Editorial Description:
A cohesive and comprehensive account of the modern theory of iterative functional equations. Many of the results included have appeared before only in research literature, making this an essential volume for all those working in functional equations and in such areas as dynamical systems and chaos, to which the theory is closely related. The authors introduce the reader to the theory and then explore the most recent developments and general results. Fundamental notions such as the existence and uniqueness of solutions to the equations are stressed throughout, as are applications of the theory to such areas as branching processes, differential equations, ergodic theory, functional analysis and geometry. Other topics covered include systems of linear and nonlinear equations of finite and infinite order in various function classes, conjugate and commutable functions, linearization, iterative roots of functions, and special functional equations
Publisher: Cambridge University Press Number Of Pages: 417 Publication Date: 1997-01-28 Sales Rank: 2381718 ISBN / ASIN: 0521452066 EAN: 9780521452069 Binding: Hardcover Manufacturer: Cambridge University Press Studio: Cambridge University Press
Book Description:
Sperner's theorem stimulated the development of a fast-growing theory dealing with external problems on finite sets and, more generally, on finite partially ordered sets. This book presents Sperner theory from a unified point of view, bringing combinatorial techniques together with methods from programming, linear algebra, Lie-algebra representations and eigenvalue methods, probability theory, and enumerative combinatorics.
Minkowski Geometry (Encyclopedia of Mathematics and its Applications)
By A. C. Thompson
Publisher: Cambridge University Press Number Of Pages: 364 Publication Date: 1996-06-28 Sales Rank: 2229376 ISBN / ASIN: 052140472X EAN: 9780521404723 Binding: Hardcover Manufacturer: Cambridge University Press Studio: Cambridge University Press Average Rating: 0 Total Reviews: 0
Book Description:
This is a comprehensive treatment of Minkowski geometry. The author begins by describing the fundamental metric properties and the topological properties of existence of Minkowski space. This is followed by a treatment of two-dimensional spaces and characterizations of Euclidean space among normed spaces. The central three chapters present the theory of area and volume in normed spaces--a fascinating geometrical interplay among the various roles of the ball in Euclidean space. Later chapters deal with trigonometry and differential geometry in Minkowski spaces. The book ends with a brief look at J. J. Schaffer's ideas on the intrinsic geometry of the unit sphere
Navier-Stokes Equations and Turbulence (Encyclopedia of Mathematics and its Applications) By Ciprian Foias, Oscar Manley, Ricardo Rosa, Roger Temam
Publisher: Cambridge University Press Number Of Pages: 362 Publication Date: 2001-08 ISBN-10 / ASIN: 0521360323 ISBN-13 / EAN: 9780521360326 Binding: Hardcover
Book Description:
This book presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. It is the result of many years of research by the authors to analyze turbulence using Sobolev spaces and functional analysis. In this way the authors have recovered parts of the conventional theory of turbulence, deriving rigorously from the Navier-Stokes equations that had been arrived at earlier by phenomenological arguments. Appendices give full details of the mathematical proofs and subtleties.
Download Description:
This book aims to bridge the gap between practising mathematicians and the practitioners of turbulence theory. It presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The book is the result of many years of research by the authors to analyze turbulence using Sobolev spaces and functional analysis. In this way the authors have recovered parts of the conventional theory of turbulence, deriving rigorously from the Navier-Stokes equations what had been arrived at earlier by phenomenological arguments. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience. Each chapter is accompanied by appendices giving full details of the mathematical proofs and subtleties. This unique presentation should ensure a volume of interest to mathematicians, engineers, and physicists
The Banach-Tarski Paradox (Encyclopedia of Mathematics and its Applications) By Stan Wagon
Publisher: Cambridge University Press Number Of Pages: 271 Publication Date: 1993-09-24 ISBN-10 / ASIN: 0521457041 ISBN-13 / EAN: 9780521457040 Binding: Paperback
Product Description:
This volume explores the consequences of the paradox for measure theory and its connections with group theory, geometry, and logic. It unifies the results of contemporary research on the paradox and presents several new results including some unusual paradoxes in hyperbolic space. It also provides up to date proofs and discusses many unsolved problems
Publisher: Addison-Wesley Number Of Pages: 330 Publication Date: 1981-12 ISBN-10 / ASIN: 0201135140 ISBN-13 / EAN: 9780201135145 Binding: Paperback
Book Description:
This volume deals with the foundations as well as the fascinating logic of quantum mechanics. The thorough presentation will guide the reader to a unified view of a theory that together with relativity is regarded as the greatest achievement in physics during this century
