Differential And Difference Dimension Polynomials
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Differential And Difference Dimension Polynomials
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Author : M.V. Kondratieva
language : en
Publisher: Springer Science & Business Media
Release Date : 1999
Differential And Difference Dimension Polynomials written by M.V. Kondratieva 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 1999 with Mathematics categories.
This book is the first monograph wholly devoted to the investigation of differential and difference dimension theory. The differential dimension polynomial describes in exact terms the degree of freedom of a dynamic system as well as the number of arbitrary constants in the general solution of a system of algebraic differential equations. Difference algebra arises from the study of algebraic difference equations and therefore bears a considerable resemblance to its differential counterpart. Difference algebra was developed in the same period as differential algebra and it has the same founder, J. Ritt. It grew to a mathematical area with its own ideas and methods mainly due to the work of R. Cohn, who raised difference algebra to the same level as differential algebra. The relatively new science of computer algebra has given strong impulses to the theory of dimension polynomials, now that packages such as MAPLE enable the solution of many problems which cannot be solved otherwise. Applications of differential and difference dimension theory can be found in many fields of mathematics, as well as in theoretical physics, system theory and other areas of science. Audience: This book will be of interest to researchers and graduate students whose work involves differential and difference equations, algebra and number theory, partial differential equations, combinatorics and mathematical physics.
Differential And Difference Dimension Polynomials
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Author : Alexander V. Mikhalev
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Differential And Difference Dimension Polynomials written by Alexander V. Mikhalev 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 2013-03-09 with Mathematics categories.
The role of Hilbert polynomials in commutative and homological algebra as well as in algebraic geometry and combinatorics is well known. A similar role in differential algebra is played by the differential dimension polynomials. The notion of differential dimension polynomial was introduced by E. Kolchin in 1964 [KoI64]' but the problems and ideas that had led to this notion (and that are reflected in this book) have essentially more long history. Actually, one can say that the differential dimension polynomial describes in exact terms the freedom degree of a dynamic system as well as the number of arbitrary constants in the general solution of a system of algebraic differential equations. The first attempts of such description were made at the end of 19th century by Jacobi [Ja890] who estimated the number of algebraically independent constants in the general solution of a system of linear ordinary differential equations. Later on, Jacobi's results were extended to some cases of nonlinear systems, but in general case the problem of such estimation (that is known as the problem of Jacobi's bound) remains open. There are some generalization of the problem of Jacobi's bound to the partial differential equations, but the results in this area are just appearing. At the beginning of the 20th century algebraic methods in the theory of differen tial equations were actively developed by F. Riquier [RiqlO] and M.
Differential And Difference Dimension Polynomials
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Author : Alexander V. Mikhalev
language : en
Publisher:
Release Date : 2014-01-15
Differential And Difference Dimension Polynomials written by Alexander V. Mikhalev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Algebraic And Algorithmic Aspects Of Differential And Integral Operators
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Author : Moulay Barkatou
language : en
Publisher: Springer
Release Date : 2014-02-25
Algebraic And Algorithmic Aspects Of Differential And Integral Operators written by Moulay Barkatou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-25 with Computers categories.
This book constitutes the proceedings of the 5th International Meeting on Algebraic and Algorithmic Aspects of Differential and Integral Operators, AADIOS 2012, held at the Applications of Computer Algebra Conference in Sofia, Bulgaria, on June 25-28, 2012. The total of 9 papers presented in this volume consists of 2 invited papers and 7 regular papers which were carefully reviewed and selected from 13 submissions. The topics of interest are: symbolic computation for operator algebras, factorization of differential/integral operators, linear boundary problems and green's operators, initial value problems for differential equations, symbolic integration and differential galois theory, symbolic operator calculi, algorithmic D-module theory, rota-baxter algebra, differential algebra, as well as discrete analogs and software aspects of the above.
