Aliprantis, Charalambos D., Burkinshaw, Owen
Positive Operators
2006, XIX, 376 p., Hardcover.
ISBN: 1-4020-5007-0
Due: August 2006
About this book
Reprinted by popular demand, this monograph presents a
comprehensive study of positive operators between Riesz spaces
and Banach lattices. Since the first publication of this book, (Academic
Press, 1985), the subject of positive operators and Riesz spaces
has found many applications in several disciplines, including
social sciences and engineering. It is well known that many
linear operators between Banach spaces arising in classical
analysis are in fact positive operators. Therefore we study here
positive operators in the setting of Riesz spaces and Banach
lattices and from both the algebraic and topological points of
view. Special emphasis is given to the compactness properties of
positive operators and their relations to the order structures of
the spaces the operators are acting upon. In order to make the
book as self-sufficient as possible, some basic results from the
theory of Riesz spaces and Banach lattices are included with
proofs where necessary. However, familiarity with the elementary
concepts of real analysis and functional analysis is assumed. The
book is divided into five chapters, each consisting of nineteen
sections all ending with exercises designed to supplement and
illustrate the material.
Table of contents
Dedication. Foreword. Historical Foreword. Preface.
Acknowledgements. List of Special Symbols.- 1. The Order
Structure of Positive Operators.- 2. Components, Homomorphisms,
and Orthomorphisms.- 3. Topological Considerations.- 4. Banach
Lattices.- 5. Compactness Properties of Positive Operators.-
Bibliography. Monographs.- Index.
Boissonnat, Jean-Daniel; Teillaud, Monique (Eds.)
Effective Computational Geometry for Curves and Surfaces
Series: Mathematics and Visualization
2006, Approx. 360 p., Hardcover.
ISBN: 3-540-33258-8
Due: September 2006
About this book
The intent of this book is to settle the foundations of non-linear
computational geometry. It covers combinatorial data structures
and algorithms, algebraic issues in geometric computing,
approximation of curves and surfaces, and computational topology.
Each chapter provides a state of the art, as well as a tutorial
introduction to important concepts and results. The focus is on
methods which are both well founded mathematically and efficient
in practice.
References to open source software and discussion of potential
applications of the presented techniques are also included.
This book can serve as a textbook on non-linear computational
geometry. It will also be useful to engineers and researchers
working in computational geometry or other fields, like
structural biology, 3-dimensional medical imaging, CAD/CAM,
robotics, and graphics
Table of contents
Lau, Dietlinde
Function Algebras on Finite Sets
Basic Course on many-valued Logic and Clone Theory
Series: Springer Monographs in Mathematics
2006, XIV, 668 p., 42 illus., Hardcover.
ISBN: 3-540-36022-0
Due: August 2, 2006
About this book
Functions, which are defined on finite sets, occur in almost all
fields of mathematics. For more than 80 years algebras whose
universes are such functions (so-called function algebras), have
been intensively studied.
This book gives a broad introduction to the theory of function
algebras and leads to the cutting edge of research. To
familiarize the reader from the very beginning on with the
algebraic side of function algebras the more general concepts of
the Universal Algebra is given in the first part of the book. The
second part on fuction algebras covers the following topics:
Galois-connection between function algebras and relation
algebras, completeness criterions, clone theory.
This book is an insdispensible source on function algebras for
graduate students and researchers in mathematical logic and
theoretical computer science.
Lindner, Marko
Infinite Matrices and their Finite Sections
An Introduction to the Limit Operator Method
Series: Frontiers in Mathematics
2006, Approx. 205 p., Softcover.
ISBN: 3-7643-7766-6
Due: August 2006
About this book
This book is concerned with the study of infinite matrices and
their approximation by matrices of finite size. Our framework
includes the simplest, important case where the matrix entries
are numbers, but also the more general case where the entries are
bounded linear operators. This generality ensures that examples
of the class of operators studied - band-dominated operators on
Lebesgue function spaces and sequence spaces - are ubiquitous in
mathematics and physics. The main concepts studied are
invertibility at infinity (closely related to Fredholmness),
limit operators, and the stability and convergence of finite
matrix approximations. Concrete examples are used to illustrate
the results throughout, including discrete Schrodinger operators
and integral and boundary integral operators arising in
mathematical physics and engineering.
This book is written for a broad audience. It will be of
particular importance to those researchers and practitioners
concerned with large finite matrices and their infinite
counterparts, for example in numerical linear algebra and
mathematical physics. More generally, the book will be of
interest to people working in operator theory and applications,
for example studying integral operators or the application of
operator algebra methods. While some basic knowledge of
functional analysis would be helpful, the presentation contains
relevant preliminary material and is largely self-contained.
Table of contents
Markowich, Peter
Applied Partial Differential Equations: A Visual Approach
2006, Approx. 160 p., Hardcover.
ISBN: 3-540-34645-7
Due: August 2006
About this textbook
The book presents topics of science and engineering, which occur
in nature or are part of our daily lives. It describes phenomena
which are modelled by partial differential equations, relating to
physical variables like mass, velocity and energy, etc. to their
spatial and temporal variations.
Typically, these equations are highly nonlinear, in many cases
they are also vectorial systems, and they represent a challenge
even for the most modern and sophisticated mathematical-analytical
and mathematical-numerical techniques.
The topics chosen reflect the longtime scientific interests of
the author. They include flow of fluids and gases, granular
flows, biological processes like pattern formation on animal
skins, kinetics of rarified gases and semiconductor devices. Each
topic is briefly presented in its scientific or engineering
context, followed by an introduction of the mathematical models
in the form of partial differential equations with a discussion
of their basic mathematical properties.
Each chapter is illustrated by a series of high quality
photographs, taken by the author. They demonstrate in an
allegoric way that partial differential equations can be used to
address a large variety of phenomena occuring in and influencing
our daily lives.
Table of contents
Onishchik, Arkadij L., Sulanke, Rolf
Projective and Cayley-Klein Geometries
Series: Springer Monographs in Mathematics
2006, Approx. 370 p., Hardcover.
ISBN: 3-540-35644-4
Due: August 17, 2006
About this book
Projective geometry, and the Cayley-Klein geometries embedded
into it, were originated in the 19th century. It is one of the
foundations of algebraic geometry and has many applications to
differential geometry.
The book presents a systematic introduction to projective
geometry as based on the notion of vector space, which is the
central topic of the first chapter. The second chapter covers the
most important classical geometries which are systematically
developed following the principle founded by Cayley and Klein,
which rely on distinguishing an absolute and then studying the
resulting invariants of geometric objects.
An appendix collects brief accounts of some fundamental notions
from algebra and topology with corresponding references to the
literature.
This self-contained introduction is a must for students,
lecturers and researchers interested in projective geometry.