Tesi sul tema "Variétés de Grassmann"
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Masala, Giovanni Batista. "Trigonométrie et polyèdres dans les variétés de Grassmann G2 (Rn)". Mulhouse, 1996. http://www.theses.fr/1996MULH0427.
Testo completoSemlali, Abdelhay. "Grassmanniennes de dimension infinie, groupes de lacets et opérateur vertex". Metz, 1996. http://docnum.univ-lorraine.fr/public/UPV-M/Theses/1996/Semlali.Abdelhay.SMZ9646.pdf.
Testo completoIn the first part of this work, we studied the infinite dimensional Grassmannians of a separable Hilbert space. More exactly, the link between hilbertian grassmannians and its connected components, the restricted general linear group, and the open sets covering of this hilbertian grassmannian. We studied also the connected components of a dense grassmannian of a hilbertian grassmannian, the link between its connected components and its cellular Schubert decomposition. At the end of this part, we show the topologic relation existing between the infinite dimensional grassmannians and the finite dimensional once. In the second part of this work, we studied the link between the loop groups and the grassmannians, we studied also the operator vertex's action on the grassmannian's elements associated to the tau function
Amine, Semaan Elias. "Lower-mobility parallel manipulators : geometrical analysis, singularities and conceptual design". Ecole Centrale de Nantes, 2011. http://www.theses.fr/2011ECDN0057.
Testo completoThis PhD thesis report deals with the geometrical analysis, the singularities and the conceptual design of lower-mobility parallel manipulators. Its main contributions consist in the formulation of a systematic method to analyze the singularities of lower-mobility parallel manipulators based on Grassmann-Cayley algebra and Grassmann geometry and an approach for the conceptual design of such manipulators based on their singularity conditions. The report is composed of six chapters. The first chapter enumerates the general characteristics of the manipulators under study and provides a state of the art on the singularities and the different methods for their determination. The second chapter recalls the fundamental concepts and tools required for the compre-hension of the methods and contributions of this PhD thesis. The third chapter develops, through several case studies, a method for the constraint analysis of lower-mobility parallel manipulators and introduces the concept of wrench graph in the 3-dimensional projective space. This wrench graph is useful for the singularity analysis and provides a conceptual aspect. The fourth chapter presents a systematic method for the singularity analysis of lower-mobility parallel manipulators based on Grassmann-Cayley algebra. This method allows the determina-tion of the parallel singularity conditions of the studied manipulator algebraically, geometrically and in a vector form and the description of the uncontrollable motions of the moving platform in these singular configurations. The fifth chapter introduces some concepts that make it possible to use Grassmann geometry for the singularity analysis of lower-mobility parallel manipulators and highlights the correspondence and the complementarity of Grassmann-Cayley algebra and Grassmann geometry in the singularity analysis of such manipulators. Finally, the sixth chapter introduces a procedure for the type synthesis of parallel Schönflies motion generators based on the concept of wrench graph, the Grassmann-Cayley algebra and the Grassmann geometry. This procedure allows one to take into account the singularities at the conceptual design of such manipulators
Gmira, Seddik. "Etude géométrique des suites d'immersions conformes du disque". Lyon 1, 1993. http://www.theses.fr/1993LYO10037.
Testo completoSchäfer, Lars. "Geometrie tt* et applications pluriharmoniques". Nancy 1, 2006. http://www.theses.fr/2006NAN10041.
