Series: Progress in Probability , Vol. 61
2009, Approx. 350 p., Hardcover
ISBN: 978-3-7643-8999-4
Due: April 2009
This book contains a collection of texts ranging from a basic introduction to the mathematical theory of spin glasses to state-of-the-art reports on current research, written by leading experts in the field. It provides a unique single reference volume that will guide the novice into the field and present an overview of recent result to the experts. The subject matter covers mean field theory of spin glasses, short range spin glasses as well as other models of statistical mechanics in random media, such as polymers in disordered potentials. Besides equilibrium statistical mechanics, nonequilibrium properties such as ageing are addressed. The focus of the book is on mathematically rigorous aspects of these topics.
The book is intended for graduate students and researchers.
Introduction.- Main lectures.- Further lectures.
Series: Applied Mathematical Sciences , Vol. 169
2009, X, 281 p. 8 illus., 2 in color., Hardcover
ISBN: 978-1-4020-9612-9
Due: April 30, 2009
A control system is called bilinear if it is described by linear differential equations in which the control inputs appear as coefficients. The study of bilinear control systems began in the 1960s and has since developed into a fascinating field, vital for the solution of many challenging practical control problems. Its methods and applications cross inter-disciplinary boundaries, proving useful in areas as diverse as spin control in quantum physics and the study of Lie semigroups.
The first half of the book is based upon matrix analysis, introducing Lie algebras and the Campbell-Baker-Hausdorff Theorem. Individual chapters are dedicated to topics such as discrete-time systems, observability and realization, examples from science and engineering, linearization of nonlinear systems, and input-output analysis.
Written by one of the leading researchers in the field in a clear and comprehensible manner and laden with proofs, exercises and Mathematica scripts, this involving text will be a vital and thorough introduction to the subject for first-year graduate students of control theory. It will also be of great value to academics and researchers with an interest in matrix analysis, Lie algebra, and semigroups.
1. Introduction.- 2. Lie Algebras, Lie Groups.- 3. Systems in Drift.- 4. Discrete Time Bilinear Systems.- 5. Systems with Outputs.- 6. Examples.- 7. Linearization.- 8. Input Structures.- A. Matrix Algebra.- B. Lie Algebras and Groups.- C. Algebraic Geometry.- D. Transitive Lie Algebras.- References.- Index.
Series: Progress in Mathematics , Vol. 274
2009, Approx. 510 p., Hardcover
ISBN: 978-3-7643-9997-9
Due: April 2009
This book contributes to important questions in the representation theory of finite groups over fields of positive characteristic ? an area of research initiated by Richard Brauer sixty years ago with the introduction of the blocks of characters. On the one hand, it introduces and develops the abstract setting of the Frobenius categories ? also called the Saturated fusion systems in the literature ? created by the author fifteen years ago for a better understanding of what was loosely called the local theory of a finite group around a prime number p or, later, around a Brauer block, and for the purpose of an eventual classification ? a reasonable concept of simple Frobenius category arises.
On the other hand, the book develops this abstract setting in parallel with its application to the Brauer blocks, giving the detailed translation of any abstract concept in the particular context of the blocks. One of the new features in this direction is a framework for a deeper understanding of one of the central open problems in modular representation theory, known as Alperinfs Weight Conjecture (AWC). Actually, this new framework suggests a more general form of AWC, and a significant result of the book is a reduction theorem of this form of AWC to quasi-simple groups.
Although this book is a research monograph, all the arguments are widely developed to make it accessible to the interested graduate students and, at the same time, to put them on the verge of the research on this new subject: the third part of the book on the localities associated to a Frobenius category gives some insight on the open question about the existence and the uniquenes of a perfect locality ? also called centric linking system in the literature. We have developed a long introduction to explain our purpose and to provide a guideline for the reader throughout the twenty four sections. A systematic appendix on the cohomology of categories completes the book
Introduction.- 1. General notation and quoted results.- 2. Frobenius P-categories: the first definition.- 3. The Frobenius P-category of a block.- 4. Nilcentralized and selfcentralizing objects in Frobenius P-categories.- 5. Alperin fusions in Frobenius P-categories.- 6. Exterior quotient of a Frobenius P-category over the selfcentralizing objects.- 7 Nilcentralized and selfcentralizing Brauer pairs in blocks.- 8. Decompositions for Dade P-algebras.- 9. Polarizations for Dade P-algebras.- 10. A gluing theorem for Dade P-algebras.- 11. The nilcentralized chain k*-functor of a block.- 12. Quotients and normal subcategories in Frobenius P-categories.- 13. The hyperfocal subcategory of a Frobenius P-category.- 14. The Grothendieck groups of a Frobenius P-category.- 15. Reduction results for the Grothendieck groups.- 16. The local-global question: reduction to the simple groups.- 17. Localities associated with Frobenius P-categories.- 18. The localizers in a Frobenius P-category.- 19 Solvability for Frobenius P-categories.- 20 A perfect F-locality from a perfect Fsc-locality.- 21. Frobenius P-categories: the second definition.- 22. The basic F-locality.- 23. Narrowing the basic Fsc-locality.- 24. Looking for a perfect Fsc-locality.- Appendix.- References.- Index.
