Idempotent mathematics is a rapidly developing new branch of the mathematical sciences that is closely related to mathematical physics. The existing literature on the subject is vast and includes numerous books and journal papers. A workshop was organized at the Erwin Schrodinger Institute for Mathematical Physics (Vienna) to give a snapshot of modern idempotent mathematics. This volume contains articles stemming from that event. Also included is an introductory paper by G. Litvinov and additional invited contributions. The resulting volume presents a comprehensive overview of the state of the art. It is suitable for graduate students and researchers interested in idempotent mathematics and tropical mathematics.
The Maslov's dequantization, idempotent and tropical mathematics: A very brief introduction by G. L. Litvinov Set coverings and invertibility of functional Galois connections by M. Akian, S. Gaubert, and V. Kolokoltsov Discrete max-plus spectral theory by M. Akian, S. Gaubert, and C. Walsh Dequantization of coadjoint orbits: Moment sets and characteristic varieties by A. Baklouti On the combinatorial aspects of max-algebra by P. Butkovic Max-plus convex sets and functions by G. Cohen, S. Gaubert, J.-P. Quadrat, and I. Singer Algebras of Lukasiewicz's logic and their semiring reducts by A. Di Nola and B. Gerla Max-plus approaches to continuous space control and dynamic programming by W. H. Fleming and W. M. McEneaney A blow-up phenomenon in the Hamilton-Jacobi equation in an unbounded domain by K. Khanin, D. Khmelev, and A. Sobolevskii The dequantization transform and generalized Newton polytopes by G. L. Litvinov and G. B. Shpiz An object-oriented approach to idempotent analysis: Integral equations as optimal control problems by P. Loreti and M. Pedicini Traffic assignment & Gibbs-Maslov semirings by P. Lotito, J.-P. Quadrat, and E. Mancinelli Viscosity solutions on Lagrangian manifolds and connections with tunnelling operators by D. McCaffrey Applications of the generated pseudo-analysis to nonlinear partial differential equations by E. Pap A generalization of the utility theory using a hybrid idempotent-probabilistic measure by E. Pap Amoebas: Their spines and their contours by M. Passare and A. Tsikh First steps in tropical geometry by J. Richter-Gebert, B. Sturmfels, and T. Theobald On minimax and idempotent generalized weak solutions to the Hamilton-Jacobi equation by I. V. Roublev Dequantisation: Semi-direct sums of idempotent semimodules by E. Wagneur On (min,max,+)-inequalities by J. van der Woude and G. J. Olsder Solution of some max-separable optimization problems with inequality constraints by K. Zimmermann.