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Front matter
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Index
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Front matter
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Issue 1-2: L'ENSEIGNEMENT MATHÉMATIQUE
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1
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Article: THE SCHUR SUBGROUP OF THE BRAUER GROUP OF A LOCAL FIELD
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1
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Chapter: K NON-DYADIC
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2
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Chapter: Remarks
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9
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Bibliography
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10
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Article: UNE CARACTÉRISATION DES NORMES EUCLIDIENNES EN DIMENSION FINIE
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13
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Chapter: Introduction
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13
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Chapter: I. Groupe des isométries linéaires
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14
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Chapter: II. La boule unité de L(E)
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15
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Chapter: III. Application au cas n = 2
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18
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Bibliography
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21
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Article: EULER'S FAMOUS PRIME GENERATING POLYNOMIAL AND THE CLASS NUMBER OF IMAGINARY QUADRATIC FIELDS
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23
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Chapter: Introduction
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23
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Chapter: A) Quadratic extensions
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25
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Chapter: B) Rings of integers
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26
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Chapter: C) Discriminant
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27
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Chapter: D) Decomposition of primes
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27
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Chapter: E) Units
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32
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Chapter: F) The class number
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33
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Chapter: G) The main theorem
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40
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Bibliography
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42
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Article: LE PROBLÈME DE GAUSS SUR LE NOMBRE DE CLASSES
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43
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Chapter: I. La classification de Gauss des formes quadratiques
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44
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Chapter: §1. FINITUDE DU NOMBRE DE CLASSES
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44
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Chapter: §2. Formes quadratiques réduites
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45
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Chapter: §3. Une méthode élémentaire pour calculer le nombre de classes
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47
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Chapter: §4. Le groupe des classes
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48
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Chapter: §5. Lien entre h(-d) et $h(-df^2)$
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51
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Chapter: II. Le problème du nombre de classes
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52
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Chapter: §1. Représentation des entiers par les formes quadratiques
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53
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Chapter: §2. Fonctions zêta
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55
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Chapter: §3. Ce que l'on espère sur le comportement de h( —d)
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57
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Chapter: §4. Minorations non effectives de h(—d)
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59
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Chapter: §5. Les cas h = 1 et h = 2
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60
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Chapter: §6. Courbes elliptiques et fonctions L
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61
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Chapter: §7. Le théorème de Goldfeld
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64
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Chapter: §8. Le théorème de Gross et Zagier
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65
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Chapter: §9. Conclusion
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66
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Article: ON TORRES-TYPE RELATIONS FOR THE ALEXANDER POLYNOMIALS OF LINKS
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69
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Chapter: §1. Introduction
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69
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Chapter: §2. Torsions of chain complexes and manifolds
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72
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Chapter: §3. Algebraic lemmas
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74
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Chapter: §4. Proof of Theorems 1 and 2
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76
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Bibliography
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82
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Article: EXTENSIONS DE MODULES ET COHOMOLOGIE DES GROUPES
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83
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Chapter: Introduction
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83
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Chapter: 1. Rappels sur les extensions
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83
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Chapter: 2. DÉRIVATIONS ET EXTENSIONS
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85
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Chapter: 3. Le groupe $H^1(G;A)$
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87
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Chapter: 4. Le groupe $H^2(G;A)$
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93
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Article: ABOUT THE PROOFS OF CALABI'S CONJECTURES ON COMPACT KÄHLER MANIFOLDS
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107
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Abstract: Abstract
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107
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Chapter: 0. Introduction
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107
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Chapter: 1. The Monge-Ampère equation
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108
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Chapter: 2. A Topological Lemma
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110
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Chapter: 3. Local inversion
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111
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Chapter: 4. Properness
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111
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Chapter: 5. A PRIORI ESTIMATES: THE ORIGINAL WAY
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114
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Chapter: 6. Coordinate free tensor calculus
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114
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Chapter: 7. HIGHER ORDER A PRIORI ESTIMATES: GENERALITIES
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115
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Chapter: 8. A PRIORI ESTIMATES OF ORDER FOUR
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118
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Chapter: 9. A PRIORI ESTIMATES OF ORDER FIVE AND MORE
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120
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Chapter: 10. The analytic point of view
