Preface Acknowledgements Part I. One-Dimensional Integrable Systems: 1. Lie groups 2. Lie algebras 3. Factorizations and homogeneous spaces 4. Hamilton's equations and Hamiltonian systems 5. Lax equations 6. Adler-Kostant-Symes 7. Adler-Kostant-Symes (continued) 8. Concluding remarks on one-dimensional Lax equations Part II. Two-Dimensional Integrable Systems: 9. Zero-curvature equations 10. Some solutions of zero-curvature equations 11. Loop groups and loop algebras 12. Factorizations and homogeneous spaces 13. The two-dimensional Toda lattice 14. T-functions and the Bruhat decomposition 15. Solutions of the two-dimensional Toda lattice 16. Harmonic maps from C to a Lie group G 17. Harmonic maps from C to a Lie group (continued) 18. Harmonic maps from C to a symmetric space 19. Harmonic maps from C to a symmetric space (continued) 20. Application: harmonic maps from S2 to CPn 21. Primitive maps 22. Weierstrass formulae for harmonic maps Part III. One-Dimensional and Two-Dimensional Integrable Systems: 23. From 2 Lax equations to 1 zero-curvature equation 24. Harmonic maps of finite type 25. Application: harmonic maps from T2 to S2 26. Epilogue References Index.
The study of geodesic flows on homogenous spaces is an area of research that has yielded some fascinating developments. This book, first published in 2000, focuses on many of these, and one of its highlights is an elementary and complete proof (due to Margulis and Dani) of Oppenheim's conjecture. Also included here: an exposition of Ratner's work on Raghunathan's conjectures; a complete proof of the Howe-Moore vanishing theorem for general semisimple Lie groups; a new treatment of Mautner's result on the geodesic flow of a Riemannian symmetric space; Mozes' result about mixing of all orders and the asymptotic distribution of lattice points in the hyperbolic plane; Ledrappier's example of a mixing action which is not a mixing of all orders. The treatment is as self-contained and elementary as possible. It should appeal to graduate students and researchers interested in dynamical systems, harmonic analysis, differential geometry, Lie theory and number theory.
Elementary differential geometry Lie groups and Lie algebras Structure of semisimple Lie algebras Symmetric spaces Decomposition of symmetric spaces Symmetric spaces of the noncompact type Symmetric spaces of the compact type Hermitian symmetric spaces On the classification of symmetric spaces Functions on symmetric spaces Bibliography List of notational conventions Symbols frequently used Author index Subject index Reviews for the first edition.
Elementary differential geometry Lie groups and Lie algebras Structure of semisimple Lie algebras Symmetric spaces Decomposition of symmetric spaces Symmetric spaces of the noncompact type Symmetric spaces of the compact type Hermitian symmetric spaces Structure of semisimple Lie groups The classification of simple Lie algebras and of symmetric spaces Solutions to exercises Some details Bibliography List of notational conventions Symbols frequently used Index Reviews for the first edition.
Spatial Dimensions of Public Policy deals with the spatial dimensions of public policy with particular reference to resource management, urban development, regional development, and poverty alleviation. Emphasis is on the geographer's actual and potential contributions to public policy. Comprised of 15 chapters, this book begins with an introduction to the nature of geographers' contributions to public policy and the reasons why they have not been as effective as the relationships between their interests and important issues of public policy might suggest. The next chapter describes how policy decisions are made in Canada and reviews the nature of disciplinary contributions to governmental decision-making at the highest level. Subsequent chapters focus on regional policy and broad issues of world strategy; specific contributions to public policy, particularly in the United Kingdom; spatial aspects of pollution policy; and policies outside the United Kingdom. Energy policy in Western Europe is discussed, together with a geographer's contribution to addressing environmental problems in New Zealand; the difficulties of achieving an accurate population census of Nigeria; and the reshaping of the legislative and congressional districts of the State of Washington. This monograph will be of interest to geographers and public policymakers.
Manufacturing Parameters and Entrepreneurship provides a guide that helps business leaders understand and apply the production parameters and estimation techniques needed for commercial success. This book covers important concepts in depth, including manufacturing space, manufacturing quality, production backorders, space consideration, quality aspects, maximum inventory control, entrepreneurial application, and quality inclusion. Key features: Covers manufacturing parameters, their estimation, and effects in a single volume. Discusses conceptualization, formulation, and analysis of space consideration. Provides basic understanding and mathematical treatment of quality aspects in detail. Discusses in detail concepts such as manufacturing space, manufacturing quality, and production backorders. Covers stock out situations in detail. Manufacturing Parameters and Entrepreneurship will be an invaluable addition to the libraries of graduate students and professionals in the field of industrial engineering, production engineering, and manufacturing science and engineering.
Introduction to Banach Spaces and their Geometry
Spacetime and Geometry is an introductory textbook on general relativity, specifically aimed at students. Using a lucid style, Carroll first covers the foundations of the theory and mathematical formalism, providing an approachable introduction to what can often be an intimidating subject. Three major applications of general relativity are then discussed: black holes, perturbation theory and gravitational waves, and cosmology. Students will learn the origin of how spacetime curves (the Einstein equation) and how matter moves through it (the geodesic equation). They will learn what black holes really are, how gravitational waves are generated and detected, and the modern view of the expansion of the universe. A brief introduction to quantum field theory in curved spacetime is also included. A student familiar with this book will be ready to tackle research-level problems in gravitational physics.
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