Cahier 1-2: L'ENSEIGNEMENT MATHÉMATIQUE
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Pages liminaires
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Table des matières
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1
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Pages liminaires
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2
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Article: CARACTÉRISATION GÉOMÉTRIQUE DES SOLUTIONS DE MINIMAX POUR L'ÉQUATION DE HAMILTON-JACOBI
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3
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Résumé
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3
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Chapitre: Introduction
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Chapitre: 1. MINIMAX D'UNE FONCTION QUADRATIQUE À L'INFINI
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Chapitre: 1.1 Préliminaires
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Chapitre: 1.2 Points critiques incidents, liés et libres
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Chapitre: 1.3 Le niveau critique de minimax
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Chapitre: 2. La solution de minimax
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Chapitre: 2.1 Rappels de géométrie symplectique
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Chapitre: 2.2 La solution géométrique de (PC)
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Chapitre: 2.3 La solution de minimax
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Chapitre: 3. Caractérisation géométrique de la solution de minimax
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Chapitre: 3.1 Notations
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Chapitre: 3.2 DÉCOMPOSITIONS ADMISSIBLES (D'APRÈS CHEKANOV ET PUSHKAR)
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Chapitre: 3.3 Caractérisation géométrique du minimax
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Chapitre: 3.4 Triangles évanescents
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Bibliographie
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33
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Article: LECTURES ON QUASI-INVARIANTS OF COXETER GROUPS AND THE CHEREDNIK ALGEBRA
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Chapitre: Introduction
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Chapitre: 1. Lecture 1
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Chapitre: 1.1 Définition of quasi-invariants
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Chapitre: 1.2 Elementary properties of $Q_m$
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Chapitre: 1.3 The variety $X_m$ and its bijective normalization
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Chapitre: 1.4 FURTHER PROPERTIES OF $X_m$
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Chapitre: 1.5 The Poincaré séries of $Q_m$
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Chapitre: 1.6 The ring of differential operators on $X_m$
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Chapitre: 2. Lecture 2
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Chapitre: 2.1 Hamiltonian mechanics and integrable Systems
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Chapitre: 2.2 The classical Calogero-Moser System
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Chapitre: 2.3 The quantum Calogero-Moser System
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Chapitre: 2.4 The algebra of differential-reflection operators
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Chapitre: 2.5 Dunkl operators and symmetric quantum integrals
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Chapitre: 2.6 Additional integrals for integer valued c
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Chapitre: 2.7 An example
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Chapitre: 3. Lecture 3
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Chapitre: 3.1 Shift operator and construction of the Baker-Akhiezer function
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Chapitre: 3.2 Berest's formula for $L_q$
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Chapitre: 3.3 Differential operators on $X_m$
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Chapitre: 3.4 The Cherednik algebra
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Chapitre: 3.5 The spherical subalgebra
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Chapitre: 3.6 Category O
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Chapitre: 3.7 Generic c
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Chapitre: 3.8 The Levasseur-Stafford theorem and its generalization
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Chapitre: 3.9 The action of the Cherednik algebra to quasi-invariants
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Chapitre: 3.10 Proof of Theorem 1.8
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Chapitre: 3.11 Proof of Theorem 1.15
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Bibliographie
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Article: SOME REMARKS ON NONCONNECTED COMPACT LIE GROUPS
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Résumé
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Chapitre: 1. Introduction
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Chapitre: 2. Compact Lie groups :a review
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Chapitre: 3. Compact Lie groups and extensions
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Chapitre: 4. Proof of the Main Theorem and examples
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Chapitre: 5. Splitting of the extension ASSOCIATED TO A NONCONNECTED COMPACT LIE GROUP
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Bibliographie
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Article: ATIYAH'S $L^2$-INDEX THEOREM
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Chapitre: 1. Introduction
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Chapitre: 2. REVIEW OF THE $L^2$ -INDEX THEOREM
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Chapitre: 3. Hilbert modules
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Chapitre: 4. On K-homology
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Chapitre: 5. Algebraic proof of Atiyah's $L2$-index theorem
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Bibliographie
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Article: UNE PREUVE DU THÉORÈME DE LIOUVILLE EN GÉOMÉTRIE CONFORME DANS LE CAS ANALYTIQUE
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Chapitre: 1. Introduction
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Chapitre: 2. Invariance conforme des géodésiques isotropes
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Chapitre: 3. Une application: le théorème de Liouville dans le cas analytique
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Bibliographie
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Article: IDEAL SOLUTIONS OF THE TARRY-ESCOTT PROBLEM OF DEGREES FOUR AND FIVE AND RELATED DIOPHANTINE SYSTEMS
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Résumé
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101
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Chapitre: 1. Introduction
