ISBN: 978-0-470-05332-4
Hardcover
344 pages
June 2007
The principal aim of the book is to make accessible the construction methods for the best possible designs to use to model human decision making in many fields from marketing to medicine.
Table of contents
Preface.
Chapter 1. Typical Stated Choice Experiments.
Chapter 2. Factorial Designs.
Chapter 3. The MNL Model and Comparing Designs.
Chapter 4. Paired Comparison Designs for Binary Attributes.
Chapter 5. Larger Choice Set Sizes for Binary Attributes.
Chapter 6. Designs for Asymmetric Attributes.
Chapter 7. Various Topics.
Chapter 8. Practical Techniques For Constructing Choice Experiments.
Bibliography.
Index.
Kendrick Press, 2007. Paperback ISBN 0-9740427-6-5 (vol.1), 0-9740427-7-3 (vol.2), 0-9740427-8-1 (vol.3), 0-9740427-9-X (series). Hardback ISBN 0-9793183-1-9 (vol. 1), 0-9793183-2-7 (vol. 2), 0-9793183-3-5 (vol. 3), 0-9793183-4-3 (series). Volume 1: xviii + 539 pp. Volume 2: xii + 553 pp. Volume 3: xii + 597 pp.
For many phenomena of the real world, observations in the past and present may have considerable influence on observations in the near future, but rather weak influence on observations in the far future. Random sequences that satisfy "strong mixing conditions" are used to model such phenomena. This three-volume series is an introduction to the theory of strong mixing conditions. All three volumes deal primarily with (1) the central limit theorem under various strong mixing conditions and (2) basic structural properties of strong mixing conditions. Well-known constructions from the literature are used to illustrate various subtleties and limitations in connection with both the central limit theory and the structural properties involving such conditions. The proofs are given in much more detail than in most papers and monographs, in order to help newcomers to the field. The main prerequisite for the study of these volumes is a graduate-level command of real analysis and measure-theoretic probability theory.
Chapter headings:
Volume 1
1. Introduction to the (Rosenblatt) strong mixing condition
2. Connections with ergodic theory
3. Five classic strong mixing conditions
4. Norms and connections with interpolation theory
5. Some other strong mixing conditions
6.Independent pairs of 6-fields
7. Markov chains
8. Second order properties
9. Stationary Gaussian sequences
10. Central limit theorems under the strong mixing condition
11. Central limit theorems under P-mixing, P*-mixing and related conditions
12. General limiting behavior of partial sums under strong mixing
13. A brief review of some other topics
Volume 2
14. Relevant material (mostly) from Volume 1
15. Direct approximation by martingale differences, a` la Gordin
16. Direct approximation by independent random variables, a` la Berkes and Philipp
17. Central limit theorems under "minimal" conditions
18. A two-part mixing assumption
19. Tightness, shift-tightness and complete dissipation under strong mixing
20. Periodicity and related topics for non-Markovian strictly stationary sequences
21. Markov chains (revisited)
22. Dichotomies for some dependence coefficients
23. Linear dependence conditions (again)
24. Some other dependence conditions
Volume 3
25. Relevant material from Volumes 1 and 2
26. Examples involving prescribed mixing rates
27. Stationary Gaussian processes (revisited)
28. Random fields I: Linear dependence conditions and spectral density
29. Random fields II: Strong mixing conditions
30. Counterexamples to the central limit theorem: Markov chains, mixing rates a` la Davydov
31. Counterexamples with arbitrarily fast mixing rates
32. Some miscellaneous counterexamples
33. Counterexamples involving quantiles
34. P-mixing counterexamples
Richard Bradley is Professor of Mathematics at Indiana University. He is
an active researcher in the field treated in this series.
NEW IN PAPERBACK
ISBN-10: 0-19-280723-4
ISBN-13: 978-0-19-280723-6
Estimated publication date: July 2007
272 pages, Line drawings & 12 halftones, 196x129 mm
Reviews
'...accessible, artfully written...it stresses the human side of the drama. Though I have been a long-time participant in the story, I found myself learning much in every chapter and not wanting to put the book down.' - Robert L. Griess Jr.
