Academic literature on the topic 'E-modules'

Le sujet de cette thèse est une approche microlocale de la transformation de Radon. Il s’agit d’appliquer à la dualité projective complexe et réelle les techniques initiées dans l’article fondateur de Sato-Kashiwara-Kawai de 1972 et de retrouver, reformuler, améliorer des travaux d’analyse plus classiques sur ce sujet, en particulier ceux de G. Henkin ou S. Gindikin. La dualité projective vue sous l’angle microlocal et faisceautique est apparue pour la première fois dans un travail important de J-L. Brylinski sur les faisceaux pervers, travail repris ensuite par D’Agnolo et Schapira dans le cadre des D-modules. Notre travail est de reprendre systématiquement cette étude avec les nouveaux outils de la théorie microlocale des faisceaux (théorie qui n’existait pas à l’époque de SKK72). Ce travail se compose essentiellement de deux parties. Dans la première, nous commençons par rappeler dans un cadre général la construction des transformations canoniques quantifiées, sous l’hypothèse de l’existence d’une section simple non-dégénérée (introduite sous un autre nom par J. Leray). Cette construction n’avait jamais été faite dans un cadre global hors du cas projectif. Nous montrons alors que ces transformations commutent à l’action des opérateurs microdifferentiels. Il s’agit là d’un résultat fondamental sans qu’aucune preuve consistante n’existe dans la littérature, ce résultat étant plus ou moins sous-entendu dans SKK72. La deuxième partie de la thèse traite des applications à la transformation de Radon “clas-sique”. L’idée de base est que cette transformation échange support des hyperfonctions (modulo analyticité) et front d’onde analytique. Nous obtenons ainsi des théorèmes de prolongement ou d’unicité sur les ouverts linéellement concave. Nous obtenons aussi un théorème des résidus pour les valeurs au bord de classes de cohomologie définies sur les cônes de signatures (1, n − 1), clarifiant substantiellement des travaux de Cordaro-Gindikin-Trèves<br>The subject of this thesis is a microlocal approach to the transformation of Radon. It is a question of applying to real and complex projective duality the techniques initiated in the founding article of Sato-Kashiwara-Kawai of 1972 and to find, reformulate, improve more classic analytical work on this subject, in particular those of G. Henkin or S. Gindikin. Pro-jective duality seen from the microlocal and sheaf point of view appeared for the first time in an important work by J-L. Brylinski on perverse sheaves, work then taken up by D'Agnolo and Schapira in the framework of D-modules. Our work is to systematically resume this study with the new tools of the microlocal sheaf theory (theory which did not exist at the time of SKK72). This work essentially consists of two parts. In the first, we begin by recalling in a general framework the construction of quantized ca-nonical transformations, under the hypothesis of the existence of a simple non-degenerate section (introduced under another name by J. Leray). This construction had never been done in a global framework outside the projective case. We then show that these transfor-mations exchange the action of the microdifferential operators. This is a fundamental re-sult without any consistent proof existing in the literature, this result being more or less implied in SKK72. The second part of the thesis deals with the applications to the “classical” Radon trans-form. The basic idea is that this transform exchanges the support of hyperfunctions (modu-lo analyticity) and the analytic wavefront set. We thus obtain theorems of continuation or uniqueness on linearly concave domain. We also get a residue theorem for the boundary values of finite cohomology classes defined on cones with (1, n-1) signature, substantially clari-fying the work of Cordaro-Gindikin-Trèves

Designons respectivement par d et e le faisceau des operateurs differentiels sur une variete complexe et le faisceau des operateurs microdifferentiels formels sur le fibre projectif cotangent de la meme variete. Alors qu'en dimension superieure ou egale a trois la classification des e et d modules microlocalement libres de rang un est relativement simple, ainsi que l'ont montre d'agnolo et schapira, le cas de la dimension deux necessite a priori une etude speciale qui est l'objet de cette these. L'existence sur tout emodule microlocalement libre de rang un d'une filtration globale canonique permet de lui associer un amodule filtre d'un type bien defini, ou a est un faisceau d'algebres generalisant le faisceau d. Il est ensuite montre que cette correspondance est biunivoque grace a la construction explicite d'un foncteur inverse. Les resultats precedents sont ensuite appliques a la construction d'une equivalence de categories entre les dmodules microlocalement libres de rang un sans torsion et certains couples (f,l) ou f est un fibre vectoriel muni d'une connexion non integrable et l un sous fibre de rang un de f. De plus, par cette correspondance, un dmodule microlocalement libre de rang un sans torsion est localement stablement libre si et seulement f n'a pas de section horizontale non nulle.

