Eric Ghysels, Denise R. Osborn
The Econometric Analysis of Seasonal Time Series
Description
Eric Ghysels and Denise R. Osborn provide a thorough and timely review of the recent developments in the econometric analysis of seasonal economic time series, summarizing a decade of theoretical advances in the area. The authors discuss the asymptotic distribution theory for linear nonstationary seasonal stochastic processes. They also cover the latest contributions to the theory and practice of seasonal adjustment, together with its implications for estimation and hypothesis testing. Moreover, a comprehensive analysis of periodic models is provided, including stationary and nonstationary cases. The book concludes with a discussion of some nonlinear seasonal and periodic models. The treatment is designed for an audience of researchers and advanced graduate students.
Chapter Contents
1. Introduction to seasonal processes; 2. Deterministic seasonality; 3. Seasonal unit root processes; 4. Seasonal adjustment programs; 5. Estimation and hypothesis testing with filtered data; 6. Periodic processes; 7. Some nonlinear seasonal models; 8. Epilogue.
ISBN: 0-521-56260-0
Binding: Hardback
ISBN: 0-521-56588-X
Binding: Paperback
Size: 237 x 159 mm
Pages: 250
Weight: 0.465kg
Figures: 15 line diagrams 2 tables
Published: 6 September 2001
Gordon James, Martin Liebeck
Representations and Characters of Groups(2nd edition)
Description
This book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside’s paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians.
Chapter Contents
1. Groups and homomorphisms; 2. Vector spaces and linear transformations; 3. Group representations; 4. FG-modules; 5. FG-submodules; 6. Group algebras; 7. FG-homomorphisms; 8. Mashcke’s theorem; 9. Schur’s lemma; 10. Irreducible modules and the group algebra; 11. More on the group algebra; 12. Conjugacy classes; 13. Characters; 14. Inner products of characters; 15. The number of irreducible characters; 16. Character tables and orthogonality relations; 17. Normal subgroups and lifted characters; 18. Some elementary character tables; 19. Tensor products; 20. Restriction to a subgroup; 21. Induced modules and characters; 22. Algebraic integers; 23. Real representations; 24. Summary of properties of character tables; 25. Characters of groups of order pq; 26. Characters of some p-groups; 27. Character table of the simple group of order 168; 28. Character table of GL(2,q); 29. Permutations and characters; 30. Applications to group theory; 31. Burnside’s theorem; 32. An application of representation theory to molecular vibration.
ISBN: 0-521-81205-4
Binding: Hardback
ISBN: 0-521-00392-X
Binding: Paperback
Pages: 472
Weight: 0kg
Figures: 28 line diagrams 163 tables
available from October 2001
Frank S. Levin
An Introduction to Quantum Theory
Description
Underpinning the axiomatic formulation of quantum theory presented in this undergraduate textbook is a review of early experiments, a comparison of classical and quantal terminology, a Schroedinger-equation treatment of the one-dimensional quantum box, and a survey of relevant mathematics. Among the many concepts comprehensively discussed are: operators; state vectors and wave functions; experimental observables; classical/quantal connections; and symmetry properties. The theory is applied to a wide variety of systems including the non-relativistic H-atom, external electromagnetic fields, and spin _. Collisions are described using wave packets. Various time-dependent and time-independent approximations are discussed; applications include electromagnetic transition rates and corrections to the H-atom energies. The final chapter deals with identical-particle symmetries and their application to the He atom, the Periodic Table and diatomic molecules. There are also brief treatments of advanced subjects such as gauge invariance and hidden variables.
Chapter Contents
Preface; Part I. Introductory: 1. The need for a non-classical description of microscopic phenomena; 2. Classical concepts and quantal inequivalencies; 3. Introducing quantum mechanics: a comparison of the classical stretched string and the quantal box; 4. Mathematical background; Part II. The Central Concepts: 5. The postulates of quantum mechanics; 6. Applications of the postulates: bound states in one dimension; 7. Applications of the postulates: continuum states in one dimension; 8. Quantal/classical connections; 9. Commuting operators, quantum numbers, symmetry properties; Part III. Systems with Few Degrees of Freedom: 10. Orbital angular momentum; 11. Two-particle systems, potential-well bound state problems; 12. Electromagnetic fields; 13. Intrinsic spin, two-state systems; 14. Generalized angular momentum and the coupling of angular momenta; 15. Three-dimensional continuum states/scattering; Part IV. Complex Systems: 16. Time-dependent approximation methods; 17. Time-independent approximation methods; 18. Many degrees of freedom: atoms and molecules; Appendix A. Elements of probability theory; Appendix B. Fourier series and integrals; Appendix C. Solution of Legendre's equation; Appendix D. Fundamental and derived quantities, conversion factors; References.
