Series: Encyclopedia of Mathematics and its Applications (No. 125)
Hardback (ISBN-13: 9780521517201)
The Hilbert transform has many uses, including solving problems in aerodynamics, condensed matter physics, optics, fluids, and engineering. Written in a style that will suit a wide audience (including the physical sciences), this book will become the reference of choice on the topic, whatever the subject background of the reader. It explains all the common Hilbert transforms, mathematical techniques for evaluating them, and has detailed discussions of their application. Especially useful for researchers are the tabulation of analytically evaluated Hilbert transforms, and an atlas that immediately illustrates how the Hilbert transform alters a function. A collection of exercises helps the reader to test their understanding of the material in each chapter. The bibliography is a wide-ranging collection of references both to the classical mathematical papers, and to a diverse array of applications.
* Informal style opens up the material to anyone working in the physical
sciences * The only book to contain an extensive table of Hilbert transforms,
and it has a mini atlas to show reader immediately how the Hilbert transform
alters a function * Exercises are included to help test understanding,
and a large bibliography points to classical papers and a wide range of
applications
Preface; 1. Introduction; 2. Review of some background mathematics; 3. Derivation of the Hilbert transform relations; 4. Some basic properties of the Hilbert transform; 5. Relationship of the Hilbert transform to some common transforms; 6. The Hilbert transform of periodic functions; 7. Inequalities for the Hilbert transforms; 8. Asymptotic behavior of the Hilbert transform; 9. Hilbert transforms of some special functions; 10. Hilbert transforms involving distributions; 11. The finite Hilbert transform; 12. Some singular integral equations; 13. Discrete Hilbert transforms; 14. Numerical evaluation of Hilbert transforms; 15. Hilbert transforms involving distributions; 16. Some further extensions of the classical Hilbert transforms; 17. Linear systems and causality; 18. The Hilbert transform of waveforms and signal processing; 19. Kramers-Kronig relations; 20. Dispersion relations for some linear optical properties; 21. Dispersion relations for magneto-optical and natural optical activity; 22. Dispersion relations for nonlinear optical properties; 23. Some further applications of Hilbert transforms; Appendix 1. Table of selected Hilbert transforms; Appendix 2. Atlas of selected Hilbert transform pairs; References; Author index; Notational index; Subject index.
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Series: Cambridge Mathematical Library
Paperback (ISBN-13: 9780521731829)
Meyn & Tweedie is back! The bible on Markov chains in general state spaces has been brought up to date to reflect developments in the field since 1996 - many of them sparked by publication of the first edition. The pursuit of more efficient simulation algorithms for complex Markovian models, or algorithms for computation of optimal policies for controlled Markov models, has opened new directions for research on Markov chains. As a result, new applications have emerged across a wide range of topics including optimisation, statistics, and economics. New commentary and an epilogue by Sean Meyn summarise recent developments and references have been fully updated. This second edition reflects the same discipline and style that marked out the original and helped it to become a classic: proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background.
* The modern classic, available in print for the first time in 10 years
* The 1994 ORSA/TIMS Best Publication on Applied Probability Award winner,
brought up to date to reflect recent developments * Now includes a prologue
by Peter W. Glynn
List of figures; Prologue to the second edition Peter W. Glynn; Preface to the second edition Sean Meyn; Preface to the first edition; Part I. Communication and Regeneration: 1. Heuristics; 2. Markov models; 3. Transition probabilities; 4. Irreducibility; 5. Pseudo-atoms; 6. Topology and continuity; 7. The nonlinear state space model; Part II. Stability Structures: 8. Transience and recurrence; 9. Harris and topological recurrence; 10. The existence of ®; 11. Drift and regularity; 12. Invariance and tightness; Part III. Convergence: 13. Ergodicity; 14. f-Ergodicity and f-regularity; 15. Geometric ergodicity; 16. V-Uniform ergodicity; 17. Sample paths and limit theorems; 18. Positivity; 19. Generalized classification criteria; 20. Epilogue to the second edition; Part IV. Appendices: A. Mud maps; B. Testing for stability; C. Glossary of model assumptions; D. Some mathematical background; Bibliography; Indexes.
Hardback (ISBN-13: 9780521424264)
This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set. The book starts with a broad introduction to the field and progresses to advanced results. Contents include: definition of Turing machines and basic time and space complexity classes, probabilistic algorithms, interactive proofs, cryptography, quantum computation, lower bounds for concrete computational models (decision trees, communication complexity, constant depth, algebraic and monotone circuits, proof complexity), average-case complexity and hardness amplification, derandomization and pseudorandom constructions, and the PCP theorem.