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Chapitre: 2. Ideal non-symmetric solutions of the Tarry-Escott problem of degree four
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Chapitre: 3. Ideal non-symmetric solutions of the Tarry-Escott problem of degree five
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Bibliographie
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Article: ADDITIVE NUMBER THEORY SHEDS EXTRA LIGHT ON THE HOPF-STIEFEL o FUNCTION
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Résumé
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Chapitre: 1. Introduction
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Chapitre: 2. Proof of Theorem 4
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Chapitre: 2.1 The lower bound
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Chapitre: 2.2 The upper bound
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Chapitre: 3. From Theorem 3 to Theorem 1
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Bibliographie
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Article: NOTE ON THE HOPF-STIEFEL FUNCTION
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Chapitre: Introduction
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Chapitre: 1. Deriving Theorem 1 from Theorem 2
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Chapitre: 2. Proof of Theorem 2
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Bibliographie
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Article: TILE HOMOTOPY GROUPS
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Résumé
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Chapitre: 1. Introduction
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Chapitre: 2. Tiling and integer programming
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Chapitre: 3. Boundary words
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Chapitre: 4. Tile homotopy groups
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Chapitre: 5. Strategy for working with tile path groups
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Chapitre: 6. Criteria for $\pi(\Tau)$ to be abelian
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Appendice: 7. Appendix: further examples
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Bibliographie
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Article: SYMPLECTIC LOOK AT SURFACES OF REVOLUTION
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Chapitre: 1. Introduction
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Chapitre: 2. Abstract surfaces of revolution
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Chapitre: 3. Metrics of specified curvature
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Bibliographie
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Article: QUADRICS, ORTHOGONAL ACTIONS AND INVOLUTIONS IN COMPLEX PROJECTIVE SPACES
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Chapitre: 0. Introduction
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Chapitre: 1. ON THE TOPOLOGY OF A QUADRIC IN $P_C^n$
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Chapitre: 2. ON THE GEOMETRY OF $P_C^n$
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Chapitre: 3. $P_C^2$ AND THE 4-SPHERE $S^4$
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Chapitre: 4. SOME APPLICATIONS AND REMARKS
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Bibliographie
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Rubrique: COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION)
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Chapitre: DISCUSSION DOCUMENT FOR THE FOURTEENTH ICMI STUDY APPLICATIONS AND MODELLING IN MATHEMATICS EDUCATION
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Chapitre: 1. Rationale for the Study
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Chapitre: 2. Framework for the Study
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Chapitre: 2.1 Concepts and notions
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Chapitre: 2.2 Structure of the topic applications and modelling in mathematics education
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Chapitre: 3. Examples of important issues
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Chapitre: 3.1 Epistemology
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Chapitre: 3.2 Application problems
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Chapitre: 3.3 Modelling abilities and competencies
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Chapitre: 3.4 Beliefs, attitudes, and emotions
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Chapitre: 3.5 Curriculum and goals
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Chapitre: 3.6 Modelling pedagogy
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Chapitre: 3.7 SUSTAINED IMPLEMENTATION
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Chapitre: 3.8 Assessment and evaluation
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Chapitre: 3.9 Technological impacts
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Chapitre: 4. Call for contributions to the Study
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Rubrique: BULLETIN BIBLIOGRAPHIQUE
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Chapitre: Généralités
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Chapitre: Histoire
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5
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Chapitre: Logique et fondements
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Chapitre: Théorie des ensembles
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Chapitre: Analyse combinatoire
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Chapitre: Ordre, treillis
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Chapitre: Théorie des nombres
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Chapitre: Corps et polynômes
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Chapitre: Géométrie algébrique
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Chapitre: Anneaux et algèbres
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Chapitre: Théorie des groupes et généralisations
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Chapitre: Mesure et intégration
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Chapitre: Fonctions d'une variable complexe
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Chapitre: Equations différentielles ordinaires
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Chapitre: Systèmes dynamiques et théorie ergodique
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Chapitre: Analyse de Fourier, analyse harmonique abstraite
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Chapitre: Analyse fonctionnelle
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Chapitre: Théorie des opérateurs
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Chapitre: Calcul des variations
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Chapitre: Géométrie
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Chapitre: Topologie générale
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Chapitre: Topologie algébrique
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Chapitre: Topologie des variétés, analyse globale et analyse des variétés
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Chapitre: Probabilités et processus stochastiques
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Chapitre: Statistique
