth varieties, equipped with Poisson structures that admit a singular locus, and singular varieties, equipped with Poisson structures, as regular as possible. We consider the affine space of dimension three F^3 (F: field of characteristic zero) and a family of singular surfaces in F^3. To each (weight) homogeneous polynomial in F[x,y,z], one associates indeed naturally a Poisson structure P on F^3 and a singular surface in F^3, on which P induces also a Poisson structure. The singular locus of P and the singularity of the surface then coincide and the Poisson structure, induced by P on the surface, is symplectic everywhere, except on the singularity. In this context, we compute the Poisson (co)homology of the obtained Poisson varieties. This result permits us to determine completly the formal deformations of these Poisson brackets. We then observe that the above singularity intervenes in the (co)homology spaces and in the deformations. The methods used permits also us to obtain, in our cases, explicit basis of the spaces associated to a homology with parameter, defined by O. Mathieu. Finally, we begin the study of the Poisson cohomology for a generalization of the singular cases given above and we give some first results, for one example
Uribe, Vargas Eduardo Ricardo. "Singularités symplectiques et de contact en géométrie différentielle des courbes et des surfaces." Paris 7, 2001. http://www.theses.fr/2001PA077154.
Повний текст джерелаKokonendji, Célestin Clotaire. "Familles exponentielles naturelles réelles de fonction variance en R Q/ par Célestin Clotaire Kokonendji." Toulouse 3, 1993. http://www.theses.fr/1993TOU30092.
Повний текст джерелаGoldsztejn, Alexandre. "Définition et applications des extensions des fonctions réelles aux intervalles généralisés : révision de la théorie des intervalles aux intervalles généralisés." Nice, 2005. http://www.theses.fr/2005NICE4056.
Повний текст джерелаThe intervals theory allows constructing supersets of the range of real functions. Therefore, in a very natural way it allows constructing some outer approximation of the solution set of systems of real equations. When it is used in conjunction to some usual existence theorems (e. G. Brouwer or Miranda theorems), the intervals theory also allows to rigorously prove the existence of solutions to such systems of equations. The modal intervals theory proposed some richer interpretations. In particular, the construction of both subjects and supersets of the range of real functions are in the scope of extensions to modal intervals. As a consequence, the extensions of real functions to modal intervals have the intrinsic power of proving the existence of solutions to systems of equations. In spite of some recent developments that have shown the promising potential applications of these richer interpretations, the modal intervals theory remains unused by most of the interval community. On one hand, a new formulation of the modal intervals theory is proposed. This new formulation uses only generalized intervals (intervals whose bounds are not constrained to be ordered) and follows the construction of the classical intervals theory. This will allow using the modal intervals theory in an easier way. On the other hand, some new preconditioning and linearization processes are proposed which are compatible with the richer interpretations provided by the modal interval theory. The new linearization process which is proposed will have the form of a new mean-value extension to generalized intervals
Bahri, Emna. "Amélioration des procédures adaptatives pour l'apprentissage supervisé des données réelles." Thesis, Lyon 2, 2010. http://www.theses.fr/2010LYO20089/document.
Повний текст джерелаMachine learning often overlooks various difficulties when confronted real data. Indeed, these data are generally complex, voluminous, and heterogeneous, due to the variety of sources. Among these problems, the most well known concern the sensitivity of the algorithms to noise and unbalanced data. Overcoming these problems is a real challenge to improve the effectiveness of the learning process against real data. In this thesis, we have chosen to improve adaptive procedures (boosting) that are less effective in the presence of noise or with unbalanced data.First, we are interested in robustifying Boosting against noise. Most boosting procedures have contributed greatly to improve the predictive power of classifiers in data mining, but they are prone to noisy data. In this case, two problems arise, (1) the over-fitting due to the noisy examples and (2) the decrease of convergence rate of boosting. Against these two problems, we propose AdaBoost-Hybrid, an adaptation of the Adaboost algorithm that takes into account mistakes made in all the previous iteration. Experimental results are very promising.Then, we are interested in another difficult problem, the prediction when the class is unbalanced. Thus, we propose an adaptive method based on boosted associative classification. The interest of using associations rules is allowing the focus on small groups of cases, which is well suited for unbalanced data. This method relies on 3 contributions: (1) FCP-Growth-P, a supervised algorithm for extracting class frequent itemsets, derived from FP-Growth by introducing the condition of pruning based on counter-examples to specify rules, (2) W-CARP associative classification method which aims to give results at least equivalent to those of existing approaches but in a faster manner, (3) CARBoost, a classification method that uses adaptive associative W-CARP as weak classifier. Finally, in a chapter devoted to the specific application of intrusion’s detection, we compared the results of AdaBoost-Hybrid and CARBoost to those of reference methods (data KDD Cup 99)
Freixas, i. Montplet Gérard. "Généralisations de la théorie de l'intersection arithmétique." Paris 11, 2007. http://www.theses.fr/2007PA112289.
Повний текст джерелаThe aim of this thesis is to extend several fundamental theorems in Arakelov Geometry, known to hold for projective arithmetic varieties, to the extended frame of quasi-projective varieties. For this one uses the formalism proposed by Burgos-Kramer-Kuhn, that generalizes that of Gillet and Soulé. We mainly establish two results : 1. Finiteness property for heights attaches to hermitian line bundles, whose metrics are singular. The singularities are of some logarithmic type ; 2. Arithmetic Riemann-Roch formula for pointed stable curves, whose tanget bundle is endowed with the hyperbolic metric singular at the cusps. Furthermore, several examples are given related to 1 –in particular a generalization of a theorem due to Wolpert on the family hyperbolic metric- and to 2 –we compute special values of the Selberg zeta funcions of modular curves
Séguy, Mathias. "Cobordisme et reliabilité équisingulière de singularités marquées de feuilletages holomorphes en dimension deux." Toulouse 3, 2003. http://www.theses.fr/2003TOU30085.
Повний текст джерелаLabruère-Chazal, Catherine. "Groupes d’Artin et mapping class groups." Dijon, 1997. http://www.theses.fr/1997DIJOS018.
Повний текст джерелаBrélivet, Thomas. "Topologie des polynômes, spectre et variance du spectre." Bordeaux 1, 2002. http://www.theses.fr/2002BOR12517.
Повний текст джерелаJamet, Guillaume. "Obstruction au prolongement des formes différentielles régulières et codimension du lieu singulier." Paris 6, 2000. http://www.theses.fr/2000PA066227.
Повний текст джерелаCapitanio, Gianmarco. "Familles Tangentielles et solutions de minimax pour l'équation de Hamilton-Jacobi." Phd thesis, Université Paris-Diderot - Paris VII, 2004. http://tel.archives-ouvertes.fr/tel-00008669.
Повний текст джерелаCes deux sujets sont reliés à des thèmes classiques en théorie des singularités, comme la théorie des enveloppes, les singularités des fronts d'onde et des caustiques, la géométrie symplectique et de contact.
Les premiers trois chapitres de la Thèse sont consacrés à l'étude des familles tangentielles, à la classification de leurs singularités stables et simples, et à leurs interprétation dans le cadre de la Géométrie de Contact.
Le dernier chapitre est dédié à l'étude des solutions de minimax pour l'équation de Hamilton--Jacobi, notamment à la classification des leurs singularités génériques de petite codimension.
Ly, Vath Vathana. "Quelques applications du contrôle stochastique aux options réelles et au risque de liquidité." Phd thesis, Université Paris-Diderot - Paris VII, 2006. http://tel.archives-ouvertes.fr/tel-00119754.
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