Idempotent mathematics and mathematical physics : international workshop, February 3-10, 2003, Erwin Schrödinger International Institute for Mathematical Physics, Vienna, Austria / G.L. Litvinov, V.P. Maslov, editors.
- Format:
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- Contributor:
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- Conference Name:
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- Language:
- English
- Subjects (All):
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- Physical Description:
- 1 online resource (378 p.)
- Edition:
- 1st ed.
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, [2005]
- Language Note:
- English
- Summary:
- 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.
- Contents:
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- ""Contents""; ""Preface""; ""The Maslov dequantization, idempotent and tropical mathematics: A very brief introduction""; ""Set coverings and invertibility of functional Galois connections""; ""Discrete max-plus spectral theory""; ""Dequantization of coadjoint orbits: Moment sets and characteristic varieties""; ""On the combinatorial aspects of max-algebra""; ""Max-plus convex sets and functions""; ""Algebras of Lukasiewicz's logic and their semiring reducts""; ""Max-plus approaches to continuous space control and dynamic programming""
- ""A blow-up phenomenon in the Hamilton�Jacobi equation in an unbounded domain""""The dequantization transform and generalized Newton polytopes""; ""An object-oriented approach to idempotent analysis: Integral equations as optimal control problems""; ""Traffic assignment & Gibbs-Maslov semirings""; ""Viscosity solutions on Lagrangian manifolds and connections with tunnelling operators""; ""Applications of the generated pseudo-analysis to nonlinear partial differential equations""; ""A generalization of the utility theory using a hybrid idempotent-probabilistic measure""
- ""Amoebas : Their spines and their contours""""First steps in tropical geometry""; ""On minimax and idempotent generalized weak solutions to the Hamilton-Jacobi equation""; ""Dequantisation: Semi-direct sums of idempotent semimodules""; ""On (min, max, + )-inequalities""; ""Solution of some max-separable optimization problems with inequality constraints""
- Notes:
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- Description based upon print version of record.
- Includes bibliographical references.
- Description based on print version record.
- ISBN:
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- 0-8218-7967-7
- 0-8218-5711-8
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