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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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1
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Front matter
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2
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Article
PROJECTIVE GEOMETRY OF POLYGONS AND DISCRETE 4-VERTEX AND 6-VERTEX THEOREMS
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3
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Abstract
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3
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Chapter
1. Introduction
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3
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Chapter
2. Theorems on plane polygons
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5
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Chapter
2.1 DISCRETE 4-VERTEX THEOREM
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5
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Chapter
2.2 DISCRETE THEOREM ON 6 AFFINE VERTICES
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6
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Chapter
2.3 DISCRETE GHYS THEOREM
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7
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Chapter
3. Main Theorem
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9
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Chapter
3.1 Intersection multiplicities
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9
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Chapter
3.2 A SIMPLEX IS STRICTLY CONVEX
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12
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Chapter
3.3 BARNER'S THEOREM FOR POLYGONS
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13
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Chapter
4. Applications of the main theorem
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15
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Chapter
4.1 Proof of Theorems 2.2, 2.6 and 2.10
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15
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Chapter
4.2 CONCLUDING REMARKS
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17
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Bibliography
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18
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Article
LATTICES OF COVARIANT QUADRATIC FORMS
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21
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Chapter
1. Introduction
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21
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Chapter
2. Covariant forms and equivalence
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23
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Chapter
3. Autoequivalences and invariants
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29
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Chapter
4. EXTRINSIC NOTIONS : USING THE UNDERLYING LATTICE
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34
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Chapter
5. Inversion and modularity
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43
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Chapter
6. Some three-dimensional lattices of covariant forms
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48
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Bibliography
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55
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Article
ON AN ASSERTION IN RIEMANN'S HABILITATIONSVORTRAG
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57
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Abstract
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57
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Chapter
1. Introduction
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57
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Chapter
2. An algebraic example
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59
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Chapter
3. Curvature zero 2-planes in $S^a \times H^a \times T^b$
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60
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Chapter
4. Curvature zero 2-planes in warped products
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61
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Chapter
5. CONCLUDING COMMENTS
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62
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Bibliography
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62
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Article
NEW EXAMPLES OF MAXIMAL SURFACES
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65
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Abstract
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65
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Chapter
1. Introduction
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65
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Chapter
2. Basic properties of simple triangle surfaces
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68
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Chapter
3. Geometric properties of systoles of simple triangle surfaces
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74
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Chapter
4. Length estimates for systoles
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82
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Chapter
5. Proof of the theorem
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89
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Bibliography
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100
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Article
CIRCULANT MODULAR HADAMARD MATRICES
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103
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Chapter
1. Introduction
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103
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Chapter
2. A FAMILY OF (p – 1)-modular circulant Hadamard matrices of size 4p.
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105
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Chapter
3. Circulant modular Hadamard matrices of type 2
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112
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Bibliography
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114
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Article
SYMPLECTIC CHARACTERISTIC CLASSES
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115
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Abstract
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115
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Chapter
1. The symplectic group
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115
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Chapter
1.1 DEFINITION
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115
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Chapter
1.2 A RELATION BETWEEN $U(\frac{p-1}{2})$ AND Sp(p-1,Z)
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116
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Chapter
2. Symplectic characteristic classes
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126
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Chapter
2.1 Characteristic classes and representations
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126
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Chapter
2.2 Symplectic characteristic classes and Chern classes
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127
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Bibliography
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129
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Article
THE POSITIVE CONE OF SPHERES AND SOME PRODUCTS OF SPHERES
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131
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Abstract
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131
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Chapter
1. Introduction
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131
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Chapter
2. PRELIMINAIRES
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133
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Chapter
3. The γ-cone and the c-cone
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139
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Chapter
4. The positive cone of the spheres
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142
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Chapter
5. FURTHER PROPERTIES OF THE CONES
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144
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Chapter
6. The cones of the products $S^n \times S^{2m-1}$
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147
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Chapter
7. The γ-cone of $S^{2n} \times S^{2m}$ and the positive cone of $S^2 \times S^{2n}$
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148
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Chapter
8. The Whitehead product and the positive cone
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150
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Chapter
9. The positive cone of some products of even-dimensional spheres
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153
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Chapter
10. "Gaps in cohomology" and the γ-cone
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155
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Chapter
11. A "DOUBLING FORMULA" FOR STIRLING NUMBERS OF THE SECOND KIND
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156
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Bibliography
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159
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Article
UNE QUINTIQUE DE GENRE 1 QUI CONTREDIT LE PRINCIPE DE HASSE
