Dritschel, Michael A. (Ed.)

The Extended Field of Operator Theory

Series: Operator Theory: Advances and Applications , Vol. 171
2006, Approx. 405 p., Hardcover
ISBN-10: 3-7643-7979-0
ISBN-13: 978-3-7643-7979-7
Due: December 2006

About this book

This volume contains contributions originating from the International Workshop on Operator Theory and Its Applications (IWOTA) held in Newcastle upon Tyne in July 2004. The articles expertly cover a broad range of material at the cutting edge of functional analysis and its applications. Topics include scattering and time varying systems, pseudodifferential and singular operators, weighted composition operators and hyperinvariant subspaces, and interpolation and lifting problems on Hilbert and Krein spaces.

Written for:

Graduates and researchers in Mathematics, Engineering and the Physical Sciences

Keywords:

functional analysis
operator theory

Table of contents

Preface.- About 24 scientific contributions.

Bunke, H., Dickinson, P.J., Kraetzl, M., Wallis, W.D.

A Graph-Theoretic Approach to Enterprise Network Dynamics

Series: Progress in Computer Science and Applied Logic (PCS) , Vol. 24
2007, Approx. 235 p., 110 illus., Hardcover
ISBN-10: 0-8176-4485-7
ISBN-13: 978-0-8176-4485-7
Due: December 2006

About this book

Networks have become nearly ubiquitous and increasingly complex, and their support of modern enterprise environments has become fundamental. Accordingly, robust network management techniques are essential to ensure optimal performance of these networks. This monograph treats the application of numerous graph-theoretic algorithms to a comprehensive analysis of dynamic enterprise networks. Network dynamics analysis yields valuable information about network performance, efficiency, fault prediction, cost optimization, indicators and warnings.

The exposition is organized into four relatively independent parts: an introduction and overview of typical enterprise networks and the graph theoretical prerequisites for all algorithms introduced later; an in-depth treatise of usage of various graph distances for event detection; a detailed exploration of properties of underlying graphs with modeling applications; and a theoretical and applied treatment of network behavior inferencing and forecasting using sequences of graphs.

Based on many years of applied research on generic network dynamics, this work covers a number of elegant applications (including many new and experimental results) of traditional graph theory algorithms and techniques to computationally tractable network dynamics analysis to motivate network analysts, practitioners and researchers alike. The material is also suitable for graduate courses addressing state-of-the-art applications of graph theory in analysis of dynamic communication networks, dynamic databasing, and knowledge management.

Written for:

Graduate students, researchers, computer scientists, network analysts, graph theorists, applied mathematicians and statisticians

Table of contents

Dedication.- Preface.- Part I: Introduction.- Intranets and Network Management.- Graph-Theoretic Concepts.- Part II: Event Detection using Graph Distance.- Matching Graphs with Unique Node Labels.- Graph Similarity Measures for Abnormal Change Detection.- Median Graphs for Abnormal Change Detection.- Graph Clustering for Abnormal Change Detection.- Graph Distance Measures based on Intragraph Clustering and Cluster Distance.- Matching Sequences of Graphs.- Part III: Properties of the Underlying Graphs.- Distances, Clustering, and Small Worlds.- Tournament Scoring.- Part IV: Prediction and Advanced Distance Measures.- Recovery of Missing Information in Graph Sequences.- Matching Hierarchical Graphs.- References.- Index.

Girard, Patrick R.

Quaternions, Clifford Algebras and Relativistic Physics

2007, Approx. 200 p., Softcover
ISBN-10: 3-7643-7790-9
ISBN-13: 978-3-7643-7790-8
Due: January 2007

About this textbook

The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have priviledged a geometric approach, the author uses an algebraic approach which can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics.

The book proposes a pedagogical introduction to this new calculus, based on quaternions, with applications mainly in special relativity, classical electromagnetism and general relativity.

The volume is intended for students, researchers and instructors in physics, applied mathematics and engineering interested in this new quaternionic Clifford calculus.

Written for:

Advanced undergraduate and graduate students, instructors, researchers in Algebra, Geometry and Physics

Keywords:

Clifford algebra
electromagnetism
quaternion
relativistic physics
rotation group
tensor product

Table of contents

Foreword.- Introduction.- 1. Quaternions.- 2. Rotation Groups SO(3) and SO(4).- 3. Complex Quaternions.- 4. Clifford Algebras.- 5. Symmetry Groups.- 6. Special Relativity.- 7. Classical Electromagnetism.- 8. General Relativity.- Conclusion.- Solutions to Exercises.- Appendices.- Bibliography.

Kurdachenko, Leonid, Otal, Javier, Subbotin, Igor Ya.

Artinian Modules over Group Rings

Series: Frontiers in Mathematics
2007, Approx. 260 p., Softcover
ISBN-10: 3-7643-7764-X
ISBN-13: 978-3-7643-7764-9
Due: October 2006

About this book

This book highlights important developments on artinian modules over group rings of generalized nilpotent groups. Along with traditional topics such as direct decompositions of artinian modules, criteria of complementability for some important modules, and criteria of semisimplicity of artinian modules, it also focuses on recent advanced results on these matters. The theory of modules over groups has its own specific character that plays an imperative role here and, for example, allows a significant generalization of the classical Maschke Theorem on some classes of infinite groups. Conversely, it leads to establishing direct decompositions of artinian modules related to important natural formations, which, in turn, find very efficient applications in infinite groups.

As self-contained as possible, this book will be useful for students as well as for experts in group theory, ring theory, and module theory.

Written for:

Graduates, postgraduates and researchers in algebra
Keywords:
Artinian module
group ring
nilpotent group Print version
Recommend to others

Table of contents

Preface.- Modules with Chain Conditions.- Ranks of Groups.- Generalized Nilpotent Groups.- Artinian Modules.- Reduction to Subgroups of Finite Index.- Modules over Dedekind Domains.- Kovacs-Newman Theorem.- Hartley Classes.- Injectivity of Some Simple Modules.- Direct Decompositions.- Countability over FC-hypercentral Groups.- Artinian Modules over Periodic Abelian Groups and over Abelian Groups of Finite Section Rank.- Nearly Injective Modules.- Injective Envelopes.- Quasifinite Modules.- Applications.- Bibliography.- Index.