ETH Zurich
E-Periodica
Alle Bände

L'Enseignement Mathématique

Volume 23 (1977)
Issue 1-2: L'ENSEIGNEMENT MATHÉMATIQUE
Front matter
Table of Contents
Front matter
Index
Front matter
Article: KRITISCHE PUNKTE UND KRÜMMUNG FÜR DIE MENGEN DES KONVEXRINGES 1
Bibliography 6
Article: QUADRATIC FORMS IN AN ADELIC SETTING 7
Chapter: 1. Introduction 7
Chapter: 2. The Mean Value Formula 7
Chapter: 3. Formulation of Siegel's Theorem 8
Chapter: 4. Derivation of Siegel's Theorem 9
Bibliography 12
Article: ON THE EVALUATION OF GAUSSIAN SUMS FOR NON-PRIMITIVE DIRICHLET CHARACTERS 13
Chapter: 1. Introduction 13
Chapter: 2. Proof of theorem B 14
Chapter: 4. Special cases 17
Bibliography 18
Article: ON THE NUMBER OF ZEROS OF FUNCTIONS 19
Chapter: 0. Introduction 19
Chapter: 1. A BASIC LEMMA 20
Chapter: 2. A USEFUL IDENTITY 21
Chapter: 3. An estimation by interpolation 23
Chapter: 4. EXPONENTIAL POLYNOMIALS 26
Chapter: 5. Further results 35
Bibliography 37
Article: STABILITY OF PROJECTIVE VARIETIES 39
Abstract: Contents 39
Chapter: Introduction 39
Chapter: §1. Stable points of représentation, examples and Chow forms 41
Chapter: §2. A CRITERION FOR $X^r \subset P^n$ TO BE STABLE 54
Chapter: §3. Effect of Singular Points on Stability 68
Chapter: §4. Asymptotic Stability of Canonically Polarized Curves 82
Chapter: §5. The Moduli Space of Stable Curves 92
Chapter: LINE BUNDLES ON THE MODULI SPACE 99
Appendix: APPENDIX 108
Bibliography 110
Article: GÉNÉRALISATION DES SUITES SPECTRALES 111
Bibliography 116
Article: PROFILS ET RÉDUITE TRANSJORDANIENNE D'UNE MATRICE CARRÉE 117
Chapter: I. Itération d'un endomorphisme (singulier) 117
Chapter: II. Analyse d'un endomorphisme f. Théorèmes préliminaires 119
Chapter: III. RÉDUITE TRANSJORDANIENNE DE f 121
Chapter: IV. Condition nécessaire et suffisante de similitude DE DEUX MATRICES 124
Chapter: V. Applications 125
Article: EXTENSION AND LIFTING OF $C^\infty$ WHITNEY FIELDS 129
Bibliography 137
Article: SISTEMI NORMALI DI GENERATORI PER GLI IDEALI DI Z [x] 139
Preface: Premessa 139
Chapter: 1. Sistemi normali 139
Chapter: 2. Segnature 141
Chapter: 3. Teorema Fondamentale 145
Chapter: Nota 147
Bibliography 148
Rubric: COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE 151
Chapter: ANNOUNCEMENT FROM THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION ABOUT AN ICMI-SYMPOSIUM TO BE HELD AT THE INTERNATIONAL CONGRESS OF MATHEMATICIANS, HELSINKI, AUGUST 1978, ON THE FOLLOWING THEME: 151
Article: THE GELFAND-NAIMARK THEOREMS FOR C*-ALGEBRAS 153
Chapter: 1. Introduction 153
Chapter: 2. Definitions and motivation 154
Chapter: 3. Historical Development 155
Chapter: 4. The Gelfand-Naimark representation theorem for commutative b*-algebras 157
Chapter: 5. The Gelfand-Naimark theorem for arbitrary B*-algebras 160
Chapter: 6. Geometrical characterizations of B*-algebras 172
Chapter: 7. Further weakening of the B*-axioms 175
Chapter: 8. Applications 177
Bibliography 178
Article: REPRESENTATION OF COMPLETELY CONVEX FUNCTIONS BY THE EXTREME-POINT METHOD 181
Chapter: 0. Introduction 181
Chapter: 1. Completely convex functions 182
Chapter: 2. Determination of the extreme rays of W 184
