Series: Trends in Logic , Vol. 27
2008, Approx. 600 p., Hardcover
ISBN: 978-1-4020-8621-2
Due: August 2008
A Geometry of Approximation addresses Rough Set Theory, a field of interdisciplinary research first proposed by Zdzislaw Pawlak in 1982, and focuses mainly on its logic-algebraic interpretation. The theory is embedded in a broader perspective that includes logical and mathematical methodologies pertaining to the theory, as well as related epistemological issues. Any mathematical technique that is introduced in the book is preceded by logical and epistemological explanations. Intuitive justifications are also provided, insofar as possible, so that the general perspective is not lost.
Such an approach endows the present treatise with a unique character. Due to this uniqueness in the treatment of the subject, the book will be useful to researchers, graduate and pre-graduate students from various disciplines, such as computer science, mathematics and philosophy. It features an impressive number of examples supported by about 40 tables and 230 figures. The comprehensive index of concepts turns the book into a sort of encyclopaedia for researchers from a number of fields.
A Geometry of Approximation links many areas of academic pursuit without losing track of its focal point, Rough Sets.
Preface.- Glossary of terms.- Introduction.- 1. A Mathematics of Perception.- 2. The Logico-algebraic Theory of Rough Sets.- 3. The Modal Logic of Rough Sets.- 4. A Relational Approach to Rough Sets.- 5. A Dialogical Approach.- Index.- Bibliography.
Series: Grundlehren der mathematischen Wissenschaften , Vol. 337
2008, Approx. 630 p. 5 illus., Hardcover
ISBN: 978-3-540-69490-8
Due: October 2008
The purpose of this book is to give a comprehensive exposition of the theory of pointwise multipliers acting in pairs of spaces of differentiable functions. The theory was essentially developed by the authors during the last thirty years and the present volume is mainly based on their results.
Part I is devoted to the theory of multipliers and encloses the following topics: trace inequalities, analytic characterization of multipliers, relations between spaces of Sobolev multipliers and other function spaces, maximal subalgebras of multiplier spaces, traces and extensions of multipliers, essential norm and compactness of multipliers, and miscellaneous properties of multipliers.
Part II concerns several applications of this theory: continuity and compactness of differential operators in pairs of Sobolev spaces, multipliers as solutions to linear and quasilinear elliptic equations, higher regularity in the single and double layer potential theory for Lipschitz domains, regularity of the boundary in $L_p$-theory of elliptic boundary value problems, and singular integral operators in Sobolev spaces.
Introduction.- Part I. Description and Properties of Multipliers.- Part II. Applications of Multipliers to Differential and Integral Operators.- References.- List of Symbols.- Subject Index.
Series: Grundlehren der mathematischen Wissenschaften , Vol. 338
2008, Approx. 1005 p., Hardcover
ISBN: 978-3-540-71049-3
Due: September 24, 2008
At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results.
PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.
Introduction.- Qualitative Description of Optimal Transport.- Optimal Transport and Riemannian Geometry.- Synthetic Treatment of Ricci Curvature.- Conclusions and Open Problems.
Series: Lecture Notes in Mathematics , Vol. 1951
2008, Approx. 160 p., Softcover
ISBN: 978-3-540-85030-4
Due: September 24, 2008
Abstract topological tools from generalized metric spaces are applied in this volume to the construction of locally uniformly rotund norms on Banach spaces. The book offers new techniques for renorming problems, all of them based on a network analysis for the topologies involved inside the problem.
Maps from a normed space X to a metric space Y, which provide locally uniformly rotund renormings on X, are studied and a new frame for the theory is obtained, with interplay between functional analysis, optimization and topology using subdifferentials of Lipschitz functions and covering methods of metrization theory. Any one-to-one operator T from a reflexive space X into c0 (T) satisfies the authors' conditions, transferring the norm to X. Nevertheless the authors' maps can be far from linear, for instance the duality map from X to X* gives a non-linear example when the norm in X is Frechet differentiable.
This volume will be interesting for the broad spectrum of specialists working in Banach space theory, and for researchers in infinite dimensional functional analysis
1. Introduction.- 2. Sigma-continuous and Co-sigma continuous maps.- 3. Generalized metric spaces and Locally Uniformly Rotund Renormings.- 4. Sigma-slicely continuous maps.- 5. Some Applications.- 6. Some Open Problems.- References, Index, and List of Symbols.
Series: Lecture Notes in Mathematics , Vol. 1959
2008, Approx. 280 p., Softcover
ISBN: 978-3-540-70564-2
Due: September 10, 2008
In this volume, the authors construct a theory of weights on the log crystalline cohomologies of families of open smooth varieties in characteristic p>0, by defining and constructing four filtered complexes. Fundamental properties of these filtered complexes are proved, in particular the p-adic purity, the functionality of three filtered complexes, the weight-filtered base change formula, the weight-filtered Kunneth formula, the weight-filtered Poincare duality, and the E2-degeneration of p-adic weight spectral sequences. In addition, the authors state some theorems on the weight filtration and the slope filtration on the rigid cohomology of a separated scheme of finite type over a perfect field of characteristic p>0.
1. Preliminaries on filtered derived categories and topoi.- 2. Weight filtrations on log crystalline cohomologies.- 3. Weight filtrations and slope filtrations on rigid cohomologies (summary).