Series: London Mathematical Society Student Texts (No. 74)
Hardback (ISBN-13: 9780521517683)
Paperback (ISBN-13: 9780521732017)
16 halftones 2 tables 335 exercises
Page extent: 385 pages
Size: 228 x 152 mm
The theory of Hardy spaces has close connections to many branches of mathematics including Fourier analysis, harmonic analysis, singular integrals, potential theory and operator theory, and has found essential applications in robust control engineering. For each application, the ability to represent elements of these classes by series or integral formulas is of utmost importance. This self-contained text provides an introduction to a wide range of representation theorems and provides a complete description of the representation theorems with direct proofs for both classes of Hardy spaces: Hardy spaces of the open unit disc and Hardy spaces of the upper half plane. With over 300 exercises, many with accompanying hints, this book is ideal for those studying Advanced Complex Analysis, Function Theory or Theory of Hardy Spaces. Advanced undergraduate and graduate students will find the book easy to follow, with a logical progression from basic theory to advanced research.
* Concise and accessible, provides complete description of representation
theorems with direct proofs for both classes of Hardy spaces * Contains
over 300 exercises, many with accompanying hints, to aid understanding
* Ideal for advanced undergraduate and graduate students taking courses
in Advanced Complex Analysis, Function Theory or Theory of Hardy Spaces
Preface; 1. Fourier series; 2. Abel*Poisson means; 3. Harmonic functions
in the unit disc; 4. Logarithmic convexity; 5. Analytic functions in the
unit disc; 6. Norm inequalities for the conjugate function; 7. Blaschke
products and their applications; 8. Interpolating linear operators; 9.
The Fourier transform; 10. Poisson integrals; 11. Harmonic functions in
the upper half plane; 12. The Plancherel transform; 13. Analytic functions
in the upper half plane; 14. The Hilbert transform on R; A. Topics from
real analysis; B. A panoramic view of the representation theorems; Bibliography;
Index.
Hardback (ISBN-13: 9780521880329)
86 halftones 180 exercises
Page extent: 670 pages
Size: 246 x 189 mm
String theory made understandable. Barton Zwiebach is once again faithful to his goal of making string theory accessible to undergraduates. He presents the main concepts of string theory in a concrete and physical way to develop intuition before formalism, often through simplified and illustrative examples. Complete and thorough in its coverage, this new edition now includes AdS/CFT correspondence and introduces superstrings. It is perfectly suited to introductory courses in string theory for students with a background in mathematics and physics. New sections cover strings on orbifolds, cosmic strings, moduli stabilization, and the string theory landscape. Now with almost 300 problems and exercises, with password-protected solutions for instructors at www.cambridge.org/zwiebach.
* Includes completely new chapters on AdS/CFT correspondence and strong
interactions, and an introduction to superstrings * A detailed and self-contained
explanation of string theory at a level that is truly understandable to
undergraduates * Presents the main concepts of string theory in a concrete
and physical way, with over 100 worked examples and over 180 homework problems
(with solutions for instructors)
Foreword; Preface; Acknowledgements; Part I. Basics: 1. A brief introduction; 2. Special relativity and extra dimensions; 3. Electromagnetism and gravitation in various dimensions; 4. Nonrelativistic strings; 5. The relativistic point particle; 6. Relativistic strings; 7. Strong parameterization and classical motion; 8. World-sheet currents; 9. Light-cone relativistic strings; 10. Light-cone fields and particles; 11. The relativistic quantum point particle; 12, Relativistic quantum closed strings; 13. Relativistic quantum closed strings; 14. A look at relativistic superstrings; Part II. Developments: 15. D-branes and gauge fields; 16. String charge and electric charge; 17. T-duality of closed strings; 18. T-duality of open strings; 19. Electromagnetism fields in D-branes; 20. Nonlinear and Born-Infeld electrodynamics; 21. Strong theory and particle physics; 22. String thermodynamics and black holes; 23. Strong interactions and AdS/CFT; 24. Covariant string quantization; 25. String interactions and Riemann surfaces; 26. Loop amplitudes in string theory; References; Index.