Testo completoIn this work we introduce the real differential geometric notion of a tt*-bundle (E,D,S), a metric tt*-bundle (E,D,S,g) and a symplectic tt*-bundle (E,D,S,omega) on an abstract vector bundle E over an almost complex manifold (M,J). With this notion we construct, generalizing Dubrovin, a correspondence between metric tt*-bundles over complex manifolds (M,J) and admissible pluriharmonic maps from (M,J) into the pseudo-Riemannian symmetric space GL(r,R)/O(p,q) where (p,q) is the signature of the metric g. Moreover, we show a rigidity result for tt*-bundles over compact Kähler manifolds and we obtain as application a special case of Lu's theorem. In addition we study solutions of tt*-bundles (TM,D,S) on the tangent bundle TM of (M,J) and characterize an interesting class of these solutions which contains special complex manifolds and flat nearly Kähler manifolds. We analyze which elements of this class admit metric or symplectic tt*-bundles. Further we consider solutions coming from varitations of Hodge structures (VHS) and harmonic bundles. Applying our correspondence to harmonic bundles we generalize a correspondence given by Simpson. Analyzing the associated pluriharmonic maps we obtain roughly speaking for special Kähler manifolds the dual Gauss map and for VHS of odd weight the period map. In the case of non-integrable complex structures, we need to generalize the notions of pluriharmonic maps and some results. Apart from the rigidity result we generalize all above results to para-complex geometry
Banos, Bertrand. "Opérateurs de Monge-Ampère symplectiques en dimensions 3 et 4". Angers, 2002. http://www.theses.fr/2002ANGE0041.
Testo completoNiglio, Louis. "Classes caractéristiques lagrangiennes". Montpellier 2, 1987. http://www.theses.fr/1987MON20282.
Testo completoMosquera, Meza Rolando. "Interpolation sur les variétés grassmanniennes et applications à la réduction de modèles en mécanique". Thesis, La Rochelle, 2018. http://www.theses.fr/2018LAROS008/document.
Testo completoThis dissertation deals with interpolation on Grassmann manifolds and its applications to reduced order methods in mechanics and more generally for systems of evolution partial differential systems. After a description of the POD method, we introduce the theoretical tools of grassmannian geometry which will be used in the rest of the thesis. This chapter gives this dissertation a mathematical rigor in the performed algorithms, their validity domain, the error estimate with respect to the grassmannian distance on one hand and also a self-contained character to the manuscript. The interpolation on Grassmann manifolds method introduced by David Amsallem and Charbel Farhat is afterward presented. This method is the starting point of the interpolation methods that we will develop in this thesis. The method of Amsallem-Farhat consists in chosing a reference interpolation point, mapping forward all interpolation points on the tangent space of this reference point via the geodesic logarithm, performing a classical interpolation on this tangent space and mapping backward the interpolated point to the Grassmann manifold by the geodesic exponential function. We carry out the influence of the reference point on the quality of the results through numerical simulations. In our first work, we present a grassmannian version of the well-known Inverse Distance Weighting (IDW) algorithm. In this method, the interpolation on a point can be considered as the barycenter of the interpolation points where the used weights are inversely proportional to the distance between the considered point and the given interpolation points. In our method, denoted by IDW-G, the geodesic distance on the Grassmann manifold replaces the euclidean distance in the standard framework of euclidean spaces. The advantage of our algorithm that we show the convergence undersome general assumptions, does not require a reference point unlike the method of Amsallem-Farhat. Moreover, to carry out this, we finally proposed a direct method, thanks to the notion of generalized barycenter instead of an earlier iterative method. However, our IDW-G algorithm depends on the choice of the used weighting coefficients. The second work deals with an optimal choice of the weighting coefficients, which take into account of the spatial autocorrelation of all interpolation points. Thus, each weighting coefficient depends of all interpolation points an not only on the distance between the considered point and the interpolation point. It is a grassmannian version of the Kriging method, widely used in Geographic Information System (GIS). Our grassmannian Kriging method require also the choice of a reference point. In our last work, we develop a grassmannian version of Neville's method which allow the computation of the Lagrange interpolation polynomial in a recursive way via the linear interpolation of two points. The generalization of this algorithm to grassmannian manifolds is based on the extension of interpolation of two points (geodesic/straightline) that we can do explicitly. This algorithm does not require the choice of a reference point, it is easy to implement and very quick. Furthermore, the obtained numerical results are notable and better than all the algorithms described in this dissertation
Molitor, Mathieu. "Grassmanniennes non-linéaires, groupes de difféomorphismes unimodulaires et quelques équations hamiltoniennes en dimension infinie". Metz, 2007. http://www.theses.fr/2007METZ015S.