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121
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Bibliography
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121
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Article: QUILLEN'S THEOREM ON BUILDINGS AND THE LOOPS ON A SYMMETRIC SPACE
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123
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Abstract: Abstract
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123
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Chapter: §1. Notation and Preliminaries
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128
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Chapter: §2. Topological Buildings
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134
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Chapter: §3. Loop Groups
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142
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Chapter: §4. Quillen's Theorem for Loop Groups
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144
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Chapter: §5. The Loops on a Symmetric Space
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147
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Chapter: §6. Examples
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152
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Chapter: §7. Bott Periodicity
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158
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Appendix: §8. Appendix : Real Forms and the generalized bruhat decomposition
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161
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Bibliography
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165
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Article: ISOCLINIC n-PLANES IN $R^{2n}$ AND THE HOPF-STEENROD SPHERE BUNDLES $S^{2n-1} \rightarrow S^n,\quad n=2,4,8$
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167
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Chapter: 0. Introduction
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167
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Chapter: 1. Some results on isoclinic n-PLANES in $R^{2n}$
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168
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Chapter: 2. SOME FURTHER RESULTS
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173
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Chapter: 3. The sphère bundles $S^{2n-1} \rightarrow \Phi_n, \quad n=2,4,or 8$, WITH FIBERS ON MUTUALLY ISOCLINIC n-PLANES IN $R^{2n}$
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181
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Chapter: 4. A UNIFIED TREATMENT OF THE THREE HOPF-STEENROD BUNDLES
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187
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Chapter: 5. COMPARISON OF OUR BUNDLES WITH THE HOPF-STEENROD BUNDLES
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194
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Appendix: Appendix 1. The Cayley numbers
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200
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Appendix: Appendix 2. The Hopf fibering and mutually isoclinic planes
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201
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Bibliography
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204
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Rubric: COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION)
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205
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Article: THE POPULARIZATION OF MATHEMATICS
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205
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Chapter: 1. A GENERAL FRAMEWORK: NEEDS AND METHODS FOR THE POPULARIZATION OF SCIENCE
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206
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Chapter: 2. Spécial features of the popularization of mathematics
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207
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Chapter: 3. The methods of popularization
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210
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Chapter: Call for papers
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212
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Chapter: Previous ICMI Studies
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213
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Article: THE THEORY OF GRÖBNER BASES
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215
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Chapter: Introduction
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215
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Chapter: 1. Notations and Definitions
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216
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Chapter: 2. The Division Algorithm
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220
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Chapter: 3. Construction of Gröbner Bases
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223
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Chapter: 4. Application to Systems of Algebraic Equations
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228
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Chapter: 5. Application to a Geometric Problem
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230
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Bibliography
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231
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Article: GEODESICS IN THE UNIT TANGENT BUNDLE OF A ROUND SPHERE
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233
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Chapter: 1. Geometry of the unit tangent bundle
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235
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Chapter: 2. Geodesics in $US^2$
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238
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Chapter: 3. Helices in $S^3$
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239
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Chapter: 4. SASAKI'S EQUATIONS
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240
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Chapter: 5. Proof of the Fundamental Constraint
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243
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Bibliography
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246
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Article: THE EULER CLASS OF ORTHOGONAL RATIONAL REPRESENTATIONS OF FINITE GROUPS
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247
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Chapter: 1. Invariant Bilinear Forms
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248
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Chapter: 2. Orthogonal representations of p-groups
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249
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Chapter: 3. Proof of the main theorem
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252
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Bibliography
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253
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Article: UNE THÉORIE DE DENJOY DES MARTINGALES DYADIQUES
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255
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Chapter: problème
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255
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Chapter: solution: totalisation dyadique
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257
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Chapter: Commentaires
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261
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Appendix: Appendice: distribution de la fonction f
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263
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Chapter: CITATIONS ET PASTICHE
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266
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Bibliography
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268
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Article: AN ELEMENTARY PROOF OF THE STRUCTURE THEOREM FOR CONNECTED SOLVABLE AFFINE ALGEBRAIC GROUPS
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269
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Abstract: Abstract
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269
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Rubric
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270
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Bibliography
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273
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Article: KALUZA-KLEIN APPROACH TO HYPERBOLIC THREE-MANIFOLDS
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275
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Chapter: §1. Introduction
