Series: Use R
2008, X, 150 p., Softcover
ISBN: 978-0-387-78166-2
Due: August 2008
Advances in statistical methodology and computing have played an important role in allowing researchers to more accurately assess the health effects of ambient air pollution. The methods and software developed in this area are applicable to a wide array of problems in environmental epidemiology. This book provides an overview of the methods used for investigating the health effects of air pollution and gives examples and case studies in R which demonstrate the application of those methods to real data. The book will be useful to statisticians, epidemiologists, and graduate students working in the area of air pollution and health and others analyzing similar data.
The authors describe the different existing approaches to statistical modeling and cover basic aspects of analyzing and understanding air pollution and health data. The case studies in each chapter demonstrate how to use R to apply and interpret different statistical models and to explore the effects of potential confounding factors. A working knowledge of R and regression modeling is assumed. In-depth knowledge of R programming is not required to understand and run the examples.
Researchers in this area will find the book useful as a ``live'' reference. Software for all of the analyses in the book is downloadable from the web and is available under a Free Software license. The reader is free to run the examples in the book and modify the code to suit their needs. In addition to providing the software for developing the statistical models, the authors provide the entire database from the National Morbidity Mortality and Air Pollution Study (NMMAPS) in a convenient R package. With the database, readers can run the examples and experiment with their own methods and ideas.
Roger D. Peng is an Assistant Professor in the Department of Biostatistics at the Johns Hopkins Bloomberg School of Public Health. He is a prominent researcher in the areas of air pollution and health risk assessment and statistical methods for spatial and temporal data. Dr. Peng is the author of numerous R packages and is a frequent contributor to the R mailing lists.
Francesca Dominici is a Professor in the Department of Biostatistics at the Johns Hopkins Bloomberg School of Public Health. She has published extensively on hierarchical and semiparametric modeling and has been the leader of major national studies of the health effects of air pollution. She has also participated in numerous panels conducted by the National Academy of Science assessing the health effects of environmental exposures and has consulted for the US Environmental Protection Agency's Clean Air Act Advisory Board.
Studies of air pollution and health. - Introduction to R and air pollution and health data. - Reproducible research tools. - Statistical issues in estimating the health effects of spatial-temporal environmental exposures. - Exploratory data analyses. - Statistical models. - Pooling risks across locations and quantifying spatial heterogeneity. -A reproducible seasonal analysis of PM10 and mortaility in the U.S.
Series: Developments in Mathematics , Vol. 17
2008, X, 188 p., Hardcover
ISBN: 978-0-387-78509-7
Due: August 2008
Number theory has a wealth of long-standing problems, the study of which over the years has led to major developments in many areas of mathematics. This volume consists of seven significant chapters on number theory and related topics. Written by distinguished mathematicians, key topics focus on multipartitions, congruences and identities (G. Andrews), the formulas of Koshliakov and Guinand in Ramanujan's Lost Notebook (B. C. Berndt, Y. Lee, and J. Sohn), alternating sign matrices and the Weyl character formulas (D. M. Bressoud), theta functions in complex analysis (H. M. Farkas), representation functions in additive number theory (M. B. Nathanson), and mock theta functions, ranks, and Maass forms (K. Ono), and elliptic functions (M. Waldschmidt).
All of the surveys were outgrowths of featured talks given during the Special Year in Number Theory and Combinatorics at the University of Florida, Gainesville, 2004-2005, and describe major progress on a broad range of topics.
This volume is intended for mathematicians and graduate students interested in number theory and related areas.
0). Preface.- 1). A Survey of Multipartitions: Congruences and Identities.- 2). Koshliakov's Formula and Guinand's Formula in Ramanujan's Lost Notebook.- 3). Exploiting Symmetries: Alternating Sign Matrices and the Weyl Character Formulas.- 4). Theta Functions in Complex Analysis and Number Theory.- 5). Inverse Problems for Representation Functions in Additive Number Theory.- 6). Mock Theta Functions, Ranks, and Maass Forms.- 7). Elliptic Functions and Transcendence.
Series: Algebra and Applications , Vol. 9
2008, Approx. 335 p. 4 illus., Hardcover
ISBN: 978-1-84800-280-7
Due: September 2008
The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical finite transformation semigroups: transformations and semigroups, ideals and Green's relations, subsemigroups, congruences, endomorphisms, nilpotent subsemigroups, presentations, actions on sets, linear representations, cross-sections and variants. The book contains many exercises and historical comments and is directed first of all to both graduate and postgraduate students looking for an introduction to the theory of transformation semigroups, but it should also prove useful to tutors and researchers.