Testo completoIn this thesis, we study the vortex filament equation, the Euler equation of an incompressible fluid which is G-invariant with respect to a Lie group action and we also study the non-linear grassmanniann. Our study is organized in three chapter and two appendices : in the first chapter, we study the local form of the vortex filament equation and we show that Hasimoto's trisk extends to the the case of a filament embedded in a general three-dimensional riemannian manifold. In the second chapter, we study the group of unimodular automorphisms of the total space of a principal bundle. We compute the Euler equations associated to this group and derive some short exact sequences. In the third chapter, we study the non-linear grassmannian, some geometrical structures on it and we consider also some hamiltonian equations associated. The first appendix treats the notion of differentiable calculus on a frechet space and the second is devoted to the group of unimodular diffeomorphisms of a compact manifold
Djament, Aurélien. "Représentations génériques des groupes linéaires : catégories de foncteurs en grassmaniennes, avec applications à la conjecture artinienne". Paris 13, 2006. http://www.theses.fr/2006PA132034.
Testo completoNguyen, Dat Dang. "Groupe de Cremona". Nice, 2009. http://www.theses.fr/2009NICE4036.
Testo completoKhayata, Mohamed. "Inversion de la transformation de Radon". Grenoble 2 : ANRT, 1987. http://catalogue.bnf.fr/ark:/12148/cb376065397.
Testo completoSmirnov, Evgeny. "Orbites d'un sous-groupe de Borel dans le produit de deux grassmanniennes". Phd thesis, Université Joseph Fourier (Grenoble), 2007. http://tel.archives-ouvertes.fr/tel-00263544.
Testo completoKfoury, Dimitry. "Calcul de Schubert affine et formules de Pieri". Electronic Thesis or Diss., Université de Lorraine, 2020. http://www.theses.fr/2020LORR0215.
Testo completoPieri's formulas are a gateway to understanding the algebra structure of the (affine) Grassmannian or even that of Flag varieties. Several are already established in a few particular types and cases. However, this problem remains open for most affine cases, especially to find Pieri formulas in "H (\mathcal{G}r_G)" in types "B", "C" and "D".In this thesis, even if some results are generalized for non-twisted affine Weyl groups, we mainly explore types A and C. In the flag variete of affine type A, we find a formula for multiplying, in the cohomology algebra of a flag variety, one element of the base "\xi^w" by another (special) element that will be called ''crochet''. This result is shown using the Pieri formula given by Lam et al in \cite{insertion}. In the affine Type "C", we propose a conjecture for a Pieri formula in Cohomology, showing that it is valid in degree "1" and "almost" all cases of degree "2". It is also checked, by testing many examples using the computer.In Homology, the Pieri formula in type C \cite{lam2010schubert}, is re-demonstrated, using a new simplified strategy. This new approach could eventually be used to establish formulas of exceptional types.In the finite dimensional flag varieties, we find an upper bound for the littlewood-Richardson's coefficients and generalize it, in all types, to particular classes that will be called ''small Schubert classes''
Ben, Hammouda Walid. "Topologie des fonctions rationnelles dans une Grassmannienne et espaces de lacets sur les espaces de configurations". Thesis, Lille 1, 2011. http://www.theses.fr/2011LIL10037/document.
Testo completoIn this thesis we study a topological point of view two spaces whose usefulness and importance beyond the scope of algebraic topology. The first space consists of all holomorphic maps of the Riemann sphere in a complex Grassmannian manifold. This space is divided into connected components and we identify the entire homotopy type of the component of degree one. We deduce explicit homological calculations. In the case of based map, we explain an action of the operad of two little disks on the space of rational functions, simplifying some work of Mann and Milgram. We also study the spaces of continuous maps and in the case of the Grassmannian of two planes complex C4, we obtain a homotopy decomposition of the space of loops. Finally the second space that we study is the free loop space of configurations of distinct points in Rn. In the case of three points, we obtain a simple and elegant result of homological splitting belonging to Fadell and Husseini
Adouani, Inès. "Quelques problèmes de géométrie Finslérienne et Kählerienne". Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066130.
