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ON INTRODUIT TOUT D'ABORD LES NOTIONS DE STRUCTURE SUR LESQUELLES CE TRAVAIL EST CONSTRUIT: CECI DANS LE CONTEXTE MATHEMATIQUE DE L'ETUDE DES FAISCEAUX DE MATRICES, DANS CELUI DES SYSTEMES AINSI QUE DANS CELUI DES MATRICES POLYNOMIALES. LES PRINCIPAUX RESULTATS CONCERNANT LA REALISATION DE PRECOMPENSATEURS SONT EGALEMENT EXPOSES. ON PRESENTE LES RESULTATS CONCERNANT LE PROBLEME DE PLACEMENT DE POLES D'UN SYSTEME LINEAIRE A PARAMETRES INVARIANTS DANS LE TEMPS DECRIT PAR L'EQUATION D'ETAT, PAR UNE COMMANDE DE TYPE RETOUR D'ETAT STATIQUE. CE PROBLEME A ETE RESOLU DANS LE CAS DE SYSTEMES COMMANDABLES PAR ROSENBROCK, ET DANS LE CAS NON COMMANDABLE PAR ZABALLA. LES DEMONSTRATIONS SONT EXPOSEES DANS LE DETAIL ET CERTAINS NOUVEAUX RESULTATS COMPLEMENTAIRES IMPORTANTS POUR LA SUITE SONT DEMONTRES. ON ABORDE LE PROBLEME DU PLACEMENT DE STRUCTURE PAR RETOUR D'ETAT STATIQUE NON REGULIER, QUI GENERALISE LES TRAVAUX DE ROSENBROCK ET ZABALLA, DANS LE CAS DES SYSTEMES EXPLICITES, COMMANDABLES OU NON. DES CONDITIONS NECESSAIRES ET SUFFISANTES EN TERME D'INDICES DE COMMANDABILITE SONT ETABLIES A PARTIR D'UNE DEMONSTRATION FAITE DANS UN CONTEXTE POLYNOMIAL. ON GENERALISE LE RESULTAT ANTERIEUR, PAR LE BIAIS D'UNE TRANSFORMATION, AU CAS DES SYSTEMES IMPLICITES INVERSIBLES A DROITE ET ON L'APPLIQUE A TROIS PROBLEMES PARTICULIERS INTERESSANTS DANS LE DOMAINE DE LA COMMANDE: LA REGULARISATION DES SYSTEMES IMPLICITES, LE PLACEMENT DE STRUCTURE DE SYSTEMES DECRITS PAR LES EQUATIONS D'ETAT ET DE SORTIE, ET L'OBTENTION DE SYSTEMES A STRUCTURES PRESCRITES PAR LE CHOIX DE L'EQUATION DE SORTIE. UN ASPECT IMPORTANT DE CE TRAVAIL EST L'EQUIVALENCE DES PROBLEMES DE COMMANDE ABORDES ET DE CERTAINS PROBLEMES DE MATRICES POLYNOMIALES OU FAISCEAUX DE MATRICES A PROPRIETES PRESCRITES CONTENANT DES SOUS-MATRICES OU SOUS-FAISCEAUX DONNES
LES SYSTEMES LINEAIRES ONT CERTAINES PROPRIETES STRUCTURELLES QUI CONDITIONNENT LA RESOLUTION DE PLUSIEURS PROBLEMES DE COMMANDE. NOUS APPELONS STRUCTURES CERTAINES LISTES D'ENTIERS ET DE POLYNOMES, PARFAITEMENT CARACTERISEES PAR LES PARAMETRES DU SYSTEME. NOUS APPELONS APPROCHE STRUCTURELLE L'ENSEMBLE DES METHODES QUI UTILISENT CES STRUCTURES POUR RESOUDRE DES PROBLEMES DE COMMANDE. DANS CE TRAVAIL, NOUS ABORDONS DANS UNE PREMIERE PARTIE LA RESOLUTION DES PROBLEMES DU REJET DE PERTURBATIONS, DE LA POURSUITE DYNAMIQUE DE MODELE, DU DECOUPLAGE REGULIER LIGNE PAR LIGNE, ET DU REJET DE PERTURBATIONS ET DECOUPLAGE SIMULTANES. NOUS PRESENTONS DE NOVUELLES CONDITIONS GEOMETRIQUES ET STRUCTURELLES (EXPRIMEES EN TERMES DE CUMULS A L'INFINI, POUR LES CAS NON STABLES, ET DE CUMULS TOTAUX POUR LE CAS STABLE) D'EXISTENCE DE LOIS DE COMMANDE PAR BOUCLAGE STATIQUE D'ETAT QUI RESOLVENT CES PROBLEMES. DANS UNE DEUXIEME PARTIE NOUS ABORDONS LES PROBLEMES DITS PARTIELS. DANS CE CAS-LA NOUS NOUS INTERESSONS AUX CONDITIONS D'EXISTENCE DE LOIS DE COMMANDE QUI FIXENT LE COMPORTEMENT D'UN NOMBRE PRE-SPECIFIE DES PREMIERS PARAMETRES DE MARKOV DU SYSTEME BOUCLE. NOUS PRESENTONS DE NOUVELLES CONDITIONS STRUCTURELLES POUR LA RESOLUTION DES PROBLEMES DU REJET DE PERTURBATIONS PARTIEL ET DU DECOUPLAGE PARTIEL LIGNE PAR LIGNE, PAR BOUCLAGE STATIQUE D'ETAT, POUR LE CAS NON STABLE, ET PAR COMPENSATION DYNAMIQUE POUR LE CAS STABLE. DANS LES DEUX CAS LES CONDITIONS SONT LES MEMES ET ELLES SONT EXPRIMEES EN TERMES D'UNE PARTIE DE LA STRUCTURE A L'INFINI DES SYSTEMES IMPLIQUES. A LA FIN DE CE MEMOIRE, NOUS ABORDONS DES EXTENSIONS POSSIBLES, ET PARTICULIEREMENT DES CONNEXIONS ENTRE LES PROBLEMES DE COMMANDE TRAITES DANS CE TRAVAIL DE THESE ET DES PROBLEMES ISSUS DE LA THEORIE H INFINI
Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly. For a better understanding of 20th century science, new mathematical tools must be introduced, like the author’s H-measures, variants by Patrick Gérard, and others yet to be discovered.
