Introduction

Chapters in this book

1. Frontmatter I
2. Preface VII
3. Contents XIII
4. Basic notations XIX
5. Part I: Elements of tropical mathematics
6. Introduction 1
7. 1 Elements of tropical algebras 5
8. 2 Elements of tropical topology 20
9. 3 Elements of tropical analysis 28
10. 4 Elements of tropical functional analysis 47
11. Part II: Some applications of tropical bi-wavelets to signal processing
12. Introduction 81
13. 5 Tropical bi-wavelets for Hölder exponents and fractal dimensions calculations 83
14. 6 Tropical bi-wavelets for multi-fractal analysis 93
15. 7 Tropical bi-wavelets for image processing 105
16. Part III: Tropical intervals
17. Introduction 113
18. 8 Tropical intervals 115
19. 9 Tropical inclusion functions 135
20. 10 Tropical probabilist set inversion 139
21. Part IV: Some applications of tropical mathematics in theoretical physics
22. Introduction 145
23. 11 Numerical applications with tropical intervals 149
24. 12 Tropical transforms for theoretical physics 150
25. 13 Contributions of tropical mathematics to statistical physics 159
26. 14 (min, +)-Path integral 163
27. 15 Tropical complex variational calculus 175
28. Postface
29. Introduction 185
30. A Tropical intervals numerical implementation 187
31. B Tropical probabilist set inversion 191
32. C Tropical intervals functions optimization examples 197
33. D Tropical intervals linear algebra examples 203
34. Bibliography 209
35. Index 219