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Issue 1-2: L'ENSEIGNEMENT MATHÉMATIQUE
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Front matter
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Table of Contents
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Front matter
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Index
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Front matter
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Article
STATE MODELS FOR LINK POLYNOMIALS
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1
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Chapter
I. Introduction
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1
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Chapter
II. Skein polynomials
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2
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Chapter
III. A SKEIN MODEL FOR THE HOMFLY POLYNOMIAL
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9
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Chapter
IV. A Skein Model for the Kauffman polynomial
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12
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Chapter
V. Graph polynomials
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14
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Chapter
VI. The Conway Polynomial
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18
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Chapter
VII. Yang-Baxter Models
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21
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Chapter
VIII. Applications and questions
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27
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Chapter
IX. Relations with mathematical physics
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28
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Appendix
Appendix on state model formalism
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31
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Bibliography
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33
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Article
GAUSS SUMS AND THEIR PRIME FACTORIZATION
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39
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Chapter
Introduction
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39
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Chapter
1. Gauss sums and some of their properties
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39
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Chapter
2. The prime factorization of p in Q(pm)
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42
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Chapter
3. The prime factorization of the Gauss sum: statement of the result
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43
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Chapter
4. A USEFUL LEMMA
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44
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Chapter
5. The prime factorization of the Gauss sum: proof of the result
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46
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Chapter
6. Annihilators of the ideal class group of a cyclotomic field
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47
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Bibliography
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51
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Article
EXCEPTIONAL POLYNOMIALS AND THE REDUCIBILITY OF SUBSTITUTION POLYNOMIALS
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53
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Chapter
1. Introduction
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53
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Chapter
2. The semi-factorable families
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55
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Chapter
3. Substitution polynomials with a quadratic factor
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58
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Chapter
4. Substitution polynomials with a cubic factor
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63
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Bibliography
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65
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Article
THE POMPEIU PROBLEM REVISITED
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67
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Abstract
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67
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Chapter
1. Introduction
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67
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Chapter
2. Spectral analysis of radial functions
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70
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Chapter
3. POMPEIU PROBLEM FOR THE M(2) ACTION ON $R^2$
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73
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Chapter
4. A LONG-STANDING CONJECTURE !
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77
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Chapter
5. Pompeiu property in non-compact symmetric spaces
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78
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Chapter
6. Symmetric spaces of the compact type
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82
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Chapter
7. Pompeiu property for two-sided translations on groups
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85
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Chapter
8. CONCLUDING REMARKS
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88
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Bibliography
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89
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Article
LINK SIGNATURE, GOERITZ MATRICES AND POLYNOMIAL INVARIANTS
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93
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Abstract
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93
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Chapter
1. P-SKEINS AND SIGNATURE
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93
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Chapter
1.1. PRELIMINARIES
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93
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Chapter
1.2. Signature and oriented skeins
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95
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Chapter
2. Goeritz matrices and the F-polynomial
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100
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Chapter
2.1. The Goeritz matrix and graph of a link
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100
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Chapter
2.2. Kauffman's polynomial and the Goeritz matrix
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104
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Bibliography
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113
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Article
TOPOLOGICAL SERIES OF ISOLATED PLANE CURVE SINGULARITIES
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115
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Abstract
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115
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Chapter
1. Introduction
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115
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Chapter
2. SPLICING AND SERIES
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117
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Chapter
3. The definition of topological series
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121
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Chapter
4. The spectrum of a plane curve singularity
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125
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Chapter
5. Invariants in the case that f has only transversal $A_1$ singularities
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130
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Chapter
6. Equations
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132
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Appendix
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136
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Bibliography
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140
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Article
VALUES OF QUADRATIC FORMS AT INTEGRAL POINTS: AN ELEMENTARY APPROACH
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143
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Appendix
Appendix Trajectories of unipotent flows and minimal sets
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162
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Bibliography
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173
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Article
ON THE INVERSIVE DIFFERENTIAL GEOMETRY OF PLANE CURVES
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175
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Chapter
§1. Introduction
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175
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Chapter
§2. THE INFINITESIMAL COXETER INVARIANT
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178
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Chapter
§3. The four vertex theorem in $R^2$
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181
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Chapter
§4. A GENERALIZATION OF THE INVARIANCE OF ω
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181
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Chapter
§5. A GENERALIZED FOUR VERTEX THEOREM
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184
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Chapter
§6. Normal form and inversive curvature
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184
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Chapter
§7. The canonical map g:γ→G
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187
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Chapter
§8. Relation with Cartan's moving frames
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188
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Chapter
§9. LOXODROMES
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189
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Chapter
§10. The complex of geometric forms on a curve in $R^2$
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192
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Bibliography
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196
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Rubric
COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION)