ISBN: 0-521-59161-9
Binding: Hardback
ISBN: 0-521-59841-9
Binding: Paperback -
Pages: 816
Figures: 263 line diagrams 2 tables
available from December 2001
Glenn Fulford, Philip Broadbridge
Industrial Mathematics
Australian Mathematical Society Lecture Series
Description
The focus in this text is on mathematical modelling stimulated by contemporary industrial problems involving heat conduction and mass diffusion. These include continuous metal casting, laser drilling, spontaneous combustion of industrial waste, water filtration and crop irrigation. The industrial problems prove to be an excellent setting for the introduction and reinforcement of modelling skills, equation solving techniques, qualitative understanding of partial differential equations and their dynamical properties. Mathematical topics include setting up partial differential equations and boundary conditions, dimensional analysis, scaling, perturbation expansions, boundary valuer problems, Fourier series, symmetry reductions, Stefan problems and bifurcations. For students of mathematics, engineering, or any other related discipline, this will be a great introduction to modelling the real world.
Chapter Contents
1. Preliminaries; 2. Case study: continuous casting; 3. Case study: water filtration; 4. Case study: laser drilling; 5. Case study: factory fires; 6. Case study: irrigation; 7. Conclusions.
ISBN: 0-521-80717-4
Binding: Hardback
ISBN: 0-521-00181-1
Binding: Paperback
Pages: 220
available from January 2002
Edited by Andrew Pressley
Quantum Groups and Lie Theory
London Mathematical Society Lecture Note Series, vol.290.
Contributors
Susumu Ariki, Edwin Beggs, Roger Carter, Robert Marsh, Vyjayanthi Chari, Andrew Pressley, Bernhard Drabant, Pavel Etingof, Olivier Schiffmann, K. R. Goodearl, Iain Gordon, Jintai Ding, Timothy J. Hodges, Shahn Majid, Ian M. Musson, Deepak Parashar, Roger J. McDermott, Hans Wenzl
Description
Since its genesis in the early 1980s, the subject of quantum groups has grown rapidly. By the late 1990s most of the foundational issues had been resolved and many of the outstanding problems clearly formulated. To take stock and to discuss the most fruitful directions for future research many of the world's leading figures in this area met at the Durham Symposium on Quantum Groups in the summer of 1999, and this volume provides an excellent overview of the material presented there. It includes important surveys of both cyclotomic Hecke algebras and the dynamical Yang-Baxter equation. Plus contributions which treat the construction and classification of quantum groups or the associated solutions of the quantum Yang-Baxter equation. The representation theory of quantum groups is discussed, as is the function algebra approach to quantum groups, and there is a new look at the origins of quantum groups in the theory of integrable systems.
Chapter Contents
Introduction; 1. Lectures on cyclotomic Hecke algebras Susumu Ariki; 2. An introduction to group doublecross products and some uses Edwin Beggs; 3. Canonical bases and piecewise-linear combinatorics Roger Carter and Robert Marsh; 4. Integrable and Weyl modules for quantum affine sl2 Vyjayanthi Chari and Andrew Pressley; 5. Notes on balanced categories and Hopf algebras Bernhard Drabant; 6. Lectures on the dynamical Yang-Baxter equations Pavel Etingof and Olivier Schiffmann; 7. Quantized primitive ideal spaces as quotients of affine algebraic varieties K. R. Goodearl; 8. Representations of semisimple Lie algebras in positive characteristic and quantum groups at roots of unity Iain Gordon; 9. The Yang-Baxter equation for operators on function fields Jintai Ding and Timothy J. Hodges; 10. Noncommutative differential geometry and twisting of quantum groups Shahn Majid; 11. Finite quantum group and pointed Hopf algebras Ian M. Musson; 12. On some two parameter quantum and Jordanian deformations, and their coloured extensions Deepak Parashar and Roger J. McDermott; 13. Tensor categories and braid representations Hans Wenzl.
ISBN: 0-521-01040-3
Binding: Paperback
Pages: 228
Figures: 22 line diagrams