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