Graduate students, post-grad students, teachers and researchers interested in semigroups, algebra or combinatronics or anyone planning to give a course in semigroups or transformation semigroups
Preface.- 1. Ordinary and partial transformations.- 2. The semigroups Tn, PT n and ISn.- 3. Generating Systems.- 4. Ideals and Green's relations.- 5. Subgroups and subsemigroups.- 6. Other relations on semigroups.- 7. Endomorphisms.- 8. Nilpotent subsemigroups.- 9. Presentation.- 10. Transitive actions.- 11. Linear representations.- 12. Cross-sections.- 13. Variants.- 14. Order-related subsemigroups.- Answers and hints to exercises.- Bibliography.- List of notation.- Index.
Series: Progress in Mathematics , Vol. 272
2008, Approx. 310 p., Hardcover
ISBN: 978-3-7643-8881-2
Due: July 2008
The main objective of this book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics. It includes the discussion of the foundations, main results, and main techniques in the rich interplay of four main areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative recurrence. It also gives a panorama of several selected topics of current research interest. All the results are included with detailed proofs, many of them simplified or rewritten on purpose for the book. The text is self-contained.
Graduate and postgraduate students and researchers in analysis, differential geometry, dynamical systems and chaos theory; for graduate courses in dimension theory of dynamical systems, multifractal analysis, and pointwise dimension and recurrence in hyperbolic dynamics
Preface.- Introduction.- Basic Notions.- I. Dimension Theory.- Dimension Theory and Thermodynamic Formalism.- Repellers and Hyperbolic Sets.- Measures of Maximal Dimension.- II. Multifractal Analysis: Core Theory.- Multifractal Analysis of Equilibrium Measures.- General Concept of Multifractal Analysis.- Dimension of Irregular Sets.- Variational Principles in Multifractal Analysis.- III. Multifractal Analysis: Further Developments.- Multidimensional Spectra and Number Theory.- Multifractal Rigidity.- Hyperbolic Sets: Past and Future.- IV. Hyperbolicity and Recurrence.- Pointwise Dimension for Hyperbolic Dynamics.- Product Structure of Hyperbolic Measures.- Quantitative Recurrence and Dimension Theory.
Series: Graduate Texts in Mathematics , Preliminary entry 935
2009, Approx. 400 p. 10 illus., Hardcover
ISBN: 978-0-387-09444-1
Due: October 2009
Symmetries play a decisive role in the natural sciences and throughout mathematics. Infinite-dimensional Lie theory deals with symmetries depending on infinitely many parameters. Infinite-dimensional Lie Groups provides a comprehensive introduction to this important subject by developing a global infinite-dimensional Lie theory on the basis that a Lie group is simply a manifold modeled on a locally convex space, equipped with a group structure with smooth group operations. The focus is on the local and global level, as well as on the translation mechanisms allowing or preventing passage between Lie groups and Lie algebras. Starting from scratch, the reader is led from the basics of the theory through to the frontiers of current research.
This introductory volume subtitled, General Theory and Main Examples, examines the structure theory of infinite-dimensional Lie groups by developing a broad framework of Lie theory and illustrating the general results through a detailed discussion of the major classes of Lie groups: linear Lie groups, groups of (smooth) maps, groups of diffeomorphisms, and direct limit groups. From these, most other relevant groups can be obtained as extensions or Lie subgroups.
Together with its companion volume subtitled, Geometry and Topology, these essentially self-contained texts provide all necessary background as regards generally locally convex spaces, finite-dimensional Lie theory and differential geometry, with modest prerequisites limited to a basic knowledge of abstract algebra, point set topology, differentiable manifolds, and functional analysis in Banach spaces. The clear exposition includes careful explanations, illustrative examples, numerous exercises, and detailed cross-references to simplify a non-linear reading of the material.
Preface.- Introduction.- Infinite-dimensional Calculus.- Infinite-dimensional Manifolds.- Lie Groups.- Locally Exponential Lie Groups.- Linear Lie Groups.- Direct Limits of Lie Groups.- Groups of Maps.- Groups of Diffeomorphisms.- Appendix A: Tools from Topology.- Appendix B: Basic Theory of Locally Convex Spaces.- Appendix C: Finite-dimensional Lie Algebras.- Appendix D: Calculus in Banach Spaces.- Appendix E: Smooth Maps into non-Lie Groups.- Appendix F: Cohomology of Lie Algebras.- Bibliography.- Index.