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161
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Chapter
1. Introduction
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161
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Chapter
2. Quintiques planes de genre 1
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162
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Chapter
3. Un corps de nombres
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164
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Chapter
4. Choix de la courbe
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165
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Chapter
5. DÉMONSTRATION DU CAS LOCAL
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166
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Chapter
6. DÉMONSTRATION DU CAS GLOBAL
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167
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Chapter
7. La jacobienne de C
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170
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Bibliography
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172
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Rubric
COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION)
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173
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Article
RAPPORTS SUR LES ACTIVITÉS DE LA CIEM POUR LES ANNÉES 1999 ET 2000
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173
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Chapter
1. À PROPOS DE LA CIEM
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173
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Chapter
2. Congrès ICME
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174
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Chapter
3. ÉTUDES DE LA CIEM
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174
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Chapter
4. Conférences régionales
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176
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Chapter
5. Autre activité
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176
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Chapter
6. Groupes d'étude affiliés
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177
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Chapter
7. Le Programme de solidarité
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177
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Chapter
8. Organisation de la Commission
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177
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Chapter
9. Informations sur la CIEM
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178
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Appendix
Appendice : Les Études de la CIEM
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178
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Rubric
INTERNATIONAL SYMPOSIUM «One Hundred Years of L'Enseignement Mathématique: Moments of Mathematics Education in the 20th Century»
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181
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Article
REPORT ON THE INTERNATIONAL SYMPOSIUM ORGANISED JOINTLY BY THE UNIVERSITY OF GENEVA AND ICMI (Geneva, 20-22 October 2000)
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181
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Rubric
COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION)
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185
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Chapter
DISCUSSION DOCUMENT FOR THE THIRTEENTH ICMI STUDY MATHEMATICS EDUCATION IN DIFFERENT CULTURAL TRADITIONS : A COMPARATIVE STUDY OF EAST ASIA AND THE WEST
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185
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Chapter
PREAMBLE
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185
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Chapter
I. WHAT IS IN THIS STUDY ?
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187
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Chapter
II. THE RATIONALE FOR THIS STUDY
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188
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Chapter
III. HOW WILL THE STUDY BE OPERATIONALISED ?
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191
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Chapter
IV. ASPECTS OF THE STUDY
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193
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Chapter
V. CONTRIBUTIONS TO THE STUDY
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199
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Rubric
BULLETIN BIBLIOGRAPHIQUE
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1
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Chapter
Généralités
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1
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Chapter
Histoire
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5
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Chapter
Logique et fondements
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7
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Chapter
Analyse combinatoire
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8
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Chapter
Théorie des nombres
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9
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Chapter
Corps et polynômes
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10
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Chapter
Géométrie algébrique
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10
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Chapter
Anneaux et algèbres
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12
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Chapter
Catégories, algèbre homologique, cohomologie des groupes
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13
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Chapter
Théorie des groupes et généralisations
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14
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Chapter
Mesure et intégration
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15
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Chapter
Fonctions d'une variable complexe
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15
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Chapter
Théorie du potentiel
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15
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Chapter
Fonctions de plusieurs variables complexes
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15
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Chapter
Fonctions spéciales
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16
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Chapter
Equations différentielles ordinaires
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16
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Chapter
Equations aux dérivées partielles
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17
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Chapter
Systèmes dynamiques et théorie ergodique
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19
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Chapter
Equations aux différences finies, équations fonctionnelles
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20
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Chapter
Analyse de Fourier, analyse harmonique abstraite
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21
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Chapter
Analyse fonctionnelle
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21
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Chapter
Théorie des opérateurs
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22
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Chapter
Calcul des variations
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23
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Chapter
Géométrie
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23
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Chapter
Géométrie différentielle
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24
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Chapter
Topologie algébrique
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24
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Chapter
Topologie des variétés, analyse globale et analyse des variétés
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25
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Chapter
Probabilités et processus stochastiques
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27
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Chapter
Statistique
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29
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Chapter
Analyse numérique
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30
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Chapter
Informatique
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31
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Chapter
Mécanique des fluides, acoustique
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33
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Chapter
Economie, recherche opérationnelle, jeux
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34
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Chapter
Systèmes, contrôle optimal
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35
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Chapter
Information, communication, circuits
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36
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Back matter
Endseiten
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38
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Back matter
Endseiten
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Back matter
Endseiten
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Heft 3-4: L'ENSEIGNEMENT MATHÉMATIQUE
