Differential algebra and related topics: proceedings of the International Workshop, Newark Campus of Rutgers, The State University of New Jersey, 2-3 November 2000

P. Cassidy, Li Guo, William F. Keigher, Phyllis J. Cassidy, William Y. Sit9810247036, 9789810247034, 9789812778437

Proceedings of the International Workshop held November 2-3, 2000 at the State University of New Jersey. Includes tutorial and survey papers presented at the workshop. For graduate students, pure mathematicians, logicians, algebraic geometers, applied mathematicians and physicists.

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Table of contents :
Contents……Page 14
Foreword……Page 6
Workshop Participants……Page 10
Workshop Program……Page 12
Preface……Page 15
1 Basic Definitions……Page 17
2 Triangular Sets and Pseudo-Division……Page 20
3 Invertibility of Initials……Page 23
4 Ranking and Reduction Concepts……Page 32
5 Characteristic Sets……Page 38
6 Reduction Algorithms……Page 41
7 Rosenfeld Properties of an Autoreduced Set……Page 45
8 Coherence and Rosenfeld’s Lemma……Page 49
9 Ritt-Raudenbush Basis Theorem……Page 56
10 Decomposition Problems……Page 58
11 Component Theorems……Page 64
12 The Low Power Theorem……Page 69
Appendix: Solutions and hints to selected exercises……Page 77
References……Page 82
1 Introduction……Page 85
2 Differential rings……Page 86
3 Differential spectrum……Page 89
4 Structure sheaf……Page 92
5 Morphisms……Page 94
7 A-Zeros……Page 95
8 Differential spectrum of R……Page 97
9 AAD modules……Page 98
10 Global sections of AAD rings……Page 100
12 AAD reduction……Page 103
13 Based schemes……Page 104
14 Products……Page 105
References……Page 107
Introduction……Page 109
1 Differential Rings……Page 110
2 Kolchin’s Irreducibility Theorem……Page 125
3 Descent for Projective Varieties……Page 129
4 Complements and Questions……Page 134
References……Page 136
2 Notation and conventions in differential algebra……Page 139
3 What is model theory?……Page 140
4 Differentially closed fields……Page 142
5 O-minimal theories……Page 156
6 Valued differential fields……Page 158
7 Model theory of difference fields……Page 160
References……Page 161
1 Introduction……Page 165
2 The derivation approach to the inverse problem……Page 169
3 The inverse problem for a 2 x 2 upper triangular matrix group……Page 172
4 Solvable groups……Page 178
References……Page 183
1 The basic concepts……Page 185
2 Universal Picard-Vessiot rings……Page 187
3 Regular singular equations……Page 192
4 Formal differential equations……Page 194
5 Multisummation and Stokes maps……Page 195
6 Meromorphic differential equations……Page 198
References……Page 202
1 Introduction……Page 205
2 Linear Differential Equations……Page 208
3 The Algorithm……Page 210
4 Remarks on the Algorithm……Page 214
5 Remarks on the Hypotheses……Page 217
6 Counterexamples……Page 218
7 An Alternate Approach……Page 220
Appendix – A MAPLE implementation……Page 223
References……Page 230
1 Integrals of Ordinary Differential Equations……Page 233
2 Linearized Equations……Page 237
3 Hamiltonian Systems – The Classical Formulation……Page 238
4 Normal Variational Equations……Page 248
5 Differential Galois Theory and Non-Integrability……Page 250
6 Preliminaries to the Applications……Page 252
7 Applications……Page 258
References……Page 267
Introduction……Page 271
1 Moving frames a tutorial……Page 272
2 Comparison of {uaK||K|>=0} with {IaK||K|>=0}……Page 283
3 Calculations with invariants……Page 287
References……Page 292
0 Introduction……Page 295
1 Definitions examples and basic properties……Page 297
2 Free Baxter algebras……Page 301
3 Further applications of free Baxter algebras……Page 312
References……Page 317