Introduction To The Algebraic Theory Of Invariants Of Differential Equations
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Introduction To The Algebraic Theory Of Invariants Of Differential Equations
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Author : Konstantin Sergeevich Sibirskiĭ
language : en
Publisher: Manchester University Press
Release Date : 1988
Introduction To The Algebraic Theory Of Invariants Of Differential Equations written by Konstantin Sergeevich Sibirskiĭ and has been published by Manchester University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Considers polynominal invariants & comitants of autonomous systems of differential equations with right-hand sides relative to various transformation groups of phase space. Contains an in-depth discussion of the two-dimensional system with quadratic right-hand sides. Features numerous applications to the qualitative theory of differential equations.
Algebraic Theory Of Differential Equations
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Author :
language : en
Publisher: Cambridge University Press
Release Date :
Algebraic Theory Of Differential Equations written by 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 with categories.
Introductory Course In Differential Equations For Students In Classical And Engineering Colleges
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Author : Daniel Alexander Murray
language : en
Publisher:
Release Date : 1897
Introductory Course In Differential Equations For Students In Classical And Engineering Colleges written by Daniel Alexander Murray and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1897 with Differential Equations categories.
Classical Invariant Theory
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Author : Peter J. Olver
language : en
Publisher: Cambridge University Press
Release Date : 1999-01-13
Classical Invariant Theory written by Peter J. Olver 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 1999-01-13 with Mathematics categories.
The book is a self-contained introduction to the results and methods in classical invariant theory.
Introductory Course In Differential Equations
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Author : Daniel Alexander Murray
language : en
Publisher:
Release Date : 1897
Introductory Course In Differential Equations written by Daniel Alexander Murray and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1897 with Mathematics categories.
Algebraic Geometry Iv
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Author : A.N. Parshin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic Geometry Iv written by A.N. Parshin 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 Mathematics categories.
The problems being solved by invariant theory are far-reaching generalizations and extensions of problems on the "reduction to canonical form" of various is almost the same thing, projective geometry. objects of linear algebra or, what Invariant theory has a ISO-year history, which has seen alternating periods of growth and stagnation, and changes in the formulation of problems, methods of solution, and fields of application. In the last two decades invariant theory has experienced a period of growth, stimulated by a previous development of the theory of algebraic groups and commutative algebra. It is now viewed as a branch of the theory of algebraic transformation groups (and under a broader interpretation can be identified with this theory). We will freely use the theory of algebraic groups, an exposition of which can be found, for example, in the first article of the present volume. We will also assume the reader is familiar with the basic concepts and simplest theorems of commutative algebra and algebraic geometry; when deeper results are needed, we will cite them in the text or provide suitable references.
Computer Algebra In Scientific Computing
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Author : Vladimir P. Gerdt
language : en
Publisher: Springer
Release Date : 2013-08-15
Computer Algebra In Scientific Computing written by Vladimir P. Gerdt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-15 with Computers categories.
This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2013, held in Berlin, Germany, in September 2013. The 33 full papers presented were carefully reviewed and selected for inclusion in this book. The papers address issues such as polynomial algebra; the solution of tropical linear systems and tropical polynomial systems; the theory of matrices; the use of computer algebra for the investigation of various mathematical and applied topics related to ordinary differential equations (ODEs); applications of symbolic computations for solving partial differential equations (PDEs) in mathematical physics; problems arising at the application of computer algebra methods for finding infinitesimal symmetries; applications of symbolic and symbolic-numeric algorithms in mechanics and physics; automatic differentiation; the application of the CAS Mathematica for the simulation of quantum error correction in quantum computing; the application of the CAS GAP for the enumeration of Schur rings over the group A5; constructive computation of zero separation bounds for arithmetic expressions; the parallel implementation of fast Fourier transforms with the aid of the Spiral library generation system; the use of object-oriented languages such as Java or Scala for implementation of categories as type classes; a survey of industrial applications of approximate computer algebra.
The Monodromy Group
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Author : Henryk Zoladek
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-10
The Monodromy Group written by Henryk Zoladek 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 2006-08-10 with Mathematics categories.
In singularity theory and algebraic geometry the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations. It has applications in the weakened 16th Hilbert problem and in mixed Hodge structures. In the theory of systems of linear differential equations one has the Riemann-Hilbert problem, the Stokes phenomena and the hypergeometric functions with their multidimensional generalizations. In the theory of homomorphic foliations there appear the Ecalle-Voronin-Martinet-Ramis moduli. On the other hand, there is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions. All this is presented in this book, underlining the unifying role of the monodromy group. The material is addressed to a wide audience, ranging from specialists in the theory of ordinary differential equations to algebraic geometers. The book contains a lot of results which are usually spread in many sources. Readers can quickly get introduced to modern and vital mathematical theories, such as singularity theory, analytic theory of ordinary differential equations, holomorphic foliations, Galois theory, and parts of algebraic geometry, without searching in vast literature.
The Center And Cyclicity Problems
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Author : Valery Romanovski
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-29
The Center And Cyclicity Problems written by Valery Romanovski 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 2009-04-29 with Mathematics categories.
In the last three decades, advances in methods for investigating polynomial ideals and their varieties have provided new possibilities for approaching two long-standing problems in the theory of differential equations: the Poincaré center problem and the cyclicity problem (the problem of bifurcation of limit cycles from singular trajectories). Using a computational algebra approach, this work addresses the center and cyclicity problems as behaviors of dynamical systems and families of polynomial systems. The text first lays the groundwork for computational algebra and gives the main properties of ideals in polynomial rings and their affine varieties; this is followed by a discussion regarding the theory of normal forms and stability of differential equations. The center and cyclicity problems are then explored in detail. The book contains numerous examples, pseudocode displays of all the computational algorithms, historical notes, nearly two hundred exercises, and an extensive bibliography. Completely self-contained, it is thus suitable mainly as a textbook for a graduate course in the subject but also as a reference for researchers.
The Center And Focus Problem
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Author : M.N. Popa
language : en
Publisher: CRC Press
Release Date : 2021-09-23
The Center And Focus Problem written by M.N. Popa and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-23 with Mathematics categories.
The Center and Focus Problem: Algebraic Solutions and Hypotheses, M. N. Popa and V.V. Pricop, ISBN: 978-1-032-01725-9 (Hardback) This book focuses on an old problem of the qualitative theory of differential equations, called the Center and Focus Problem. It is intended for mathematicians, researchers, professors and Ph.D. students working in the field of differential equations, as well as other specialists who are interested in the theory of Lie algebras, commutative graded algebras, the theory of generating functions and Hilbert series. The book reflects the results obtained by the authors in the last decades. A rather essential result is obtained in solving Poincaré's problem. Namely, there are given the upper estimations of the number of Poincaré-Lyapunov quantities, which are algebraically independent and participate in solving the Center and Focus Problem that have not been known so far. These estimations are equal to Krull dimensions of Sibirsky graded algebras of comitants and invariants of systems of differential equations.