* Contains the modern take on computational complexity as well as the classical
* Covers the basics plus advanced topics that appear for the first time
in a graduate textbook * More than 300 exercises are included
Part I. Basic Complexity Classes: 1. The computational model - and why
it doesnft matter; 2. NP and NP completeness; 3. Diagonalization; 4. Space
complexity; 5. The polynomial hierarchy and alternations; 6. Boolean circuits;
7. Randomized computation; 8. Interactive proofs; 9. Cryptography; 10.
Quantum computation; 11. PCP theorem and hardness of approximation: an
introduction; Part II. Lower Bounds for Concrete Computational Models:
12. Decision trees; 13. Communication complexity; 14. Circuit lower bounds;
15. Proof complexity; 16. Algebraic computation models; Part III. Advanced
Topics: 17. Complexity of counting; 18. Average case complexity: Levinfs
theory; 19. Hardness amplification and error correcting codes; 20. Derandomization;
21. Pseudorandom constructions: expanders and extractors; 22. Proofs of
PCP theorems and the Fourier transform technique; 23. Why are circuit lower
bounds so difficult*; Appendix A: mathematical background.
Series: London Mathematical Society Lecture Note Series (No. 359)
Paperback (ISBN-13: 9780521734714)
Vector bundles and their associated moduli spaces are of fundamental importance in algebraic geometry. In recent decades this subject has been greatly enhanced by its relationships with other areas of mathematics, including differential geometry, topology and even theoretical physics, specifically gauge theory, quantum field theory and string theory. Peter E. Newstead has been a leading figure in this field almost from its inception and has made many seminal contributions to our understanding of moduli spaces of stable bundles. This volume has been assembled in tribute to Professor Newstead and his contribution to algebraic geometry. Some of the subjectfs leading experts cover foundational material, while the survey and research papers focus on topics at the forefront of the field. This volume is suitable for both graduate students and more experienced researchers.
* Written by acknowledged experts in the field * Covers both foundational
material and the latest research * Designed to appeal to both new and more
experienced researchers
Preface; Acknowledgments; Part I. Lecture Notes: 1. Lectures on principal
bundles V. Balaji; 2. Brill-Noether theory for stable vector bundles Ivona
Grzegorczyk and Montserrat Teixidor i Bigas; 3. Fourier-Mukai and Nahm
transforms U. Bruzzo, D. Hernandez Ruiperez and C. Tejero Prieto; 4. Geometric
invariant theory P. E. Newstead; 5. Deformation theory for vector bundles
N. Nitsure; 6. The theory of vector bundles S. Ramanan; Part II. Survey
articles: 7. Moduli of sheaves from moduli of Kronecker modules L. Alvarez-Consul
and A. King; 8. Coherent Systems: a brief survey S. B. Bradlow; 9. Higgs
bundles surface group representations Oscar Garcia-Prada; 10. Quotients
by non-reductive algebraic group actions Frances Kirwan; 11. Dualities
on T*SUx(2,Ox) E. Previato; 12. Moduli spaces for principal bundles A.
H. W. Schmitt; Part III. Research Articles: 13. Beilinson type spectral
sequences on scrolls M. Aprodu and V. Brinz*nescu; 14. Coherent systems
on a nodal curve Usha N. Bhosle; 15. Brill-Noether bundles and coherent
systems on special curves L. Brambila-Paz and Angela Ortega; 16. Higgs
bundles in the vector representation N. Hitchin; 17. Moduli spaces of torsion
free sheaves on nodal curves C. S. Seshadri.
Series: Cambridge Tracts in Mathematics (No. 179)
Hardback (ISBN-13: 9780521514965)
The dynamics of linear operators is a young and rapidly evolving branch of functional analysis. In this book, which focuses on hypercyclicity and supercyclicity, the authors assemble the wide body of theory that has received much attention over the last fifteen years and present it for the first time in book form. Selected topics include various kinds of eexistence theoremsf, the role of connectedness in hypercyclicity, linear dynamics and ergodic theory, frequently hypercyclic and chaotic operators, hypercyclic subspaces, the angle criterion, universality of the Riemann zeta function, and an introduction to operators without non-trivial invariant subspaces. Many original results are included, along with important simplifications of proofs from the existing research literature, making this an invaluable guide for students of the subject. This book will be useful for researchers in operator theory, but also accessible to anyone with a reasonable background in functional analysis at the graduate level.
* Self-contained for easier reading * Includes a ereader-friendlyf introduction
to the work of C. J. Read on operators without non-trivial invariant subspaces
* Contains original results, simplifications of existing research and over
100 carefully selected exercises
Introduction; 1. Hypercyclic and supercyclic operators; 2. Hypercyclicity everywhere; 3. Connectedness and hypercyclicity; 4. Weakly mixing operators; 5. Ergodic theory and linear dynamics; 6. Beyond hypercyclicity; 7. Common hypercyclic vectors; 8. Hypercyclic subspaces; 9. Supercyclicity and the angle criterion; 10. Linear dynamics and the weak topology; 11. Universality of the Riemann zeta function; 12. About ethef Read operator; Appendices; Notations; Index; Bibliography.