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Introduction To The Algebraic Theory Of Invariants Of Differential Equations
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Author :Konstantin Sergeevich Sibirskiĭ Publisher :Manchester University Press ISBN 13 :9780719026690 Total Pages :210 pages Book Rating :4.0/5 (266 download)
Book Synopsis Introduction to the Algebraic Theory of Invariants of Differential Equations by : Konstantin Sergeevich Sibirskiĭ
Download or read book Introduction to the Algebraic Theory of Invariants of Differential Equations written by Konstantin Sergeevich Sibirskiĭ and published by Manchester University Press. This book was released on 1988 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Classical Invariant Theory by : Peter J. Olver
Download or read book Classical Invariant Theory written by Peter J. Olver and published by Cambridge University Press. This book was released on 1999-01-13 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a self-contained introduction to the results and methods in classical invariant theory.
Book Synopsis Lectures On The Theory Of Group Properties Of Differential Equations by : Lev Vasilyevich Ovsyannikov
Download or read book Lectures On The Theory Of Group Properties Of Differential Equations written by Lev Vasilyevich Ovsyannikov and published by World Scientific Publishing Company. This book was released on 2013-05-20 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecturers provide a clear introduction to Lie group methods for determining and using symmetries of differential equations, a variety of their applications in gas dynamics and other nonlinear models as well as the author's remarkable contribution to this classical subject. It contains material that is useful for students and teachers but cannot be found in modern texts. For example, the theory of partially invariant solutions developed by Ovsyannikov provides a powerful tool for solving systems of nonlinear differential equations and investigating complicated mathematical models.
Book Synopsis Invariant Theory by : Sebastian S. Koh
Download or read book Invariant Theory written by Sebastian S. Koh and published by Springer. This book was released on 2006-11-15 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of expository papers is the outgrowth of a conference in combinatorics and invariant theory. In recent years, newly developed techniques from algebraic geometry and combinatorics have been applied with great success to some of the outstanding problems of invariant theory, moving it back to the forefront of mathematical research once again. This collection of papers centers on constructive aspects of invariant theory and opens with an introduction to the subject by F. Grosshans. Its purpose is to make the current research more accesssible to mathematicians in related fields.
Book Synopsis Invariants of Quadratic Differential Forms by : Joseph Edmund Wright
Download or read book Invariants of Quadratic Differential Forms written by Joseph Edmund Wright and published by Courier Corporation. This book was released on 2013-10-21 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic monograph offers a brief account of the invariant theory connected with a single quadratic differential form. Includes historical overview; methods of Christoffel, Lie, Maschke; and geometrical, dynamical methods. 1960 edition.
Book Synopsis The Theory of Algebraic Number Fields by : David Hilbert
Download or read book The Theory of Algebraic Number Fields written by David Hilbert and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: A translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher.
Book Synopsis Algebraic Theory of Differential Equations by : Malcolm A. H. MacCallum
Download or read book Algebraic Theory of Differential Equations written by Malcolm A. H. MacCallum and published by . This book was released on 2009 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique introduction to the subject, reflecting different approaches to the integration of differential equations.
Book Synopsis Introduction to Groups, Invariants and Particles by : Frank W. K. Firk
Download or read book Introduction to Groups, Invariants and Particles written by Frank W. K. Firk and published by CreateSpace. This book was released on 2014-05-07 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group Theory, with its emphasis on Lie Groups and their application to the study of symmetries of the fundamental constituents of matter is introduced at a level suitable for Seniors and advanced Juniors majoring in the Physical Sciences. The book has its origin in a one-semester course that Professor Firk taught at Yale University for more than ten years. It is not generally appreciated by Physicists that continuous transformation groups (Lie Groups) originated in the Theory of Differential Equations. The infinitesimal generators of Lie Groups therefore have forms that involve differential operators and their commutators, and these operators and their algebraic properties have found, and continue to find, a natural place in the development of Quantum Physics. Topics covered include:Galois Groups Algebraic Invariants Invariants of Physics Groups − Concrete and Abstract Lie's Differential Equation Lie's Continuous Transformation Groups Matrix Representations of Groups Lie Groups of Transformations Group Structure of Lorentz Transformations Groups and the Structure of Matter Lie Groups and the Conservation Laws of the Physical Universe
Book Synopsis Arithmetic Differential Equations by : Alexandru Buium
Download or read book Arithmetic Differential Equations written by Alexandru Buium and published by American Mathematical Soc.. This book was released on 2005 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: For most of the book the only prerequisites are the basic facts of algebraic geometry and number theory."--BOOK JACKET.
