eBook ISBN:  9780821879672 
Product Code:  CONM/377.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821879672 
Product Code:  CONM/377.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 377; 2005; 370 ppMSC: Primary 00; 81; 06; 35; 49; 46; 52; 14
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.
ReadershipGraduate students and research mathematicians interested in idempotent and tropical mathematics.

Table of Contents

Articles

G. L. Litvinov — The Maslov Dequantization, idempotent and tropical mathematics: a very brief introduction

Marianne Akian, Stéphane Gaubert and Vassili Kolokoltsov — Set coverings and invertibility of functional Galois connections [ MR 2148996 ]

Marianne Akian, Stéphane Gaubert and Cormac Walsh — Discrete maxplus spectral theory [ MR 2148997 ]

Ali Baklouti — Dequantization of coadjoint orbits: moment sets and characteristic varieties [ MR 2148998 ]

Peter Butkovič — On the combinatorial aspects of maxalgebra [ MR 2148999 ]

Guy Cohen, Stéphane Gaubert, JeanPierre Quadrat and Ivan Singer — Maxplus convex sets and functions [ MR 2149000 ]

A. Di Nola and B. Gerla — Algebras of Lukasiewicz’s logic and their semiring reducts [ MR 2149001 ]

Wendell H. Fleming and William M. McEneaney — Maxplus approaches to continuous space control and dynamic programming [ MR 2149002 ]

K. Khanin, D. Khmelev and A. Sobolevskiĭ — A blowup phenomenon in the HamiltonJacobi equation in an unbounded domain [ MR 2149003 ]

G. L. Litvinov and G. B. Shpiz — The dequantization transform and generalized Newton polytopes [ MR 2149004 ]

Paola Loreti and Marco Pedicini — An objectoriented approach to idempotent analysis: integral equations as optimal control problems [ MR 2149005 ]

P. Lotito, J.P. Quadrat and E. Mancinelli — Traffic assignment & GibbsMaslov semirings [ MR 2149006 ]

D. McCaffrey — Viscosity solutions on Lagrangian manifolds and connections with tunnelling operators [ MR 2149007 ]

Endre Pap — Applications of the generated pseudoanalysis to nonlinear partial differential equations [ MR 2149008 ]

Endre Pap — A generalization of the utility theory using a hybrid idempotentprobabilistic measure [ MR 2149009 ]

Mikael Passare and August Tsikh — Amoebas: their spines and their contours [ MR 2149010 ]

Jürgen RichterGebert, Bernd Sturmfels and Thorsten Theobald — First steps in tropical geometry [ MR 2149011 ]

Ilya V. Roublev — On minimax and idempotent generalized weak solutions to the HamiltonJacobi equation [ MR 2149012 ]

Edouard Wagneur — Dequantisation: semidirect sums of idempotent semimodules [ MR 2149013 ]

Jacob van der Woude and Geert Jan Olsder — On $(\min ,\max ,+)$inequalities [ MR 2149014 ]

Karel Zimmermann — Solution of some maxseparable optimization problems with inequality constraints [ MR 2149015 ]


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

Articles

G. L. Litvinov — The Maslov Dequantization, idempotent and tropical mathematics: a very brief introduction

Marianne Akian, Stéphane Gaubert and Vassili Kolokoltsov — Set coverings and invertibility of functional Galois connections [ MR 2148996 ]

Marianne Akian, Stéphane Gaubert and Cormac Walsh — Discrete maxplus spectral theory [ MR 2148997 ]

Ali Baklouti — Dequantization of coadjoint orbits: moment sets and characteristic varieties [ MR 2148998 ]

Peter Butkovič — On the combinatorial aspects of maxalgebra [ MR 2148999 ]

Guy Cohen, Stéphane Gaubert, JeanPierre Quadrat and Ivan Singer — Maxplus convex sets and functions [ MR 2149000 ]

A. Di Nola and B. Gerla — Algebras of Lukasiewicz’s logic and their semiring reducts [ MR 2149001 ]

Wendell H. Fleming and William M. McEneaney — Maxplus approaches to continuous space control and dynamic programming [ MR 2149002 ]

K. Khanin, D. Khmelev and A. Sobolevskiĭ — A blowup phenomenon in the HamiltonJacobi equation in an unbounded domain [ MR 2149003 ]

G. L. Litvinov and G. B. Shpiz — The dequantization transform and generalized Newton polytopes [ MR 2149004 ]

Paola Loreti and Marco Pedicini — An objectoriented approach to idempotent analysis: integral equations as optimal control problems [ MR 2149005 ]

P. Lotito, J.P. Quadrat and E. Mancinelli — Traffic assignment & GibbsMaslov semirings [ MR 2149006 ]

D. McCaffrey — Viscosity solutions on Lagrangian manifolds and connections with tunnelling operators [ MR 2149007 ]

Endre Pap — Applications of the generated pseudoanalysis to nonlinear partial differential equations [ MR 2149008 ]

Endre Pap — A generalization of the utility theory using a hybrid idempotentprobabilistic measure [ MR 2149009 ]

Mikael Passare and August Tsikh — Amoebas: their spines and their contours [ MR 2149010 ]

Jürgen RichterGebert, Bernd Sturmfels and Thorsten Theobald — First steps in tropical geometry [ MR 2149011 ]

Ilya V. Roublev — On minimax and idempotent generalized weak solutions to the HamiltonJacobi equation [ MR 2149012 ]

Edouard Wagneur — Dequantisation: semidirect sums of idempotent semimodules [ MR 2149013 ]

Jacob van der Woude and Geert Jan Olsder — On $(\min ,\max ,+)$inequalities [ MR 2149014 ]

Karel Zimmermann — Solution of some maxseparable optimization problems with inequality constraints [ MR 2149015 ]