Series: London Mathematical Society Lecture Note Series (No. 366)
Paperback (ISBN-13: 9780521134439)
The first book to approach high oscillation as a subject of its own, Highly Oscillatory Problems begins a new dialogue and lays the groundwork for future research. It ensues from the six-month programme held at the Newton Institute of Mathematical Sciences, which was the first time that different specialists in highly oscillatory research, from diverse areas of mathematics and applications, had been brought together for a single intellectual agenda. This ground-breaking volume consists of eight review papers by leading experts in subject areas of active research, with an emphasis on computation: numerical Hamiltonian problems, highly oscillatory quadrature, rapid approximation of functions, high frequency wave propagation, numerical homogenization, discretization of the wave equation, high frequency scattering and the solution of elliptic boundary value problems.
* The first book devoted to high oscillation, covering the full breadth of the subject area * Authored by leading experts in their respective fields * Surveys the current state of the field and paves the way for future research
Preface; 1. Oscillations over long times in numerical Hamiltonian systems E. Hairer and C. Lubich; 2. Highly oscillatory quadrature D. Huybrechs and S. Olver; 3. Rapid function approximation by modified Fourier series D. Huybrechs and S. Olver; 4. Approximation of high frequency wave propagation M. Motamed and O. Runborg; 5. Wavelet-based numerical homogenization B. Engquist and O. Runborg; 6. Plane wave methods for approximating the time harmonic wave equation T. Luostari, T. Huttunen and P. Monk; 7. Boundary integral methods in high frequency scattering S. N. Chandler-Wilde and I. G. Graham; 8. Novel analytical and numerical methods for elliptic boundary value problems A. S. Fokas and E. A. Spence.
Series: Cambridge Tracts in Theoretical Computer Science (No. 50)
Hardback (ISBN-13: 9780521820493)
Process algebra is a widely accepted and much used technique in the specification and verification of parallel and distributed software systems. This book sets the standard for the field. It assembles the relevant results of most process algebras currently in use, and presents them in a unified framework and notation. The authors describe the theory underlying the development, realization and maintenance of software that occurs in parallel or distributed systems. A system can be specified in the syntax provided, and the axioms can be used to verify that a composed system has the required external behaviour. As examples, two protocols are completely specified and verified in the text: the Alternating-Bit Protocol for Data Communication, and Fischer’s Protocol of Mutual Exclusion. The book serves as a reference text for researchers and graduate students in computer science, offering a complete overview of the field and referring to further literature where appropriate.
* Presents a unified overview of process algebra, which makes it suitable as a reference book, course text or self-study aid * Contains over 300 exercises ranging in difficulty to suit all readers * Accompanying website (www.win.tue.nl/processalgebra) offers exercise solutions, software tools and more
Preface; 1. Process algebra; 2. Preliminaries; 3. Transition systems; 4. Basic process theory; 5. Recursion; 6. Sequential processes; 7. Parallel and communicating processes; 8. Abstraction; 9. Timing; 10. Data and states; 11. Features; 12. Semantics; Bibliography; Index of symbols and notations; Index of authors; Index of subjects.
Series: New Mathematical Monographs (No. 13)
Hardback (ISBN-13: 9780521760362)
This is the first authored book to be dedicated to the new field of directed algebraic topology that arose in the 1990s, in homotopy theory and in the theory of concurrent processes. Its general aim can be stated as 'modelling non-reversible phenomena' and its domain should be distinguished from that of classical algebraic topology by the principle that directed spaces have privileged directions and directed paths therein need not be reversible. Its homotopical tools (corresponding in the classical case to ordinary homotopies), fundamental group and fundamental groupoid should be similarly 'non-reversible': directed homotopies, fundamental monoid and fundamental category. Homotopy constructions occur here in a directed version, which gives rise to new 'shapes', like directed cones and directed spheres. Applications will deal with domains where privileged directions appear, including rewrite systems, traffic networks and biological systems. The most developed examples can be found in the area of concurrency.
* The first book to emerge from this new and exciting research field * The author establishes a new mathematical foundation for the subject * Intended for graduate students and researchers in mathematics and computer sciences
Introduction; Part I. First Order Directed Homotopy and Homology: 1. Directed structures and first order homotopy properties; 2. Directed homology and noncommutative geometry; 3. Modelling the fundamental category; Part II. Higher Directed Homotopy Theory: 4. Settings for higher order homotopy; 5. Categories of functors and algebras, relative settings; 6. Elements of weighted algebraic topology; Appendix A. Some points of category theory; References; Index of symbols; General index.
Series: London Mathematical Society Student Texts (No. 75)
Paperback (ISBN-13: 9780521134088)
Hardback (ISBN-13: 9780521118392)
This introductory text explores the theory of graph spectra: a topic with applications across a wide range of subjects, including computer science, quantum chemistry and electrical engineering. The spectra examined here are those of the adjacency matrix, the Seidel matrix, the Laplacian, the normalized Laplacian and the signless Laplacian of a finite simple graph. The underlying theme of the book is the relation between the eigenvalues and structure of a graph. Designed as an introductory text for graduate students, or anyone using the theory of graph spectra, this self-contained treatment assumes only a little knowledge of graph theory and linear algebra. The authors include many new developments in the field which arise as a result of rapidly expanding interest in the area. Exercises, spectral data and proofs of required results are also provided. The end-of-chapter notes serve as a practical guide to the extensive bibliography of over 500 items.
* Fills a gap left by out-of-print books at a time of rapidly expanding interest in the subject * Only a little familiarity with graph theory and linear algebra is assumed * Contains over 100 exercises, spectral data for small graphs and an extensive bibliography
Preface; 1. Introduction; 2. Graph operations and modifications; 3. Spectrum and structure; 4. Characterizations by spectra; 5. Structure and one eigenvalue; 6. Spectral techniques; 7. Laplacians; 8. Additional topics; 9. Applications; Appendix; Bibliography; Index of symbols; Index.
Series: New Mathematical Monographs (No. 12)
Hardback (ISBN-13: 9780521760379)
The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which are needed in the presentation of results, proven by Cohen, Moore, and the author, on the exponents of homotopy groups. The author introduces various aspects of unstable homotopy theory, including: homotopy groups with coefficients; localization and completion; the Hopf invariants of Hilton, James, and Toda; Samelson products; homotopy Bockstein spectral sequences; graded Lie algebras; differential homological algebra; and the exponent theorems concerning the homotopy groups of spheres and Moore spaces. This book is suitable for a course in unstable homotopy theory, following a first course in homotopy theory. It is also a valuable reference for both experts and graduate students wishing to enter the field.
* Methods are introduced one-by-one in chapters that are largely self-contained * Suitable as a course text and also a valuable reference for experts and graduate students wishing to enter the field * Contains over 270 exercises
Preface; Introduction; 1. Homotopy groups with coefficients; 2. A general theory of localization; 3. Fibre extensions of squares and the Peterson-Stein formula; 4. Hilton-Hopf invariants and the EHP sequence; 5. James-Hopf invariants and Toda-Hopf invariants; 6. Samelson products; 7. Bockstein spectral sequences; 8. Lie algebras and universal enveloping algebras; 9. Applications of graded Lie algebras; 10. Differential homological algebra; 11. Odd primary exponent theorems; 12. Differential homological algebra of classifying spaces; Bibliography; Index.