**Contemporary Mathematics**

Volume: 377;
2005;
370 pp;
Softcover

MSC: Primary 00; 81; 06; 35; 49; 46; 52; 14;

Print ISBN: 978-0-8218-3538-8

Product Code: CONM/377

List Price: $109.00

Individual Member Price: $87.20

**Electronic ISBN: 978-0-8218-7967-2
Product Code: CONM/377.E**

List Price: $109.00

Individual Member Price: $87.20

# Idempotent Mathematics and Mathematical Physics

Share this page *Edited by *
*G. L. Litvinov; V. P. Maslov*

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 Schrödinger 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.

#### Table of Contents

# Table of Contents

## Idempotent Mathematics and Mathematical Physics

- Contents iii4 free
- Preface v6 free
- The Maslov dequantization, idempotent and tropical mathematics: A very brief introduction 18 free
- Set coverings and invertibility of functional Galois connections 1926
- Discrete max-plus spectral theory 5360
- Dequantization of coadjoint orbits: Moment sets and characteristic varieties 7986
- On the combinatorial aspects of max-algebra 93100
- Max-plus convex sets and functions 105112
- Algebras of Lukasiewicz's logic and their semiring reducts 131138
- Max-plus approaches to continuous space control and dynamic programming 145152
- A blow-up phenomenon in the Hamilton–Jacobi equation in an unbounded domain 161168
- The dequantization transform and generalized Newton polytopes 181188
- An object-oriented approach to idempotent analysis: Integral equations as optimal control problems 187194
- Traffic assignment & Gibbs-Maslov semirings 209216
- Viscosity solutions on Lagrangian manifolds and connections with tunnelling operators 221228
- Applications of the generated pseudo-analysis to nonlinear partial differential equations 239246
- A generalization of the utility theory using a hybrid idempotent-probabilistic measure 261268
- Amoebas : Their spines and their contours 275282
- First steps in tropical geometry 289296
- On minimax and idempotent generalized weak solutions to the Hamilton-Jacobi equation 319326
- Dequantisation: Semi-direct sums of idempotent semimodules 339346
- On (min, max, + )-inequalities 353360
- Solution of some max-separable optimization problems with inequality constraints 363370

#### Readership

Graduate students and research mathematicians interested in idempotent and tropical mathematics.