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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: THE COSET WEIGHT DISTRIBUTIONS OF CERTAIN BCH CODES AND A FAMILY OF CURVES
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3
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Chapter: Introduction
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3
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Chapter: §1. A FAMILY OF CURVES
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5
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Chapter: §2. DISSECTING THE JACOBIAN
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8
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Chapter: §3. BOUNDS FOR N(A,B)
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13
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Chapter: §4. Numerical results
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17
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Chapter: §5. The covering radius
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19
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Bibliography
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20
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Article: HOLONOMY AND SUBMANIFOLD GEOMETRY
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23
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Abstract
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23
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Chapter: 1. Introduction
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23
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Chapter: 2. Riemannian holonomy
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25
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Chapter: 3. Normal holonomy
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27
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Chapter: 4. Homogeneity and holonomy
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39
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Chapter: 5. Lorentzian holonomy and homogeneous submanifolds of $H^n$
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45
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Bibliography
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48
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Article: TRIPLE RATIO ON THE UNITARY STIEFEL MANIFOLD
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51
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Abstract
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51
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Chapter: Introduction
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51
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Chapter: 1. Geometric setting
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52
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Chapter: 2. Action of G on $S \times S$ and $S \times S \times S$
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55
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Chapter: 3. Orbits for the $GL_q$-action on $\tilde{T}_q$
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58
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Chapter: 4. The triple ratio on S
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68
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Bibliography
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70
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Article: THE HILBERT METRIC AND GROMOV HYPERBOLICITY
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73
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Abstract
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73
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Chapter: Introduction
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73
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Chapter: 1. Intersecting chords in convex domains
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75
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Chapter: 1.1 Intersecting line segments and Menger curvature
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76
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Chapter: 1.2 Chords larger than δ
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77
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Chapter: 2. Hyperbolicity of Hilbert's metric
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78
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Chapter: 3. Intersecting chords theorem for convex $C^2$-domains
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81
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Chapter: 3.1 The two-dimensional case
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81
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Chapter: 3.2 The proof of Theorem 3.1
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83
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Chapter: 4. CONSEQUENCES OF GROMOV HYPERBOLICITY FOR THE SHAPE OF THE BOUNDARY
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84
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Chapter: 5. NON-STRICTLY CONVEX DOMAINS
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86
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Bibliography
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88
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Article: SEMISTABLE K3-SURFACES WITH ICOSAHEDRAL SYMMETRY
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91
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Abstract
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91
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Chapter: Introduction
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91
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Chapter: 1. Semistable degenerations of K3 -surfaces
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93
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Chapter: 2. Tetrahedra
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96
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Chapter: 3. DEFORMATION THEORY
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105
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Chapter: 4. HODGE ALGEBRAS
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113
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Chapter: 5. The dodecahedron
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115
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Bibliography
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125
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Article: EXPOSANT ET INDICE D'ALGÈBRES SIMPLES CENTRALES NON RAMIFIÉES
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127
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Chapter: 1. Quelques résultats et exemples classiques
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129
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Chapter: 2. Algèbres non ramifiées via la réduction d'indice
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133
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Chapter: 3. Algèbres non ramifiées sur les produits de courbes
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137
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Appendix: APPENDICE
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139
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Bibliography
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145
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Article: L'ÉQUATION DE NAGELL-LJUNGGREN $\frac{x^n – 1}{x – 1} = y^q$
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147
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Chapter: 1. Introduction
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147
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Chapter: 2. Les résultats de Nagell et Ljunggren
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149
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Chapter: 3. Application des formes linéaires de logarithmes : RÉSULTATS DE FINITUDE
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150
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Chapter: 4. Un outil important : les formes linéaires de logarithmes
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152
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Chapter: 5. Un exemple de résolution complète de l'équation (1)
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155
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Chapter: 6. OÙ APPARAISSENT LES FORMES LINÉAIRES DE LOGARITHMES p-ADIQUES
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157
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Chapter: 7. A NOUVEAU LES CONGRUENCES
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159
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Chapter: 8. Une extension du théorème de Nagell et Ljunggren
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160
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Chapter: 9. Autres résultats
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161
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Chapter: 10. L'ÉQUATION $\frac{x^n – 1}{x – 1} = y^q$
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163
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Chapter: 11. Le cas x < 0
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164
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Chapter: 12. Applications
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164
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Bibliography
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165
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Article: THE FANNING METHOD FOR CONSTRUCTING EVEN UNIMODULAR LATTICES. I
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169
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Abstract
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169
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Chapter: Introduction
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169
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Chapter: 1. Lattices
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170
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Chapter: 2. ISOFOLDS AND ISOFANS
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174
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Chapter: 3. Elementary isofans and isofolds
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180
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Bibliography
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186
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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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3
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Chapter: Logique et fondements
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4
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Chapter: Analyse combinatoire
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5
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Chapter: Ordre, treillis
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6
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Chapter: Théorie des nombres
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6
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Chapter: Corps et polynômes
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7
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Chapter: Géométrie algébrique
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7
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Chapter: Algèbre linéaire et multilinéaire, théorie des matrices
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8
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Chapter: Anneaux et algèbres
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8
