Volume II focuses on the optimal control problem over a finite time interval for hyperbolic dynamical systems. The chapters consider some abstract models, each motivated by a particular canonical hyperbolic dynamics, and present numerous new results.

This self-contained account of the main results in large deviation theory includes recent developments and emphasizes the Freidlin-Wentzell results on small random perturbations. Metastability is described on physical grounds, followed by the development of more exacting approaches to its description. The first part of the book then develops such pertinent tools as the theory of large deviations which is used to provide a physically relevant dynamical description of metastability. Written for graduate students, this book affords an excellent route into contemporary research as well.

This second volume in a two-volume set provides a complete self-contained proof of the classification of geometries associated with sporadic simple groups: Petersen and tilde geometries. It contains a study of the representations of the geometries under consideration in GF(2)-vector spaces as well as in some non-Abelian groups. The central part is the classification of the amalgam of maximal parabolics, associated with a flag transitive action on a Petersen or tilde geometry. By way of their systematic treatment of group amalgams, the authors establish a deep and important mathematical...

Ticciati's approach to quantum field theory falls between building a mathematical model of the subject and presenting the mathematics that physicists actually use. It begins with the need to combine special relativity and quantum mechanics and culminates in a basic understanding of the standard model of electroweak and strong interactions. The book is divided into five parts: canonical quantization of scalar fields, Weyl, Dirac and vector fields, functional integral quantization, the standard model of the electroweak and strong interactions, renormalization. This should be a useful reference...

One century after Hilbert constructed the first example of a non-classical affine plane, this book aims to summarize all the major results about geometries on surfaces. Acting both as a reference and a monograph, the authors have included detailed sections on what is known as well as outlining problems that remain to be solved. There are sections on classical geometries, methods for constructing non-classical geometries and classifications and characterizations of geometries. This work is related to a host of other fields including approximation, convexity, differential geometry topology and...

This treatise covers most of the known results on reducibility of polynomials over arbitrary fields, algebraically closed fields, and finitely generated fields. The author includes several theorems on reducibility of polynomials over number fields that are either totally real or complex multiplication fields. Some of these results are based on the recent work of E. Bombieri and U. Zannier, presented here by Zannier in an appendix. The book also treats other subjects such as Ritt's theory of composition of polynomials, and properties of the Mahler measure and concludes with a bibliography of...

Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes. It is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient. The subject overlaps with convex geometry and employs many tools from that area, including some formulas from integral geometry. It also has connections to discrete tomography, geometric probing in robotics and to stereology. This comprehensive study provides a rigorous treatment of the subject. Although...

This second edition of the first comprehensive, accessible account of the subject is intended for a diverse audience: graduate students who wish to learn the subject, researchers in the various fields of application who want to concentrate on certain theoretical aspects, and specialists who need a thorough reference work. For the second edition, the authors have greatly expanded the bibliography to ensure that it is comprehensive and up-to-date, and have also added an appendix surveying research since the first edition. A list of exercises and open problems ends each chapter.

Here is a lucid and comprehensive introduction to the differential geometric study of partial differential equations (PDE). The first book to present substantial results on local solvability of general and nonlinear PDE systems without using power series techniques, it describes a general approach to PDE systems based on ideas developed by Lie, Cartan and Vessiot. The central theme is the exploitation of singular vector field systems and their first integrals. These considerations naturally lead to local Lie groups, Lie pseudogroups and the equivalence problem, all of which are covered in...

Asymptotics and Mellin-Barnes Integrals provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behavior of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic...