Les radars à synthèse d'ouverture (Synthetic Aperture Radar ou SAR) permettent de fournir des images à très haute résolution de la surface de la Terre. Les algorithmes de classification traditionnels se basent sur une hypothèse de bruit gaussien comme modèle de signal, qui est rapidement mise en défaut lorsque l'environnement devient inhomogène ou impulsionnel, comme c'est particulièrement le cas dans les images SAR polarimétriques haute résolution, notamment au niveau des zones urbaines. L'utilisation d'un modèle de bruit composé, appelé modèle SIRV, permet de mieux prendre en compte ces phénomènes et de représenter la réalité de manière plus adéquate. Cette thèse s'emploie alors à étudier l'application et l'impact de ce modèle pour la classification des images SAR polarimétriques afin d'améliorer l'interprétation des classifications au sens de la polarimétrie et à proposer des outils adaptés à ce nouveau modèle. En effet, il apparaît rapidement que les techniques classiques utilisent en réalité beaucoup plus l'information relative à la puissance de chaque pixel plutôt qu'à la polarimétrie pour la classification. Par ailleurs, les techniques de classification traditionnelles font régulièrement appel à la moyenne de matrices de covariance, calculée comme une moyenne arithmétique. Cependant, étant donnée la nature riemannienne de l'espace des matrices de covariance, cette définition n'est pas applicable et il est nécessaire d'employer une définition plus adaptée à cette structure riemannienne. Nous mettons en évidence l'intérêt d'utiliser un modèle de bruit non gaussien sur des données réelles et nous proposons plusieurs approches pour tirer parti de l'information polarimétrique qu'il apporte. L'apport de la géométrie de l'information pour le calcul de la moyenne est de même étudié, sur des données simulées mais également sur des données réelles acquises par l'ONERA. Enfin, une étude préliminaire d'une extension de ces travaux au cas de l'imagerie hyperspectrale est proposée, de par la proximité de ce type de données avec les données SAR polarimétriques. / Synthetic Aperture Radars (SAR) now provide high resolution images of the Earth surface. Traditional classification algorithms are based on a Gaussian assumption for the distribution of the signal, which is no longer valid when the background is heterogeneous, which is particularly the case for polarimetric SAR images, especially in urban areas. A compound Gaussian model, called the SIRV model, allows to take into account these phenomena. This thesis is then devoted to studying the impact of this model for the classification of polarimetric SAR images in order to improve the interpretation of classification results in a polarimetric sense, and to propose tools better suited to this model. Indeed, classical techniques using the Gaussian assumption actually use the power information of each pixel much more than the polarimetric information. Furthermore, it is often necessary to compute a mean of covariance matrices, usually by taking the standard arithmetical mean. However, the space of covariance matrices has a Riemannian structure, not an Euclidean one, which means this definition of the mean is not correct. We will then present several methods to use the actual polarimetric information thanks to the SIRV model to improve the classification results. The benefit of using a correct, Riemannian definition of the mean will also be demonstrated on simulated and real data. Finally, a preliminary study of an extension of this work to hyperspectral imagery will be presented.

We study the Cauchy problem of the derivative nonlinear Schrodinger equation in one space dimension. Using the method of inverse scattering, we prove global well-posedness of the derivative nonlinear Schrodinger equation for initial conditions in a dense and open subset of weighted Sobolev space that can support bright solitons.

No description available.

The theory of Riemann surfaces is quite old, consequently it is well developed. Riemann surfaces originated in complex analysis as a means of dealing with the problem of multi-valued functions. Such multi-valued functions occur because the analytic continuation of a given holomorphic function element along different paths leads in general to different branches of that function. The theory splits in two parts; the compact and the non-compact case. The function theory developed on these cases are quite dissimilar. The main difficulty one encounters in the compact case is the scarcity of global holomorphic functions, which limits one’s study to meromorphic functions. This however is not an issue in non-compact Riemann surfaces, where one enjoys a vast variety of global holomorphic functions. While the function theory of compact Riemann surfaces is centered around the Riemann-Roch theorem, which essentially tells us how many linearly independent meromorphic functions there are having certain restrictions on their poles, the function theory developed on non-compact Riemann surface engages tools for approximation of functions on certain subsets by holomorphic maps on larger domains. The most powerful tool in this regard is the Runge’s approximation theorem. An intriguing application of this is the Gunning-Narasimhan theorem, which says that every connected open Riemann surface has an immersion into the complex plane. The main goal of this project is to prove Runge’s approximation theorem and illustrate its effectiveness in proving the Gunning-Narasimhan theorem. Finally we look at an analogue of Gunning-Narasimhan theorem in the case of a compact Riemann surface.

