Tropical And Idempotent Mathematics And Applications

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Tropical and Idempotent Mathematics

Grigoriĭ Lazarevich Litvinov,S. N. Sergeev
Tropical and Idempotent Mathematics Book PDF

Author : Grigoriĭ Lazarevich Litvinov,S. N. Sergeev
Publisher : American Mathematical Soc.
Page : 395 pages
File Size : 51,6 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.

Tropical and Idempotent Mathematics and Applications

Grigoriĭ Lazarevich Litvinov,S. N. Sergeev
Tropical and Idempotent Mathematics and Applications Book PDF

Author : Grigoriĭ Lazarevich Litvinov,S. N. Sergeev
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 51,7 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.

Idempotent Mathematics and Mathematical Physics

Grigoriĭ Lazarevich Litvinov,Viktor Pavlovich Maslov
Idempotent Mathematics and Mathematical Physics Book PDF

Author : Grigoriĭ Lazarevich Litvinov,Viktor Pavlovich Maslov
Publisher : American Mathematical Soc.
Page : 378 pages
File Size : 53,9 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.

Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

Yves Achdou,Guy Barles,Hitoshi Ishii,Grigory L. Litvinov
Hamilton Jacobi Equations Approximations Numerical Analysis and Applications Book PDF

Author : Yves Achdou,Guy Barles,Hitoshi Ishii,Grigory L. Litvinov
Publisher : Springer
Page : 301 pages
File Size : 55,9 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).

Relational and Algebraic Methods in Computer Science

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

Author : Peter Höfner,Peter Jipsen,Wolfram Kahl,Martin Eric Müller
Publisher : Springer
Page : 463 pages
File Size : 50,9 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.

Tropical Mathematics and Applications to Theoretical Physics and Scientific Computing

Abdel O Kenoufi,Michel Gondran,Alexandre Gondran,Thierry Lehner
Tropical Mathematics and Applications to Theoretical Physics and Scientific Computing Book PDF

Author : Abdel O Kenoufi,Michel Gondran,Alexandre Gondran,Thierry Lehner
Publisher : Unknown
Page : 0 pages
File Size : 45,7 Mb
Release : 2025-01-15
Category : Mathematics
ISBN : 3110769093

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Tropical Mathematics and Applications to Theoretical Physics and Scientific Computing by Abdel O Kenoufi,Michel Gondran,Alexandre Gondran,Thierry Lehner Pdf

Tropical Mathematics built on Idempotent Semi-Rings and Dioids permits an extension of the usual Linear methods to Non-Linear problems and provides powerful analyzing and computing in Theoretical Physics and Applied Mathematics. Until recently, solutions in mathematics and physics were organized around algebraic structures such as groups, rings, and fields. These techniques are not well-suited to modeling and solving non-linear problems.

Rings, Modules and Codes

André Leroy,Christian Lomp,Sergio López-Permouth,Frédérique Oggier
Rings Modules and Codes Book PDF

Author : André Leroy,Christian Lomp,Sergio López-Permouth,Frédérique Oggier
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 54,8 Mb
Release : 2019-04-12
Category : Modules (Algebra)
ISBN : 9781470441043

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Rings, Modules and Codes by André Leroy,Christian Lomp,Sergio López-Permouth,Frédérique Oggier Pdf

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.

Decision Making and Optimization

Martin Gavalec,Jaroslav Ramík,Karel Zimmermann
Decision Making and Optimization Book PDF

Author : Martin Gavalec,Jaroslav Ramík,Karel Zimmermann
Publisher : Springer
Page : 231 pages
File Size : 54,9 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.

Spectral Theory and Geometric Analysis

Mikhail Aleksandrovich Shubin,Maxim Braverman
Spectral Theory and Geometric Analysis Book PDF

Author : Mikhail Aleksandrovich Shubin,Maxim Braverman
Publisher : American Mathematical Soc.
Page : 223 pages
File Size : 45,8 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.

Biological Fluid Dynamics: Modeling, Computations, and Applications

Anita T. Layton, Sarah D. Olson
Biological Fluid Dynamics Modeling Computations and Applications Book PDF

Author : Anita T. Layton, Sarah D. Olson
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 45,9 Mb
Release : 2014-10-14
Category : Mathematics
ISBN : 9780821898505

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Biological Fluid Dynamics: Modeling, Computations, and Applications by Anita T. Layton, Sarah D. Olson Pdf

This volume contains the Proceedings of the AMS Special Session on Biological Fluid Dynamics: Modeling, Computation, and Applications, held on October 13, 2012, at Tulane University, New Orleans, Louisiana. In recent years, there has been increasing interest in the development and application of advanced computational techniques for simulating fluid motion driven by immersed flexible structures. That interest is motivated, in large part, by the multitude of applications in physiology and biology. In some biological systems, fluid motion is driven by active biological tissues, which are typically constructed of fibers that are surrounded by fluid. Not only do the fibers hold the tissues together, they also transmit forces that ultimately result in fluid motion. In other examples, the fluid may flow through conduits such as blood vessels or airways that are flexible or active. That is, those conduits may react to and affect the fluid dynamics. This volume responds to the widespread interest among mathematicians, biologists, and engineers in fluid-structure interactions problems. Included are expository and review articles in biological fluid dynamics. Applications that are considered include ciliary motion, upside-down jellyfish, biological feedback in the kidney, peristalsis and dynamic suction pumping, and platelet cohesion and adhesion.

