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Surveys investigations of Banach-space isometries. This volume emphasizes the characterization of isometries and focuses on establishing the type of explicit, canonical form in a variety of settings. It describes the isometries on classical function spaces. It explores isometries on Banach algebras.

Models for the mechanical behavior of porous media introduced more than 50 years ago are still relied upon today, but more recent work shows that they may sometimes violate the laws of thermodynamics. This monograph shows that physical consistency requires a unique description of dynamic processes that involve porous media and that new dynamic variables naturally enter into the large-scale description of porous media. The implications of the physical theory presented in this book are significant, particularly in applications in geophysics and the petroleum industry. The Thermophysics of Porous Media offers a unique opportunity to examine the dynamic role that porosity plays in porous materials.

The interest of these authors lies in explicit, canonical-form characterizations of isometries on Banach spaces, and in this monograph, they explore the topic in the context of classical function spaces. Designed for both experts and beginners in the field, their treatment presents a history of the subject, the important results, and a look at some of the wide variety of methods used in addressing the characterization problem in various types of spaces. The authors faithfully report the results of other researchers' original papers and offer some enlightening clarifications. Each chapter is self-contained and includes notes and remarks that touch upon related results and other approaches not addressed in the main text.

This book offers a systematic presentation of the modern theory of the stability of stochastic differential equations in infinite dimensional spaces - particularly Hilbert spaces. The treatment includes a review of basic concepts and investigation of the stability theory of linear and nonlinear stochastic differential equations and stochastic functional differential equations in infinite dimensions. The final chapter explores topics and applications such as stochastic optimal control and feedback stabilization, stochastic reaction-diffusion, Navier-Stokes equations, and stochastic population dynamics. This book makes up-to-date material accessible and lays the foundation for future advances.

This book presents a systematic, detailed development of approaches to construct ¿ uniformly convergent finite difference schemes for wide classes of singularly perturbed boundary value problems. The first part of the book explores boundary value problems for elliptic and parabolic reaction-diffusion and convection-diffusion equations in n-dimensional domains with smooth and piecewise-smooth boundaries. Containing material published mainly in the last four years, the second section focuses on problems with boundary layers and additional singularities generated by nonsmooth data, unboundedness of the domain, and the perturbation vector parameter.

Since higher order derivatives are useful in many places, nth order derivatives are often defined directly. These derivatives are more general than the ordinary derivative and are useful in many purposes. This book discusses higher order derivatives and the relations among them. It covers higher order generalized derivatives, including Peano derivative, d.l.V.P. derivative, symmetric and unsymmetric Riemann derivative, symmetric and unsymmetric Cesàro derivative, symmetric and unsymmetric Borel derivative, symmetric and unsymmetric LP-derivative, symmetric and unsymmetric Laplace derivative, and Abel derivative.

Details the construction of a Lorentz invariant thermodynamic lattice gas model and shows how the associated nonrelativistic, Galilean invariant model can be used to describe flow in porous media. This work develops the equations of seismic wave propagation in porous media, the associated boundary conditions, and surface waves.

Presents a comprehensive description of various aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. This work systematizes methods for overcoming the difficulties inherent in the solution of hyperbolic systems. It is suitable for those interested in the development of numerical methods.

This text presents a theory of generalized Cauchy-Riemann systems with the order of the polar singularities not less than one and discusses its application to the study of infinitesimal bendings of positive curvature surfaces with an isolated flat point.

Part of the "Pitman Monographs and Surveys in Pure and Applied Mathematics" series, this text examines mathematical problems of classical nonlinear electromagnetic theory.

Examines periodic solutions of impulsive differential equations. Periodic linear impulsive differential equations, the use of the small parameter method in noncritical and critical cases, and the existence of periodic solutions of nonlinear differential equations are discussed.

Focuses on concrete analytic questions, with functional analysis providing the general framework. This work features discussions including radial limits, exceptional sets, zeros, factorization, and the relations between fractional Cauchy transforms and Dirichlet and Besov spaces.

Elastic plates form a class of very important mechanical structures that occur in a wide range of practical applications. This book explores a number of problems encountered in working with elastic plates. It considers various fundamental boundary value problems in conjunction with variational and potential methods for finite and infinite domains.

Presents the theoretical framework for developing methods that allow the treatment of a variety of discontinuous initial and boundary value problems for both ordinary and partial differential equations, in explicit and implicit forms. This work is suitable for researchers in engineering as well as advanced students in these fields.

Includes results that open perspectives on fields in mechanics and their methodological counterparts in mathematics. This work also surveys advances in the areas where mathematics and mechanics interact. It is suitable for applied mathematicians, physicists, scientists and engineers.

Focuses on the principal spectral theory for general time-dependent and random parabolic equations and systems. This book addresses Faber-Krahn inequalities for elliptic and time-periodic problems and extends the linear theory for scalar nonautonomous and random parabolic equations to cooperative systems.

This text describes the development of the theory of J-symmetric operator algebras and representations of *-algebras on indefinite metric spaces in a systematic form. It also covers the application of different techniques from the theory of J-Symmetric representations on Krein spaces.

A monograph that examines a variety of phenomena in which interfaces play a crucial role. It studies developments related to the Marangoni effect, including patterned convection and instabilities, oscillatory/wavy phenomena, and turbulent phenomena.

Hamiltonian fluid dynamics and stability theory work hand-in-hand in a variety of engineering, physics, and physical science fields. This book offers an introduction to Hamiltonian fluid dynamics and describes aspects of hydrodynamic stability theory within the context of the Hamiltonian formalism.

Inverse boundary problems are an area of applied mathematics with applications throughout physics and the engineering sciences. This book considers the following: Can the unknown coefficients of an elliptic partial differential equation be determined from the eigen values and the boundary values of the eigen functions?

Progress in the field of SCQM (supersymmetric classical and quantum mechanics) has been dramatic and the literature continues to grow. This monograph offers an overview of the field and summarizes the major developments over the years. It provides both a review of the literature and an exposition of the underlying SCQM principles.

Presents the ray method for studying nonlinear wave propagation in fluid dynamics and plasma physics. Topics covered are shock wave propagation, the derivation of model equations in several dimensions (dissipative and dispersive) and the interaction of waves, both hyperbolic and dispersive.

Part of the "Pitman Monographs in Pure and Applied Mathematics" series, this text presents various problems of partial differential equations. It covers elliptic systems degenerated at the boundary, overdetermined boundary value problems and initial boundary value problems.

Focuses on canonical-form characterizations of isometries on Banach spaces. This monograph explores the topic in the context of vector-valued function spaces and operator spaces. It looks at some of the wide variety of methods used in addressing the characterization problem in various types of spaces.

Presents most of the developments in continuous matrix variate distribution theory. This work investigates the range of matrix variate distributions, including: matrix variate normal distribution; Wishart distribution; Matrix variate t-distribution; Matrix variate beta distribution; F-distribution; and, Matrix variate Dirichlet distribution.

The computational power available means that practitioners can find accurate approximations to the solutions of more sophisticated mathematical models. This book describes a class of techniques that fulfill this need by providing closed-form solutions to many boundary value problems that arise in science and engineering.

This text deals with the two-dimensional Riemann problem for Euler equations in gas dynamics and its mathematical simplification. For Euler equations it is classified into 18 cases according to the different combinations of four elementary plane waves emanated by initial discontinuities.

Often perceived as dry and abstract, homological algebra has important applications in a number of important areas, including ring theory, group theory, representation theory, and algebraic topology and geometry. Suitable for graduate students, this book presents the material in an easy-to-understand manner with various examples and exercises.