Testo completoThis thesis deals with some classical problems in complex geometry. The first part is devoted to a problem in complex Finsler Geometry. Giving two holomorphic vector bundles E1 and E2, respectively endowed with two Finsler structures F1 and F2, we build a Finsler metric F on E 1 ⊗ E 2 involving the two initial Finsler structures. This is done under some assumptions on global sections of E1* and E2*. We give an optimal condition under which F is strictly pseudo convex with negative curvature. This result is preceded by a chapter containing a background material in complex Finsler geometry and some personal attempts. The second part of this thesis deals with a problem in Kähler Geometry. We prove the existence of an "extremal" function lower bounding all admissible functions (ie plurisubharmonic functions modulo a metric) with sup equal to zero on the complex Grassmann manifold G m,nm ( C ). The functions considered are invariant under a suitable automorphisms group. This gives a conceptually simple method to compute Tian's invariant in the case of a non toric manifold
Alashkar, Taleb. "3D dynamic facial sequences analysis for face recognition and emotion detection". Thesis, Lille 1, 2015. http://www.theses.fr/2015LIL10109/document.
Testo completoIn this thesis, we have investigated the problems of identity recognition and emotion detection from facial 3D shapes animations (called 4D faces). In particular, we have studied the role of facial (shapes) dynamics in revealing the human identity and their exhibited spontaneous emotion. To this end, we have adopted a comprehensive geometric framework for the purpose of analyzing 3D faces and their dynamics across time. That is, a sequence of 3D faces is first split to an indexed collection of short-term sub-sequences that are represented as matrix (subspace) which define a special matrix manifold called, Grassmann manifold (set of k-dimensional linear subspaces). The geometry of the underlying space is used to effectively compare the 3D sub-sequences, compute statistical summaries (e.g. sample mean, etc.) and quantify densely the divergence between subspaces. Two different representations have been proposed to address the problems of face recognition and emotion detection. They are respectively (1) a dictionary (of subspaces) representation associated to Dictionary Learning and Sparse Coding techniques and (2) a time-parameterized curve (trajectory) representation on the underlying space associated with the Structured-Output SVM classifier for early emotion detection. Experimental evaluations conducted on publicly available BU-4DFE, BU4D-Spontaneous and Cam3D Kinect datasets illustrate the effectiveness of these representations and the algorithmic solutions for identity recognition and emotion detection proposed in this thesis
Chen, Zongbin. "Pureté des fibres de Springer affines pour GL_4". Thesis, Paris 11, 2011. http://www.theses.fr/2011PA112266/document.
Testo completoThis thesis consists of two parts. In the first part, we prove the purity of affine Springer fibers for $\gl_{4}$ in the unramified case. More precisely, we have constructed a family of non standard affine pavings for the affine grassmannian, which induce an affine paving for the affine Springer fiber. In the second part, we introduce a notion of $\xi$-stability on the affine grassmannian $\xx$ for the group $G=\gl_{d}$, and we calculate the Poincaré polynomial of the quotient $\xx^{\xi}/T$ of the stable part $\xxs$ by the maximal torus $T$ by a process analogue to the Harder-Narasimhan reduction
Ngo, Khac Hoang. "Non-coherent wireless communications : fundamental limits and system design". Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASC031.