Dans cette thèse, on introduit la notion de revêtement potentiellement inséparable et on se propose de développer une théorie de la ramification pour ces derniers. Le langage utilisé est celui des schémas en groupoïdes. Après avoir établi quelques résultats préliminaires au chapitre 1, on prouve au chapitre 2 un théorème de quotient d'un schéma en groupoïdes par un sous-groupoïde. Au chapitre 3, on utilise ces résultats pour entreprendre l'étude générale du formalisme des revêtements inséparables. Enfin, au chapitre 4, on spécialise au cas des revêtements sous un schéma en groupes diagonalisable et on étudie en détail la structure de ces derniers. En particulier, on exprime le lieu Gorenstein de ces morphismes en fonction des constantes de structure du revêtement et on prouve dans ce cadre une formule analogue à la formule de Riemann-Hurwitz des revêtements ramifiés classiques. / In this thesis, we introduce the notion of inseparable coverings and we try to develop a ramification theory for such objects. We make use of the groupoid scheme formalism. In section 1, we establish preliminary results on scheme epimorphisms. We use these results in the next section to prove a quotient theorem for groupoid schemes.Then in section 3 we introduce the general formalism of inseparable coverings.Finally, in the last section we consider in greater details inseparable coverings given by the action of a diagonalizable group scheme. We compute the Gorenstein locus of these morphisms and we prove a formula analogous to the classical Riemann-Hurwitz formula.

We consider diffeomorphisms of a compact Riemann Surface. A development of Oseledec's Multiplicative Ergodic Theorem is given, along with a development of measure theoretic entropy and dimension. The main result, due to L.S. Young, is that for certain diffeomorphisms of a surface, there is a beautiful relationship between these three concepts; namely that the entropy equals dimension times expansion.

Music dictation as a discipline is over a century old but, to date, there has been no research that has shed light on its origins and background in Spain. The objective of this research is: 1. To clarify the idea behind music dictation prior to its systematization as a discipline by Albert Lavignac (1882) and Hugo Riemann (1889); and 2. To determine what methodology changes these works introduced regarding the previous practice. To this end, the origin of music dictation in Spain in official syllabuses of music pedagogy has been established and the works of sol-fa and music dictation relevant to its constitution and development have been identified, analysed and described. For each of these works, the implicit and explicit objectives have been drawn. A description has been made of the theoretical-musical approaches they put forward and an analysis has been carried out of the predominant elements of music and their treatment. The aim of this thesis is to put music dictation into its historical perspective, whose purpose focuses on the conscious and explicit perception of the melody. The conclusions reached in this thesis should prove to be of fundamental importance in the design and development of methodological tools and proposals related to the fields of music theory and ear training. / El dictado musical como disciplina tiene más de un siglo de antigüedad pero, hasta la fecha, no ha habido estudios que arrojaran luz sobres sus orígenes y antecedentes en España. El presente trabajo tiene como objetivos: 1. Esclarecer la concepción que se tenía del dictado musical antes de su sistematización como disciplina por Albert Lavignac (1882) y Hugo Riemann (1889); y 2. Determinar qué cambios metodológicos introdujeron estas obras con respecto a la praxis anterior. Para ello: se ha establecido el origen del dictado musical en España en las enseñanzas regladas de música, y se han identificado, analizado y descrito las obras de solfeo y dictado musical relevantes en su constitución y desarrollo. Se han extraído los objetivos implícitos y explícitos de cada una de estas obras; se han descrito qué planteamientos teórico-musicales proponen, y se han analizado qué elementos de la música predominaban y cómo se abordaban. Con esta tesis se pretende hacer un seguimiento histórico del dictado musical, primera disciplina cuya finalidad se centra en la percepción consciente y explícita de la melodía. Las conclusiones obtenidas en esta tesis serán un pilar clave para el diseño y el desarrollo de herramientas y propuestas metodológicas relacionadas con las áreas de lenguaje musical y educación auditiva. / El dictat musical com a disciplina té més d'un segle d'antiguitat però, fins avui, no hi ha hagut estudis que llançaren llum sobres els seus orígens i antecedents a Espanya. El present treball té com a objectius: 1. Esclarir la concepció que es tenia del dictat musical abans de la seua sistematització com a disciplina per Albert Lavignac (1882) i Hugo Riemann (1889); i 2. Determinar què canvis metodològics van introduir aquestes obres pel que fa a la praxi anterior. Per açò: s'ha establert l'origen del dictat musical a Espanya en els ensenyaments reglats de música, i s'han identificat, analitzat i descrit les obres de solfeig i dictat musical rellevants en la seua constitució i desenvolupament. S'han extret els objectius implícits i explícits de cadascuna d'aquestes obres; s'han descrit què plantejaments teòric-musicals proposen, i s'han analitzat què elements de la música predominaven i com s'abordaven. Amb aquesta tesi es pretén fer un seguiment històric del dictat musical, primera disciplina la finalitat de la qual se centra en la percepció conscient i explícita de la melodia. Les conclusions obtingudes en aquesta tesi seran un pilar clau per al disseny i el desenvolupament d'eines i propostes metodològiques relacionades amb les àrees de llenguatge musical i educació auditiva. / Gorbe Ferrer, L. (2017). Origen, fundamentación y sistematización de la educación auditiva en España: Caracterización del dictado musical como estrategia complementaria al solfeo [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/86194 / TESIS