'Ronan does a good job of describing the mathematics in broad strokes and giving a flavour of what is happening and - more importantly - why mathematicians get excited about these questions.' - The Mathematical Association of America
'This book tells for the first time the fascinating story of the biggest theorem ever to have been proved. Mark Ronan graphically describes not only the last few decades of the chase and the intriguing characters who led it, but also some of the more interesting byways, including my personal favourite, the one I called "Monstrous Moonshine".' - John H. Conway, F.R.S.
'Ronan tells a good story, and in doing so he paints a convincing picture of how mathematicians conduct their research.' - Gareth Jones, London Mathematical Society Newsletter
Description
The exciting story of one of the great mathematical quests, combining mathematics with stories of the extraordinary characters involved.
Very accessible writing - dazzling concepts such as multi-dimensional snowflakes are explained for the general reader.
An exciting, pacy, historical narrative covering two centuries - from the young genius Everiste Galois to the present day.
Imagine a giant snowflake in 196,884 dimensions...
This is the story of a mathematical quest that began two hundred years ago in revolutionary France, led to the biggest collaboration ever between mathematicians across the world, and revealed the 'Monster' - not monstrous at all, but a structure of exquisite beauty and complexity. Told here for the first time in accessible prose, it is a story that involves brilliant yet tragic characters, curious number 'coincidences' that led to breakthroughs in the mathematics of symmetry, and strange crystals that reach into many dimensions. And it is a story that is not yet over, for we have yet to understand the deep significance of the Monster - and its tantalizing hints of connections with the physical structure of spacetime. Once we understand the full nature of the Monster, we may well have revealed a whole new and deeper understanding of the nature of our Universe.
Readership: This book will appeal to readers of popular science and popular mathematics, both non-specialists and also specialists attracted by the biographical details and narrative of the quest for 'the Monster'
Contents
Prologue
1. Theaetetus's Icosahedron
2. Galois: Death of a Genius
3. Irrational Solutions
4. Groups
5. Sophus Lie
6. Lie Groups and Physics
7. Going Finite
8. After the War
9. The Man from Uccle
10. The Big Theorum
11. Pandora's Box
12. The Leech Lattice
13. Fischer's Monsters
14. The Atlas
15. A Monstrous Mystery
16. Construction
17. Moonshine
Appendix 1: The Golden Section
Appendix 2: The Witt Design
Appendix 3: The Leech Lattice
Appendix4: The 26 Exceptions
(hardback)
ISBN-10: 0-19-856495-3
ISBN-13: 978-0-19-856495-9
Estimated publication date: October 2007
614 pages, 234x156 mm
Series: Oxford Mathematical Monographs
Description
Modern treatment of many classical topics in the area of Sasakian geometry.
Up-to-date discussion of all recent results.
Numerous examples and exercises.
Extensive bibliography and appendices.
This book is an extensive monograph on Sasakian manifolds , focusing on the intricate relationship between Kahler and Sasakian geometries. The subject is introduced by discussion of several background topics, icluding the theory of Riemannian foliations, compact complex and Kahler orbifolds, and the existence and and obstruction theory of Kahler-Einstein metrics on complex compact orbifolds. There is then a discussion of contact and almost contact structures in the Riemannian setting, in which compact quasi-regular Sasakian manifolds emerge as algebraic objects. There is an extensive discussion of the symmetries of Sasakian manifolds, leading to a study of Sasakian structures on links of isolated hypersurface singularities. This is followed by an in-depth study of compact sasakian manifolds in dimensions three and five. The final section of the book deals with the existence of Sasaki-Einstein metrics. 3-Sasakian manifolds and the role of sasakian-Einstein geometry in String Theory are discussed separately.
Authors, editors, and contributors
Charles Boyer, University of New Mexico and
Krzysztof Galicki, University of New Mexico