Book Synopsis Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers by : Kenji Iohara
Download or read book Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers written by Kenji Iohara and published by Springer Nature. This book was released on 2020-02-20 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Gröbner bases) and geometry (via quiver theory). Gröbner bases serve as effective models for computation in algebras of various types. Although the theory of Gröbner bases was developed in the second half of the 20th century, many works on computational methods in algebra were published well before the introduction of the modern algebraic language. Since then, new algorithms have been developed and the theory itself has greatly expanded. In comparison, diagrammatic methods in representation theory are relatively new, with the quiver varieties only being introduced – with big impact – in the 1990s. Divided into two parts, the book first discusses the theory of Gröbner bases in their commutative and noncommutative contexts, with a focus on algorithmic aspects and applications of Gröbner bases to analysis on systems of partial differential equations, effective analysis on rings of differential operators, and homological algebra. It then introduces representations of quivers, quiver varieties and their applications to the moduli spaces of meromorphic connections on the complex projective line. While no particular reader background is assumed, the book is intended for graduate students in mathematics, engineering and related fields, as well as researchers and scholars.
Book Synopsis Differential Algebra And Related Topics - Proceedings Of The International Workshop by : Phyllis J Cassidy
Download or read book Differential Algebra And Related Topics - Proceedings Of The International Workshop written by Phyllis J Cassidy and published by World Scientific. This book was released on 2002-05-30 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential algebra explores properties of solutions to systems of (ordinary or partial, linear or nonlinear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with algebraic constraints. This algebraic theory of Joseph F Ritt and Ellis R Kolchin is further enriched by its interactions with algebraic geometry, Diophantine geometry, differential geometry, model theory, control theory, automatic theorem proving, combinatorics, and difference equations. Differential algebra now plays an important role in computational methods such as symbolic integration, and symmetry analysis of differential equations. This volume includes tutorial and survey papers presented at workshop.
Book Synopsis Group Analysis of Differential Equations by : L. V. Ovsiannikov
Download or read book Group Analysis of Differential Equations written by L. V. Ovsiannikov and published by Academic Press. This book was released on 2014-05-10 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations. This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the given differential equation with a known admitted group. The theory of differential invariants that is developed on an infinitesimal basis is elaborated in Chapter VII. The last chapter outlines the ways in which the methods of group analysis are used in special issues involving differential equations. This publication is a good source for students and specialists concerned with areas in which ordinary and partial differential equations play an important role.
Book Synopsis Galois Theory of Linear Differential Equations by : Marius van der Put
Download or read book Galois Theory of Linear Differential Equations written by Marius van der Put and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews
Book Synopsis The Theory of Equations by : William Snow Burnside
Download or read book The Theory of Equations written by William Snow Burnside and published by . This book was released on 1904 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Theory of Equations, Vol. 2 by : William Snow Burnside
Download or read book The Theory of Equations, Vol. 2 written by William Snow Burnside and published by Forgotten Books. This book was released on 2017-10-15 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Theory of Equations, Vol. 2: Introduction to the Theory of Binary Algebraic Forms Definitions, Formation of covariants and invariants, 168. Properties of covariants and invariants, Formation of covariants by the operator 170. Theorem relating to covariants and semicovariants, 171. Double linear transformation applied to the theory of covariants, 172. Properties of covariants derived from linear transformation, 173 - 176. Propositions relating to the formation of invariants and covariants of quantics transformed by a linear transformation, 177. Derivation of invariants and covariants by differential symbols, Examples. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Book Synopsis Algebraic Invariants by : Leonard Eugene Dickson
Download or read book Algebraic Invariants written by Leonard Eugene Dickson and published by CreateSpace. This book was released on 2014-02-11 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: AUTHOR'S PREFACE. This introduction to the classical theory of invariants of algebraic forms is divided into three parts of approximately equal length. Part I treats of linear transformations both from the standpoint of a change of the two points of reference or the triangle of reference used in the definition of the homogeneous coordinates of points in a line or plane, and also from the standpoint of projective geometry. Examples are given of invariants of forms f/ of low degrees in two or three variables, and the vanishing of an invariant of f is shown to give a geometrical property of the locus f = 0, which, on the one hand, is independent of the points of reference or triangle of reference, and, on the other hand, is unchanged by projection. Certain covariants such as Jacobians and Hessians are discussed and their algebraic and geometrical interpretations given; in particular, the use of the Hessian in the solution of a cubic equation and in the discussion of the points of inflexion of a plane