Information and Communication Technology (ICT) projects are being initiated and deployed in marginalized areas to help improve the standard of living for community members. This has lead to a new field, which is responsible for information processing and knowledge development in rural areas, called Information and Communication Technology for Development (ICT4D). An ICT4D projects has been implemented in a marginalized area called Dwesa; this is a rural area situated in the wild coast of the former homelandof Transkei, in the Eastern Cape Province of South Africa. In this rural community there are e-Service projects which have been developed and deployed to support the already existent ICT infrastructure. Some of these projects include the e-Commerce platform, e-Judiciary service, e-Health and e-Government portal. Although these projects are deployed in this area, community members face a language and literacy barrier because these services are typically accessed through English textual interfaces. This becomes a challenge because their language of communication is isiXhosa and some of the community members are illiterate. Most of the rural areas consist of illiterate people who cannot read and write isiXhosa but can only speak the language. This problem of illiteracy in rural areas affects both the youth and the elderly. This research seeks to design, develop and implement software modules that can be used to convert isiXhosa text into natural sounding isiXhosa speech. Such an application is called a Text-to-Speech (TTS) system. The main objective of this research is to improve ICT4D eServices’ usability through the development of an isiXhosa Text-to-Speech system. This research is undertaken within the context of Siyakhula Living Lab (SLL), an ICT4D intervention towards improving the lives of rural communities of South Africa in an attempt to bridge the digital divide. Thedeveloped TTS modules were subsequently tested to determine their applicability to improve eServices usability. The results show acceptable levels of usability as having produced audio utterances for the isiXhosa Text-To-Speech system for marginalized areas.

Dans cette thèse nous rappelons la notion de L-algèbre, qui a pour objet d'être un modèle algébrique des types d'homotopie. L'objectif principal de cette thèse est la description d'une structure de E-infini-coalgèbre sur l'élément principal d'une L-algèbre. Ceci peut être vu comme une généralisation de la structure de E-infini-coalgèbre sur le complexe des chaînes d'un ensemble simplicial, telle que décrite par Smith dans Iterating the cobar construction, 1994. Nous construisons une E-infini-opérade, notée K, utilisée pour construire la E-infini-coalgèbre sur l'élément principal d'une L-algèbre. Cette structure de E-infini-coalgèbre montre que la L-algèbre canoniquement associée à un ensemble simplicial contient au moins autant d'information homotopique que la E-infini-coalgèbre couramment associée à un ensemble simplicial<br>In this thesis we recall the notion of L-algebra. L-algebras are intended as algebraic models for homotopy types. L-algebras were introduced by Alain Prouté in several talks since the eighties. The principal objective of this thesis is the description of an E-infinity-coalgebra structure on the main element of an L-algebra. This can be seen as a generalization of the E-infinity-coalgebra structure on the chain complex associated to a simplicial set given by Smith in Iterating the cobar construction, 1994. We construct an E-inifity-operad, denoted K, used to construct the E-inifity-coalgebra on the main element of a L-algebra. This E-inifity-coalgebra structure shows that the canonical L-algebra associated to a simplicial set contains at least as much homotopy information as the E-inifity-coalgebras usually associated to simplicial sets

The involvement of carers in oncology is important for the health of people diagnosed with cancer as well as carers themselves. To improve their involvement, three groups; patients, their carers, and  clinicians should maintain good communication. The e-learning interface, eTRIO, has a learning module for each of these three groups. The design of eTRIO is based on research from psycho- oncologists. This study aims to answer the question; What are the strengths and weaknesses of the eTRIO interfaces for clinicians, carers, and patients in terms of their usability? Heuristic evaluation and think-alouds have been conducted to answer this. The results of this study show that interactive activities, as well as neatly presented content, are engaging the user, buttons and content should have clear purposes. The eTRIO interface will enhance carers' involvement with good usability, making it easy for users to retain important information. Strengths and areas for improvement will be presented in this study.<br>Inkludera cancerpatienters närstående i onkologi är viktigt för både cancerpatienter och deras närstående. För att förbättra de närståendes inkludering måste tre grupper; patienter, deras närstående och läkare ha god kommunikation mellan varandra. E-lärande platformen, eTRIO, har en modul för varje ovannämnd grupp. Designen av eTRIO är baserad på forskning av psyko-onkologer. Denna studie har som syfte att besvara frågan; Vad är eTRIOs gränssnitts styrkor och svagheter för läkare, cancerpatienter och närstående med avseende på användarvänlighet? En heuristisk utvärdering och think-alouds har gjorts för att svara på denna fråga. Resultaten av denna studie visar att interaktiva aktiviteter och visuellt tilltalande presenterat innehåll engagerar användarna samt att knappar och innehåll behöver tydliga syften. Gränssnitten av eTRIO kommer att förbättra närståendes inkludering med bra användarvänlighet och gör det lätt för användare att komma ihåg viktig information. Styrkor och områden för förbättring kommer att presenteras i denna studie.

