Idempotent Analysis And Its Applications

Author : Vassili N. Kolokoltsov,Victor P. Maslov
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 45,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401589017

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Idempotent Analysis and Its Applications by Vassili N. Kolokoltsov,Victor P. Maslov Pdf

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 .

Author : Vasily Kolokoltsov,Victor P. Maslov
Publisher : Springer
Page : 305 pages
File Size : 44,8 Mb
Release : 2014-10-09
Category : Mathematics
ISBN : 940158902X

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Idempotent Analysis and Its Applications by Vasily Kolokoltsov,Victor P. Maslov Pdf

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 .

Author : Grigoriĭ Lazarevich Litvinov,S. N. Sergeev
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 41,9 Mb
Release : 2014
Category : Mathematics
ISBN : 9780821894965

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Tropical and Idempotent Mathematics and Applications by Grigoriĭ Lazarevich Litvinov,S. N. Sergeev Pdf

This volume contains the proceedings of the International Workshop on Tropical and Idempotent Mathematics, held at the Independent University of Moscow, Russia, from August 26-31, 2012. The main purpose of the conference was to bring together and unite researchers and specialists in various areas of tropical and idempotent mathematics and applications. This volume contains articles on algebraic foundations of tropical mathematics as well as articles on applications of tropical mathematics in various fields as diverse as economics, electroenergetic networks, chemical reactions, representation theory, and foundations of classical thermodynamics. This volume is intended for graduate students and researchers interested in tropical and idempotent mathematics or in their applications in other areas of mathematics and in technical sciences.

Author : Grigoriĭ Lazarevich Litvinov,S. N. Sergeev
Publisher : American Mathematical Soc.
Page : 395 pages
File Size : 43,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821847824

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Tropical and Idempotent Mathematics by Grigoriĭ Lazarevich Litvinov,S. N. Sergeev Pdf

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.

Author : Grigoriĭ Lazarevich Litvinov,Viktor Pavlovich Maslov
Publisher : American Mathematical Soc.
Page : 378 pages
File Size : 50,7 Mb
Release : 2005
Category : Mathematical physics
ISBN : 9780821835388

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Idempotent Mathematics and Mathematical Physics by Grigoriĭ Lazarevich Litvinov,Viktor Pavlovich Maslov Pdf

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.

Author : Yves Achdou,Guy Barles,Hitoshi Ishii,Grigory L. Litvinov
Publisher : Springer
Page : 316 pages
File Size : 48,9 Mb
Release : 2013-05-24
Category : Mathematics
ISBN : 9783642364334

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Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications by Yves Achdou,Guy Barles,Hitoshi Ishii,Grigory L. Litvinov Pdf

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).

Author : V. P. Maslov
Publisher : American Mathematical Soc.
Page : 228 pages
File Size : 45,7 Mb
Release : 1992
Category : Function spaces
ISBN : 0821841149

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Idempotent Analysis by V. P. Maslov Pdf

Author : Endre Pap
Publisher : Springer Science & Business Media
Page : 342 pages
File Size : 49,9 Mb
Release : 2012-10-20
Category : Technology & Engineering
ISBN : 9783642339592

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Intelligent Systems: Models and Applications by Endre Pap Pdf

The theory and applications of intelligent systems is today an important field of research. This book is an up-to-date collection of seventeen chapters, written by recognized experts in the field. In an introductory mathematical foundations part an overview of generalizations of the integral inequalities for nonadditive integrals and a construction of the General Prioritized Fuzzy Satisfaction Problem is given. Then different aspects of robotics are presented, such as the differences between human beings and robots, the motion of bipedal humanoid robots, and an evaluation of different autonomous quadrotor flight controllers. Also Fuzzy Systems are presented by a model of basic planar imprecise geometric objects allowing various applications in image analysis , GIS, and robotics, as well as a type-2 fuzzy logic in a software library for developing perceptual computers, and a two--degree--of--freedom speed control solutions for a brushless Direct Current motor. The book also presents recent applications in medicine such as a Virtual Doctor System, methods for a face to face human machine interaction, and an emotion estimation, with applications for multiple diseases and the effect of the applied therapy. The last part of the book covers different applications in transportation, network monitoring, and localization of pedestrians in images.

Author : Vasily N Kolokoltsov,Oleg A Malafeyev
Publisher : World Scientific
Page : 411 pages
File Size : 55,6 Mb
Release : 2020-08-21
Category : Mathematics
ISBN : 9789811214875

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Understanding Game Theory: Introduction To The Analysis Of Many Agent Systems With Competition And Cooperation (Second Edition) by Vasily N Kolokoltsov,Oleg A Malafeyev Pdf

Steadily growing applications of game theory in modern science (including psychology, biology and economics) require sources to provide rapid access in both classical tools and recent developments to readers with diverse backgrounds. This book on game theory, its applications and mathematical methods, is written with this objective in mind.The book gives a concise but wide-ranging introduction to games including older (pre-game theory) party games and more recent topics like elections and evolutionary games and is generously spiced with excursions into philosophy, history, literature and politics. A distinguished feature is the clear separation of the text into two parts: elementary and advanced, which makes the book ideal for study at various levels.Part I displays basic ideas using no more than four arithmetic operations and requiring from the reader only some inclination to logical thinking. It can be used in a university degree course without any (or minimal) prerequisite in mathematics (say, in economics, business, systems biology), as well as for self-study by school teachers, social and natural scientists, businessmen or laymen. Part II is a rapid introduction to the mathematical methods of game theory, suitable for a mathematics degree course of various levels.To stimulate the mathematical and scientific imagination, graphics by a world-renowned mathematician and mathematics imaging artist, A T Fomenko, are used. The carefully selected works of this artist fit remarkably into the many ideas expressed in the book.This new edition has been updated and enlarged. In particular, two new chapters were added on statistical limit of games with many agents and on quantum games, reflecting possibly the two most stunning trends in the game theory of the 21st century.