The declension of variation. On the notion of multiplicity in Gilles Deleuze This paper aims at a reconstruction of the notion of multiplicity in the thought of the French philosopher Gilles Deleuze. To this end, our guiding thread corresponds to the relationship that this thinker establishes between the mathematical doctrine of Bernhard Riemann and the philosophy of Henri Bergson. Our purpose is to go through the various appearances of this relationship and to reconstruct the fundamental axes of an original concept of multiplicity that we believe Deleuze's thought holds. Thus, our inquiry, via a strategic journey through the Bergsonism, A Thousand Plateaus and Difference and Repetition, uncovers a double articulation for the deleuzian multiplicity. This double articulation is expressed in the two axes of thematization that we develop, namely coherence and inherence, or in other terms, a multidimensional organization and an activity of internal division. From these two axes, we believe, the notion of multiplicity describes the dynamics proper to a mouvement of continuous change or variation of nature. Keywords : Deleuze, Multiplicity, Variation, Bergson, Riemann, Bergsonism, A Thousand Plateaus, Difference and repetition.

Orientador: Fabiano Borges da Silva / Resumo: Neste trabalho apresentamos a definição da integral de Riemann por meio de so­matórios de retângulos que aproximam pela falta e pelo excesso a região sob uma curva definida por uma função. Posteriormente mostramos que as funções contínuas definidas num intervalo fechado e limitado [a, b] são integráveis e fornecemos um exemplo de função não integrável. Finalmente apresentamos o Teorema Fundamental do Cálculo e uma abor­dagem para a teoria de integração que pode ser aplicada no contexto do Ensino Médio. / Abstract: ln this work we present the definition of the Riemann integral by summing rectangles that approximate the region under a curve defined by a function due to lack and excess. Then we show that continuous functions defined in a closed and limited interval [a, b] are integrable, and after we provide an example of an unintegrable function. Finally we present the Fundamental Calculus Theorem and an approach to integration theory that can be applied in the High School context. / Mestre

We consider orthogonal polynomials P_n satisfying orthogonality relations where the measure of orthogonality is, in general, a complex-valued Borel measure supported on subsets of the complex plane. In our consideration we will focus on measures of the form d\mu(z) = \rho(z) dz where the function \rho may depend on other auxiliary parameters. Much of the asymptotic analysis is done via the Riemann-Hilbert problem and the Deift-Zhou nonlinear steepest descent method, and relies heavily on notions from logarithmic potential theory.