We give a thorough account of the various equivalent notions for \sheaf" on a locale, namely the separated and complete presheaves, the local home- omorphisms, and the local sets, and to provide a new approach based on quantale modules whereby we see that sheaves can be identi¯ed with certain Hilbert modules in the sense of Paseka. This formulation provides us with an interesting category that has immediate meaningful relations to those of sheaves, local homeomorphisms and local sets. The concept of B-set (local set over the locale B) present in [3] is seen as a simetric idempotent matrix with entries on B, and a map of B-sets as de¯ned in [8] is shown to be also a matrix satisfying some conditions. This gives us useful tools that permit the algebraic manipulation of B-sets. The main result is to show that the existing notions of \sheaf" on a locale B are also equivalent to a new concept what we call a Hilbert module with an Hilbert base. These modules are the projective modules since they are the image of a free module by a idempotent automorphism On the ¯rst chapter, we recall some well known results about partially ordered sets and lattices. On chapter two we introduce the category of Sup-lattices, and the cate- gory of locales, Loc. We describe the adjunction between this category and the category Top of topological spaces whose restriction to spacial locales give us a duality between this category and the category of sober spaces. We ¯nish this chapter with the de¯nitions of module over a quantale and Hilbert Module. Chapter three concerns with various equivalent notions namely: sheaves of sets, local homeomorphisms and local sets (projection matrices with entries on a locale). We ¯nish giving a direct algebraic proof that each local set is isomorphic to a complete local set, whose rows correspond to the singletons. On chapter four we de¯ne B-locale, study open maps and local homeo- morphims. The main new result is on the ¯fth chapter where we de¯ne the Hilbert modules and Hilbert modules with an Hilbert and show this latter concept is equivalent to the previous notions of sheaf over a locale.<br>Orientador: Pedro Manuel Agostinho Resende

Orientadores: Adriano Adrega de Moura, Daniel Ken Nakano<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-22T17:19:06Z (GMT). No. of bitstreams: 1 Macedo_TiagoRodrigues_D.pdf: 1593692 bytes, checksum: 0f44184671f53844f40df83e883c05ea (MD5) Previous issue date: 2013<br>Resumo: Nesta tese nós estudamos dois problemas principais. O primeiro problema aborda extensões de módulos para álgebras de corrente associadas a álgebras de Lie simples, complexa e de dimensão finita. Primeiro nós calculamos 1-extensões entre módulos simples de dimensão finita dessas álgebras, recuperando parcialmente um resultado de Kodera. A seguir nós desenvolvemos uma técnica para calcular extensões mais altas entre módulos simples, com a qual nós calculamos certas 2-extensões. Por fim nós mostramos que os grupos de cohomologia da álgebra de corrente são isomorfos aos da álgebra de Lie simples associada a ela, confirmando uma afirmação de Feigin. Essa parte da tese foi desenvolvida em colaboração com B. Boe, C. Drupieski e D. Nakano. O segundo problema aborda certa classe de módulos para hiperálgebras de álgebras de corrente. Quando a álgebra de Lie a qual a álgebra de corrente é associada é de tipo ADE, nós mostramos que módulos de Weyl locais são isomorfos a certos módulos de Demazure, estendendo para característica positiva um resultado de Fourier-Littelmann. Em geral, nós estendemos um resultado de Naoi, provando que módulos de Weyl locais admitem uma bandeira de Demazure, i.e., uma filtração cujos fatores são isomorfos a módulos de Demazure. Usando esse resultado, nós provamos uma conjectura de Jakelic-Moura que afirma que o caracter dos módulos de Weyl locais para hiperálgebras de laços são independentes do corpo base, desde que este seja algebricamente fechado<br>Abstract: In this thesis we consider two main problems. The first problem concerns extensions between simple modules for current algebras associated to complex, simple, finite-dimensional Lie algebras. To begin, we compute 1-extensions between finite-dimensional simple modules, partially recovering a result due to Kodera. Then we develop a technique aimed to compute higher extensions, and which we use to compute 2-extensions between certain simple modules. Finally we prove that cohomology groups of current algebras are isomorphic to the cohomology groups of its underlying simple Lie algebra, a result stated by Feigin. This part of the thesis arises from collaboration with B. Boe, C. Drupieski and D. Nakano. The second problem is concerned with the study of certain classes of modules for hyper algebras of current algebras. In the case that the underlying Lie algebra is simply laced, we show that local Weyl modules are isomorphic to certain Demazure modules, extending to positive characteristic a result due to Fourier-Littelmann. More generally, we extend a result of Naoi by proving that local Weyl modules admit a Demazure flag, i.e., a filtration with factors isomorphic to Demazure modules. Using this, we prove a conjecture of Jakelic-Moura stating that the character of local Weyl modules for hyper loop algebras are independent of the (algebraically closed) ground field<br>Doutorado<br>Matematica<br>Doutor em Matemática