Testo completoIn wireless communication over fading channels, especially multiple-antenna communication, the instantaneous knowledge of channel coefficients, so-called channel state information (CSI), is critical because it enables to adapt the transmission and reception to current channel conditions. The communication with a priori CSI at the receiver is said to be coherent. In practice, however, CSI is not granted for free prior to communication and needs to be estimated at a cost that should not be ignored, especially in a highly mobile environment. Thus, communication without a priori CSI, also known as noncoherent communication, is a more practical and general framework. This thesis contributes to the understanding of the theoretical limits of noncoherent communications, as well as the design of a practical noncoherent communication system in block fading. We consider three scenarios: the point-topoint (P2P) channel, the multiple-access channel (MAC), and the broadcast channel (BC).In the first part, we study the fundamental limits of noncoherent communications in terms of achievable data rate and degrees of freedom (DoF). We consider generic block fading in which the channel has finite differential entropy and finite second moment. First, we derive the optimal DoF for the noncoherent multiple-input multiple-output (MIMO) P2P channel by using the duality approach to bound the input-output mutual information. Second, using a similar duality approach, we derive the optimal DoF region for the two-user noncoherent single-input multiple-output (SIMO) MAC, which can be achieved by time sharing between simple pilot-based schemes. Third, we derive achievable rate and DoF regions for the noncoherent MIMO BC with spatially correlated fading by exploiting the transmit correlation diversity, which is the difference between the correlation experienced by different users. In doing so, we carefully design pilot-based transmission schemes based on rate splitting, product superposition, and a combination of them to effectively transmit signals in both the common and mutually exclusive parts of the correlation subspaces. In the second part, we design the constellation and efficient detection schemes for noncoherent communications over Rayleigh block fading channel. First, we propose a structured Grassmannian constellation for the SIMO P2P channel that is simple to generate, has high packing efficiency, admits a simple yet effective binary labeling, and allows for efficient soft and hard detection. Second, we investigate joint constellation design for the MIMO MAC. We introduce some simple and effective design criteria so as to minimize the joint detection error, and propose some simple constellation constructions. Third, we propose a noncoherent multi-user soft detection scheme for the SIMO MAC in spatially correlated Rayleigh fading based on expectation propagation approximate inference. This scheme has polynomial complexity in the channel dimension while producing accurate approximate per-user posterior marginals leading to near-optimal error performance
Kammoun, Inès. "Codage spatio-temporel sans connaissance a priori du canal". Paris, ENST, 2004. http://www.theses.fr/2004ENST0026.
Testo completoWireless communications multiple input multiple output systems promise very high data rates on scattering-rich wireless channels. Most of the proposed schemes that achieve these high rates require the channel to be known to the receiver. In practice, knowledge of the channel is often obtained via training, which can decrease significantly the spectral efficiency. We propose an EM-based maximum a posteriori semi-blind receiver which. This iterative receiver uses pilots as well as unknown data symbols in order to improve the channel estimation quality. The space-time scheme considered for the transmission is the Alamouti's two-branch scheme. However, it is not always feasible or advantageous to use training-based schemes. Hence, we propose to use a space-time transmission scheme that do not require channel state information either at the transmitter or at the receiver end. This scheme is referenced as non coherent one. In this context, we proposed to design new schemes that lead to efficient encoding/decoding for the noncoherent MIMO communication. First, we proved that the design of a good non coherent code is equivalent to the design of codes on the Grassmann manifold with a distance criterion deduced from the expression of the pairwise error probability. By the study of the existant parameterizations of the Grassmann manifold, we concluded that a new one must be introduced. Hence, we proposed an exponential parameterization of this manifold. We proposed a simplification of the code conception criterion in the Grassmann manifold. We have introduced a new family of space-time codes suited for non coherent MIMO systems. These codes have a lot of advantages. The number of conveyed information symbols is maximized, maximum order of diversity is reached by using similar tools as in the coherent case. They permit a larger spectral efficiency than existing non coherent codes for similar or better performance. We also proposed how to simplify the GLRT (Generalized Likelihood Ratio Test) decoding process
Ernst, Romuald. "Dynamique des opérateurs sur les Grassmanniennes". Phd thesis, Université Blaise Pascal - Clermont-Ferrand II, 2013. http://tel.archives-ouvertes.fr/tel-00949228.
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