ISBN: 966-8849-32-9
Pages: 220
Format: 145x215 mm
Cover: hardcover
Abstract:
The present monograph is devoted mostly to general properties of the ball structures, which simultaneously generalize the coarse structures introduced in the large scale geometry by J. Roe as well as the uniform structures. Chapter 1 contains the definition of the ball structures (baleans), provides their different examples and briefly discusses their connections with coarse structures. The topological coarse structures are also considered. The different morphisms of balleans and coarse spaces are defined and some categories of balleans and coarse structures are introduced. Chapter 2 is devoted to relations between the ball structures and metric structures, important morphisms between metric spaces. Chapter 3 concerns the property of cellularity of balleans and contains the notion of asymptotic dimension of balleans in the spirit of Gromov. It turns out that cellularity can be described in terms of asymptotic dimension zero, which makes it close to the non-Archimedean (ultrametric) spaces. Chapter 4 is devoted to the property of normality. In Chapters 5 and 6 the graph balleans and the group balleans are investigated. In Chapter 7 the functions on balleans which are slowly oscillating with respect to given filter are studied. The counterpart of the Higson corona in the context of balleans is investigated in Chapter 8. Some cardinal invariants of balleans are introduced and discussed in Chapter 9. The concluding Chapter 10 is devoted to the notion of maximality of balleans. Bibliography: 86 items.
Additional Info:
Mathematical Studies: Monograph Series. Volume 12
AUTHORS:
Ihor Protasov, Kyiv University
Michael Zarichnyi, Lviv University and University of Rzesz
2007. VIII, 270 p. w. figs. 24 cm
ISBN: 9783834803191
This is an elementary introduction to the representation theory of real and complex matrix groups. The text is written for students in mathematics and physics who have a good knowledge of differential/integral calculus and linear algebra and are familiar with basic facts from algebra, number theory and complex analysis. The goal is to present the fundamental concepts of representation theory, to describe the connection between them,and to explain some of their background. The focus is on groups which are of particular interest for applications in physics and number theory (e.g. Gell-Mann's eightfold way and theta functions, automorphic forms). The reader finds a large variety of examples which are presented in detail and from different points of view. The examples motivate the general theory well covered already by the existing literature. Hence for complete proofs of most of the essential statements and theorems the reader is often referred to the standard sources. Plenty of exercises are included in the text. Some of these exercises and/or omitted proofs may give a starting point for a bachelor thesis and further studies in a master program.
Autoreninfo
Prof. Dr. Rolf Berndt ist am Mathematischen Seminar der Universitat Hamburg tatig.
This unique book focuses on critical point theory for strongly indefinite functionals in order to deal with nonlinear variational problems in areas such as physics, mechanics and economics. With the original ingredients of Lipschitz partitions of unity of gage spaces (nonmetrizable spaces), Lipschitz normality, and sufficient conditions for the normality, as well as existence-uniqueness of flow of ODE on gage spaces, the book presents for the first time a deformation theory in locally convex topological vector spaces. It also offers satisfying variational settings for homoclinic-type solutions to Hamiltonian systems, Schrödinger equations, Dirac equations and diffusion systems, and describes recent developments in studying these problems. The concepts and methods used open up new topics worthy of in-depth exploration, and link the subject with other branches of mathematics, such as topology and geometry, providing a perspective for further studies in these areas. The analytical framework can be used to handle more infinite-dimensional Hamiltonian systems.
Contents:
Readership: Researchers and graduate students in analysis & differential equations, mathematical physics, geometry & topology, mechanics and control theory.
176pp Pub. date: Aug 2007
ISBN 978-981-270-962-2
Industrial mathematics is evolving into an important branch of mathematics. Mathematicians, in particular in Italy, are becoming increasingly aware of this new trend and are engaged in bridging the gap between highly specialized mathematical research and the emerging demand for innovation from industry. The contributions in this volume provide both R&D workers in industry with a general view of existing skills, and academics with state-of-the-art applications of mathematics to real-world problems, which may also be incorporated in advanced courses.
Contents:
Readership: Researchers in mathematical modeling, numerical and computational mathematics, and computer science.
640pp Pub. date: Aug 2007
ISBN 978-981-270-938-7
Contrary to the conventional wisdom held by many contemporaries in our time, the popularity of studying complexity is fast becoming a new fad in the intellectual scene. However, can the study of complex phenomena truly reveal recognizable patterns (with predictable outcomes) to enhance our understanding of reality, especially when it is embedded within the messy web of complexity? If so, what then are the limits? This book strives to demolish some of the myths surrounding the nature of complexity and, in the process, to provide an original theory to understand it in this world and beyond. It introduces the authors dialectic theory of complexity, together with the theoretical debate in the literature. It expounds on the concept of complexity from various perspectives, including chemistry, micro- and macro-physics, biology and psychology. It also examines the nature of complexity from societal and cultural perspectives.
This book presents a broad view on the nature of complexity, adequately introducing the reader to this emerging field.
Contents:
Readership: General readers and academia.
300pp (approx.) Pub. date: Scheduled Fall 2007
ISBN 978-981-270-898-4
ISBN 978-981-270-899-1(paperback)
This book brings together two emerging research areas: synchronization in coupled nonlinear systems and complex networks, and study conditions under which a complex network of dynamical systems synchronizes. While there are many texts that study synchronization in chaotic systems or properties of complex networks, there are few texts that consider the intersection of these two very active and interdisciplinary research areas.
The main theme of this book is that synchronization conditions can be related to graph theoretical properties of the underlying coupling topology. The book introduces ideas from systems theory, linear algebra and graph theory and the synergy between them that are necessary to derive synchronization conditions. Many of the results, which have been obtained fairly recently and have until now not appeared in textbook form, are presented with complete proofs. This text is suitable for graduate-level study or for researchers who would like to be better acquainted with the latest research in this area.
Contents:
Readership: Graduate students and researchers in physics, applied mathematics and engineering.
150pp (approx.) Pub. date: Scheduled Fall 2007
ISBN 978-981-270-973-8
Unique in its field, this book uses a methodology that is entirely new, creating the simplest and most abstract foundations for physics to date. The author proposes a fundamental description of process in a universal computational rewrite system, leading to an irreducible form of relativistic quantum mechanics from a single operator. This is not only simpler, and more fundamental, but also seemingly more powerful than any other quantum mechanics formalism available. The methodology finds immediate applications in particle physics, theoretical physics and theoretical computing. In addition, taking the rewrite structure more generally as a description of process, the book shows how it can be applied to large-scale structures beyond the realm of fundamental physics.
Contents:
Readership: Researchers in quantum, theoretical and high energy physics.
680pp (approx.) Pub. date: Scheduled Winter 2007
ISBN 978-981-270-914-1