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.
G. L. Litvinov, Independent University of Moscow, Russia. S. N. Sergeev, University of Birmingham, United Kingdom.
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