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Tropical and idempotent mathematics and applications / [edited by] G.L. Litvinov and S.N. Sergeev.

By: Contributor(s): Material type: TextTextSeries: Contemporary mathematics ; 616Publication details: Providence : American Mathematical Society, c2014.Description: xii, 300 p. : illustrations ; 26 cmISBN:
  • 9780821894965 (pbk. : acidfree paper)
Subject(s): DDC classification:
  • 510 23 Am512c
Contents:
Tropical Cramer determinants revisited by M. Akian, S. Gaubert, and A. Guterman-- An approximation of Hopf-Lax type formula via idempotent analysis by A. Avantaggiati and P. Loreti-- Ideals of MV-semirings and MV-algebras by L. P. Belluce, A. Di Nola, and A. R. Ferraioli-- Tropical Plucker functions and Kashiwara crystals by V. I. Danilov, A. V. Karzanov, and G. A. Koshevoy-- A metric on max-min algebra by J. Eskeldson, M. Jaffe, and V. Nitica-- Optimization on the range of a max-separable operator by M. Gavalec and K. Zimmermann-- Algebraic structures of tropical mathematics by Z. Izhakian, M. Knebusch, and L. Rowen-- Parametric dequantization, tropical reduction of hyperfields and steady states of AC electrical networks by B. Kh. Kirshtein-- A constrained tropical optimization problem: Complete solution and application example by N. Krivulin-- On the mathematical foundations of classical thermodynamics by V. P. Maslov-- Tropical support sets in analysis of weak links and complementarity by V. Matveenko-- Idempotent algebra models of single-agent and multi-agent dynamics by D. Nikolayev-- Tropical convexity over max-min semiring by V. Nitica and S. Sergeev-- Tropicalization and tropical equilibration of chemical reactions by V. Noel, D. Grigoriev, S. Vakulenko, and O. Radulescu-- An overview of transience bounds in max-plus algebra by T. Nowak and B. Charron-Bost-- Strong independence and injectivity in tropical modules by E. Wagneur.
Summary: This volume contains the proceedings of the International Workshop on Tropical and Idempotent Mathematics, held at the Independent University of Moscow, Russia, from August 26-31, 2012. The main purpose of the conference was to bring together and unite researchers and specialists in various areas of tropical and idempotent mathematics and applications. This volume contains articles on algebraic foundations of tropical mathematics as well as articles on applications of tropical mathematics in various fields as diverse as economics, electroenergetic networks, chemical reactions, representation theory, and foundations of classical thermodynamics. This volume is intended for graduate students and researchers interested in tropical and idempotent mathematics or in their applications in other areas of mathematics and in technical sciences.
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Includes bibliographical references.

Tropical Cramer determinants revisited by M. Akian, S. Gaubert, and A. Guterman--
An approximation of Hopf-Lax type formula via idempotent analysis by A. Avantaggiati and P. Loreti--
Ideals of MV-semirings and MV-algebras by L. P. Belluce, A. Di Nola, and A. R. Ferraioli--
Tropical Plucker functions and Kashiwara crystals by V. I. Danilov, A. V. Karzanov, and G. A. Koshevoy--
A metric on max-min algebra by J. Eskeldson, M. Jaffe, and V. Nitica--
Optimization on the range of a max-separable operator by M. Gavalec and K. Zimmermann--
Algebraic structures of tropical mathematics by Z. Izhakian, M. Knebusch, and L. Rowen--
Parametric dequantization, tropical reduction of hyperfields and steady states of AC electrical networks by B. Kh. Kirshtein--
A constrained tropical optimization problem: Complete solution and application example by N. Krivulin--
On the mathematical foundations of classical thermodynamics by V. P. Maslov--
Tropical support sets in analysis of weak links and complementarity by V. Matveenko--
Idempotent algebra models of single-agent and multi-agent dynamics by D. Nikolayev--
Tropical convexity over max-min semiring by V. Nitica and S. Sergeev--
Tropicalization and tropical equilibration of chemical reactions by V. Noel, D. Grigoriev, S. Vakulenko, and O. Radulescu--
An overview of transience bounds in max-plus algebra by T. Nowak and B. Charron-Bost--
Strong independence and injectivity in tropical modules by E. Wagneur.

This volume contains the proceedings of the International Workshop on Tropical and Idempotent Mathematics, held at the Independent University of Moscow, Russia, from August 26-31, 2012. The main purpose of the conference was to bring together and unite researchers and specialists in various areas of tropical and idempotent mathematics and applications. This volume contains articles on algebraic foundations of tropical mathematics as well as articles on applications of tropical mathematics in various fields as diverse as economics, electroenergetic networks, chemical reactions, representation theory, and foundations of classical thermodynamics. This volume is intended for graduate students and researchers interested in tropical and idempotent mathematics or in their applications in other areas of mathematics and in technical sciences.

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