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