Literatura académica sobre el tema "Equation canonique"
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Artículos de revistas sobre el tema "Equation canonique"
Debiard, Amédée y Bernard Gaveau. "Equations de Cauchy-Riemann Sur SU(2) et Leurs Enveloppes D'Holomorphie". Canadian Journal of Mathematics 38, n.º 4 (1 de agosto de 1986): 1009–24. http://dx.doi.org/10.4153/cjm-1986-049-8.
Texto completoTesis sobre el tema "Equation canonique"
Lovera, Stéphanie. "Propriétés spectrales de l'opérateur solution canonique du d-bar et des opérateurs de Hankel de symbole antiholomorphe". Phd thesis, Université de Provence - Aix-Marseille I, 2005. http://tel.archives-ouvertes.fr/tel-00011986.
Texto completoDans un premier temps, on étudie les propriétés spectrales de l'opérateur solution canonique du dbar restreint aux (0,1)-formes à coefficients holomorphes. Nous donnons des conditions nécessaires et suffisantes, pour que l'opérateur solution canonique du dbar soit borné, compact et appartienne à la p-ème classe de Schatten, et ce dans le cas d'une ou plusieurs variables et pour toute une classe d'espaces de Hilbert contenant des espaces de Hilbert de fonctions holomorphes classiques comme des espaces de Bergman à poids, des espaces de Fock, des espaces de Sobolev de fonctions holomorphes, des espaces de Hardy-Sobolev, l'espace de Hardy ou l'espace invariant de Moebius.
Dans un second temps, on s'intéresse à l'existence d'un opérateur de Hankel défini sur un espace de Hilbert de fonctions holomorphes, de symbole antiholomorphe non trivial dans une classe de Schatten donnée et on cherche à étudier le rapport entre la croissance d'une fonction f et la taille des valeurs singulières de l'opérateur de Hankel induit par f-bar.
Dans ce travail, on considère les grands opérateurs de Hankel de symbole antiholomorphe définis sur l'espace de Hardy du disque unité de C, l'espace de Dirichlet ou des espaces de Sobolev de fonctions holomorphes sur le disque unité de C. On donne d'abord une condition nécessaire et suffisante sur p pour que la p-ème classe de Schatten contienne un opérateur de Hankel de symbole antiholomorphe non trivial. Ensuite, on caractérise les fonctions f pour lesquelles l'opérateur de Hankel de symbole f-bar est un opérateur de Hilbert-Schmidt. En outre, on établit des conditions nécessaires sur f pour que l'opérateur induit par f-bar soit un opérateur borné, compact et appartienne à la p-ème classe de Schatten, excepté dans le cas de l'espace de Dirichlet.
Hass, Vincent. "Modèles individu-centrés en dynamiques adaptatives, comportement asymptotique et équation canonique : le cas des mutations petites et fréquentes". Electronic Thesis or Diss., Université de Lorraine, 2023. http://www.theses.fr/2023LORR0165.
Texto completoAdaptive dynamics theory is a branch of evolutionary biology which studies the links between ecology and evolution. The biological assumptions that define its framework are those of rare and small mutations and large asexual populations. Adaptive dynamics models describe the population at the level of individuals, which are characterised by their phenotypes, and aim to study the influence of heredity, mutation and selection mechanisms on the long term evolution of the population. The success of this theory comes in particular from its ability to provide a description of the long term evolution of the dominant phenotype in the population as a solution to the “Canonical Equation of Adaptive Dynamics” driven by a fitness gradient, where fitness describes the possibility of mutant invasions, and is constructed from ecological parameters. Two main mathematical approaches to the canonical equation have been developed so far: an approach based on PDEs and a stochastic approach. Despite its success, the stochastic approach is criticised by biologists as it is based on a non-realistic assumption of too rare mutations. The goal of this thesis is to correct this biological controversy by proposing more realistic probabilistic models. More precisely, the aim is to investigate mathematically, under a double asymptotic of large population and small mutations, the consequences of a new biological assumption of frequent mutations on the canonical equation. The goal is to determine, from a stochastic individual-based model, the long term behaviour of the mean phenotypic trait of the population. The question we ask is reformulated into a slow-fast asymptotic analysis acting on two eco-evolutionary time scales. A slow scale corresponding to the dynamics of the mean trait, and a fast scale corresponding to the evolutionary dynamics of the centred and dilated distribution of traits. This slow-fast asymptotic analysis is based on averaging techniques. This method requires the identification and characterisation of the asymptotic behaviour of the fast component and that the latter has ergodicity properties. More precisely, the long time behaviour of the fast component is non-classical and corresponds to that of an original measure-valued diffusion which is interpreted as a centered Fleming-Viot process that is characterised as the unique solution of a certain martingale problem. Part of these results is based on a duality relation on this non-classical process and requires moment conditions on the initial data. Using coupling techniques and the correspondence between Moran's particle processes and Kingman's genealogies, we establish that the centered Fleming-Viot process satisfies an ergodicity property with exponential convergence result in total variation. The implementation of averaging methods, inspired by Kurtz, is based on compactness-uniqueness arguments. The idea is to prove the compactness of the laws of the couple made up of the slow component and the occupation measure of the fast component and then to establish a martingale problem for all accumulation points of the family of laws of this couple. The last step is to identify these accumulation points. This method requires in particular the introduction of stopping times to control the moments of the fast component and to prove that they tend to infinity using large deviation arguments, to reduce the problem initially posed on the real line to the torus case in order to prove compactness, to identify the limit of the fast component by adapting an argument based on Dawson duality, to identify the limit of the slow component and then to move from the torus to the real line
Keller, Julien. "Equations de type Vortex et métriques canoniques". Phd thesis, Université Paul Sabatier - Toulouse III, 2005. http://tel.archives-ouvertes.fr/tel-00012107.
