Jeremy Gunawardena (ed.)

Idempotency

Herausgeber: Gunawardena, J.; Gunawardena, Jeremy

• Gebundenes Buch

Produktbeschreibung

Certain nonlinear optimisation problems arising in such disparate areas as the theory of computation, pure and applied probability and mathematical physics, can be solved by linear methods, provided one replaces the usual number system with one in which addition satisfies the idempotent law. Only recently has a systematic study of the subject emerged, triggered in part by a workshop organised by Hewlett-Packard's Basic Research Institute in the Mathematical Sciences (BRIMS), which brought together for the first time many leading researchers in the area. This volume is a record of that workshop, but it also includes other invited contributions, a broad Introduction to Idempotency, written specially for the book, and a bibliography of the subject. In sum, this is the most up-to-date survey currently available of research in this developing area of mathematics; the articles cover both practical and more theoretical considerations, making it essential reading for all workers in the area.

Table of contents:
An introduction to idempotency J. Gunawardena; 1. Tropical semirings J.-E. Pin; 2. Some automata-theoretic aspects of min-max-plus semirings D. Krob; 3. The finite power property for rational sets of free groups F. d'Alessandro and J. Sakarovitch; 4. The topological approach to the limitedness problem on distance automata H. Leung; 5. Types and dynamics in partially additive categories G. Mascari and M. Pedicini; 6. Task resource models and (max,+) automata S. Gaubert and J. Mairesse; 7. Algebraic system analysis of timed Petri nets G. Cohen, S. Gaubert and J.-P. Quadrat; 8. Ergodic theorems for stochastic operators and discrete event systems F. Baccelli and J. Mairesse; 9. Computational issues in recursive stochastic systems B. Gaujal and A. Jean-Marie; 10. Periodic points of nonexpansive maps R. D. Nussbaum; 11. A system-theoretic approach for discrete-event control of manufacturing systems A. Gürel, O. C. Pastravanu and F. L. Lewis; 12. Idempotent structures in the supervisory control of discrete event systems D. D. Cofer and V. K. Garg; 13. Maxpolynomials and discrete-event dynamic systems R. Cuninghame-Green; 14. Stochastic HJB equation and WKB method V. N. Kolokoltsov; 15. Lagrange problem from the point of view of idempotent analysis S. Samborskii; 16. New differential equation for the dynamics of the Pareto sets V. N. Kolokoltsov and V. P. Maslov; 17. Duality between probability and optimization M. Akian, J.-P. Quadrat and M. Viot; 18. Maslov optimisation theory: topological aspects P. Del Moral; 19. Random particle methods in (max,+) optimization problems P. Del Moral and G. Salut; 20. The geometry of finite dimensional pseudomodules E. Wagneur; 21. A general linear max-plus solution technique E. A. Walkup and G. Borriello; 22. Axiomatics of thermodynamics and idempotent analysis V. P. Maslov; 23. Correspondence principle for idempotent calculus and some computer applications G. L. Litvinov and V. P. Maslov.

A record of a workshop organised by Hewlett-Packard's Basic Research Institute in the Mathematical Sciences, which brought together for the first time many leading researchers in the subject. It is the most up-to-date survey of this developing area of mathematics; the articles cover both practical and more theoretical considerations, making it essential reading for all workers in the area.

The most up-to-date survey of this developing area of mathematics.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 456
• Erscheinungstermin: 9. September 2004
• Englisch
• Abmessung: 235mm x 157mm x 31mm
• Gewicht: 886g
• ISBN-13: 9780521553445
• ISBN-10: 052155344X
• Artikelnr.: 20968700

Inhaltsangabe

Foreword; Preface; List of participants; 1. An introduction to idempotency
Jeremy Gunawardena; 2. Tropical semirings Jean-Eric Pin; 3. Some
automata-theoretic aspects of min-max-plus semirings Daniel Krob; 4. The
finite power property for rational sets of a free group Flavio d'Alessandro
and Jacques Sakarovitch; 5. The topological approach to the limitedness
problem on distance automata Hing Leung; 6. Types and dynamics in partially
additive categories Gianfranco Mascari and Marco Pedicini; 7. Task resource
models and (max,+) automata Stéphane Gaubert and Jean Mairesse; 8.
Algebraic system analysis of timed Petri nets Guy Cohen, Stéphane Gaubert
and Jean-Pierre Quadrat; 9. Ergodic theorems for stochastic operators and
discrete event networks François Baccelli and Jean Mairesse; 10.
Computational issues in recursive stochastic systems Bruno Gaujal and Alain
Jean-Marie; 11. Periodic points of nonexpansive maps Roger D. Nussbaum; 12.
A system-theoretic approach for discrete-event control of manufacturing
systems Ayla Gürel, Octavian C. Pastravanu and Frank L. Lewis; 13.
Idempotent structures in the supervisory control of discrete event systems
Darren D. Cofer and Vijay K. Garg; 14. Maxpolynomials and discrete-event
dynamic systems Raymond A. Cunninghame-Green; 15. The Stochastic HJB
equation and WKB method Vassili N. Kolokoltsov; 16. The Lagrange problem
from the point of view of idempotent analysis Serguei Samborskii; 17. A new
differential equation for the dynamics of the Pareto sets Vassili N.
Kolokoltsov and Victor P. Maslov; 18. Duality between probability and
optimization Marianne Akian, Jean-Pierre Quadrat and Michel Viot; 19.
Maslov optimization theory: topological aspects Pierre Del Moral; 20.
Random particle methods in (max,+) optimization problems Pierre Del Moral
and Gérard Salut; 21. The geometry of finite dimensional pseudomodules
Edouard Wagneur; 22. A general linear max-plus solution technique Elizabeth
A. Walkup and Gaetano Borriello; 23. Axiomatics of thermodynamics and
idempotent analysis Victor P. Maslov; 24. The correspondence principle for
idempotent calculus and some computer applications Grigori L. Litvinov and
Victor P. Maslov.