Tropical And Idempotent Mathematics

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Tropical and Idempotent Mathematics

Author : Grigoriĭ Lazarevich Litvinov
Publisher : American Mathematical Soc.
ISBN 13 : 0821847821
Total Pages : 395 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tropical and Idempotent Mathematics by : Grigoriĭ Lazarevich Litvinov

Download or read book Tropical and Idempotent Mathematics written by Grigoriĭ Lazarevich Litvinov and published by American Mathematical Soc.. This book was released on 2009 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Tropical and Idempotent Mathematics and Applications

Author : Grigoriĭ Lazarevich Litvinov
Publisher : American Mathematical Soc.
ISBN 13 : 082189496X
Total Pages : 314 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tropical and Idempotent Mathematics and Applications by : Grigoriĭ Lazarevich Litvinov

Download or read book Tropical and Idempotent Mathematics and Applications written by Grigoriĭ Lazarevich Litvinov and published by American Mathematical Soc.. This book was released on 2014 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Idempotent Mathematics and Mathematical Physics

Author : Grigoriĭ Lazarevich Litvinov
Publisher : American Mathematical Soc.
ISBN 13 : 0821835386
Total Pages : 378 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Idempotent Mathematics and Mathematical Physics by : Grigoriĭ Lazarevich Litvinov

Download or read book Idempotent Mathematics and Mathematical Physics written by Grigoriĭ Lazarevich Litvinov and published by American Mathematical Soc.. This book was released on 2005 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Analysis

Author : V. P. Maslov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821841143
Total Pages : 228 pages
Book Rating : 4.8/5 (411 download)

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Book Synopsis Idempotent Analysis by : V. P. Maslov

Download or read book Idempotent Analysis written by V. P. Maslov and published by American Mathematical Soc.. This book was released on 1992 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Tropical Geometry

Author : Diane Maclagan
Publisher : American Mathematical Society
ISBN 13 : 1470468565
Total Pages : 363 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Introduction to Tropical Geometry by : Diane Maclagan

Download or read book Introduction to Tropical Geometry written by Diane Maclagan and published by American Mathematical Society. This book was released on 2021-12-13 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of the six chapters concludes with problems that will help the readers to practice their tropical skills, and to gain access to the research literature. This wonderful book will appeal to students and researchers of all stripes: it begins at an undergraduate level and ends with deep connections to toric varieties, compactifications, and degenerations. In between, the authors provide the first complete proofs in book form of many fundamental results in the subject. The pages are sprinkled with illuminating examples, applications, and exercises, and the writing is lucid and meticulous throughout. It is that rare kind of book which will be used equally as an introductory text by students and as a reference for experts. —Matt Baker, Georgia Institute of Technology Tropical geometry is an exciting new field, which requires tools from various parts of mathematics and has connections with many areas. A short definition is given by Maclagan and Sturmfels: “Tropical geometry is a marriage between algebraic and polyhedral geometry”. This wonderful book is a pleasant and rewarding journey through different landscapes, inviting the readers from a day at a beach to the hills of modern algebraic geometry. The authors present building blocks, examples and exercises as well as recent results in tropical geometry, with ingredients from algebra, combinatorics, symbolic computation, polyhedral geometry and algebraic geometry. The volume will appeal both to beginning graduate students willing to enter the field and to researchers, including experts. —Alicia Dickenstein, University of Buenos Aires, Argentina

Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

Author : Yves Achdou
Publisher : Springer
ISBN 13 : 3642364330
Total Pages : 316 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications by : Yves Achdou

Download or read book Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications written by Yves Achdou and published by Springer. This book was released on 2013-05-24 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Spectral Theory and Geometric Analysis

Author : Mikhail Aleksandrovich Shubin
Publisher : American Mathematical Soc.
ISBN 13 : 0821849484
Total Pages : 223 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Spectral Theory and Geometric Analysis by : Mikhail Aleksandrovich Shubin