This textbook presents the core of recent advances in design theory and its implications for design methods and design organization. Providing a unified perspective on different design methods and approaches, from the most classic (systematic design) to the most advanced (C-K theory), it offers a unique and integrated presentation of traditional and contemporary theories in the field. Examining the principles of each theory, this guide utilizes numerous real life industrial applications, with clear links to engineering design, industrial design, management, economics, psychology and creativity. Containing a section of exams with detailed answers, it is useful for courses in design theory, engineering design and advanced innovation management. "Students and professors, practitioners and researchers in diverse disciplines, interested in design, will find in this book a rich and vital source for studying fundamental design methods and tools as well as the most advanced design theories that work in practice". Professor Yoram Reich, Tel Aviv University, Editor-in-Chief, Research In Engineering Design. "Twenty years of research in design theory and engineering have shown that training in creative design is indeed possible and offers remarkably operational methods - this book is indispensable for all leaders and practitioners who wish to strengthen theinnovation capacity of their company." Pascal Daloz, Executive Vice President, Dassault Systèmes
This new, third volume of Cohen-Tannoudji's groundbreaking textbook covers advanced topics of quantum mechanics such as uncorrelated and correlated identical particles, the quantum theory of the electromagnetic field, absorption, emission and scattering of photons by atoms, and quantum entanglement. Written in a didactically unrivalled manner, the textbook explains the fundamental concepts in seven chapters which are elaborated in accompanying complements that provide more detailed discussions, examples and applications. * Completing the success story: the third and final volume of the quantum mechanics textbook written by 1997 Nobel laureate Claude Cohen-Tannoudji and his colleagues Bernard Diu and Franck Laloë * As easily comprehensible as possible: all steps of the physical background and its mathematical representation are spelled out explicitly * Comprehensive: in addition to the fundamentals themselves, the books comes with a wealth of elaborately explained examples and applications Claude Cohen-Tannoudji was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Supérieure in Paris where he also studied and received his PhD in 1962. In 1973 he became Professor of atomic and molecular physics at the Collège des France. His main research interests were optical pumping, quantum optics and atom-photon interactions. In 1997, Claude Cohen-Tannoudji, together with Steven Chu and William D. Phillips, was awarded the Nobel Prize in Physics for his research on laser cooling and trapping of neutral atoms. Bernard Diu was Professor at the Denis Diderot University (Paris VII). He was engaged in research at the Laboratory of Theoretical Physics and High Energy where his focus was on strong interactions physics and statistical mechanics. Franck Laloë was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Supérieure in Paris. His first assignment was with the University of Paris VI before he was appointed to the CNRS, the French National Research Center. His research was focused on optical pumping, statistical mechanics of quantum gases, musical acoustics and the foundations of quantum mechanics.
This new edition of the near-legendary textbook by Schlichting and revised by Gersten presents a comprehensive overview of boundary-layer theory and its application to all areas of fluid mechanics, with particular emphasis on the flow past bodies (e.g. aircraft aerodynamics). The new edition features an updated reference list and over 100 additional changes throughout the book, reflecting the latest advances on the subject.
This book presents the main research veins developed within the framework of the Anthropological Theory of the Didactic (ATD), a paradigm that originated in French didactics of mathematics. While a great number of publications on ATD are available in French and Spanish, Working with the Anthropological Theory of the Didactic in Mathematics Education is the first directed at English-speaking international audiences. Written and edited by leading researchers in ATD, the book covers all aspects of ATD theory and practice, including teaching applications. The chapters feature the most relevant and recent investigations presented at the 6th international conference on the ATD, offering a unique opportunity for an international audience interested in the study of mathematics teaching and learning to keep in touch with advances in educational research. The book is divided into four sections and the contributions explore key topics such as: The core concept of ‘praxeology’, including its development and functionalities The need for new teaching praxeologies in the paradigm of questioning the world The impact of ATD on the teaching profession and the education of teachers This is the second volume in the New Perspectives on Research in Mathematics Education. This comprehensive casebook is an indispensable resource for researchers, teachers and graduate students around the world.