Publication is planned for January 2003 | Hardback | 240 pages | ISBN: 0-521-82538-5
available from January 2003 |
The main focus of this book is the exploration of the geometric and dynamic properties of a far reaching generalization of a conformal iterated function system - a Graph Directed Markov System. These systems are very robust in that they apply to many settings that do not fit into the scheme of conformal iterated systems. The basic theory is laid out here and the authors have touched on many natural questions arising in its context. However, they also emphasise the many issues and current research topics which can be found in original papers. For example the detailed analysis of the structure of harmonic measures of limit sets, the examination the doubling property of conformal measures, the extensive study of generalized polynomial like mapping or multifractal analysis of geometrically finite Kleinian groups. This book leads readers onto frontier research in the field, making it ideal for both established researchers and graduate students.
Contents Introduction; 1. Symbolic dynamics; 3. Holder families of functions; 4. Conformal graph directed Markov systems; 5. Examples of graph directed Markov systems; 6. Conformal iterated function systems; 7. Dynamical rigidity of conformal iterated function systems; 8. Parabolic iterated function systems; 9. Parabolic systems: Hausdorff and packing measures.
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Publication is planned for January 2003 | Hardback (Paperback) | 300 pages 300 line diagrams | ISBN: 0-521-82451-6
available from January 2003
Celebrating a century of geometry and geometry teaching, this book will give the reader an enjoyable insight into all things geometrical. There are a wealth of popular articles including sections on Pythagoras, the golden ratio and recreational geometry. Historical items, drawn principally from the Mathematical Gazette, are authored by mathematicians such as G. H. Hardy, Rouse Ball, Thomas Heath and Bertrand Russell as well as some more recent expositors. Thirty eDesert Island Theoremsf from distinguished mathematicians and educationalists give light to some surprising and beautiful results. Contributors include H. S. M. Coxeter, Michael Atiyah, Tom Apostol, Solomon Golomb, Keith Devlin, Nobel Laureate Leon Lederman, Carlo Sequin, Simon Singh, Christopher Zeeman and Pulitzer Prizewinner Douglas Hofstadter. The book also features the wonderful Eyeball Theorems of Peruvian geometer and web designer, Antonio Gutierrez. For anyone with an interest in mathematics and mathematics education this book will be an enjoyable and rewarding read.
Contents Introduction; 1. The nature of geometry; 2. Desert island theorems - Greek geometry; 3. The history of geometry; 4. Desert island theorems - elementary Euclidean geometry; 5. Pythagorasf theorem; 6. Desert island theorems - advanced Euclidean geometry; 7. The golden ratio; 8. Desert island theorems - non-Euclidean geometry and topology; 9. Recreational geometry; 10. Desert island theorems - geometrical physics; 11. The teaching of geometry; Appendices.
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Publication is planned for January 2003 | Paperback | 172 pages 150 line diagrams | ISBN: 0-521-53103-9
available from January 2003
The homotopy type of a closed simply connected 4-manifold is determined by the intersection form. The homotopy classes of maps between two such manifolds, however, do not coincide with the algebraic morphisms between intersection forms. Therefore the problem arises of computing the homotopy classes of maps algebraically and determining the law of composition for such maps. This problem is solved in the book by introducing new algebraic models of a 4-manifold. The book has been written to appeal to both established researchers in the field and graduate students interested in topology and algebra. There are many references to the literature for those interested in further reading.
Contents Introduction; 1. The homotopy category of (2,4)-complexes; 2. The homotopy category of simply connected 4-manifolds; 3. Track categories; 4. The splitting of the linear extension TL; 5. The category T Gamma and an algebraic model of CW(2,4); 6. Crossed chain complexes and algebraic models of tracks; 7. Quadratic chain complexes and algebraic models of tracks; 8. On the cohomology of the category nil.
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Publication is planned for March 2003 | Hardback | 200 pages | ISBN: 0-521-82472-9
available from March 2003
In recent years there has developed a satisfactory and coherent theory of orthogonal polynomials in several variables, attached to root systems, and depending on two or more parameters. These polynomials include as special cases: symmetric functions; zonal spherical functions on real and p-adic reductive Lie groups; the Jacobi polynomials of Heckman and Opdam; and the AskeyWilson polynomials, which themselves include as special or limiting cases all the classical families of orthogonal polynomials in one variable. This first comprehensive and organised account of the subject aims to provide a unified foundation for this theory, to which the author has been a principal contributor. It is an essentially self-contained treatment, accessible to graduate students familiar with root systems and Weyl groups. The first four chapters are preparatory to Chapter V, which is the heart of the book and contains all the main results in full generality.
Contents Introduction; 1. Affine root systems; 2. The extended affine Weyl group; 3. The braid group; 4. The affine Hecke algebra; 5. Orthogonal polynomials; 6. The rank 1 case; Bibliography; Index.
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Publication is planned for April 2003 | Hardback (Paperback) | 320 pages 86 line diagrams 167 half-tones 101 colour figures | ISBN: 0-521-56418-2 Publication is planned for April 2003 | Paperback (Hardback) | 320 pages 86 line diagrams 167 half-tones 101 colour figures | ISBN: 0-521-56457-3 available from April 2003
Following the success of The Quantum Universe, first published in 1987, a host of exciting new discoveries have been made in the field of quantum mechanics. The New Quantum Universe provides an up-to-date and accessible introduction to the essential ideas of quantum physics, and demonstrates how it affects our everyday life. Quantum mechanics gives an understanding of not only atoms and nuclei, but also all the elements and even the stars. The book explains quantum paradoxes and the eventful life of Schroedingerfs Cat, along with the Einstein-Podolsky-Rosen paradox and Bellfs Inequality. It then looks ahead to the nanotechnology revolution, describing quantum cryptography, quantum computing and quantum teleportation, and ends with an account of quantum mechanics and science fiction. Using simple non-mathematical language, this book is suitable for final-year school students, science undergraduates, and anyone wishing to appreciate how physics allows the new technologies that are changing our lives.
Reviews eThe Quantum Universe has a quotation from me in every chapter - but itfs a damn good book anyway.f Richard P. Feynman
eA lively, informative read, beautifully illustrated, about the most powerful scientific theory known to mankind.f P. C. W. Davies
ec a pleasure to both the mind and eye.f Science
eThis book will amaze, baffle and delight cf Nature
eIf you want a eway inf to the most successful and wide-ranging theory devised by human ingenuity, read The Quantum Universe.f New Scientist
Contents Preface; 1. Waves versus particles; 2. Heisenberg and uncertainty; 3. Schrodinger and matter waves; 4. Atoms and nuclei; 5. Quantum tunnelling; 6. Pauli and the elements; 7. Quantum co-operation and superfluids; 8. Quantum jumps; 9. Quantum engineering; 10. Death of a star; 11. Feynman rules; 12. Weak photons and strong glue; 13. Afterword - quantum physics and science fiction; Epilogue; Appendices.