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275
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Chapter: §2. CONFORMAL COMPACTIFICATIONS AND THEIR TOPOLOGY
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277
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Chapter: §3. Classification of Γ with $dim_H\Lambda(\Gamma)\leq 1$
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284
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Chapter: §4. HODGE THEORY FOR HYPERBOLIC 3-MANIFOLDS
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287
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Chapter: §5. Monopoles and Instantons
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291
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Chapter: §6. Twistor spaces
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295
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Chapter: §7. Atiyah-Ward ansatzes, summing 't Hooft solutions and elsenstein series
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305
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Bibliography
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310
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Article: SOME ALMOST HOMOGENEOUS GROUP ACTIONS ON SMOOTH COMPLETE RATIONAL SURFACES
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313
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Chapter: §1. Minimal embeddings: définitions and preliminary remarks
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314
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Chapter: §2. The minimal B/Γ-embeddings
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317
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Chapter: §3. Application to SL(2)-embeddings
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331
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Bibliography
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332
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Article: REPRÉSENTATIONS ET TRACES DES ALGÈBRES DE HECKE POLYNÔME DE JONES-CONWAY
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333
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Chapter: §0. Introduction
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333
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Chapter: §1. Une description du polynôme de Jones-Conway
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336
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Chapter: §2. Représentations des algèbres de Hecke
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340
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Chapter: §3. Traces des algèbres de Hecke
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342
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Chapter: §4. La trace T
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345
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Chapter: §5. La trace de Jones-Ocneanu
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348
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Chapter: §6. Une généralisation du polynôme de Jones-Conway
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349
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Bibliography
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355
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Article: GLOBAL CONSTRUCTION OF THE NORMALIZATION OF STEIN SPACES
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357
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Chapter: Introduction
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357
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Chapter: 1. Example of a Stein space X with $\widetilde{O(X)} \neq O(\tilde{X})$
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358
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Chapter: 2. Construction of $O(\tilde{X})$ from O(X) for Stein spaces X
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360
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Chapter: 3. Applications
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361
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Bibliography
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363
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Article: LES ÉQUATIONS DIFFÉRENTIELLES ONT 350 ANS
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365
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Chapter: problèmes de Debeaune
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365
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Chapter: «Discorsi» de Galilée
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366
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Chapter: Newton
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367
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Chapter: Solution du premier problème de Debeaune
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369
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Chapter: problème de l'isochrone
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370
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Chapter: caténaire
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371
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Chapter: tractrice
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373
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Chapter: L'ÉQUATION DIFFÉRENTIELLE «DE BERNOULLI»
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374
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Chapter: Brachystochrone
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375
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Chapter: PROBLÈMES ISOPÉRIMÉTRIQUES
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377
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Chapter: Euler et Lagrange
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379
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Chapter: Problèmes isopérimétriques, suite
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380
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Chapter: Epilogue
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381
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Chapter: Exercices
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382
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Bibliography
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384
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Article: LES GRANDS THÈMES DE FRANÇOIS CHÂTELET
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387
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Chapter: 1. Variétés de Severi-Brauer
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387
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Chapter: 1.1. Avant Châtelet.
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387
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Chapter: 1.2. La contribution de F. Châtelet [1943a] [1943b] [1944].
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389
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Chapter: 1.3. Après les travaux de Châtelet.
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391
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Chapter: 1.4. Importance des variétés de Severi-Brauer.
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391
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Chapter: 2. Courbes de genre 1
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392
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Chapter: 2.1. Avant Châtelet.
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392
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Chapter: 2.2. La contribution de Châtelet [1938] [1941] [1946a] [1947a].
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393
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Chapter: 2.3. Après Châtelet.
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395
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Chapter: 2.4. Points de torsion.
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395
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Chapter: 3. Surfaces cubiques
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396
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Chapter: 3.1. Avant Châtelet.
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396
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Chapter: 3.2. La contribution de Châtelet [1953] [1954 a] [1954b] [1958] [1959b] [1966].
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397
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Chapter: 3.3. Après Châtelet.
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399
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Chapter: ARTICLES DE FRANÇOIS CHÂTELET
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401
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Bibliography
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403
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Rubric: BULLETIN BIBLIOGRAPHIQUE
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1
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Rubric: BULLETIN BIBLIOGRAPHIQUE
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41
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Back matter
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