Part of Cambridge Monographs on Mathematical Physics
Publication planned for: October 2017
availability: Not yet published - available from October 2017
format: Hardback
isbn: 9781107147898
A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravities, and therefore providing graduates and researchers with an invaluable resource on this important topic in gravitational physics.
Preface
1. Introduction
2. Point particles
3. Dust solutions
4. AdS cyclic symmetric stationary solutions
5. Perfect fluid static stars
6. Static perfect fluid stars with ĩ
7. Hydrodynamic equilibrium
8. Stationary perfect fluid with ĩ
9. Friedmann?Robertson?Walker cosmologies
10. Dilaton-inflaton FRW cosmologies
11. Einstein?Maxwell solutions
12. Nonlinear electrodynamics black hole
13. Dilaton minimally coupled to gravity
14. Dilaton non-minimally coupled to gravity
15. Low energy 2+1 string gravity
16. Topologically massive gravity
17. Bianchi type spacetimes in TMG
18. Petrov type N wave metrics
19. Kundt spacetimes in TMG
20. Cotton tensor in Riemannian spacetimes
References
Index.
August 4, 2015 by Chapman and Hall/CRC
Reference - 568 Pages - 86 B/W Illustrations
ISBN 9781482248197
Series: Chapman & Hall/CRC Biostatistics Series
paperback
ISBN 9781138894044
Explores the Bayesian approach to the analysis of repeated measures
Includes the necessary introductory material for understanding Bayesian inference and WinBUGS
Incorporates many real examples throughout as well as exercises at the end of each chapter
Provides the WinBUGS code online so that readers can implement the code as they progress through the book
Analyze Repeated Measures Studies Using Bayesian Techniques
Going beyond standard non-Bayesian books, Bayesian Methods for Repeated Measures presents the main ideas for the analysis of repeated measures and associated designs from a Bayesian viewpoint. It describes many inferential methods for analyzing repeated measures in various scientific areas, especially biostatistics.
The author takes a practical approach to the analysis of repeated measures. He bases all the computing and analysis on the WinBUGS package, which provides readers with a platform that efficiently uses prior information. The book includes the WinBUGS code needed to implement posterior analysis and offers the code for download online.
Accessible to both graduate students in statistics and consulting statisticians, the book introduces Bayesian regression techniques, preliminary concepts and techniques fundamental to the analysis of repeated measures, and the most important topic for repeated measures studies: linear models. It presents an in-depth explanation of estimating the mean profile for repeated measures studies, discusses choosing and estimating the covariance structure of the response, and expands the representation of a repeated measure to general mixed linear models. The author also explains the Bayesian analysis of categorical response data in a repeated measures study, Bayesian analysis for repeated measures when the mean profile is nonlinear, and a Bayesian approach to missing values in the response variable.
EMS Series of Congress Reports
ISBN print 978-3-03719-175-0,
May 2017, 597 pages, hardcover, 16.5 x 23.5 cm.
This volume is dedicated to Pavel Exner on the occasion of his 70th anniversary. It collects contributions by numerous scientists with expertise in mathematical physics and in particular in problems arising from quantum mechanics. The questions addressed in the contributions cover a large range of topics. A lot of attention was paid to differential operators with zero range interactions, which are often used as models in quantum mechanics. Several authors considered problems related to systems with mixed-dimensions such as quantum waveguides, quantum layers and quantum graphs. Eigenvalues and eigenfunctions of Laplace and Schrodinger operators are discussed too, as well as systems with adiabatic time evolution. Although most of the problems treated in the book have a quantum mechanical background, some contributions deal with issues which go well beyond this framework; for example the Cayley?Hamilton theorem, approximation formulae for contraction semigroups or factorization of analytic operator-valued Fredholm functions. As for the mathematical tools involved, the book provides a wide variety of techniques from functional analysis and operator theory.
Altogether the volume presents a collection of research papers which will be of interest to any active scientist working in one of the above mentioned fields.
Keywords: Schrodinger operators, point interactions, metric graphs, quantum
waveguides, eigenvalue estimates, operator-valued functions, Cayley-Hamilton
theorem, adiabatic theorem
EMS Textbooks in Mathematics
ISBN print 978-3-03719-174-3
May 2017, 629 pages, hardcover, 16.5 x 23.5 cm.
This is the second of three volumes which will provide a comprehensive introduction to the modern representation theory of Frobenius algebras. The first part of the book is devoted to fundamental results of the representation theory of finite dimensional hereditary algebras and their tilted algebras, which allow to describe the representation theory of prominent classes of Frobenius algebras.
The second part is devoted to basic classical and recent results concerning the Hochschild extensions of finite dimensional algebras by duality bimodules and their module categories. Moreover, the shapes of connected components of the stable Auslander-Reiten quivers of Frobenius algebras are described.
The only prerequisite in this volume is a basic knowledge of linear algebra and some results of the fi rst volume. It includes complete proofs of all results presented and provides a rich supply of examples and exercises.
The text is primarily addressed to graduate students starting research in the representation theory of algebras as well mathematicians working in other fi elds.
Keywords: Algebra, module, bimodule, representation, quiver, ideal, radical, simple module, semisimple module, uniserial module, projective module, injective module, tilting module, hereditary algebra, tilted algebra, Frobenius algebra, symmetric algebra, selfinjective algebra, Hochschild extension algebra, category, functor, torsion pair, projective dimension, injective dimension, global dimension, Euler form, Grothendieck group, irreducible homomorphism, almost split sequence, Auslander-Reiten translation, Auslander-Reiten quiver, stable equivalence, syzygy module, duality bimodule, Hochschild extension
Texts and Readings in Mathematics/74
2017, 9789386279637, 180 pages, Hard cover
trim 74 cover n This book combines the spirit of a textbook and of a monograph on the topic of Semigroups and their applications. It is expected to have potential users across a broad spectrum including operator theory, partial differential equations, harmonic analysis, probability and statistics and classical and quantum mechanics. A reasonable amount of familiarity with real analysis, including the Lebesgue-integration theory, basic functional analysis and bounded linear operators is assumed. However, any discourse on a theory of semigroups needs an introduction to unbounded linear operators, some elements of which have been included in the Appendix, along with the basic ideas of the Fourier transform and of Sobolev spaces. The chapters 4 through 6 contain advanced material, not often found in textbooks, but which have many interesting applications such as the Feynman-Kac formula, the central limit theorem and the construction of Markov semigroups. The exercises are given in the text as the topics are developed, so that the interested reader can be persuaded to solve these as a part of learning that topic.
1 Vector-valued functions
2 C0-semigroups
3 Dissipative operators and holomorphic semigroups
4 Perturbation and convergence of semigroups
5 Chernoff's Theorem and its applications
6 Markov semigroups
7 Applications to partial differential equations
Appendix
A.1 Unbounded operators
A.2 Fourier transforms
A.3 Sobolev spaces
References
Index