Computer Algebra in Scientific Computing

François Boulier,Matthew England,Timur M. Sadykov,Evgenii V. Vorozhtsov
Computer Algebra in Scientific Computing Book PDF

Author : François Boulier,Matthew England,Timur M. Sadykov,Evgenii V. Vorozhtsov
Publisher : Springer Nature
Page : 644 pages
File Size : 47,5 Mb
Release : 2020-10-17
Category : Computers
ISBN : 9783030600266

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Computer Algebra in Scientific Computing by François Boulier,Matthew England,Timur M. Sadykov,Evgenii V. Vorozhtsov Pdf

This book constitutes the refereed proceedings of the 22nd International Workshop on Computer Algebra in Scientific Computing, CASC 2020, held in Linz, Austria, in September 2020. The conference was held virtually due to the COVID-19 pandemic. The 34 full papers presented together with 2 invited talks were carefully reviewed and selected from 41 submissions. They deal with cutting-edge research in all major disciplines of computer algebra. The papers cover topics such as polynomial algebra, symbolic and symbolic-numerical computation, applications of symbolic computation for investigating and solving ordinary differential equations, applications of CAS in the investigation and solution of celestial mechanics problems, and in mechanics, physics, and robotics.

Computer Algebra in Scientific Computing

Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov
Computer Algebra in Scientific Computing Book PDF

Author : Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov
Publisher : Springer
Page : 494 pages
File Size : 43,6 Mb
Release : 2015-09-10
Category : Computers
ISBN : 9783319240213

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Computer Algebra in Scientific Computing by Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov Pdf

This book constitutes the proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing, CASC 2015, held in Aachen, Germany, in September 2015. The 35 full papers presented in this volume were carefully reviewed and selected from 42 submissions. They deal with the ongoing progress both in theoretical computer algebra and its expanding applications. New and closer interactions are fostered by combining the area of computer algebra methods and systems and the application of the tools of computer algebra for the solution of problems in scientific computing.

Computational Methods in Systems Biology

Ezio Bartocci,Pietro Lio,Nicola Paoletti
Computational Methods in Systems Biology Book PDF

Author : Ezio Bartocci,Pietro Lio,Nicola Paoletti
Publisher : Springer
Page : 356 pages
File Size : 48,8 Mb
Release : 2016-09-03
Category : Computers
ISBN : 9783319451770

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Computational Methods in Systems Biology by Ezio Bartocci,Pietro Lio,Nicola Paoletti Pdf

This book constitutes the refereed proceedings of the 14th International Conference on Computational Methods in Systems Biology, CMSB 2016, held in Cambridge, UK, in September 2016. The 20 full papers, 3 tool papers and 9 posters presented were carefully reviewed and selected from 37 regular paper submissions. The topics include formalisms for modeling biological processes; models and their biological applications; frameworks for model verification, validation, analysis, and simulation of biological systems; high-performance computational systems biology and parallel implementations; model inference from experimental data; model integration from biological databases; multi-scale modeling and analysis methods; and computational approaches for synthetic biology.

Analysis, Complex Geometry, and Mathematical Physics

Paul M. N. Feehan,Jian Song, Ben Weinkove,Richard A. Wentworth
Analysis Complex Geometry and Mathematical Physics Book PDF

Author : Paul M. N. Feehan,Jian Song, Ben Weinkove,Richard A. Wentworth
Publisher : American Mathematical Soc.
Page : 359 pages
File Size : 40,6 Mb
Release : 2015-07-21
Category : Geometry, Differential
ISBN : 9781470414641

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Analysis, Complex Geometry, and Mathematical Physics by Paul M. N. Feehan,Jian Song, Ben Weinkove,Richard A. Wentworth Pdf

This volume contains the proceedings of the Conference on Analysis, Complex Geometry and Mathematical Physics: In Honor of Duong H. Phong, which was held from May 7-11, 2013, at Columbia University, New York. The conference featured thirty speakers who spoke on a range of topics reflecting the breadth and depth of the research interests of Duong H. Phong on the occasion of his sixtieth birthday. A common thread, familiar from Phong's own work, was the focus on the interplay between the deep tools of analysis and the rich structures of geometry and physics. Papers included in this volume cover topics such as the complex Monge-Ampère equation, pluripotential theory, geometric partial differential equations, theories of integral operators, integrable systems and perturbative superstring theory.

Discrete Geometry and Algebraic Combinatorics

Alexander Barg,Oleg R. Musin
Discrete Geometry and Algebraic Combinatorics Book PDF

Author : Alexander Barg,Oleg R. Musin
Publisher : American Mathematical Society
Page : 202 pages
File Size : 46,8 Mb
Release : 2014-08-28
Category : Mathematics
ISBN : 9781470409050

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Discrete Geometry and Algebraic Combinatorics by Alexander Barg,Oleg R. Musin Pdf

This volume contains the proceedings of the AMS Special Session on Discrete Geometry and Algebraic Combinatorics held on January 11, 2013, in San Diego, California. The collection of articles in this volume is devoted to packings of metric spaces and related questions, and contains new results as well as surveys of some areas of discrete geometry. This volume consists of papers on combinatorics of transportation polytopes, including results on the diameter of graphs of such polytopes; the generalized Steiner problem and related topics of the minimal fillings theory; a survey of distance graphs and graphs of diameters, and a group of papers on applications of algebraic combinatorics to packings of metric spaces including sphere packings and topics in coding theory. In particular, this volume presents a new approach to duality in sphere packing based on the Poisson summation formula, applications of semidefinite programming to spherical codes and equiangular lines, new results in list decoding of a family of algebraic codes, and constructions of bent and semi-bent functions.