Chapter: 3. Determination of a base for W 187
Bibliography 190
Article: SOME CONTRIBUTIONS OF BENO ECKMANN TO THE DEVELOPMENT OF TOPOLOGY AND RELATED FIELDS 191
Chapter: Introduction 191
Chapter: 1. Continuous solutions of Systems of linear equations 193
Chapter: 2. A group theoretical proof of the Hurwitz-Radon Theorem 195
Chapter: 3. Complexes with operators 197
Chapter: 5. Simple homotopy type 202
Bibliography 204
Article: ON THE CHARACTERISTIC CLASSES OF GROUPS OF DIFFEOMORPHISMS 209
Bibliography 219
Article: ALTERNATIVE HOMOTOPY THEORIES 221
Chapter: 1. Introduction 221
Chapter: 2. EQUIVARIANT HOMOTOPY THEORY 223
Chapter: 3. Some examples 225
Chapter: 4. Ex-HOMOTOPY THEORY 227
Chapter: 5. The register theorem 229
Chapter: 6. The exact sequence 230
Chapter: 7. The adjoint G-bundle 232
Chapter: 8. Examples 235
Bibliography 237
Article: LA (2p+1)-ÈME DÉVIATION D'UN ANNEAU LOCAL 239
Chapter: Introduction 240
Chapter: 2p premières déviations 241
Chapter: 2p + 1-ème déviation 243
Chapter: Situation générique 245
Chapter: Conclusion 246
Bibliography 247
Article: CHARACTERISTIC NUMBERS OF 3-MANIFOLDS 249
Bibliography 254
Article: ON REPRESENTATION OF FUNCTIONS BY MEANS OF SUPERPOSITIONS AND RELATED TOPICS 255
Abstract: CONTENTS 255
Chapter: Preface 256
Chapter: Chapter 1. — Survey of results 257
Chapter: §1. Superpositions of analytic functions 258
Chapter: §2. The problem of resolvents 259
Chapter: §3. Superpositions of smooth functions and the theory of approximation 261
Chapter: §4. Superpositions of continuons functions 263
Chapter: §5. Linear superpositions 265
Chapter: Chapter 2. — Superpositions of smooth functions 267
Chapter: §1. The notion of entropy 267
Chapter: §2. The entropy of the space of smooth functions 269
Chapter: §3. Theorem on superpositions of smooth functions 276
Chapter: Chapter 3. — Superpositions of continuous functions 277
Chapter: §1. Certain improvements of Kolmogorov 's theorem 277
Chapter: §2. The theorem of Kahane 279
Chapter: §3. The main lemma 280
Chapter: §4. The proof of the theorem 282
Chapter: Chapter 4. — Linear superpositions 283
Chapter: §1. Notation 283
Chapter: §2. Estimate of the difference of the integrais of one term of a superposition along nearby level curves 284
Chapter: §3. Deletion of dependent terms 288
Chapter: §4. Reduction of linear superpositions to a form with independent terms 292
Chapter: §5. The set of linear superpositions in the space of continuous functions is closed 296
Chapter: §6. The set of linear superpositions in the space of continuous functions is nowhere dense 299
Chapter: Chapter 5. — Dimension of the space of linear superpositions 302
Chapter: §1. (ε,δ)-entropy and the "dimension" of function spaces 302
Chapter: §2. (ε,δ)-entropy of the set of linear superpositions 306
Chapter: §3. Functional "dimension" of the space of linear superpositions 311
Chapter: §4. Variation of superpositions of smooth functions 312
Chapter: §5. Instability of the representation of functions as superpositions of smooth functions 316
Bibliography 317
Rubric: BULLETIN BIBLIOGRAPHIQUE 1
Rubrik: BULLETIN BIBLIOGRAPHIQUE 49
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