Download or read book Spectral Theory and Geometric Analysis written by Mikhail Aleksandrovich Shubin and published by American Mathematical Soc.. This book was released on 2011-02-10 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Linear Algebra

Author : Leslie Hogben
Publisher : CRC Press
ISBN 13 : 1498785603
Total Pages : 1906 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Handbook of Linear Algebra by : Leslie Hogben

Download or read book Handbook of Linear Algebra written by Leslie Hogben and published by CRC Press. This book was released on 2013-11-26 with total page 1906 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and

Tropical Algebraic Geometry

Author : Ilia Itenberg
Publisher : Springer Science & Business Media
ISBN 13 : 3034600488
Total Pages : 113 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Tropical Algebraic Geometry by : Ilia Itenberg

Download or read book Tropical Algebraic Geometry written by Ilia Itenberg and published by Springer Science & Business Media. This book was released on 2009-05-30 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes present a polished introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject. It consists of three chapters which complete each other and give a possibility for non-specialists to make the first steps in the subject which is not yet well represented in the literature. The notes are based on a seminar at the Mathematical Research Center in Oberwolfach in October 2004. The intended audience is graduate, post-graduate, and Ph.D. students as well as established researchers in mathematics.

Max-linear Systems: Theory and Algorithms

Author : Peter Butkovič
Publisher : Springer Science & Business Media
ISBN 13 : 1849962995
Total Pages : 281 pages
Book Rating : 4.8/5 (499 download)

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Book Synopsis Max-linear Systems: Theory and Algorithms by : Peter Butkovič

Download or read book Max-linear Systems: Theory and Algorithms written by Peter Butkovič and published by Springer Science & Business Media. This book was released on 2010-08-05 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent years have seen a significant rise of interest in max-linear theory and techniques. Specialised international conferences and seminars or special sessions devoted to max-algebra have been organised. This book aims to provide a first detailed and self-contained account of linear-algebraic aspects of max-algebra for general (that is both irreducible and reducible) matrices. Among the main features of the book is the presentation of the fundamental max-algebraic theory (Chapters 1-4), often scattered in research articles, reports and theses, in one place in a comprehensive and unified form. This presentation is made with all proofs and in full generality (that is for both irreducible and reducible matrices). Another feature is the presence of advanced material (Chapters 5-10), most of which has not appeared in a book before and in many cases has not been published at all. Intended for a wide-ranging readership, this book will be useful for anyone with basic mathematical knowledge (including undergraduate students) who wish to learn fundamental max-algebraic ideas and techniques. It will also be useful for researchers working in tropical geometry or idempotent analysis.

Idempotency

Author : Jeremy Gunawardena
Publisher : Cambridge University Press
ISBN 13 : 052155344X
Total Pages : 457 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis Idempotency by : Jeremy Gunawardena

Download or read book Idempotency written by Jeremy Gunawardena and published by Cambridge University Press. This book was released on 1998-01-13 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Certain nonlinear optimization problems arising in such disparate areas as the theory of computation, pure and applied probability and mathematical physics, can be solved by linear methods, provided one replaces the usual number system with one in which addition satisfies the idempotent law. This systematic study of the subject has emerged, triggered in part by a workshop organized by Hewlett-Packard's Basic Research Institute in the Mathematical Sciences (BRIMS), which brought together many leading researchers in the area. This volume is a record of that workshop, but it also includes other invited contributions, a broad Introduction to Idempotency, written specially for the book, and a bibliography of the subject. In sum, the articles cover both practical and more theoretical considerations, making it essential reading for all workers in the area.

Relational and Algebraic Methods in Computer Science

Author : Peter Höfner
Publisher : Springer
ISBN 13 : 3319062514
Total Pages : 463 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Relational and Algebraic Methods in Computer Science by : Peter Höfner

Download or read book Relational and Algebraic Methods in Computer Science written by Peter Höfner and published by Springer. This book was released on 2014-04-08 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory

Author : Gebhard Böckle
Publisher : Springer
ISBN 13 : 3319705660
Total Pages : 753 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory by : Gebhard Böckle

Download or read book Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory written by Gebhard Böckle and published by Springer. This book was released on 2018-03-22 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.