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Front matter
Titelseiten
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Table of Contents
Inhaltsverzeichnis
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203
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Front matter
Titelseiten
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204
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Article
INVERTING RADON TRANSFORMS : THE GROUP-THEORETIC APPROACH
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205
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Abstract
Kurzfassung
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205
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Abstract
Contents
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205
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Chapter
1. Introduction
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206
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Chapter
2. Geometric setting
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210
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Chapter
2.1 Double fibrations of homogeneous spaces
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210
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Chapter
2.2 Group-theoretic Radon transforms
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212
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Chapter
3. Convolution on X and inversion of R
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215
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Chapter
3.1 A CONVOLUTION FORMULA
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215
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Chapter
3.2 Radon inversion by convolution
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220
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Chapter
4. Radon transforms on isotropic spaces
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221
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Chapter
4.1 Totally geodesic submanifolds
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221
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Chapter
4.2 An inversion formula
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224
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Chapter
4.3 Examples
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227
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Chapter
5. HARMONIC ANALYSIS ON X AND INVERSION OF R
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230
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Chapter
6. Shifted Radon transforms, waves, and the amusing formula
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232
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Chapter
6.1 SHIFTS
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233
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Chapter
6.2 Radon inversion by shifts
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234
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Chapter
6.3 Examples
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235
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Chapter
6.4 The amusing formula generalized
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241
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Chapter
6.5 MULTITEMPORAL WAVES
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244
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Chapter
6.6 Examples
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247
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Bibliography
Bibliographie
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251
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Article
SUR L'HYPERBOLICITÉ DE CERTAINS COMPLÉMENTAIRES
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253
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Abstract
Kurzfassung
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253
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Chapter
0. Introduction
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253
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Chapter
1. Préliminaires
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255
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Chapter
2. Le théorème de Green
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257
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Chapter
3. Linéarisation des courbes entières dans $(C*)^k$
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258
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Chapter
4. Complémentaire d'une courbe à trois composantes dans $P^2(C)$
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260
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Appendix
5. Appendice. Courbes de Brody dans $(C*)^k$
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265
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Bibliography
Bibliographie
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267
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Article
VITALI'S CONVERGENCE THEOREM ON TERM BY TERM INTEGRATION
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269
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Chapter
1. Introduction
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269
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Chapter
2. Vitali's convergence theorem
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272
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Chapter
3. The Vitali-Hahn-Saks Theorem
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279
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Bibliography
Bibliographie
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284
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Article
PROPOS D'UN THÉORÈME DE VERSHIK ET KARPUSHEV
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287
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Abstract
Kurzfassung
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287
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Chapter
1. Introduction
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287
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Chapter
2. Exemples
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289
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Chapter
3. Représentations, cohomologie et fonctions (conditionnellement) de type positif
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298
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Chapter
3.1 Représentations irréductibles et factorielles
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298
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Chapter
3.2 Fonctions de type positif
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298
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Chapter
3.3 Construction GNS
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299
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Chapter
3.4 Topologie sur le dual
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300
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Chapter
3.5 COHOMOLOGIE ET ACTIONS AFFINES
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301
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Chapter
3.6 Fonctions conditionnellement de type positif
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302
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Chapter
4. Preuve du théorème
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303
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Chapter
4.1 Stratégie
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303
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Chapter
4.2 Théorème de Schoenberg
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304
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Chapter
4.3 DÉCOMPOSITION DE CHOQUET
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304
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Chapter
4.4 Localisation
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305
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Chapter
4.5. PROPOSITION. On conserve les notations précédentes.
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306
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Chapter
4.6 Constructions GNS
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309
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Bibliography
Bibliographie
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313
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Article
