Series: Acta Numerica
7 Paperback books (ISBN-13: 9780521176002)
Page extent: 3662 pages
Size: 244 x 170 mm
Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide useful techniques and analysis.
1. Linear algebra algorithms as dynamical systems Moody T. Chu; 2. Accurate and efficient expression evaluation and linear algebra James Demmel, Iona Dumitriu, Olga Holtz and Plamen Koeu; 3. Asymptotic and numerical homogenization B. Engquist and P. E. Souganidis; 4. Interior-point methods for optimization Arkadi S. Nemirovski and Michael J. Todd; 5. Greedy approximation V. N. Temlyakov.
Moody T. Chu, James Demmel, Iona Dumitriu, Olga Holtz, Plamen Koeu, B. Engquist, P. E. Souganidis, Arkadi S. Nemirovski, Michael J. Todd, V. N. Temlyakov
Series: Cambridge Tracts in Mathematics (No. 186)
Hardback (ISBN-13: 9780521898058)
10 b/w illus. 60 exercises
Page extent: 225 pages
Size: 228 x 152 mm
This accessible research monograph investigates how 'finite-dimensional' sets can be embedded into finite-dimensional Euclidean spaces. The first part brings together a number of abstract embedding results, and provides a unified treatment of four definitions of dimension that arise in disparate fields: Lebesgue covering dimension (from classical 'dimension theory'), Hausdorff dimension (from geometric measure theory), upper box-counting dimension (from dynamical systems), and Assouad dimension (from the theory of metric spaces). These abstract embedding results are applied in the second part of the book to the finite-dimensional global attractors that arise in certain infinite-dimensional dynamical systems, deducing practical consequences from the existence of such attractors: a version of the Takens time-delay embedding theorem valid in spatially extended systems, and a result on parametrisation by point values. This book will appeal to all researchers with an interest in dimension theory, particularly those working in dynamical systems.
* Introduces alternative definitions to researchers who traditionally use only one * An authoritative summary which assembles results scattered through the literature * Provides up-to-date results and abstract background for researchers in dynamical systems
Preface; Introduction; Part I. Finite-Dimensional Sets: 1. Lebesgue covering dimension; 2. Hausdorff measure and Hausdorff dimension; 3. Box-counting dimension; 4. An embedding theorem for subsets of RN; 5. Prevalence, probe spaces, and a crucial inequality; 6. Embedding sets with dH(X-X) finite; 7. Thickness exponents; 8. Embedding sets of finite box-counting dimension; 9. Assouad dimension; Part II. Finite-Dimensional Attractors: 10. Partial differential equations and nonlinear semigroups; 11. Attracting sets in infinite-dimensional systems; 12. Bounding the box-counting dimension of attractors; 13. Thickness exponents of attractors; 14. The Takens time-delay embedding theorem; 15. Parametrisation of attractors via point values; Solutions to exercises; References; Index.
Series: Cambridge Studies in Advanced Mathematics (No. 129)
Hardback (ISBN-13: 9780521474238)
250 exercises
Page extent: 550 pages
Size: 228 x 152 mm
This graduate-level textbook provides an elementary exposition of the theory of automorphic representations and L-functions for the general linear group in an adelic setting. The authors keep definitions to a minimum and repeat them when reintroduced so that the book is accessible from any entry point, and with no prior knowledge of representation theory. They also include concrete examples of both global and local representations of GL(n), and present their associated L-functions. The theory is developed from first principles for GL(1), then carefully extended to GL(2) with complete detailed proofs of key theorems. Several of the proofs are here presented for the first time, including Jacquet's simple and elegant proof of the tensor product theorem. Finally, the higher rank situation of GL(n) is given a detailed treatment. Containing numerous exercises, this book will motivate students and researchers to begin working in this fertile field of research.
* Presents clear, detailed proofs suitable for graduate students * Immediately engages students using simple, concrete examples * Contains over 250 exercises with solutions
Preface; 1. Adeles over Q; 2. Automorphic representations and L-functions for GL(1,AQ); 3. The classical theory of automorphic forms for GL(2); 4. Automorphic forms for GL(2,AQ); 5. Automorphic representations for GL(2,AQ); 6. Theory of admissible representations of GL(2,Qp); 7. Theory of admissible (g,K∞) modules for GL(2,R); 8. The contragredient representation for GL(2); 9. Unitary representations of GL(2); 10. Tensor products of local representations; 11. The Godement*Jacquet L-function for GL(2,AQ); 12. The classical theory of automorphic forms for GL(n,R); 13. Automorphic forms and representations for GL(n,A); 14. Theory of local representations for GL(n); 15. The Godement*Jacquet L-function for GL(n,AQ); References; Index.
Series: Encyclopedia of Mathematics and its Applications (No. 138)
Hardback (ISBN-13: 9780521898331)
25 b/w illus.
Page extent: 700 pages
Size: 234 x 156 mm
The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The author not only provides a thorough description of the theory, but also details its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.
* Synthesizes the author's substantial body of research over the last 20 years * Contains useful tools for readers interested in graph theory * Book's coverage and style makes it the definitive reference for graduate students and researchers
Foreword Maurice Nivat; Introduction; 1. Overview; 2. Graph algebras and widths of graphs; 3. Equational and recognizable sets in many-sorted algebras; 4. Equational and recognizable sets of graphs; 5. Monadic second-order logic; 6. Algorithmic applications; 7. Monadic second-order transductions; 8. Transductions of terms and words J. Engelfriet; 9. Relational structures; 10. Conclusion and open problems; References; Index.
Series: London Mathematical Society Lecture Note Series (No. 381)
Paperback (ISBN-13: 9780521136587)
23 b/w illus.
Page extent: 350 pages
Size: 228 x 152 mm
Difference equations are playing an increasingly important role in the natural sciences. Indeed many phenomena are inherently discrete and are naturally described by difference equations. Phenomena described by differential equations are therefore approximations of more basic discrete ones. Moreover, in their study it is very often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference equations. This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference ones. Each of the eleven chapters is a self-contained treatment of a topic, containing introductory material as well as the latest research results. The book will be welcomed by graduate students and researchers seeking an introduction to the field. As a survey of the current state of the art it will also serve as a valuable reference.
* Shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted for difference equations * Each chapter covers a single topic, and includes introductory material as well as the latest research results * An ideal introduction to the subject for students and researchers
Preface; Introduction; 1. Lagrangian and Hamiltonian formalism for discrete equations: symmetries and first integrals V. Dorodnitsyn and R. Kozlov; 2. Painleve equations: continuous, discrete and ultradiscrete B. Grammaticos and A. Ramani; 3. Definitions and predictions of integrability for difference equations J. Hietarinta; 4. Orthogonal polynomials, their recursions, and functional equations M. Ismail; 5. Discrete Painleve equations and orthogonal polynomials A. Its; 6. Generalized Lie symmetries for difference equations D. Levi and R. I. Yamilov; 7. Complete integrability of discrete nonlinear systems S. Novikov; 8. Lectures on moving frames P. Olver; 9. Lattices of compact semisimple Lie groups J. Patera; 10. Lectures on discrete differential geometry Y. B. Suris; 11. Lie point symmetries of difference equations and symmetry preserving discretization of differential equations Pavel Winternitz.