These days, the term Noncommutative Dynamics has several interpretations. It is used in this book to refer to a set of phenomena associated with the dynamical evo- lution of quantum systems of the simplest kind that involve rigorous mathematical structures associated with infinitely many degrees of freedom. The dynamics of such a system is represented by a one-parameter group of automorphisms of a non- commutative algebra of observables, and we focus primarily on the most concrete case in which that algebra consists of all bounded operators on a Hilbert space. If one introduces a natural...
These days, the term Noncommutative Dynamics has several interpretations. It is used in this book to refer to a set of phenomena associated with the d...
The aim of this monograph is to give a unified account of the classical topics in fixed point theory that lie on the border-line of topology and non- linear functional analysis, emphasizing developments related to the Leray- Schauder theory. Using for the most part geometric methods, our study cen- ters around formulating those general principles of the theory that provide the foundation for many of the modern results in diverse areas of mathe- matics. The main text is self-contained for readers with a modest knowledge of topology and functional analysis; the necessary background material is...
The aim of this monograph is to give a unified account of the classical topics in fixed point theory that lie on the border-line of topology and non- ...
The subject of antenna design, primarily a discipline within electrical en- neering, is devoted to the manipulation of structural elements of and/or the electrical currents present on a physical object capable of supporting such a current. Almost as soon as one begins to look at the subject, it becomes clear that there are interesting mathematical problems which need to be addressed, in the ?rst instance, simply for the accurate modelling of the electromagnetic ?elds produced by an antenna. The description of the electromagnetic ?elds depends on the physical structure and the background...
The subject of antenna design, primarily a discipline within electrical en- neering, is devoted to the manipulation of structural elements of and/or t...
This book is the first serious attempt to gather all of the available theory of "nonharmonic Fourier series" in one place, combining published results with new results by the authors.
This book is the first serious attempt to gather all of the available theory of "nonharmonic Fourier series" in one place, combining published resu...
The present monograph is intended to provide a comprehensive and accessible introduction to the optimization of elliptic systems. This area of mathematical research, which has many important applications in science and technology. has experienced an impressive development during the past two decades. There are already many good textbooks dealing with various aspects of optimal design problems. In this regard, we refer to the works of Pironneau 1984], Haslinger and Neittaanmaki 1988], 1996], Sokolowski and Zolksio 1992], Litvinov 2000], Allaire 2001], Mohammadi and Pironneau 2001],...
The present monograph is intended to provide a comprehensive and accessible introduction to the optimization of elliptic systems. This area of mathema...
This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. It provides a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method.
This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth con...
General relativity is the modern theory of the gravitational ?eld. It is a deep subject that couples ?uid dynamics to the geometry of spacetime through the Einstein equations. The subject has seen a resurgence of interest recently, partlybecauseofthespectacularsatellitedatathatcontinuestoshednewlight on the nature of the universe. . . Einstein's theory of gravity is still the basic theorywehavetodescribetheexpandinguniverseofgalaxies. ButtheEinstein equations are of great physical, mathematical and intellectual interest in their own right. They are the granddaddy of all modern ?eld equations,...
General relativity is the modern theory of the gravitational ?eld. It is a deep subject that couples ?uid dynamics to the geometry of spacetime throug...
This book is meant for an audience of advanced undergraduates and graduate students taking courses on the statistical mechanics approach to turbulent ?ows and on stochastic simulations. It is also suitable for the self-study of professionals involved in the research and modelling of large scale stochastic ?uid ?ows with a substantial vortical component. Several related ideas motivate the approach in this book, namely, the application of equilibrium statistical mechanics to two-dimensional and 2- dimensional ?uid ?ows in the spirit of Onsager 337], and Kraichnan 227], is taken to be a valid...
This book is meant for an audience of advanced undergraduates and graduate students taking courses on the statistical mechanics approach to turbulent ...
This is the first of two books in the Calculus of Variations and Measure Theory where many results, some now classical and others at the forefront of research in the subject, are gathered in a unified, consistent way. Contemporary arguments are used throughout the text, streamlining well-known aspects of the theory, while providing novel contributions. The first book prepares the ground for the second in that it introduces and develops the basic tools in the Calculus of Variations and in Measure Theory needed to address fundamental questions in the treatment of functionals involving...
This is the first of two books in the Calculus of Variations and Measure Theory where many results, some now classical and others at the forefront of ...
Quite simply, this book offers the most comprehensive survey to date of the theory of semiparallel submanifolds. It begins with the necessary background material, detailing symmetric and semisymmetric Riemannian manifolds, smooth manifolds in space forms, and parallel submanifolds. The book then introduces semiparallel submanifolds and gives some characterizations for their class as well as several subclasses. The coverage moves on to discuss the concept of main symmetric orbit and presents all known results concerning umbilic-like main symmetric orbits. With more than 40 published papers...
Quite simply, this book offers the most comprehensive survey to date of the theory of semiparallel submanifolds. It begins with the necessary backg...