Author : V. P. Maslov,S. N. Samborskiĭ
Publisher : American Mathematical Society(RI)
Page : 232 pages
File Size : 49,6 Mb
Release : 1992
Category : Mathematics
ISBN : CORNELL:31924063695369

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Idempotent Analysis by V. P. Maslov,S. N. Samborskiĭ Pdf

Idempotent analysis is a new branch of mathematical analysis concerned with functional spaces and their mappings when the algebraic structure is generated by an idempotent operation. The articles in this collection show how idempotent analysis is playing a unifying role in many branches of mathematics related to external phenomena and structures---a role similar to that played by functional analysis in mathematical physics, or numerical methods in partial differential equations. Such a unification necessitates study of the algebraic and analytic structures appearing in spaces of functions with values in idempotent semirings. The papers collected here constitute an advance in this direction.

Author : K. Glazek
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 55,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401599641

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A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences by K. Glazek Pdf

This volume presents a short guide to the extensive literature concerning semir ings along with a complete bibliography. The literature has been created over many years, in variety of languages, by authors representing different schools of mathematics and working in various related fields. In many instances the terminology used is not universal, which further compounds the difficulty of locating pertinent sources even in this age of the Internet and electronic dis semination of research results. So far there has been no single reference that could guide the interested scholar or student to the relevant publications. This book is an attempt to fill this gap. My interest in the theory of semirings began in the early sixties, when to gether with Bogdan W ~glorz I tried to investigate some algebraic aspects of compactifications of topological spaces, semirings of semicontinuous functions, and the general ideal theory for special semirings. (Unfortunately, local alge braists in Poland told me at that time that there was nothing interesting in investigating semiring theory because ring theory was still being developed). However, some time later we became aware of some similar investigations hav ing already been done. The theory of semirings has remained "my first love" ever since, and I have been interested in the results in this field that have been appearing in literature (even though I have not been active in this area myself).

Author : Mikhail Aleksandrovich Shubin,Maxim Braverman
Publisher : American Mathematical Soc.
Page : 223 pages
File Size : 44,6 Mb
Release : 2011-02-10
Category : Mathematics
ISBN : 9780821849484

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Spectral Theory and Geometric Analysis by Mikhail Aleksandrovich Shubin,Maxim Braverman Pdf

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.

Author : Peter Höfner,Peter Jipsen,Wolfram Kahl,Martin Eric Müller
Publisher : Springer
Page : 463 pages
File Size : 54,5 Mb
Release : 2014-04-08
Category : Mathematics
ISBN : 9783319062518

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Relational and Algebraic Methods in Computer Science by Peter Höfner,Peter Jipsen,Wolfram Kahl,Martin Eric Müller Pdf

This book constitutes the proceedings of the 14th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2014 held in Marienstatt, Germany, in April/May 2014. The 25 revised full papers presented were carefully selected from 37 submissions. The papers are structured in specific fields on concurrent Kleene algebras and related formalisms, reasoning about computations and programs, heterogeneous and categorical approaches, applications of relational and algebraic methods and developments related to modal logics and lattices.

Author : Martin Gavalec,Jaroslav Ramík,Karel Zimmermann
Publisher : Springer
Page : 231 pages
File Size : 41,5 Mb
Release : 2014-10-08
Category : Business & Economics
ISBN : 9783319083230

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Decision Making and Optimization by Martin Gavalec,Jaroslav Ramík,Karel Zimmermann Pdf

The book is a benefit for graduate and postgraduate students in the areas of operations research, decision theory, optimization theory, linear algebra, interval analysis and fuzzy sets. The book will also be useful for the researchers in the respective areas. The first part of the book deals with decision making problems and procedures that have been established to combine opinions about alternatives related to different points of view. Procedures based on pairwise comparisons are thoroughly investigated. In the second part we investigate optimization problems where objective functions and constraints are characterized by extremal operators such as maximum, minimum or various triangular norms (t-norms). Matrices in max-min algebra are useful in applications such as automata theory, design of switching circuits, logic of binary relations, medical diagnosis, Markov chains, social choice, models of organizations, information systems, political systems and clustering. The input data in real problems are usually not exact and can be characterized by interval values.

Author : Vincenc Torra,Yasuo Narukawa,Guillermo Navarro-Arribas,David Megías
Publisher : Springer
Page : 325 pages
File Size : 42,6 Mb
Release : 2014-07-08
Category : Computers
ISBN : 9783642415500

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Modeling Decisions for Artificial Intelligence by Vincenc Torra,Yasuo Narukawa,Guillermo Navarro-Arribas,David Megías Pdf

This book constitutes the proceedings of the 10th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2013, held in Barcelona, Spain, in November 2013. The 24 papers presented in this volume were carefully reviewed and selected from 40 submissions. They deal with the theory and tools for modeling decisions, as well as applications that encompass decision making processes and information fusion techniques.