ISBN: 9789048151417

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. Alexander V. Mikhalev, Alexander Levin, E.V. Pankratiev, Books, Science and Nature, Differential and Difference Dimension Polynomials Books>Science and Nature, Springer Netherlands

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ISBN: 9789048151417

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. Books List_Books

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ISBN: 9789048151417

Mathematics; Algebra; Partial Differential Equations; Combinatorics Combinatorics, algebra, difference equation, number theory, partial differential equation Books, Springer Nature

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ISBN: 9789048151417

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 de… Meer...

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ISBN: 9789048151417

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 b… Meer...

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## ISBN: 9789048151417

Mathematics; Algebra; Partial Differential Equations; Combinatorics Combinatorics, algebra, difference equation, number theory, partial differential equation Books, Springer Nature

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2010, ISBN: 9789048151417

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Softcover reprint of hardcover 1st ed. 1999, Softcover, Buch, [PU: Springer]

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** Gedetalleerde informatie over het boek. - Differential and Difference Dimension Polynomials**

EAN (ISBN-13): 9789048151417

ISBN (ISBN-10): 9048151414

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pocket book

Verschijningsjaar: 2010

Uitgever: Springer-Verlag GmbH

440 Bladzijden

Gewicht: 0,661 kg

Taal: eng/Englisch

Boek bevindt zich in het datenbestand sinds 2012-01-02T00:02:31+01:00 (Amsterdam)

Detailpagina laatst gewijzigd op 2020-12-27T16:47:54+01:00 (Amsterdam)

ISBN/EAN: 9789048151417

ISBN - alternatieve schrijfwijzen:

90-481-5141-4, 978-90-481-5141-7

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