ETH Zurich
E-Periodica
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L'Enseignement Mathématique

Band 33 (1987)
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Heft 1-2: L'ENSEIGNEMENT MATHÉMATIQUE 1
Artikel: FORMULES POUR LES TRISÉCANTES DES SURFACES ALGÉBRIQUES 1
Kapitel: Première partie : $P^4$ 9
Kapitel: I) Rappels et définitions; schémas Σ et $\Sigma_0$ 9
Kapitel: II) Trisécantes dans $P^4$: la théorie 17
Kapitel: III) Trisécantes dans $P^4$: les calculs 26
Kapitel: Deuxième partie: $P^5$, $P^6$, $P^7$ 32
Kapitel: IV) Trisécantes dans $P^5$ 32
Kapitel: V) Trisécantes dans $P^N$, N>s 42
Anhang: VI) Annexe 48
Bibliographie 65
Artikel: SUITES RÉCURRENTES LINÉAIRES Propriétés algébriques et arithmétiques 67
Chapter: Introduction 67
Chapter: A. PROPRIÉTÉS ALGÉBRIQUES 69
Chapter: I. SÉRIES RATIONNELLES SUR UN CORPS K 69
Chapter: II. Quelques exemples 71
Chapter: III. Espaces de s.r.l. sur K 75
Chapter: IV. 81
Chapter: B. ÉTUDE ARITHMÉTIQUE 87
Chapter: I. MÉTHODES ÉLÉMENTAIRES 87
Chapter: II. MÉTHODES p-ADIQUES 96
Chapter: III. MÉTHODES TRANSCENDANTES 102
Bibliography 106
Article: NONLINEAR ANALYSIS IN GEOMETRY 109
Chapter: §1. Eigenvalues and Harmonic Functions 112
Chapter: §2. Yamabe's Equation and Conformally Flat Manifolds 118
Chapter: §3. Harmonic Maps 120
Chapter: 1. Existence, uniqueness and regularity 120
Chapter: 2. Noncompact manifolds 121
Chapter: 3. Rigidity 122
Chapter: 4. Harmonic maps in physics 123
Chapter: §4. Minimal submanifolds 124
Chapter: §5. Kähler Geometry 129
Chapter: 1. Complex and almost complex structures 129
Chapter: 2. KÄHLER AND ALGEBRAIC STRUCTURES 130
Chapter: 3. Uniformization 132
Chapter: 4. Analytic objects 136
Chapter: §6. Canonical Metrics Over Complex Manifolds 138
Chapter: 1. The Bergman, Kobayashi-Royden and Caratheodory metrics 138
Chapter: 2. Kähler-Einstein Metrics on Compact Kähler Manifolds 141
Chapter: 3. Hermitian Manifolds and Stable Vector Bundles 144
Chapter: 4. Chern Number Inequalities 146
Chapter: 5. Kähler-Einstein Metrics on Noncompact Manifolds 148
Chapter: 6. Ricci Flat Metrics on Noncompact Manifolds 150
Bibliography 152
Article: HOMOLOGIE DE DEGRÉ TROIS D'ALGÈBRES DE LIE SIMPLES DÉPLOYÉES ÉTENDUES À UNE ALGÈBRE COMMUTATIVE 159
Chapter: 1. Introduction 159
Chapter: 2. Préliminaires et énoncé des résultats 161
Chapter: 3. Cas où g n'est pas de type A_n(n \geq 2) 165
Chapter: 4. Remarques sur le cas de sl(r, A), r≥ 3 170
Bibliography 173
Rubric 174
Article: APPROXIMATION DES MOYENNES ARITHMÉTICO-GÉOMÉTRIQUES 175
Bibliography 181
Rubric 182
Article: ON THE GALOIS GROUPS OF THE EXPONENTIAL TAYLOR POLYNOMIALS 183
Chapter: I. Review of the Newton Polygon 183
Chapter: II. Application to the Exponential Taylor Polynomials 185
Chapter: III. Global Conclusions A and B 186
Chapter: IV. CALCULATION OF THE DISCRIMINANT 187
Chapter: V. End of Proof 187
Chapter: VI. Final Remarks 187
Bibliography 189
Rubric 190
Article: THE VARIETY OF MODULI OF FOLIATIONS ON A COMPLEX SPACE 191
Bibliography 197
Rubric 198
Article: THE THEOREM OF BROWN AND SARD 199
Bibliography 202
Article: SIMPLE PROOF OF THE MURASUGI AND KAUFFMAN THEOREMS ON ALTERNATING LINKS 203
Chapter: §1. Introduction 203
Chapter: §2. The extended dual state lemma 208
Chapter: §3. Kauffman's state model for the Jones polynomial 215
Chapter: §4. Proof of Theorem 1 215
Chapter: §5. Proof of Theorem 2 218
Appendix: Appendix: an improvement of the inequality of Theorem 1 224
Bibliography 225
Rubric 226
Article: SKETCH OF THE EVOLUTION OF (NONCOMMUTATIVE) RING THEORY 227
Chapter: I. Sources 229
Chapter: II. Exploration 233
Chapter: III. Classification 237
Chapter: IV. Structure of algebras 241
Chapter: V. Interlude 250
Chapter: VI. Structure of rings with minimum condition 253
Chapter: VII. SOME SUBSEQUENT DEVELOPMENTS 257
Bibliography 264
Rubric 268
Article: AN ELEMENTARY ACCOUNT OF SELBERG'S LEMMA 269
Bibliography 273
Rubric 274
Article: INVOLUTIONS IN SURFACE MAPPING CLASS GROUPS 275
Chapter: 1. Introduction 275
Chapter: 2. The subgroup generated by involutions 276
Chapter: 3. Thurston's classification of mapping classes 284
Chapter: 4. Products of involutions 286
Chapter: 5. Remarks and examples 287
Bibliography 290
Article: THE COMPLEX CROSS RATIO ON THE HEISENBERG GROUP 291
Chapter: Introduction 291
Bibliography 300
Article: ON A CONSTRUCTION FOR THE REPRESENTATION OF A POSITIVE INTEGER AS THE SUM OF FOUR SQUARES 301
Bibliography 306
Article: SOME EXAMPLES OF GROUP ALGEBRAS WITHOUT FILTRED MULTIPLICATIVE BASIS 307
Chapter: §1. Preliminary remarks 308
Chapter: §2. Examples where the ground field is irrelevant 309
Chapter: §3. The group of quaternion units 312
Bibliography 314
Article: AN ORBIT CLOSING PROOF OF BROUWER'S LEMMA ON TRANSLATION ARCS 315
Abstract: Abstract 315
Chapter: 1. An isotopy closing lemma 316
Chapter: 2. Fixed points for homeomorphisms of the sphere 320
Bibliography 322
Article: RADICALS AND HILBERT NULLSTELLENSATZ FOR NOT NECESSARILY ALGEBRAICALLY CLOSED FIELDS 323
Chapter: §1. The main result and definitions 323
Chapter: §2. SOME PROPERTIES OF THE K-RADICAL 326
Chapter: §3. Proof of the Hilbert K-Nullstellensatz 329
Chapter: §4. Connections with previous results 333
Chapter: §5. TWO EXAMPLES 334
Bibliography 338
Rubric: COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION) 339
Rubric: BULLETIN BIBLIOGRAPHIQUE 1
Rubric: BULLETIN BIBLIOGRAPHIQUE 33