Rings, Modules and Codes

Author : André Leroy
Publisher : American Mathematical Soc.
ISBN 13 : 1470441047
Total Pages : 355 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Rings, Modules and Codes by : André Leroy

Download or read book Rings, Modules and Codes written by André Leroy and published by American Mathematical Soc.. This book was released on 2019-04-12 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the Fifth International Conference on Noncommutative Rings and their Applications, held from June 12–15, 2017, at the University of Artois, Lens, France. The papers are related to noncommutative rings, covering topics such as: ring theory, with both the elementwise and more structural approaches developed; module theory with popular topics such as automorphism invariance, almost injectivity, ADS, and extending modules; and coding theory, both the theoretical aspects such as the extension theorem and the more applied ones such as Construction A or Reed–Muller codes. Classical topics like enveloping skewfields, weak Hopf algebras, and tropical algebras are also presented.

Nonarchimedean and Tropical Geometry

Author : Matthew Baker
Publisher : Springer
ISBN 13 : 3319309455
Total Pages : 526 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Nonarchimedean and Tropical Geometry by : Matthew Baker

Download or read book Nonarchimedean and Tropical Geometry written by Matthew Baker and published by Springer. This book was released on 2016-08-18 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume grew out of two Simons Symposia on "Nonarchimedean and tropical geometry" which took place on the island of St. John in April 2013 and in Puerto Rico in February 2015. Each meeting gathered a small group of experts working near the interface between tropical geometry and nonarchimedean analytic spaces for a series of inspiring and provocative lectures on cutting edge research, interspersed with lively discussions and collaborative work in small groups. The articles collected here, which include high-level surveys as well as original research, mirror the main themes of the two Symposia. Topics covered in this volume include: Differential forms and currents, and solutions of Monge-Ampere type differential equations on Berkovich spaces and their skeletons; The homotopy types of nonarchimedean analytifications; The existence of "faithful tropicalizations" which encode the topology and geometry of analytifications; Relations between nonarchimedean analytic spaces and algebraic geometry, including logarithmic schemes, birational geometry, and the geometry of algebraic curves; Extended notions of tropical varieties which relate to Huber's theory of adic spaces analogously to the way that usual tropical varieties relate to Berkovich spaces; and Relations between nonarchimedean geometry and combinatorics, including deep and fascinating connections between matroid theory, tropical geometry, and Hodge theory.

Introduction to Tropical Geometry

Author : Diane Maclagan
Publisher : American Mathematical Soc.
ISBN 13 : 0821851985
Total Pages : 363 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Introduction to Tropical Geometry by : Diane Maclagan

Download or read book Introduction to Tropical Geometry written by Diane Maclagan and published by American Mathematical Soc.. This book was released on 2015-04-15 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of the six chapters concludes with problems that will help the readers to practice their tropical skills, and to gain access to the research literature.

Relational and Algebraic Methods in Computer Science

Author : Wolfram Kahl
Publisher : Springer
ISBN 13 : 3319247042
Total Pages : 395 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Relational and Algebraic Methods in Computer Science by : Wolfram Kahl

Download or read book Relational and Algebraic Methods in Computer Science written by Wolfram Kahl and published by Springer. This book was released on 2015-09-24 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 15th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2015, held in Braga, Portugal, in September/October 2015. The 20 revised full papers and 3 invited papers presented were carefully selected from 25 submissions. The papers deal with the theory of relation algebras and Kleene algebras, process algebras; fixed point calculi; idempotent semirings; quantales, allegories, and dynamic algebras; cylindric algebras, and about their application in areas such as verification, analysis and development of programs and algorithms, algebraic approaches to logics of programs, modal and dynamic logics, interval and temporal logics.