ETH Zurich

E-Periodica Schweizer Zeitschriften online. Revues suisses en ligne. Swiss journals online.

Journal
Volume 27 (1981)
Issue 1-2: L'ENSEIGNEMENT MATHÉMATIQUE
Front matter
Table of Contents
Front matter
Index
Front matter
Front matter 1
Article: SUR LA FONCTION: NOMBRE DE FACTEURS PREMIERS DE N 3
Abstract 3
Chapter: Introduction 3
Chapter: §1. DÉMONSTRATION DU THÉORÈME 1 6
Chapter: §2. DÉMONSTRATION DU THÉORÈME 2 10
Chapter: §3. Valeurs extrêmes de f(n) + f(n +1) 12
Chapter: §4. Nombres ω-intéressants 17
Chapter: §5. DÉMONSTRATION DU THÉORÈME 4 19
Bibliography 25
Article: THE HYPER-KLOOSTERMAN SUM 29
Chapter: 1. Introduction 29
Chapter: 2. Lemmas 30
Chapter: 3. Proof of Theorems 1 and 2 32
Bibliography 40
Article: THÉORÈMES DE GAUSS-BONNET, DE HOPF, ET RÉSIDUS DES CONNEXIONS MÉTRIQUES A SINGULARITÉS 41
Chapter: 1. Introduction 41
Chapter: 2. Connexions métriques sur une surface (Rappels) 43
Chapter: 3. Résidus et formule locale de Gauss-Bonnet 45
Chapter: 4. Théorème des résidus 47
Chapter: 5. Connexions métriques sans singularités 48
Chapter: 6. Connexions métriques plates a singularités isolées 50
Bibliography 55
Article: SCHUBERT CALCULUS OF A COXETER GROUP 57
Chapter: Introduction 57
Chapter: 1. Coxeter groups 59
Chapter: 2. Demazure's basis theorem 63
Chapter: 3. GIAMBELLI FORMULA 66
Chapter: 4. Pieri formula 71
Chapter: 5. $H_w$ AS A AND PARABOLICS 74
Chapter: 6. Application: The combinatorics of the classical Pieri formula 76
Bibliography 83
Article: SPECKER'S MATHEMATICAL WORK FROM 1949 TO 1979 85
Chapter: From doctorate to professorship 87
Chapter: Enjoyment of interaction 88
Chapter: Topology and recursive analysis 88
Chapter: An example of beginning with concrete problems 89
Chapter: Logic and quantum mechanics 90
Chapter: Typical ambiguity and model theory 92
Chapter: Complexity of algorithms 94
Chapter: Specker's Mathematical Publications (1949-79) 96
Article: TOWARDS A COMPLEXITY THEORY OF SYNCHRONOUS PARALLEL COMPUTATION 99
Abstract 99
Chapter: 1. Introduction 99
Chapter: 2. Circuits and Alternating Turing Machines 102
Chapter: 3. Log Depth vs Log Space 109
Chapter: 4. Conglomerates and Aggregates 111
Chapter: 5. Hardware Modification Machines 116
Chapter: 6. Other Modifiable Models 117
Chapter: 7. Simultaneous Resource Bounds 118
Chapter: 8. Open Questions 122
Bibliography 123
Article: ZUR AXIOMATISIERUNG GEWISSER AFFINER GEOMETRIEN 125
Chapter: 1. EINFÜHRUNG UND PROBLEMSTELLUNG 125
Chapter: 2. Beweis der Charakterisierungslemmas 128
Chapter: 3. Die Nicht-Charakterisierbarkeit 132
Chapter: 4. SCHLUSSBEMERKUNGEN 134
Bibliography 135
Article: ALTERNATION AND THE ACKERMANN CASE OF THE DECISION PROBLEM 137
Abstract 137
Chapter: 1. Introduction and historical background 137
Chapter: 2. Some notions from logic 141
Chapter: 3. Some notions from computational complexity 142
Chapter: 4. Alternating Turing machines 144
Chapter: 5. Upper bounds 147
Chapter: 6. Lower bounds 154
Chapter: Conclusions 159
Chapter: Acknowledgment 160
Bibliography 160
Article: PROBLEMS AND RESULTS ON FINITE AND INFINITE COMBINATORIAL ANALYSIS II 163
Article: HOMÉOMORPHIE DES ROTATIONS DE $S^m$ ÉVOLUTION D'UN PROBLÈME, SOUVENIRS 177