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-12-19T18:27:28Z No. of bitstreams: 1 santiagomilerquispemamani.pdf: 952447 bytes, checksum: 6008ae3816024f866eea3c17d560372d (MD5)<br>Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-02-07T12:39:21Z (GMT) No. of bitstreams: 1 santiagomilerquispemamani.pdf: 952447 bytes, checksum: 6008ae3816024f866eea3c17d560372d (MD5)<br>Made available in DSpace on 2017-02-07T12:39:21Z (GMT). No. of bitstreams: 1 santiagomilerquispemamani.pdf: 952447 bytes, checksum: 6008ae3816024f866eea3c17d560372d (MD5) Previous issue date: 2016-04-25<br>O objetivo deste trabalho é apresentar o resultado dado por Bass em [4], que determina uma condição no domínio de integridade R para que todo módulo finitamente gerado e livre de torção seja escrito como soma direta de módulos de posto 1. Mostramos que uma condição necessária é que todo ideal em R seja gerado por dois elementos, ou seja, que esses domínios sejam quase domínios de Dedekind. Em seguida, aplicamos o resultado na descrição de módulos livres de torção e de posto finito sobre os anéis de coordenadas de curvas singulares, cujas singularidades são nós ou cúspides.<br>The aim of this paper is to present the result given by Bass in [4], which determines a condition on the integral domain R so that every finitely generated torsion free module is written as a direct sum of modules of rank 1. We show that a necessary condition is that all ideal in R is generated by two elements, in other words, that these domains are almost Dedekind domains. Then, we apply the result in the description of torsion free modules of finite rank over the coordinate rings of singular curves, whose singularities are nodal or cuspidal.

L’augmentation de la puissance électrique consommée à bord des avions a récemment conduit à introduire des convertisseurs électroniques de puissance à base d'interrupteurs à IGBT dans de nombreuses applications aéronautiques. L'utilisation de ces interrupteurs diffère de leurs emplois traditionnels dans les domaines du ferroviaire ou de l'automobile. En effet, les sollicitations environnementales ainsi que les cycles de commandes électriques sont différents de ceux rencontrés jusqu’alors, ce qui amène à remettre en cause les résultats actuels au sujet de la durée de vie et de la fiabilité de ces interrupteurs. Face à ces interrogations, les sociétés THALES et Hispano-Suiza se sont associées au sein du programme de l’avion plus électrique MODERNE (MODular ElectRical NEtwork) initié par Airbus, en vue de développer des solutions à haut niveau de fiabilité pour des applications aéronautiques sévères. C’est dans ce contexte que prennent place les présents travaux, dont les objectifs sont dans un premier temps de proposer de nouvelles architectures de modules susceptibles de présenter de meilleures performances d’intégration, et dans un second temps d’en étudier la fiabilité. Pour répondre à ces questions, un état de l'art des technologies utilisables a été mené. La confrontation de ses technologies aux contraintes et recommandations aéronautiques a conduit au choix de deux approches d'assemblage, proposées avec un jeu de matériaux sélectionnés pour leurs propriétés physiques et en conformité avec les réglementations sur l’utilisation de matériaux polluants. À l'issue d'une analyse de défaillances, différents développements ont été conduits afin de modéliser et caractériser le comportement thermique, mécanique puis à défaillance des modules. Des modèles Éléments Finis de structures représentatives des solutions proposées ont alors été mis au point et exploités pour l'élaboration de règles de conception, sur la base de plans d'expériences couplés à de la simulation numériques. Les informations générées ont servi à la conception de trois prototypes destinés à des applications différentes. Les performances de ces prototypes ont été évaluées, notamment leurs fiabilités obtenues par des calculs mécano-fiabilistes ayant permis l'optimisation de la conception des différents modules.