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Date
Editeur
Auteur
Titre
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Jérémie Joudioux - Hertz potentials and the decay of higher spin fields
/ Fanny Bastien
/ 03-07-2014
/ Canal-u.fr
Joudioux Jérémie
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The study of the asymptotic behavior of higher spin fields has proven to be a key point in understanding the stability properties of the Einstein equations. Penrose derived in the 60s the asymptotic behavior of these higher spin fields from a representation by Hertz potentiels satisfying a wave equation and a decay Ansatz for the solutions of the wave equation. The purpose of this talk is to perform the construction by Penrose in the context of the Cauchy problem on Minkowski space -time for Maxwell fields and linearized gravity. Considering a Cauchy problem for Maxwell fields and linearized gravity with data in weighted Sobolev spaces, a Hertz potential is build from a generalization of the de Rham complex to arbitrary spin. The asymptotic behavior of these higher spin fields is then derived from the asymptotic behavior of the solutions of the wave equation. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
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Serguei Ivachkovitch - Method of pseudoholomorphic curves and applications (Part 3)
/ Fanny Bastien
/ 28-06-2012
/ Canal-u.fr
Ivachkovitch Serguei
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Voir le résumé
The method of « pseudoholomorphic » curves proved itself to be extremely useful in different fields. In symplectic topology, for instance Gromov’s Nonsqueezing Theorem, Arnold’s conjecture and the Floer homology, the Gromov-Witten invariants. In complex analysis and geometry, for instane polynomial hulls of totally real surfaces, envelopes of meromorphy, holomorphic foliations. We shall develop the theory of complex curves in almost complex manifolds and discuss some of these applications in our lectures. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
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De Fourier à la compression d’images et de vidéos
/ Inria / Interstices
/ 16-04-2019
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Guillemot Christine, Roumy Aline
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Voir le résumé
Grâce à la transformée de Fourier, de nombreuses évolutions technologiques ont pu voir le jour. Cet outil mathématique essentiel en traitement d'images a rendu possible la compression d'images fixes avec le format JPEG et de vidéos avec le format MPEG ! Mot(s) clés libre(s) : traitement d'images, transformée de Fourier, transformée en cosinus discrète, compression image, réseaux auto-encodeurs, JPEG, MPEG
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De la transformée de Fourier à l’imagerie médicale
/ Inria / Interstices
/ 29-04-2019
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Grenier Denis
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Voir le résumé
L'imagerie médicale ne serait pas ce qu'elle est aujourd'hui sans la fameuse transformée de Fourier. 150 ans après sa découverte, cette technique reste d'actualité et même si de nouvelles pistes voient le jour, c'est bien à elle que l'on doit les immenses progrès réalisés en imagerie médicale ! Mot(s) clés libre(s) : transformée de Fourier, imagerie médicale, FFT, résonance magnétique nucléaire, IRM
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Transferts thermiques, : Conduction, Convection, Rayonnement
/ SILLAGES
/ 19-01-2010
/ Unisciel
Granier Olivier
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Voir le résumé
Ce cours est composé de 3 parties: conduction (diffusion) thermique, transfert thermique convectif (convection), rayonnement thermique . Mot(s) clés libre(s) : loi de Fourier, chaleur, flux thermique, résistance thermique, loi d'Ohm, loi de Newton, corps noir, loi de Wien du déplacement, loi de Stefan
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TP réalisation d’un analyseur de spectres
/ SILLAGES
/ 27-07-2011
/ Unisciel
Granier Olivier
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Ce TP, après le rappel des caractéristiques du filtre passe-bande, propose la réalisation d'un analyseur de spectres. Mot(s) clés libre(s) : analyse de Fourier, multiplieur, diodes, wobulation, filtre passe-bande, facteur de qualité, diagramme de Bode
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TP Electricité n°6 Utilisation de l'analyse de Fourier en électronique
/ SILLAGES
/ 27-07-2011
/ Unisciel
Granier Olivier
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Voir le résumé
Ce TP aborde la mise en évidence des harmoniques d'un signal carré et d'un signal triangulaire, puis étudie la réponse d'un filtre passe-bas à différentes tensions d'entrée. Mot(s) clés libre(s) : analyse de Fourier, passe-bande, passe-bas, facteurs de qualité, harmoniques, fondamental, signal carré, signal triangulaire
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Rod Gover - An introduction to conformal geometry and tractor calculus (Part 4)
/ Fanny Bastien
/ 25-06-2014
/ Canal-u.fr
Gover Rod
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Voir le résumé
After recalling some features (and the value of) the invariant ``Ricci calculus'' of pseudo-‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal covariance is visited and some covariant/invariant equations from physics are recovered in this framework. Motivated by the need to develop a more effective approach to such problems we are led into the idea of conformal geometry and a conformally invariant calculus; this``tractor calculus'' is then developed explicitly. We will discuss how to calculate using this, and touch on applications to the construction of conformal invariants and conformally invariant differential operators. The second part of the course is concerned with the application of conformal geometry and tractor calculus for the treatment of conformal compactification and the geometry of conformal infinity. The link with Friedrich’s conformal field equations will be made. As part of this part we also dedicate some time to the general problem of treating hypersurfaces in a conformal manifold, and in particular arrive at a conformal Gauss equation. Finally we show how these tools maybe applied to treat aspects of the asymptotic analysis of boundary problems on conformally compact manifolds. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
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Rod Gover - An introduction to conformal geometry and tractor calculus (Part 3)
/ Fanny Bastien
/ 25-06-2014
/ Canal-u.fr
Gover Rod
Voir le résumé
Voir le résumé
After recalling some features (and the value of) the invariant ``Ricci calculus'' of pseudo-‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal covariance is visited and some covariant/invariant equations from physics are recovered in this framework. Motivated by the need to develop a more effective approach to such problems we are led into the idea of conformal geometry and a conformally invariant calculus; this``tractor calculus'' is then developed explicitly. We will discuss how to calculate using this, and touch on applications to the construction of conformal invariants and conformally invariant differential operators. The second part of the course is concerned with the application of conformal geometry and tractor calculus for the treatment of conformal compactification and the geometry of conformal infinity. The link with Friedrich’s conformal field equations will be made. As part of this part we also dedicate some time to the general problem of treating hypersurfaces in a conformal manifold, and in particular arrive at a conformal Gauss equation. Finally we show how these tools maybe applied to treat aspects of the asymptotic analysis of boundary problems on conformally compact manifolds. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
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Rod Gover - An introduction to conformal geometry and tractor calculus (Part 2)
/ Fanny Bastien
/ 24-06-2014
/ Canal-u.fr
Gover Rod
Voir le résumé
Voir le résumé
After recalling some features (and the value of) the invariant ``Ricci calculus'' of pseudo-‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal covariance is visited and some covariant/invariant equations from physics are recovered in this framework. Motivated by the need to develop a more effective approach to such problems we are led into the idea of conformal geometry and a conformally invariant calculus; this``tractor calculus'' is then developed explicitly. We will discuss how to calculate using this, and touch on applications to the construction of conformal invariants and conformally invariant differential operators. The second part of the course is concerned with the application of conformal geometry and tractor calculus for the treatment of conformal compactification and the geometry of conformal infinity. The link with Friedrich’s conformal field equations will be made. As part of this part we also dedicate some time to the general problem of treating hypersurfaces in a conformal manifold, and in particular arrive at a conformal Gauss equation. Finally we show how these tools maybe applied to treat aspects of the asymptotic analysis of boundary problems on conformally compact manifolds. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
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