FINITE TYPE LINK-HOMOTOPY INVARIANTS
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315
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Abstract
Kurzfassung
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315
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Chapter
1. Introduction
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315
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Chapter
2. CONJUGATION AND PARTIAL CONJUGATION
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317
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Chapter
3. Construction of the invariant
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323
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Bibliography
Bibliographie
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327
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Article
GROUPS ACTING ON THE CIRCLE
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329
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Chapter
1. Introduction
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329
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Abstract
Contents
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330
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Chapter
2. Some classical definitions
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330
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Chapter
3. TWO BASIC EXAMPLES
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332
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Chapter
3.1 The projective group
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333
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Chapter
3.2 Piecewise linear groups
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336
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Chapter
4. The group of homeomorphisms of the circle
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338
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Chapter
4.1 Locally compact groups acting on the circle
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345
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Chapter
5. Rotation numbers
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349
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Chapter
5.1 Dynamics of a single homeomorphism
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349
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Chapter
5.2 Tits' alternative
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359
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Chapter
6. BOUNDED EULER CLASS
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363
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Chapter
6.1 Group cohomology
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363
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Chapter
6.2 The Euler class of a group action on the circle
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366
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Chapter
6.3 BOUNDED COHOMOLOGY AND THE MILNOR-WOOD INEQUALITY
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367
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Chapter
6.4 EXPLICIT BOUNDS ON THE EULER CLASS
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372
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Chapter
6.5 Actions on the real line and orderings
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373
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Chapter
6.6 SOME EXAMPLES
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382
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Chapter
7. HIGHER RANK LATTICES
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386
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Chapter
7.1 WITTE'S THEOREM
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387
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Chapter
7.2 Actions of higher rank lattices
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390
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Chapter
7.3 Lattices in linear groups
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392
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Chapter
7.4 Some groups that do act...
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401
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Bibliography
Bibliographie
|
404
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Rubric
COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION)
|
409
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Article
REPORT ON THE ICMI STUDY : «WHAT IS RESEARCH IN MATHEMATICS EDUCATION, AND WHAT ARE ITS RESULTS?»
|
409
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Bibliography
Bibliographie
|
411
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Rubric
BULLETIN BIBLIOGRAPHIQUE
|
39
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Chapter
Généralités
|
39
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Chapter
Analyse combinatoire
|
44
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Chapter
Théorie des nombres
|
45
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Chapter
Corps et polynômes
|
46
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Chapter
Géométrie algébrique
|
46
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Chapter
Algèbre linéaire et multilinéaire, théorie des matrices
|
47
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Chapter
Anneaux et algèbres
|
48
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Chapter
Catégories, algèbre homologique, cohomologie des groupes
|
49
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|
Chapter
Théorie des groupes et généralisations
|
49
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|
Chapter
Mesure et intégration
|
51
|
|
Chapter
Fonctions d'une variable complexe
|
51
|
|
Chapter
Équations différentielles ordinaires
|
51
|
|
Chapter
Equations aux dérivées partielles
|
52
|
|
Chapter
Systèmes dynamiques et théorie ergodique
|
53
|
|
Chapter
Équations aux différences finies, équations fonctionnelles
|
54
|
|
Chapter
Analyse de Fourier, analyse harmonique abstraite
|
54
|
|
Chapter
Transformations intégrales, calcul opérationnel
|
54
|
|
Chapter
Analyse fonctionnelle
|
55
|
|
Chapter
Théorie des opérateurs
|
56
|
|
Chapter
Calcul des variations
|
58
|
|
Chapter
Géométrie
|
58
|
|
Chapter
Ensembles convexes et inégalités géométriques
|
60
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|
Chapter
Géométrie différentielle
|
60
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|
Chapter
Topologie générale
|
61
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|
Chapter
Topologie algébrique
|
62
|
|
Chapter
Topologie des variétés, analyse globale et analyse des variétés
|
62
|
|
Chapter
Probabilités et processus stochastiques
|
63
|
|
Chapter
Statistique
|
65
|
|
Chapter
Analyse numérique
|
67
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|
Chapter
Informatique
|
68
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|
Chapter
Mécanique des particules et systèmes
|
70
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|
Chapter
Mécanique des solides, élasticité et plasticité
|
70
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|
Chapter
Mécanique des fluides, acoustique
|
71
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|
Chapter
Thermodynamique classique, propagation de la chaleur
|
71
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Chapter
Physique statistique, structure de la matière
|
71
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Chapter
Astronomie et astrophysique
|
71
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|
Chapter
Économie, recherche opérationnelle, jeux
|
72
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|
Chapter
Biologie et sciences du comportement
|
72
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|
Chapter
Systèmes, contrôle optimal
|
72
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|
Chapter
Information, communication, circuits
|
73
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Back matter
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Front matter
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Index
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Back matter
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Back matter
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Back matter
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Back matter
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Back matter
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