Series: Progress in Mathematics, Vol. 203
2010, XV, 343 p. 12 illus., 6 in color., Hardcover
ISBN: 978-0-8176-4958-6
Second Edition features new material in most chapters, but particularly in Chapters 3, 7, and 12 Covers major new topics, such as a complex geodesic flow and the accompanying geometry of the projectivized holomorphic tangent bundle Features improvements and general corrections based off of the first edition throughout the text Intended for a broad audience of mathematicians, researchers and students in Riemannian geometry
This second edition, divided into fourteen chapters, presents a comprehensive treatment of contact and symplectic manifolds from the Riemannian point of view. The monograph examines the basic ideas in detail and provides many illustrative examples for the reader.
Riemannian Geometry of Contact and Symplectic Manifolds, Second Edition provides new material in most chapters, but a particular emphasis remains on contact manifolds. New principal topics include a complex geodesic flow and the accompanying geometry of the projectivized holomorphic tangent bundle and a complex version of the special directions discussed in Chapter 11 for the real case. Both of these topics make use of Etienne Ghys's attractive notion of a holomorphic Anosov flow.
Researchers, mathematicians, and graduate students in contact and symplectic manifold theory and in Riemannian geometry will benefit from this work. A basic course in Riemannian geometry is a prerequisite.
Preface * 1. Symplectic Manifolds * 2. Principal S1-bundles * 3. Contact Manifolds * 4. Associated Metrics * 5. Integral Submanifolds and Contact Transformations * 6. Sasakian and Cosymplectic Manifolds * 7. Curvature of Contact Metric Manifolds * 8. Submanifolds of Kahler and Sasakian Manifolds * 9. Tangent Bundles and Tangent Sphere Bundles * 10. Curvature Functionals and Spaces of Associated Metrics * 11. Negative Xi-sectional Curvature * 12. Complex Contact Manifolds * 13. Additional Topics in Complex Geometry * 14. 3-Sasakian Manifolds * Bibliography * Subject Index * Author Index
Series: Springer Series in Statistics
2010, XIV, 262 p., Hardcover
ISBN: 978-1-4419-6823-4
Integrates conceptual and computational treatment of tree representations of complex pathways to important outcomes across diverse scientific applications Introduces random and alternative deterministic forests to facilitate interpretability of pathways with many contributing conditions and non-linear relationships Illustrates the interplay between scientific judgments and constraints on allowed pathway constructions; comparisons with conventional statistical methods
The routes to many important outcomes including diseases and ultimately death as well as financial credit consist of multiple complex pathways containing interrelated events and conditions. We have historically lacked effective methodologies for identifying these pathways and their non-linear and interacting features. This book focuses on recursive partitioning strategies as a response to the challenge of pathway characterization. A highlight of the second edition is the many worked examples, most of them from epidemiology, bioinformatics, molecular genetics, physiology, social demography, banking, and marketing. The statistical issues, conceptual and computational, are not only treated in detail in the context of important scientific questions, but also an array of substantively-driven judgments are explicitly integrated in the presentation of examples. Going considerably beyond the standard treatments of recursive partitioning that focus on pathway representations via single trees, this second edition has entirely new material devoted to forests from predictive and interpretive perspectives. For contexts where identification of factors contributing to outcomes is a central issue, both random and deterministic forest generation methods are introduced via examples in genetics and epidemiology. The trees in deterministic forests are reproducible and more easily interpretable than the components of random forests. Also new in the second edition is an extensive treatment of survival forests and post-market evaluation of treatment effectiveness. Heping Zhang is Professor of Public Health, Statistics, and Child Study, and director of the Collaborative Center for Statistics in Science, at Yale University. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics, a Myrto Lefkopoulou Distinguished Lecturer Awarded by Harvard School of Public Health, and a Medallion lecturer selected by the Institute of Mathematical Statistics. Burton Singer is Courtesy Professor in the Emerging Pathogens Institute at University of Florida, and previously Charles and Marie Robertson Professor of Public and International Affairs at Princeton University. He is a member of the National Academy of Sciences and Institute of Medicine of the National Academies, and a Fellow of the American Statistical Association.
Series: Universitext
2010, XIV, 474 p. 2 illus., 1 in color., Softcover
ISBN: 978-1-4419-6093-1
Due: September 29, 2010
Fully updated and revised second edition Explores harmonic analysis techniques for the study of the mathematical concept of Hilbert space Focusing mainly on operator theories and developments, the text discusses two specific operator classes
The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory.
This second edition, in addition to revising and amending the original text, focuses on further developments of the theory. Specifically, the last two chapters of the book continue and complete the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.
Preface.- Contractions and their dilations.- Properties of unitary dilations.- Functional calculus.- Extended functional calculus.- Operator valued analytic functions.- Functional models.- Regular factorizations and invariant subspaces.- Weak contractions.- The structure of C_{\cdot0} contractions.- The structire of Operators of class C_0.- Further results.- Bibliography.- Author Index.- Subject index.- Notation index.
2010, 388 p. 80 illus., 40 in color., Hardcover
ISBN: 978-3-642-14036-5
Due: September 2010
Formalism of classical mechanics underlies a number of powerful mathematical methods that are widely used in theoretical and mathematical physics. This book considers the basics facts of Lagrangian and Hamiltonian mechanics, as well as related topics, such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyond the traditional level adopted in the standard textbooks on classical mechanics, only elementary mathematical methods are used in the exposition of the material. The mathematical constructions involved are explicitly described and explained, so the book can be a good starting point for the undergraduate student new to this field. At the same time and where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for the graduate students intending to work in one of the branches of the vast field of theoretical physics. To illustrate how classical-mechanics formalism works in other branches of theoretical physics, examples related to electrodynamics, as well as to relativistic and quantum mechanics, are included.
Sketch of Lagrangian Formalism.- Hamiltonian Formalism - Canonical Transformations on Two- Dimensional Phase Space - Properties of Canonical Transformations - Integral Invariants - Potential Motion in a Geometric Setting - Transformations, Symmetries and Noether Theorem.- Hamiltonian Formalism for Singular Theories.
Series: Universitext
Original French edition published by EDP Sciences, CNRS Editions, France, 1997
2010, XXX, 234 p., Softcover
ISBN: 978-0-85729-029-8
Due: September 29, 2010
This book provides an introduction to complex analysis in several variables. The viewpoint of integral representation theory together with Grauert's bumping method offers a natural extension of single variable techniques to several variables analysis and leads rapidly to important global results. Applications focus on global extension problems for CR functions, such as the Hartogs-Bochner phenomenon and removable singularities for CR functions. Three appendices on differential manifolds, sheaf theory and functional analysis make the book self-contained.
Each chapter begins with a detailed abstract, clearly demonstrating the structure and relations of following chapters. New concepts are clearly defined and theorems and propositions are proved in detail. Historical notes are also provided at the end of each chapter.
Clear and succinct, this book will appeal to post-graduate students, young researchers seeking an introduction to holomorphic function theory in several variables and lecturers seeking a concise book on the subject.
Elementary local properties of holomorphic functions of several complex variables.- Currents and complex structures.- The Bochner-Martinelli-Koppelman kernel and formula applications.- Extensions of CR functions.- Extensions of holomorphic and CR functions on manifolds.- Domains of holomorphy and pseudoconvexity.- The Levi problem and the resolution of ? in strictly pseudoconvex domains.- Characterisation of removable singularities of CR functions on a strictly pseudoconvex boundary.- Appendices.