Texto completo$$\sqrt\Lambda F_h = \sum_i \widetilde_i\pi^_$$
alors nous prouvons que la suite de métriques équilibrées existe, converge et sa limite est, à un changement conforme, solution de l'équation précédente. De ce résultat nous déduisons, par réduction dimensionnelle, un théorème d'approximation dans le cas des équations Vortex de Bradlow ainsi que leurs généralisations aux équations couplées Vortex.
Chen, Yahao. "Geometric analysis of differential-algebraic equations and control systems : linear, nonlinear and linearizable". Thesis, Normandie, 2019. http://www.theses.fr/2019NORMIR04.
Texto completoIn the first part of this thesis, we study linear differential-algebraic equations (shortly, DAEs) and linear control systems given by DAEs (shortly, DAECSs). The discussed problems and obtained results are summarized as follows. 1. Geometric connections between linear DAEs and linear ODE control systems ODECSs. We propose a procedure, named explicitation, to associate a linear ODECS to any linear DAE. The explicitation of a DAE is a class of ODECSs, or more precisely, an ODECS defined up to a coordinates change, a feedback transformation and an output injection. Then we compare the Wong sequences of a DAE with invariant subspaces of its explicitation. We prove that the basic canonical forms, the Kronecker canonical form KCF of linear DAEs and the Morse canonical form MCF of ODECSs, have a perfect correspondence and their invariants (indices and subspaces) are related. Furthermore, we define the internal equivalence of two DAEs and show its difference with the external equivalence by discussing their relations with internal regularity, i.e., the existence and uniqueness of solutions. 2. Transform a linear DAECS into its feedback canonical form via the explicitation with driving variables. We study connections between the feedback canonical form FBCF of DAE control systems DAECSs proposed in the literature and the famous Morse canonical form MCF of ODECSs. In order to connect DAECSs with ODECSs, we use a procedure named explicitation (with driving variables). This procedure attaches a class of ODECSs with two kinds of inputs (the original control input and the vector of driving variables) to a given DAECS. On the other hand, for classical linear ODECSs (without driving variables), we propose a Morse triangular form MTF to modify the construction of the classical MCF. Based on the MTF, we propose an extended MTF and an extended MCF for ODECSs with two kinds of inputs. Finally, an algorithm is proposed to transform a given DAECS into its FBCF. This algorithm is based on the extended MCF of an ODECS given by the explication procedure. Finally, a numerical example is given to show the structure and efficiency of the proposed algorithm. For nonlinear DAEs and DAECSs (of quasi-linear form), we study the following problems: 3. Explicitations, external and internal analysis, and normal forms of nonlinear DAEs. We generalize the two explicitation procedures (with or without driving variable) proposed in the linear case for nonlinear DAEs of quasi-linear form. The purpose of these two explicitation procedures is to associate a nonlinear ODECS to any nonlinear DAE such that we can use the classical nonlinear ODE control theory to analyze nonlinear DAEs. We discuss differences of internal and external equivalence of nonlinear DAEs by showing their relations with the existence and uniqueness of solutions (internal regularity). Then we show that the internal analysis of nonlinear DAEs is closely related to the zero dynamics in the classical nonlinear control theory. Moreover, we show relations of DAEs of pure semi-explicit form with the two explicitation procedures. Furthermore, a nonlinear generalization of the Weierstrass form WE is proposed based on the zero dynamics of a nonlinear ODECS given by the explicitation procedure
Schiffmann, Olivier. "Algebres de hall, algebres affines quantiques et bases canoniques equations de yang-baxter dynamiques, groupes quantiques dynamiques, systemes integrables". Cergy-Pontoise, 2000. http://www.theses.fr/2000CERG0105.
Texto completoGoulart, José Henrique De Morais. "Estimation de modèles tensoriels structurés et récupération de tenseurs de rang faible". Thesis, Université Côte d'Azur (ComUE), 2016. http://www.theses.fr/2016AZUR4147/document.
Texto completoIn the first part of this thesis, we formulate two methods for computing a canonical polyadic decomposition having linearly structured matrix factors (such as, e.g., Toeplitz or banded factors): a general constrained alternating least squares (CALS) algorithm and an algebraic solution for the case where all factors are circulant. Exact and approximate versions of the former method are studied. The latter method relies on a multidimensional discrete-time Fourier transform of the target tensor, which leads to a system of homogeneous monomial equations whose resolution provides the desired circulant factors. Our simulations show that combining these approaches yields a statistically efficient estimator, which is also true for other combinations of CALS in scenarios involving non-circulant factors. The second part of the thesis concerns low-rank tensor recovery (LRTR) and, in particular, the tensor completion (TC) problem. We propose an efficient algorithm, called SeMPIHT, employing sequentially optimal modal projections as its hard thresholding operator. Then, a performance bound is derived under usual restricted isometry conditions, which however yield suboptimal sampling bounds. Yet, our simulations suggest SeMPIHT obeys optimal sampling bounds for Gaussian measurements. Step size selection and gradual rank increase heuristics are also elaborated in order to improve performance. We also devise an imputation scheme for TC based on soft thresholding of a Tucker model core and illustrate its utility in completing real-world road traffic data acquired by an intelligent transportation