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Chapter: Théorie des groupes et généralisations
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9
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Chapter: Groupes topologiques; groupes et algèbres de Lie
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10
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Chapter: Fonctions de variables réelles
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10
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Chapter: Fonctions d'une variable complexe
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10
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Chapter: Équations différentielles ordinaires
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11
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Chapter: Équations aux dérivées partielles
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11
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Chapter: Systèmes dynamiques et théorie ergodique
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12
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Chapter: Équations aux différences finies, équations fonctionnelles
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12
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Chapter: Analyse de Fourier, analyse harmonique abstraite
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12
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Chapter: Analyse fonctionnelle
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13
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Chapter: Théorie des opérateurs
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15
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Chapter: Calcul des variations
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16
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Chapter: Géométrie
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16
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Chapter: Géométrie différentielle
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16
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Chapter: Topologie algébrique
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18
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Chapter: Topologie des variétés, analyse globale et analyse des variétés
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18
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Chapter: Probabilités et processus stochastiques
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20
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Chapter: Statistique
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21
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Chapter: Analyse numérique
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21
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Chapter: Informatique
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22
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Chapter: Mécanique des solides, élasticité et plasticité
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23
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Chapter: Mécanique des fluides, acoustique
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24
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Chapter: Thermodynamique classique, propagation de la chaleur
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24
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Chapter: Mécanique quantique
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24
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Chapter: Astronomie et astrophysique
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24
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Chapter: Économie, recherche opérationnelle, jeux
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25
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Chapter: Biologie et sciences du comportement
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25
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Chapter: Information, communication, circuits
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26
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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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Issue 3-4: L'ENSEIGNEMENT MATHÉMATIQUE
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Front matter
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Table of Contents
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189
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Front matter
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190
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Article: ON THE RATIONAL FORMS OF NILPOTENT LIE ALGEBRAS AND LATTICES IN NILPOTENT LIE GROUPS
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191
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Abstract
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191
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Chapter: 1. Introduction
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191
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Chapter: 2. Nilpotent Lie algebras with a unique rational form up to isomorphism
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194
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Chapter: 2.1 HEISENBERG ALGEBRAS
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194
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Chapter: 2.2 Example of a free nilpotent algebra
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196
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Chapter: 2.3 More examples
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196
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Chapter: 3. Malcev's example
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197
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Chapter: 4. Nilpotent Lie algebras with infinitely many non-isomorphic rational forms
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201
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Chapter: 4.1 Basic lemma
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201
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Chapter: 4.2 Proof of Theorem 2
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201
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Chapter: 4.3 Classification of rational forms for some 6-dimensional Lie ALGEBRAS
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203
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Bibliography
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207
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Article: MM-SPACES AND GROUP ACTIONS
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209
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Abstract
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209
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Chapter: 1. Introduction
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209
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Chapter: 2. Some concepts of asymptotic geometric analysis
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210
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Chapter: 3. A TRANSFORMATION GROUP FRAMEWORK
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212
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Chapter: 4. Concentration property and fixed points
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217
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Chapter: 5. Invariant means on spheres
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222
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Chapter: 6. Ramsey-Dvoretzky-Milman property
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226
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Chapter: 6.1 EXTREME AMENABILITY AND SMALL OSCILLATIONS
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226
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Chapter: 6.2 Dvoretzky's theorem
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227
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Chapter: 6.3 Ramsey's theorem
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228
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Chapter: 6.4 Extreme amenability and minimal flows
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230
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Chapter: 6.5 The Urysohn metric space
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231
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Chapter: 7. Concentration to a non-trivial space
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232
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Chapter: 8. Reading suggestions
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234
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Bibliography
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235
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Article: TOPOLOGICAL PROOF OF THE GROTHENDIECK FORMULA IN REAL ALGEBRAIC GEOMETRY
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237
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Chapter: Introduction
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237
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Chapter: 1. The Grothendieck formula
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238
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Chapter: 2. Proof of the Grothendieck formula
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244
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Bibliography
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257
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Article: AN HOMOLOGY 4-SPHERE GROUP WITH NEGATIVE DEFICIENCY
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259
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Abstract
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259
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Rubric
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260
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Bibliography
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262
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Article: ON THE CLASSIFICATION OF CERTAIN PIECEWISE LINEAR AND DIFFERENTIABLE MANIFOLDS IN DIMENSION EIGHT AND AUTOMORPHISMS OF $\sharp_{i=1}^b (S^2 \times S^5)$
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263
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Abstract
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263
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Chapter: 1. Introduction
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263
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Chapter: 2. STATEMENT OF THE RESULT
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264
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Chapter: 2.1 The classical invariants
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265
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Chapter: 2.2 Manifolds with trivial cup form $\delta_x$
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267
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Chapter: 3. Preliminaries
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269
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Chapter: 3.1 The structure of manifolds: handle attachment and surgery
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269
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Chapter: 3.2 CONSEQUENCES FOR E-MANIFOLDS OF DIMENSION EIGHT WITH $W_2 = 0$
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271
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Chapter: 3.3 Homotopy vs. isotopy
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271
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Chapter: 3.4 SOME 4-DIMENSIONAL CW-COMPLEXES