Mathematical Aspects Of Computer And Information Sciences
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Author : Daniel Slamanig
language : en
Publisher: Springer Nature
Release Date : 2020-03-18
Mathematical Aspects Of Computer And Information Sciences written by Daniel Slamanig and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-18 with Computers categories.
This book constitutes the refereed proceedings of the 8th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2019, held in Gebze, Turkey, in November 2019. The 22 revised papers and 14 short papers presented were carefully reviewed and selected from 66 submissions. The papers are organized in the following topical sections: algorithms and foundation; security and cryptography; combinatorics, codes, designs and graphs; data modeling and machine learning; tools and software track.
Mathematical Aspects Of Computer And Information Sciences
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Author : Ilias S. Kotsireas
language : en
Publisher: Springer
Release Date : 2016-04-16
Mathematical Aspects Of Computer And Information Sciences written by Ilias S. Kotsireas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-16 with Computers categories.
This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015, held in Berlin, Germany, in November 2015. The 48 revised papers presented together with 7 invited papers were carefully reviewed and selected from numerous submissions. The papers are grouped in topical sections on curves and surfaces, applied algebraic geometry, cryptography, verified numerical computation, polynomial system solving, managing massive data, computational theory of differential and difference equations, data and knowledge exploration, algorithm engineering in geometric computing, real complexity: theory and practice, global optimization, and general session.
Handbook Of Algebra
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Author : M. Hazewinkel
language : en
Publisher: Elsevier
Release Date : 2006-05-30
Handbook Of Algebra written by M. Hazewinkel and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-30 with Mathematics categories.
Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed.- Thorough and practical source for information- Provides in-depth coverage of new topics in algebra- Includes references to relevant articles, books and lecture notes
Symmetries Of Partial Differential Equations
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Author : A.M. Vinogradov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Symmetries Of Partial Differential Equations written by A.M. Vinogradov 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.
2 The authors of these issues involve not only mathematicians, but also speci alists in (mathematical) physics and computer sciences. So here the reader will find different points of view and approaches to the considered field. A. M. VINOGRADOV 3 Acta Applicandae Mathematicae 15: 3-21, 1989. © 1989 Kluwer Academic Publishers. Symmetries and Conservation Laws of Partial Differential Equations: Basic Notions and Results A. M. VINOORADOV Department of Mathematics, Moscow State University, 117234, Moscow, U. S. S. R. (Received: 22 August 1988) Abstract. The main notions and results which are necessary for finding higher symmetries and conservation laws for general systems of partial differential equations are given. These constitute the starting point for the subsequent papers of this volume. Some problems are also discussed. AMS subject classifications (1980). 35A30, 58005, 58035, 58H05. Key words. Higher symmetries, conservation laws, partial differential equations, infinitely prolonged equations, generating functions. o. Introduction In this paper we present the basic notions and results from the general theory of local symmetries and conservation laws of partial differential equations. More exactly, we will focus our attention on the main conceptual points as well as on the problem of how to find all higher symmetries and conservation laws for a given system of partial differential equations. Also, some general views and perspectives will be discussed.
Mathematical Aspects Of Computer And Information Sciences
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Author : Johannes Blömer
language : en
Publisher: Springer
Release Date : 2017-12-20
Mathematical Aspects Of Computer And Information Sciences written by Johannes Blömer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-20 with Computers categories.
This book constitutes the refereed proceedings of the 7th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2017, held in Vienna, Austria, in November 2017. The 28 revised papers and 8 short papers presented were carefully reviewed and selected from 67 submissions. The papers are organized in the following topical sections: foundation of algorithms in mathematics, engineering and scientific computation; combinatorics and codes in computer science; data modeling and analysis; and mathematical aspects of information security and cryptography.
Library Of Congress Subject Headings
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Author : Library of Congress
language : en
Publisher:
Release Date : 2004
Library Of Congress Subject Headings written by Library of Congress and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Subject headings, Library of Congress categories.