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197
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Chapter
ASSESSMENT IN MATHEMATICS EDUCATION AND ITS EFFECTS
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197
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Chapter
DISCUSSION DOCUMENT
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197
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Chapter
Background and outline of the study
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197
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Chapter
Call for papers
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205
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Obituary
GEORGES DE RHAM 1903-1990
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207
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Bibliography
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213
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Article
CONTACT GEOMETRY AND WAVE PROPAGATION
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215
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Chapter
§1. Basic definitions
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215
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Chapter
§2. Characteristics
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222
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Chapter
§3. Submanifolds
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235
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Chapter
§4. Legendre fibrations and singularities
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246
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Chapter
§5. Legendre varieties and the obstacle problem
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252
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Bibliography
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265
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Article
YANGIANS AND R-MATRICES
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267
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Chapter
0. Introduction
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267
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Chapter
1. Yangians
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271
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Chapter
2. Highest weight representations
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276
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Chapter
3. A COMBINATORIAL INTERLUDE
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280
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Chapter
4. Classification
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283
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Chapter
5. R-MATRICES AND INTERTWINING OPERATORS
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294
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Chapter
6. CONCLUDING REMARKS
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299
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Bibliography
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302
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Article
EXTERIOR ALGEBRAS AND THE QUADRATIC RECIPROCITY LAW
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303
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Abstract
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303
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Rubric
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304
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Bibliography
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307
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Article
THE HADAMARD-CARTAN THEOREM IN LOCALLY CONVEX METRIC SPACES
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309
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Chapter
1. Introduction
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309
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Chapter
2. Conjugate points
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311
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Chapter
3. Proof of Theorem 1
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315
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Chapter
4. COHN-VOSSEN'S THEOREM AND SPACES WITHOUT CONJUGATE POINTS
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317
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Bibliography
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320
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Article
THE DISTANCE BETWEEN IDEALS IN THE ORDERS OF A REAL QUADRATIC FIELD
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321
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Chapter
1. Introduction
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321
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Chapter
2. Basic definitions
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322
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Chapter
3. The homomorphism θ
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330
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Chapter
4. Reduced ideals
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335
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Chapter
5. Lagrange's reduction procedure
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337
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Chapter
6. Periods of reduced cycles
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343
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Chapter
7. COMPARISON OF DISTANCES BETWEEN CORRESPONDING IDEALS IN DIFFERENT ORDERS
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350
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Chapter
8. GAUSS'S REDUCTION PROCESS
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352
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Bibliography
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357
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Article
THE ROLE OF GAMES AND PUZZLES IN THE POPULARIZATION OF MATHEMATICS
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359
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Abstract
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359
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Chapter
popularization of mathematics
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359
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Chapter
Games and mathematics
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362
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Chapter
Games and puzzles as a means for popularization
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364
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Bibliography
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368
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Article
CATÉGORIES DÉRIVÉES ET DUALITÉ, TRAVAUX DE J.-L. VERDIER
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369
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Chapter
1. Catégories dérivées
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369
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Chapter
2. Dualité
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378
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Bibliography
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388
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Bibliography
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389
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Bibliography
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390
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Chapter
Note sur la bibliographie
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391
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Article
MANIN'S PROOF OF THE MORDELL CONJECTURE OVER FUNCTION FIELDS
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393
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Chapter
I. The Theorem of the Kernel
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393
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Chapter
0. Review of connections and hypercohomology
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393
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Chapter
1. Extensions of connections
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395
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Chapter
2. The Gauss-Manin connection
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398
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Chapter
3. Sections of a family and extensions of connections
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399
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Chapter
4. Abelian schemes
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402
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Chapter
5. The algebraic proof
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403
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Chapter
6. The analytic proof
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409
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Chapter
II. PICARD-FUCHS EQUATIONS
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412
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Chapter
1. PICARD-FUCHS DIFFERENTIAL EQUATIONS
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412
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Chapter
2. PICARD-FUCHS COMPUTATIONS
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415
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Chapter
III. MORDELL'S CONJECTURE
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417
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Chapter
1. Sets of bounded height
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417
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Chapter
2. Lang-Siegel towers
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418
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Chapter
3. COROLLARIES OF THE THEOREM OF THE KERNEL
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419
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Chapter
4. Proof of Mordell's conjecture
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420
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Appendix
Appendix: Chai's proof of the Theorem of the Kernel
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424
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Bibliography
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427
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Rubric
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Rubric
BULLETIN BIBLIOGRAPHIQUE
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1
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Rubric
BULLETIN BIBLIOGRAPHIQUE
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27
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Back matter
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Back matter
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