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273
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Chapter: 3.5 Pontrjagin classes and $\pi_3(SO(4))$
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274
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Chapter: 3.6 Links of 3-spheres in $\sharp_{i=1}^b (S^2 \times S^5)$
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274
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Chapter: 3.7 Links of 5-spheres in $S^8$
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275
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Chapter: 4. Proof of Theorem 2.2 and Theorem 2.4
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278
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Chapter: 4.1 Proof of Theorem 2.2
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278
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Chapter: 4.2 THE DETERMINATION OF $W_4$ IN THE GENERAL CASE
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280
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Chapter: 4.3 Manifolds with given invariants
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281
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Chapter: 5. Structure of the group $Aut_0^{PL}(\sharp_{i=1}^b (S^2 \times S^5))/Aut_0^{PL}(\sharp_{i=1}^b (S^2 \times D^6))$
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285
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Bibliography
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288
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Article: UNE PREUVE GÉOMÉTRIQUE DU THÉORÈME DE JUNG
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291
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Chapter: 1. Introduction
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291
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Chapter: 2. Applications birationnelles entre surfaces
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296
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Chapter: 3. Preuve du théorème de Jung
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302
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Chapter: 4. Compléments
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310
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Chapter: 4.1 Un exemple
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310
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Chapter: 4.2 Structure de produit amalgamé
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312
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Chapter: 4.3 Preuve sur un corps quelconque
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312
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Bibliography
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314
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Article: TORSION NUMBERS OF AUGMENTED GROUPS WITH APPLICATIONS TO KNOTS AND LINKS
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317
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Abstract
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317
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Chapter: 1. Introduction
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317
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Chapter: 2. Augmented groups and torsion numbers
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319
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Chapter: 3. EXTENDED FOX FORMULA AND RECURRENCE
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326
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Chapter: 4. Prime parts of torsion numbers
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333
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Chapter: 5. Torsion numbers and links
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337
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Bibliography
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342
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Article: PROJECTIVE MODULES OVER SOME PRÜFER RINGS
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345
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Chapter: 1. Introduction
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345
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Chapter: 2. A GENERAL STEINITZ ISOMORPHISM THEOREM
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347
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Chapter: 3. DECOMPOSITION OF FINITELY GENERATED PROJECTIVE MODULES
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349
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Chapter: 4. Rings with the strong $1\frac{1}{2}$ -generator property
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351
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Chapter: 5. Non finitely generated projective modules
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353
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Bibliography
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356
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Article: THE NONAMENABILITY OF SCHREIER GRAPHS FOR INFINITE INDEX QUASICONVEX SUBGROUPS OF HYPERBOLIC GROUPS
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359
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Abstract
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359
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Chapter: 1. Introduction
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359
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Chapter: 2. Nonamenability for graphs
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363
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Chapter: 3. Hyperbolic metric spaces
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366
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Chapter: 4. Quasiconvex subgroups of hyperbolic groups
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367
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Chapter: 5. PROOF OF THE MAIN RESULT
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368
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Bibliography
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371
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Rubric: COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION)
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377
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Chapter: THE ICMI AWARDS IN MATHEMATICS EDUCATION RESEARCH
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377
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Rubric: BULLETIN BIBLIOGRAPHIQUE
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27
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Chapter: Généralités
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27
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Chapter: Histoire
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32
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Chapter: Logique et fondements
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33
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Chapter: Analyse combinatoire
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33
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Chapter: Théorie des nombres
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34
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Chapter: Corps et polynômes
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35
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Chapter: Géométrie algébrique
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35
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Chapter: Anneaux et algèbres
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36
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Chapter: K-théorie
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37
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Chapter: Théorie des groupes et généralisations
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38
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Chapter: Groupes topologiques : groupes et algèbres de Lie
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39
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Chapter: Fonctions de variables réelles
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40
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Chapter: Fonctions d'une variable complexe
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40
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Chapter: Fonctions de plusieurs variables complexes
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41
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Chapter: Équations aux dérivées partielles
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42
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Chapter: Systèmes dynamiques et théorie ergodique
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43
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Chapter: Équations aux différences finies, équations fonctionnelles
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45
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Chapter: Approximations et développements en série
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45
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Chapter: Analyse de Fourier, analyse harmonique abstraite
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45
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Chapter: Analyse fonctionnelle
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46
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Chapter: Théorie des opérateurs
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47
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Chapter: Calcul des variations
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48
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Chapter: Géométrie
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49
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Chapter: Ensembles convexes et inégalités géométriques
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49
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Chapter: Géométrie différentielle
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49
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Chapter: Topologie algébrique
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50
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Chapter: Topologie des variétés, analyse globale et analyse des variétés
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50
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Chapter: Probabilités et processus stochastiques
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52
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Chapter: Statistique
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56
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Chapter: Analyse numérique
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57
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Chapter: Informatique
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58
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Chapter: Mécanique des fluides, acoustique
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58
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Chapter: Économie, recherche opérationnelle, jeux
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59
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Chapter: Biologie et sciences du comportement
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60
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Chapter: Information, communication, circuits
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60
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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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