Series: Progress in Mathematics , Vol. 275
2009, Approx. 500 p., Hardcover
ISBN: 978-3-7643-9899-6
Due: May 2009
The central object of the book is a subtle scalar Riemannian curvature quantity in even dimensions which is called Bransonfs Q-curvature. It was introduced by Thomas Branson about 15 years ago in connection with an attempt to systematise the structure of conformal anomalies of determinants of conformally covariant differential operators on Riemannian manifolds. Since then, numerous relations of Q-curvature to other subjects have been discovered, and the comprehension of its geometric significance in four dimensions was substantially enhanced through the studies of higher analogues of the Yamabe problem.
The book attempts to reveal some of the structural properties of Q-curvature in general dimensions. This is achieved by the development of a new framework for such studies. One of the main properties of Q-curvature is that its transformation law under conformal changes of the metric is governed by a remarkable linear differential operator: a conformally covariant higher order generalization of the conformal Laplacian. In the new approach, these operators and the associated Q-curvatures are regarded as derived quantities of certain conformally covariant families of differential operators which are naturally associated to hypersurfaces in Riemannian manifolds. This method is at the cutting edge of several central developments in conformal differential geometry in the last two decades (Fefferman-Graham ambient metrics, spectral theory on Poincar\'e-Einstein spaces, tractor calculus, Cartan geometry). In addition, the present theory is strongly inspired by the realization of the idea of holography in the AdS/CFT-duality. This motivates to speak here about holographic descriptions of Q-curvature. The text is self-contained and accessible by postgraduate students.
Preface.- 1. Introduction.- 2. Spaces, Actions, Representations and Curvature.- 3. Powers of the Laplacian, Q-Curvature and Scattering.- 4. Paneitz Operator and Paneitz Curvature.- 5. Intertwining Families.- 6. Conformally Covariant Families.- Bibliography.- Index.
Series: Trends in Mathematics
2009, Approx. 500 p., Hardcover
ISBN: 978-3-7643-9905-4
Due: June 2009
Our knowledge of objects of complex and potential analysis has been enhanced recently by ideas and constructions of theoretical and mathematical physics, such as quantum field theory, nonlinear hydrodynamics, material science. These are some of the themes of this refereed collection of papers, which grew out of the first conference of the European Science Foundation Networking Programme 'Harmonic and Complex Analysis and Applications' held in Norway 2007.
Preface.- Contributions by Helene Airault, Andrei Bogatyrev, Ovidiu Calin, Der-Chen Chang, A.S. Demidov, C. D. Fassnacht, Konstantin Fedorovskiy, Stephen J. Gardiner, Anatoly Golberg, Pavel Gumenyuk, Vladimir Gutlyanskii, Ruben A. Hidalgo, Vojkan Jaksic, Nguyen Thanh Nguyet, Henrik Kalisch, Anatolii A. Karatsuba, Ekatherina A. Karatsuba, C. R. Keeton, D. Khavinson, Igor Kondrashuk, Anatoly Kotikov, Samuel Krushkal, Alexander Kuznetsov, E. Liflyand, Jean-Pierre Loheac, Irina Markina, Xavier Massaneda, Marco Merkli, Yuri A. Neretin, Joaquim Ortega-Cerd`a, Myriam Ounaes, Philippe Poulin, Dmitri Prokhorov, Alexander Rashkovskii, Tomas Sjoedin, Alexander Yu. Solynin, S. Tikhonov, Xavier Tolsa, Alexander Vasil'ev.
Series: Springer Texts in Statistics
2009, Hardcover
ISBN: 978-0-387-93838-7
Due: September 2009
A broad range of material is covered in this book, essential for students of theoretical statistics.
This book is based on a three semester sequence of core courses on theoretical statistics.
Introduction.- Probability and measure: a gentle introduction.- Exponential families.- Sufficiency, completeness, and ancillarity.- Unbiased estimation.- Curved exponential families.- Conditional distributions.- Variance bounds and information.- Bayesian estimation.- Large sample theory.- Estimating equations and maximum likelihood.- Equivariant estimation.- Empirical bayes and shrinkage estimators.- Hypothesis testing.- Optimal tests in higher dimensions.- General linear model.- Asymptotic optimality.- Large sample theory for likelihood ratio tests.- Nonparametric regression.- Weak convergence in metric spaces.- Weak convergence in applications.- Bootstrap methods.- Sequential analysis.- Solutions to selected problems.