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Chapitre: Analyse numérique
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Chapitre: Informatique
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Chapitre: Mécanique des solides, élasticité et plasticité
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Chapitre: Optique, électromagnétique
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Chapitre: Economie, recherche opérationnelle, jeux
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Chapitre: Systèmes, contrôle optimal
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Pages complémentaires
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Pages complémentaires
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Pages complémentaires
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Pages complémentaires
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Pages complémentaires
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Cahier 3-4: L'ENSEIGNEMENT MATHÉMATIQUE
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Pages liminaires
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Table des matières
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215
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Pages liminaires
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216
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Article: ON THE ENTROPY OF HOLOMORPHIC MAPS
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217
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Chapitre: §1. Notation and definitions
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Chapitre: §2. ESTIMATES OF DENSITY
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Chapitre: §3. KÄHLER MANIFOLDS
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Chapitre: §4. Real algebraic maps
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Chapitre: §5. Quasiconformal maps
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Chapitre: §6. Mean curvature
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Appendice: Appendix : Examples of holomorphic endomorphisms
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Bibliographie
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231
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Chapitre: Note des Éditeurs
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Article: NOTES SUR L'ARTICLE DE M. GROMOV
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Bibliographie
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Article: ENDOMORPHISMES DES VARIÉTÉS HOMOGÈNES
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Chapitre: 1. Introduction
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Chapitre: 2. Endomorphismes des variétés complexes compactes
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Chapitre: 2.1 Dimension de Kodaira
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Chapitre: 2.2 Action d'un endomorphisme et ramification
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Chapitre: 2.3 Fibration d'Albanese
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Chapitre: 2.4 Petite dimension
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Chapitre: 2.5 Une question proche
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Chapitre: 3. Variétés homogènes kählériennes
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Chapitre: 3.1 Tores
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Chapitre: 3.2 Variétés de drapeaux
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Chapitre: 3.3 Cas général
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Chapitre: 4. Invariance de la fibration de Tits
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Chapitre: 4.1 La fibration de Tits
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Chapitre: 4.2 Première application
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Chapitre: 5. Quelques exemples
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Chapitre: 6. Existence de facteurs inversibles.
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Chapitre: 6.1 Structure de la fibration de Tits
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Chapitre: 6.2 Un théorème de Jörg Winkelmann
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Chapitre: 6.3 Endomorphismes agissant par automorphismes dans les fibres
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Chapitre: 6.4 Application
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Chapitre: 7. Endomorphismes irréductibles
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Bibliographie
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Article: HYPERBOLICITY OF MAPPING-TORUS GROUPS AND SPACES
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Résumé
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Chapitre: Introduction
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Chapitre: 1. An illustration
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Chapitre: 2. Mapping-telescopes and forest-stacks
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Chapitre: 3. Metrics
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Chapitre: 3.1 Horizontal and vertical metrics
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Chapitre: 3.2 Telescopic metric
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Chapitre: 4. Main theorem
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Chapitre: 5. PRELIMINARY WORK
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Chapitre: 5.1 About dilatation in cancellations
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Chapitre: 5.2 Straight telescopic paths
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Chapitre: 6. About straight quasi geodesics
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Chapitre: 7. Substitution of quasi geodesics
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Chapitre: 8. Approximation of straight quasi geodesics in fine position
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Chapitre: 9. PUTTING PATHS IN FINE POSITION
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Chapitre: 10. Straight quasi geodesic bigons are thin
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Chapitre: 11. Geodesic triangles are thin
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Chapitre: 12. Back to mapping-telescopes
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Chapitre: 12.1 Statement of the theorem
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Chapitre: 12.2 Proof of Theorem 12.4
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Chapitre: 13. About mapping-torus groups
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Chapitre: 13.1 Relationships with mapping-telescopes
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Chapitre: 13.2 Free group endomorphisms and forest-maps
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Chapitre: 13.3 Proof of Theorem 13.2
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Bibliographie
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Article: THE BASIC GERBE OVER A COMPACT SIMPLE LIE GROUP
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Résumé
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Chapitre: 1. Introduction
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Chapitre: 2. Gerbes with connections