Bibliography 183
Article: THE RIEMANN-ROCH THEOREM FOR COMPACT RIEMANN SURFACES 185
Chapter: §1. Introduction 185
Chapter: §2. Line bundles and vector bundles. Sheaf theoretic preliminaries 185
Chapter: §3. RIEMANN-ROCH THEOREM (PRELIMINARY FORM) 189
Chapter: §4. The degree of the canonical line bundle 191
Chapter: §5. RIEMANN-ROCH THEOREM (FINAL FORM). SERRE DUALITY 193
Bibliography 196
Article: IDENTITIES FOR PRODUCTS OF GAUSS SUMS OVER FINITE FIELDS 197
Chapter: 1. Introduction 197
Chapter: 2. Notation and the identities 198
Chapter: 3. Theorems of Stickelberger and Davenport-Hasse 200
Chapter: 4. Proof of (2) 200
Chapter: 5. Proof of (3) 201
Chapter: 6. Proof of (4) 204
Chapter: 7. Proof of (5) 206
Chapter: 8. Character sum analogues of (1), (1a) and (1b) 207
Bibliography 209
Article: ON THE GENUS OF GENERALIZED FLAG MANIFOLDS 211
Chapter: Introduction 211
Chapter: §1. Genus and self maps 213
Chapter: §2. The case of generalized flag manifolds 216
Bibliography 219
Article: SUR L'USAGE DE CRITÈRES POUR RECONNAÎTRE UN GROUPE LIBRE, UN PRODUIT AMALGAMÉ OU UNE HNN-EXTENSION 221
Chapter: Introduction 221
Chapter: 2. DÉFINITIONS ET GÉNÉRALITÉS SUR LES ACTIONS DE GROUPES ET LES GRAPHES 222
Chapter: 3. Critère pour groupes libres 225
Chapter: 4. Critères pour produits amalgamés 230
Chapter: 5. Critère pour les HNN-extensions 232
Chapter: 6. Structures bipolaires 236
Bibliography 242
Article: LOCALLY HOMOGENEOUS VARIATIONS OF HODGE STRUCTURE 243
Chapter: Introduction 243
Abstract: TABLE OF CONTENTS 246
Chapter: §1. Preliminaries 246
Chapter: §2. Vector bundles on Γ\M 250
Chapter: §3. The cohomology groups $H^n(\Gamma; \rho, V)$ 254
Chapter: §4. The variation of Hodge structure associated to (ρ, V) 261
Chapter: §5. Hodge theory for $H^n(\Gamma; \rho, V)$, FROM THE VARIATION OF HODGE STRUCTURE 264
Bibliography 276
Article: APPLICATION OF TOPOLOGY TO PROBLEMS ON SUMS OF SQUARES 277
Bibliography 283
Article: FINITENESS THEOREMS IN GEOMETRIC CLASSFIELD THEORY 285
Chapter: 0. Introduction 285
Chapter: II. Preliminaries 288
Chapter: II. The Main theorem 294
Chapter: III. A VARIANT 306
Chapter: IV. Absolute Finiteness theorems 311
Chapter: V. Application to l-adic representations 312
Bibliography 314
Article: APPENDIX: TORSION POINTS OF ABELIAN VARIETIES IN CYCLOTOMIC EXTENSIONS 315
Bibliography 319
Article: ON COUSIN-I COMPLEX SPACES 321
Abstract: Summary 321
Rubric 322
Bibliography 325
Article: DESCARTES, EULER, POINCARÉ, PÓLYA—AND POLYHEDRA 327
Chapter: 1. Introduction 327
Chapter: 2. Pólya's proof of Descartes' theorem 331
Chapter: 3. The angular defect in higher dimensions 335
Chapter: 3. Historical comment and summary 342
Bibliography 343
Rubric: COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE 345
Chapter: FIFTH INTERNATIONAL CONGRESS ON MATHEMATICS EDUCATION 345
Article: INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION, 1980-81 347
Chapter: 1. THE PRESIDENT'S REPORT 347
Chapter: 2. ICME iv 348
Chapter: 3. BULLETIN OF ICMI 350
Chapter: 4. FUTURE ACTIVITIES 350
Rubric: BULLETIN BIBLIOGRAPHIQUE 1
Rubric: BULLETIN BIBLIOGRAPHIQUE 57
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