Asymptotics and Mellin-Barnes Integrals (Encyclopedia of Mathematics and its Applications) By R. B. Paris, D. Kaminski
Publisher: Cambridge University Press Number Of Pages: 438 Publication Date: 2001-09-24 ISBN-10 / ASIN: 0521790018 ISBN-13 / EAN: 9780521790017 Binding: Hardcover
Product Description:
Asymptotics and Mellin-Barnes Integrals provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behavior of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of Mellin-Barnes integrals that is otherwise not available in standard references on asymptotics
Publisher: Cambridge University Press Number Of Pages: 628 Publication Date: 2003-04-21 Sales Rank: 1588942 ISBN / ASIN: 0521803381 EAN: 9780521803380 Binding: Hardcover Manufacturer: Cambridge University Press Studio: Cambridge University Press Average Rating: 0 Total Reviews: 0
Book Description:
Information content and programming semantics are just two of the applications of the mathematical concepts of order, continuity and domains. This authoritative and comprehensive account of the subject will be an essential handbook for all those working in the area. An extensive index and bibliography make this an ideal sourcebook for all those working in domain theory
Publisher: Cambridge University Press Number Of Pages: 518 Publication Date: 2007-01-15 Sales Rank: 3250426 ISBN / ASIN: 0521824761 EAN: 9780521824767 Binding: Hardcover Manufacturer: Cambridge University Press Studio: Cambridge University Press
Book Description:
Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential equations are considered as a part of contact and symplectic geometry, so that all the machinery of Hodge-deRham calculus can be applied. In this way a wide class of equations can be tackled, including quasi-linear equations and Monge-Ampere equations (which play an important role in modern theoretical physics and meteorology).
Publisher: Cambridge University Press Number Of Pages: 264 Publication Date: 1992-04-24 Sales Rank: 3115208 ISBN / ASIN: 0521415349 EAN: 9780521415347 Binding: Hardcover Manufacturer: Cambridge University Press Studio: Cambridge University Press
Book Description:
In this treatise, the authors present the general theory of orthogonal polynomials on the complex plane and several of its applications. The assumptions on the measure of orthogonality are general, the only restriction is that it has compact support on the complex plane. In the development of the theory the main emphasis is on asymptotic behavior and the distribution of zeros. In the first two chapters exact upper and lower bounds are given for the orthonormal polynomials and for the location of their zeros. The next three chapters deal with regular n-th root asymptotic behavior, which plays a key role both in the theory and in its applications. Orthogonal polynomials with this behavior correspond to classical orthogonal polynomials in the general case, and many extremal properties of measures in mathematical analysis and approximation theory with this type of regularity turn out to be equivalent. Several easy-to-use criteria are presented for regular behavior. The last chapter contains applications of the theory, including exact rates for convergence of rational interpolants, best rational approximants and non-diagonal Pade approximants to Markov functions (Cauchy transforms of measures). The results are based on potential theoretic methods, so both the methods and the results can be extended to extremal polynomials in norms other than L2 norms. A sketch of the theory of logarithmic potentials is given in an in appendix
Publisher: Cambridge University Press Number Of Pages: 382 Publication Date: 2003-09-15 Sales Rank: 2109165 ISBN / ASIN: 0521827213 EAN: 9780521827218 Binding: Hardcover Manufacturer: Cambridge University Press Studio: Cambridge University Press
Book Description:
Joussef Jabri presents min-max methods through a comprehensive study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. Jabri clarifies the extensions and variants of the MPT in a complete and unified way and covers standard topics: the classical and dual MPT; second-order information from PS sequences; symmetry and topological index theory; perturbations from symmetry; convexity and more. He also covers the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants. A bibliography and detailed index are also included
byAnders Björner Michel Las Vergnas Bernd Sturmfels Neil White G|nter M. Ziegler
Publisher: Cambridge University Press Number Of Pages: 560 Publication Date: 2000-01-28 Sales Rank: 1015926 ISBN / ASIN: 052177750X EAN: 9780521777506 Binding: Paperback Manufacturer: Cambridge University Press Studio: Cambridge University Press
Book Description:
This second edition of the first comprehensive, accessible account of the subject is intended for a diverse audience : graduate students who wish to learn the subject, researchers in the various fields of application who want to concentrate on certain theoretical aspects, and specialists who need a thorough reference work. For the second edition, the authors have greatly expanded the bibliography to ensure that it is comprehensive and up-to-date, and have also added an appendix surveying research since the first edition. A list of exercises and open problems ends each chapter.