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Chapitre: 2.1 Chatterjee-Hitchin gerbes
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Chapitre: 2.2 Bundle gerbes
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Chapitre: 2.3 Simplicial gerbes
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Chapitre: 2.4 Equivariant bundle gerbes
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Chapitre: 3. Gerbes from principal bundles
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Chapitre: 4. Gluing data
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Chapitre: 5. The basic gerbe over a compact simple Lie group
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Chapitre: 5.1 Notation
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Chapitre: 5.2 The basic 3-form on G
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Chapitre: 5.3 The special unitary group
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Chapitre: 6. Pre-quantization of conjugacy classes
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Appendice: Appendix A. Proof of Lemma 4.4
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Bibliographie
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Article: ANALYSE DE FOURIER DES FRACTIONS CONTINUES À QUOTIENTS RESTREINTS
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Résumé
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Chapitre: 1. Introduction
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Chapitre: 2. Les ensembles F(A)
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Chapitre: 3. Dimension de Hausdorff
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Chapitre: 4. Une mesure spéciale
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Chapitre: 5. Intégrales oscillantes
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Chapitre: 6. Estimation de la transformée de Fourier
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Chapitre: 7. Une question de Montgomery
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Chapitre: 8. COMMENTAIRES ET QUESTIONS
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Bibliographie
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Article: ON THE CLASSIFICATION OF RATIONAL KNOTS
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Résumé
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Chapitre: 1. Introduction
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Chapitre: 2. Rational tangles and their invariant fractions
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Chapitre: 3. The classification of unoriented rational knots
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Chapitre: 3.1 The cuts
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Chapitre: 3.2 The flypes
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Chapitre: 4. Rational knots and their mirror images
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Chapitre: 5. On connectivity
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Chapitre: 6. The oriented case
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Chapitre: 7. Strongly invertible links
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Bibliographie
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Rubrique: BULLETIN BIBLIOGRAPHIQUE
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Chapitre: Généralités
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Chapitre: Histoire
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Chapitre: Logique et fondements
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Chapitre: Analyse combinatoire
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Chapitre: Théorie des nombres
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Chapitre: Corps et polynômes
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Chapitre: Géométrie algébrique
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Chapitre: Anneaux et algèbres
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Chapitre: K-théorie
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Chapitre: Théorie des groupes et généralisations
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Chapitre: Groupes topologiques ; groupes et algèbres de Lie
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Chapter: Fonctions d'une variable complexe
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Chapter: Fonctions de plusieurs variables complexes
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Chapter: Équations différentielles ordinaires
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Chapter: Équations aux dérivées partielles
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Chapter: Systèmes dynamiques et théorie ergodique
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Chapter: Approximations et développements en série
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Chapter: Analyse de Fourier, analyse harmonique abstraite
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46
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Chapter: Analyse fonctionnelle
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46
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Chapter: Théorie des opérateurs
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47
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Chapter: Calcul des variations et contrôle optimal
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47
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Chapter: Géométrie
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48
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Chapter: Géométrie différentielle
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48
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Chapter: Topologie algébrique
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49
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Chapter: Topologie des variétés, analyse globale et analyse des variétés
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50
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Chapter: Probabilités et processus stochastiques
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51
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Chapter: Statistique
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51
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Chapter: Analyse numérique
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52
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Chapter: Informatique
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53
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Chapter: Mécanique des fluides, acoustique
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53
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Chapter: Biologie et sciences du comportement
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54
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Chapter: Information, communication, circuits
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54
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Back matter
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Front matter
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Index
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Back matter
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Back matter
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Back matter
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