Books in the Chapman & Hall/CRC Research Notes in Mathematics Series series

Presents the theory of growth and continuity envelopes in function spaces. This book includes various concepts that originate from the classical result of the Sobolev embedding theorem, ubiquitous in various areas of functional analysis. It discusses classical spaces, such as Lebesgue and Lorentz, and defines growth and continuity envelopes.

The seminal 1989 work of Douglas and Paulsen in the theory of analytic Hilbert modules precipitated a number of major research efforts. This title reports on the progress made by the authors and others, including the characteristic space theory, rigidity, the equivalence problem, and reproducing Hilbert spaces on n-dimensional complex space.

Presents concepts and basic tools that are needed to explore and exploit the wide-ranging applicability of the quantum integrable systems. This book discusses the applications of integrable systems in statistical mechanics and mathematical physics.

Addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure set of zeroes of a general class of nonlinear operators.

Offers an account of the graph dynamics system SER (Scheduling by Edge Reversal). This book discusses the main applications and properties of SER, provides data from statistics and correlations computed over several graph classes, and gives an overview of the algorithmic aspects of the construction of the catalogue.

Suitable for numerical analysts, this text contains the proceedings of the 18th Dundee Biennial Conference on Numerical Analysis. It covers things ranging from partial differential equations to linear algebra and approximation theory.

Presents the work and results of experts at the forefront of research in mathematics, material sciences, chemical engineering, biology and physics. This work contains the plenary lectures and contributed papers of the 1997 International Interdisciplinary Congress proceedings held in Crete.

Boundary element methods relate to a wide range of engineering applications. This book illustrates the connections between the modeling of applied problems, the derivation and analysis of corresponding boundary integral equations, and their efficient numerical solutions.

A second collection of articles taken from 10 years of the "Twistor Newsletter", produced at the Mathematics Institute, Oxford. It traces the development of twistor theory, and covers topics such as the hypersurface twistors and Cauchy-Riemann structures.

Offers a survey of developments in inverse acoustic and electromagnetic scattering theory. This book uses point sources combined with several far-reaching techniques to obtain qualitative reconstruction methods while addressing questions of uniqueness, stability, and reconstructions for both two-and three-dimensional problems.

Introduces a Morse (index) theory that is easier to use, less technical, and flexible than theories for strongly indefinite functionals. This book presents a self-contained treatment with full proofs of the major results and with applications of the theory to Hamiltonian systems and other areas of research.

Introduces readers to the inherent characteristics of nonlinear DAE systems and the methods used to address their control. This work then discusses the significance of DAE systems to the modeling and control of chemical processes. It presents results on the stabilization and disturbance elimination for a large class of nonlinear DAE systems.

This book provides a new mathematical theory for the treatment of an ample series of spatial problems of electrodynamics, particle physics, quantum mechanics and elasticity theory

Presents the basic techniques of using Lie algebraic concepts to explore the domain of nonlinear integrable systems. This book begins by establishing a practical basis in Lie algebra, including discussions of structure Lie, loop, and Virasor groups, quantum tori and Kac-Moody algebras, and gradation.

When a dynamical system has a large number of parameters it is not possible to get a completely comprehensive picture of all the types of behavior that it may display and one must be content with surveying the system along various corridors of lower dimension

This volume collects the proceedings of conferences given at the University of Metz during the 1992 "Metz Days". Various important topics in partial differential equations are examined: phase transition, evolution problems, bifurcation, stability and parabolic problems.

The index theorem is a central result of modern mathematics and all students of global analysis need to be familiar with it. This edition preserves the brevity of the first edition, but includes new material and reworkings of some of the more difficult arguments.

This text provides a unifying approach to the valuation of different kinds of options, arranged so it presents a natural transition from the theory of optimal stopping problems to the valuation of options. The book also introduces generalized optimal stopping problems.

Despite their importance and the amount of research published on the theory of the Navier-Stokes equations, some very elementary and fundamental questions remain unanswered. This book explores two main topics: the search for mild solutions using the tools of real harmonic analysis, and the 1982 regularity criterion of Caffarelli et al.