1 edition of **Idempotent Analysis and Its Applications** found in the catalog.

- 338 Want to read
- 8 Currently reading

Published
**1997**
by Springer Netherlands in Dordrecht
.

Written in English

- Mathematics,
- Differential equations, partial,
- Economics,
- Mathematical optimization,
- Algebra

This monograph is about a branch of calculus the authors have called Idempotent Analysis, which deals with the semimodules of functions ranging in a semiring with idempotent addition. The theory is developed together with numerous applications to discrete mathematics, turnpike theory, mathematical economics, games and controlled Markov processes, the theory of generalised solutions of the Hamilton-Jacobi-Bellman differential equation, the theory of continuously observed and controlled quantum systems and the construction of WKB-like asymptotics of the heat equation and the Schrödinger equation. Audience: This book will be of interest to mathematicians, engineers, college teachers and students.

**Edition Notes**

Statement | by Vassili N. Kolokoltsov, Victor P. Maslov |

Series | Mathematics and Its Applications -- 401, Mathematics and Its Applications -- 401 |

Contributions | Maslov, Victor P. |

Classifications | |
---|---|

LC Classifications | QA172-172.4, QA171.5 |

The Physical Object | |

Format | [electronic resource] / |

Pagination | 1 online resource (324 p.) |

Number of Pages | 324 |

ID Numbers | |

Open Library | OL27044688M |

ISBN 10 | 9048148340, 9401589011 |

ISBN 10 | 9789048148349, 9789401589017 |

OCLC/WorldCa | 851371593 |

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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, Cited by: About this book. 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. Presently, the literature on idempotent algebra and its applications to theoretical computer science (linguistic problems, finite Idempotent Analysis and Its Applications book, 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. Presently, the literature on idempotent algebra and its applications to theoretical computer science (linguistic problems, finite automata, discrete event systems, and Petri nets), biomathematics.

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. ISBN: OCLC Number: Description: xii, pages: illustrations ; 25 cm. Contents: 1. Idempotent Analysis Analysis of Operators on Idempotent Semimodules Generalized Solutions of Bellman's Differential Equation Quantization of the Bellman Equation and Multiplicative Asymptotics Optimization Theory.

The first chapter deals with idempotent analysis per se. [Read or Download] Idempotent Analysis and Its Applications Full Books [ePub/PDF/Audible/Kindle] 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 Analysis and Its Applications, Hardcover by Kolokoltsov, Vassili N.; Maslov, V. P., ISBNISBNBrand New, Free shipping A translation of a presentation of the idempotent theory, a branch of calculus dealing with the semimodules of functions ranging in a semiring with idempotent addition.

Idempotent Analysis and Its Applications by Vassili N. Kolokoltsov Department of Mathematical Statistics, Nottingham Trent University, Nottingham, England and Institute of New Technologies, Moscow, Russia and Victor P.

Maslov Department of Physics, Moscow State University, Moscow, Russia KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON.

Idempotent Analysis Volume 13 of Advances in Soviet mathematics, ISSN Volume 13 of Advances in the mathematical sciences, ISSN.

Application of idempotent mathematics are numerous in mathematical physics (de-quantization, thermodynamics), chemical engineering and system biology (including chemical kinetics and the analysis of multiscale dynamics), the theory of dimension and entropy (including fractal and negative dimensions), in models of economics and finances, in the theory of complexity, approximation theory in high.

MATHEMATICS AND ITS APPLICATIONS ebook. Springer. Hardcover. Book Condition: New. Hardcover. pages. Dimensions: in.

x in. x 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 F unctional Analysis is an abstract version of Idempotent Analysis in the sense of [1–8].

Idempotent Analysis is closely related to optimal cont rol theory, optimization theory. 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 optimization, 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.

Journals & Books; Help In this survey article we give a brief overview of various aspects of the recently emerging field of idempotent analysis and suggest potential connections with domain theory. Idempotent Analysis and its Applications, Kluwer, Dordrecht () Google Scholar.

important examples. In sections 4–7 we consider the notion of linearity in Idempotent Analysis and indicate some of its applications to idempotent linear algebra. Due to imprecision of sources of input data in real-world problems, the data usu-ally come in a form of conﬁdence intervals or other number sets rather than exact quantities.

Tropical and Idempotent Mathematics and Applications International Workshop on Tropical and Idempotent Mathematics, August, Independent University, Moscow, Russia.

0 Comment. TROPICAL AND IDEMPOTENT MATHEMATICS. 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.

Its Applications Third edition Time Series Analysis and. ISSN X described in the landmark work of Box and Jenkins (). This book is designed to be useful as a text for courses in time series on several di erent This fact accounts for the basic engineering Time Series Analysis and Its Applications.

the book is written in an informal style and has many elementary examples, the propositions and theorems are generally carefully proved, and the inter- ested student will certainly be able to experience the theorem-proof style of. This book contains the basics of linear algebra with an emphasis on non- The Vandermonde determinant and its application.

The Cauchy deter- Projections. Idempotent matrices &2. Theorem. An idempotent operator P is an Hermitian one if .Key-words: Idempotent semiring, Dioid, Max-plus algebra, Continuous lattice, Idempotent measure, Optimization, Large deviations.

(Resume: tsvp) e-mail: @ Unit de recherche. Using this framework we will see that the Bellman optimality principle is the idempotent version of the classical Markov causality principle.

Applications to optimal control problems, Hamilton--Jacobi equations, and mathematical morphology are discussed in the second part of this study.