Idempotent Mathematics And Mathematical Physics
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Idempotent Mathematics And Mathematical Physics
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Author : Grigoriĭ Lazarevich Litvinov
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Idempotent Mathematics And Mathematical Physics written by Grigoriĭ Lazarevich Litvinov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
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.
Idempotent Mathematics And Mathematical Physics
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Idempotent Mathematics And Mathematical Physics written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematical physics categories.
Idempotent Mathematics And Mathematical Physics
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Author : Grigoriĭ Lazarevich Litvinov
language : en
Publisher: University of Chicago Press
Release Date : 2005
Idempotent Mathematics And Mathematical Physics written by Grigoriĭ Lazarevich Litvinov and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
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.
Tropical And Idempotent Mathematics
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Author : Grigoriĭ Lazarevich Litvinov
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Tropical And Idempotent Mathematics written by Grigoriĭ Lazarevich Litvinov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
This volume is a collection of papers from the International Conference on Tropical and Idempotent Mathematics, held in Moscow, Russia in August 2007. This is a relatively new branch of mathematical sciences that has been rapidly developing and gaining popularity over the last decade. Tropical mathematics can be viewed as a result of the Maslov dequantization applied to 'traditional' mathematics over fields. Importantly, applications in econophysics and statistical mechanics lead to an explanation of the nature of financial crises. Another original application provides an analysis of instabilities in electrical power networks. Idempotent analysis, tropical algebra, and tropical geometry are the building blocks of the subject. Contributions to idempotent analysis are focused on the Hamilton-Jacobi semigroup, the max-plus finite element method, and on the representations of eigenfunctions of idempotent linear operators. Tropical algebras, consisting of plurisubharmonic functions and their germs, are examined. The volume also contains important surveys and research papers on tropical linear algebra and tropical convex geometry.
Idempotent Analysis And Its Applications
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Author : Vassili N. Kolokoltsov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Idempotent Analysis And Its Applications written by Vassili N. Kolokoltsov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
The first chapter deals with idempotent analysis per se . To make the pres- tation self-contained, in the first two sections we define idempotent semirings, give a concise exposition of idempotent linear algebra, and survey some of its applications. Idempotent linear algebra studies the properties of the semirn- ules An , n E N , over a semiring A with idempotent addition; in other words, it studies systems of equations that are linear in an idempotent semiring. Pr- ably the first interesting and nontrivial idempotent semiring , namely, that of all languages over a finite alphabet, as well as linear equations in this sern- ing, was examined by S. Kleene [107] in 1956 . This noncommutative semiring was used in applications to compiling and parsing (see also [1]) . Presently, the literature on idempotent algebra and its applications to theoretical computer science (linguistic problems, finite automata, discrete event systems, and Petri nets), biomathematics, logic , mathematical physics , mathematical economics, and optimizat ion, is immense; e. g. , see [9, 10, 11, 12, 13, 15, 16 , 17, 22, 31 , 32, 35,36,37,38,39 ,40,41,52,53 ,54,55,61,62 ,63,64,68, 71, 72, 73,74,77,78, 79,80,81,82,83,84,85,86,88,114,125 ,128,135,136, 138,139,141,159,160, 167,170,173,174,175,176,177,178,179,180,185,186 , 187, 188, 189]. In §1. 2 we present the most important facts of the idempotent algebra formalism . The semimodules An are idempotent analogs of the finite-dimensional v- n, tor spaces lR and hence endomorphisms of these semi modules can naturally be called (idempotent) linear operators on An .
Idempotency
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Author : Jeremy Gunawardena
language : en
Publisher: Cambridge University Press
Release Date : 1998-01-13
Idempotency written by Jeremy Gunawardena and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-13 with Mathematics categories.
Certain nonlinear optimization problems arise in such areas as the theory of computation, pure and applied probability, and mathematical physics. These problems can be solved through linear methods, providing the usual number system is replaced with one that satisfies the idempotent law. Only recently has a systematic study of idempotency analysis emerged, triggered in part by a workshop organized by Hewlett-Packard's Basic Research Institute in the Mathematical Sciences (BRIMS), which brought together for the first time many leading researchers in the area. This volume, a record of that workshop, includes a variety of contributions, a broad introduction to idempotency, written especially for the book, and a bibliography of the subject. It is the most up-to-date survey currently available of research in this developing area of mathematics; the articles cover both practical and more theoretical considerations, making it essential reading for all workers in the area.
Asymptotic Combinatorics With Application To Mathematical Physics
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Author : V.A. Malyshev
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Combinatorics With Application To Mathematical Physics written by V.A. Malyshev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
New and striking results obtained in recent years from an intensive study of asymptotic combinatorics have led to a new, higher level of understanding of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory.
Spectral Theory And Geometric Analysis
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Author : Mikhail Aleksandrovich Shubin
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-02-10
Spectral Theory And Geometric Analysis written by Mikhail Aleksandrovich Shubin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-10 with Mathematics categories.
The papers in this volume cover important topics in spectral theory and geometric analysis such as resolutions of smooth group actions, spectral asymptotics, solutions of the Ginzburg-Landau equation, scattering theory, Riemann surfaces of infinite genus and tropical mathematics.
Hamilton Jacobi Equations Approximations Numerical Analysis And Applications
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Author : Yves Achdou
language : en
Publisher: Springer
Release Date : 2013-05-24
Hamilton Jacobi Equations Approximations Numerical Analysis And Applications written by Yves Achdou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-24 with Mathematics categories.
These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).
Relations And Kleene Algebra In Computer Science
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Author : Renate Schmidt
language : en
Publisher: Springer
Release Date : 2006-10-04
Relations And Kleene Algebra In Computer Science written by Renate Schmidt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-04 with Mathematics categories.
The book constitutes the joint refereed proceedings of the 9th International Conference on Relational Methods in Computer Science, RelMiCS 2006, and the 4th International Workshop on Applications of Kleene Algebras, AKA 2006, held in Manchester, UK in August/September 2006. The 25 revised full papers presented together with two invited papers and the abstract of an invited talk were carefully reviewed and selected from 44 submissions.