cubic curve. In brief, beginning with ample illustrations from plane analytics, the reader is led by easy stages to the standpoint of linear transformations, their invariants and interpretations, employed in analytic projective geometry and modern algebra. Part II treats of the algebraic properties of invariants and covariants, chiefly of binary forms: homogeneity, weight, annihilators, semi-invariant leaders of covariants, law of reciprocity, fundamental systems, properties as functions of the roots, and production by means of differential operators. Any quartic equation is solved by reducing it to a canonical form by means of the Hessian (§ 33). Irrational invariants are illustrated by a carefully selected set of exercises (§ 35). Part III gives an introduction to the symbolic notation of Aronhold and Clebsch. The notation is first explained at length for a simple case; likewise the fundamental theorem on the types of symbolic factors of a term of a covariant of binary forms is first proved for a simple example by the method later used for the general theorem. In view of these and similar attentions to the needs of those making their first acquaintance with the symbolic notation, the difficulties usually encountered will, it is believed, be largely avoided. This notation must be mastered by those who would go deeply into the theory of invariants and its applications. Hilbert's theorem on the expression of the forms of a set linearly in terms of a finite number of forms of the set is proved and applied to establish the finiteness of a fundamental set of covariants of a system of binary forms. The theory of transvectants is developed as far as needed in the discussion of apolarity of binary forms and its application to rational curves (§§ 53-57), and in the determination by induction of a fundamental system of covariants of a binary form without the aid of the more technical supplementary concepts employed by Gordan. Finally, there is a discussion of the types of symbolic factors in any term of a concomitant of a system of forms in three or four variables, with remarks on fine and plane coordinates. For further developments reference is made at appropriate places to the texts in English by Salmon, Elliott, and Grace and Young, as well as to Gordan's Invariantentheorie. The standard work on the geometrical side of invariants is Clebsch-Lindemann, Vorlesungen über Geometrie. Reference may be made to books by W. F. Meyer, Apolaritdt und Rationale Curve, Bericht uber den gegenwarligen Stand der Invariantentheorie, and Formentheorie. Concerning invariant-factors, elementary divisors, and pairs of quadratic or bilinear forms, not treated here, see Muth, Elementartheiler, Bromwich, Quadratic Forms and their Classification by Means of Invariant Factors, and Bocher's Introduction to Higher Algebra....
Book Synopsis Qualitative Theory of Differential Equations by : Zhifen Zhang
Download or read book Qualitative Theory of Differential Equations written by Zhifen Zhang and published by American Mathematical Soc.. This book was released on 1992 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Subriemannian geometries, also known as Carnot-Caratheodory geometries, can be viewed as limits of Riemannian geometries. They also arise in physical phenomenon involving ``geometric phases'' or holonomy. Very roughly speaking, a subriemannian geometry consists of a manifold endowed with a distribution (meaning a $k$-plane field, or subbundle of the tangent bundle), called horizontal together with an inner product on that distribution. If $k=n$, the dimension of the manifold, we get the usual Riemannian geometry. Given a subriemannian geometry, we can define the distance between two points just as in the Riemannian case, except we are only allowed to travel along the horizontal lines between two points. The book is devoted to the study of subriemannian geometries, their geodesics, and their applications. It starts with the simplest nontrivial example of a subriemannian geometry: the two-dimensional isoperimetric problem reformulated as a problem of finding subriemannian geodesics. Among topics discussed in other chapters of the first part of the book the author mentions an elementary exposition of Gromov's surprising idea to use subriemannian geometry for proving a theorem in discrete group theory and Cartan's method of equivalence applied to the problem of understanding invariants (diffeomorphism types) of distributions. There is also a chapter devoted to open problems. The second part of the book is devoted to applications of subriemannian geometry. In particular, the author describes in detail the following four physical problems: Berry's phase in quantum mechanics, the problem of a falling cat righting herself, that of a microorganism swimming, and a phase problem arising in the $N$-body problem. He shows that all these problems can be studied using the same underlying type of subriemannian geometry: that of a principal bundle endowed with $G$-invariant metrics. Reading the book requires introductory knowledge of differential geometry, and it can serve as a good introduction to this new, exciting area of mathematics. This book provides an introduction to and a comprehensive study of the qualitative theory of ordinary differential equations. It begins with fundamental theorems on existence, uniqueness, and initial conditions, and discusses basic principles in dynamical systems and Poincare-Bendixson theory. The authors present a careful analysis of solutions near critical points of linear and nonlinear planar systems and discuss indices of planar critical points. A very thorough study of limit cycles is given, including many results on quadratic systems and recent developments in China. Other topics included are: the critical point at infinity, harmonic solutions for periodic differential equations, systems of ordinary differential equations on the torus, and structural stability for systems on two-dimensional manifolds. This books is accessible to graduate students and advanced undergraduates and is also of interest to researchers in this area. Exercises are included at the end of each chapter.