Series: Interdisciplinary Statistics Volume: 20
ISBN: 9781584888406
Publication Date: 8/4/2008
Number of Pages: 360
Shows how to apply Bayesian hierarchical modeling to geographical analyses of disease
Deals with both population and individual analyses resulting from cancer registry data
Discusses the survival and longitudinal analyses of data in health services and designed studies
Covers standard topics, such as relative risk estimation and clustering
Uses a range of actual data sets to illustrate concepts
Provides the data sets, WinBUGS ODC files, and R code on the author's website
Focusing on data commonly found in public health databases and clinical settings, Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiology provides an overview of the main areas of Bayesian hierarchical modeling and its application to the geographical analysis of disease.
The book explores a range of topics in Bayesian inference and modeling,
including Markov chain Monte Carlo methods, Gibbs sampling, the Metropolis-Hastings
algorithm, goodness-of-fit measures, and residual diagnostics. It also
focuses on special topics, such as cluster detection; space-time modeling;
and multivariate, survival, and longitudinal analyses. The author explains
how to apply these methods to disease mapping using numerous real-world
data sets pertaining to cancer, asthma, epilepsy, foot and mouth disease,
influenza, and other diseases. In the appendices, he shows how R and WinBUGS
can be useful tools in data manipulation and simulation.
Applying Bayesian methods to the modeling of georeferenced health data, Bayesian Disease Mapping proves that the application of these approaches to biostatistical problems can yield important insights into data.
Series: Chapman & Hall/CRC Applied Mathematics & Nonlinear Science Volume: 17
ISBN: 9781420089042
IPublication Date: 9/26/2008
Number of Pages: 376
Provides a selection of standard finite difference and finite elements
Covers novel techniques, such as high-order compact finite difference and meshless methods
Presents applications from the fields of mechanical and electrical engineering as well as the physical sciences
Contains computer projects and problems
Includes a CD-ROM with MATLAB code
Offers a solutions manual for qualifying instructors
This textbook introduces several major numerical methods for solving partial differential equations. It presents new techniques, such as the high-order compact difference method and the radial basis function meshless method, as well as traditional techniques that include the classic finite difference method and the finite element method. Ideal for a one- or two-semester course, the text only requires some knowledge of computer programming, advanced calculus, and difference equations. It provides practical examples, exercises, references, and problems, along with a solutions manual for qualifying instructors. An accompanying CD-ROM contains MATLABŪ source code.
Brief Overview of Partial Differential Equations. Finite Difference Methods for Parabolic Equations. Finite Difference Methods for Hyperbolic Equations. Finite Difference Methods for Elliptic Equations. High-Order Compact Difference Methods. Finite Element Methods: Basic Theory. Finite Element Methods: Programming. Mixed Finite Element Methods. Finite Element Methods for Electromagnetics. Meshless Methods with Radial Basis Functions. Other Meshless Methods
Series: Lecture Notes in Pure and Applied Mathematics
ISBN: 9781420090468
Publication Date: 11/15/2008
Number of Pages: 280
Discusses the classification of cyclic groups with periodic factorizations and with non-full-rank factorizations
Covers quasi-periodicity and the factoring of the group of integers
Provides a self-contained treatment of the more general theory of factorization to aid practitioners in using the theory without having to immerse in the details of the full generality
Presents applications to variable length codes and integer codes
The factorization theory of abelian groups has a number of applications in the geometry of tilings, coding theory, combinatorics, Fourier analysis, graph theory, and number theory. Focusing on this theory and its interesting applications, this book explores problems in which the underlying factored group is cyclic. The authors consider factorizations of finite cyclic groups that lead to a rich theory with its own techniques and applications. They discuss the problem of tiling the number line with copies of a given tile and factoring finite cyclic groups. The book also presents the theory of variable length codes and certain problems from Fourier analysis where factoring finite cyclic groups plays a prominent part.