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Idempotent Mathematics and Mathematical Physics
 
Edited by: G. L. Litvinov Independent University of Moscow, Moscow, Russia
V. P. Maslov Moscow Institute of Electrical Engineering, Moscow, Russia
Idempotent Mathematics and Mathematical Physics
Softcover ISBN:  978-0-8218-3538-8
Product Code:  CONM/377
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7967-2
Product Code:  CONM/377.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-3538-8
eBook: ISBN:  978-0-8218-7967-2
Product Code:  CONM/377.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
Idempotent Mathematics and Mathematical Physics
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Idempotent Mathematics and Mathematical Physics
Edited by: G. L. Litvinov Independent University of Moscow, Moscow, Russia
V. P. Maslov Moscow Institute of Electrical Engineering, Moscow, Russia
Softcover ISBN:  978-0-8218-3538-8
Product Code:  CONM/377
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7967-2
Product Code:  CONM/377.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-3538-8
eBook ISBN:  978-0-8218-7967-2
Product Code:  CONM/377.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 3772005; 370 pp
    MSC: 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.

    Readership

    Graduate 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 max-plus spectral theory [ MR 2148997 ]
    • Ali Baklouti — Dequantization of coadjoint orbits: moment sets and characteristic varieties [ MR 2148998 ]
    • Peter Butkovič — On the combinatorial aspects of max-algebra [ MR 2148999 ]
    • Guy Cohen, Stéphane Gaubert, Jean-Pierre Quadrat and Ivan Singer — Max-plus 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 — Max-plus approaches to continuous space control and dynamic programming [ MR 2149002 ]
    • K. Khanin, D. Khmelev and A. Sobolevskiĭ — A blow-up phenomenon in the Hamilton-Jacobi 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 object-oriented approach to idempotent analysis: integral equations as optimal control problems [ MR 2149005 ]
    • P. Lotito, J.-P. Quadrat and E. Mancinelli — Traffic assignment & Gibbs-Maslov semirings [ MR 2149006 ]
    • D. McCaffrey — Viscosity solutions on Lagrangian manifolds and connections with tunnelling operators [ MR 2149007 ]
    • Endre Pap — Applications of the generated pseudo-analysis to nonlinear partial differential equations [ MR 2149008 ]
    • Endre Pap — A generalization of the utility theory using a hybrid idempotent-probabilistic measure [ MR 2149009 ]
    • Mikael Passare and August Tsikh — Amoebas: their spines and their contours [ MR 2149010 ]
    • Jürgen Richter-Gebert, Bernd Sturmfels and Thorsten Theobald — First steps in tropical geometry [ MR 2149011 ]
    • Ilya V. Roublev — On minimax and idempotent generalized weak solutions to the Hamilton-Jacobi equation [ MR 2149012 ]
    • Edouard Wagneur — Dequantisation: semi-direct 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 max-separable optimization problems with inequality constraints [ MR 2149015 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 3772005; 370 pp
MSC: 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.

Readership

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 max-plus spectral theory [ MR 2148997 ]
  • Ali Baklouti — Dequantization of coadjoint orbits: moment sets and characteristic varieties [ MR 2148998 ]
  • Peter Butkovič — On the combinatorial aspects of max-algebra [ MR 2148999 ]
  • Guy Cohen, Stéphane Gaubert, Jean-Pierre Quadrat and Ivan Singer — Max-plus 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 — Max-plus approaches to continuous space control and dynamic programming [ MR 2149002 ]
  • K. Khanin, D. Khmelev and A. Sobolevskiĭ — A blow-up phenomenon in the Hamilton-Jacobi 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 object-oriented approach to idempotent analysis: integral equations as optimal control problems [ MR 2149005 ]
  • P. Lotito, J.-P. Quadrat and E. Mancinelli — Traffic assignment & Gibbs-Maslov semirings [ MR 2149006 ]
  • D. McCaffrey — Viscosity solutions on Lagrangian manifolds and connections with tunnelling operators [ MR 2149007 ]
  • Endre Pap — Applications of the generated pseudo-analysis to nonlinear partial differential equations [ MR 2149008 ]
  • Endre Pap — A generalization of the utility theory using a hybrid idempotent-probabilistic measure [ MR 2149009 ]
  • Mikael Passare and August Tsikh — Amoebas: their spines and their contours [ MR 2149010 ]
  • Jürgen Richter-Gebert, Bernd Sturmfels and Thorsten Theobald — First steps in tropical geometry [ MR 2149011 ]
  • Ilya V. Roublev — On minimax and idempotent generalized weak solutions to the Hamilton-Jacobi equation [ MR 2149012 ]
  • Edouard Wagneur — Dequantisation: semi-direct 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 max-separable optimization problems with inequality constraints [ MR 2149015 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.