David P. Blecher, Department of Mathematics, University of Houston and Christian Le Merdy, Laboratoire de Mathematiques, Universite de Besancon

Operator Algebras and Their Modules - An operator space approach

0-19-852659-8
Publication date: 7 October 2004
Clarendon Press 398 pages, 234mm x 156mm
Series: London Mathematical Society Monographs

A unique reference presenting the general theory of algebras of operators on a Hilbert space and the modules over such algebras
All the basic tools and constructions in one comprehensive volume with detailed notes
Authoritative first-hand account from major contributors to the field

Description

This invaluable reference tool is the first to present the general theory of algebras of operators on a Hilbert space, and the modules over such algebras. The new theory of operator spaces is presented early on and the text assembles the basic concepts, theory and methodologies needed to equip a beginning researcher in this area.

Readership: Graduate students and researchers in functional analysis, operator algebras, and operator spaces. Also researchers in related areas such as Banach algebras, function spaces, or Banach space theory.

Contents

Preface
1 Operator spaces
2 Basic theory of operator algebras
3 Basic theory of operator modules
4 Some 'extremal theory'
5 Completely isomorphic theory of operator algebras
6 Tensor products of operator algebras
7 Selfadjointness criteria
8 C*-modules and operator spaces
Appendix
References
Index

Alexander A. Ivanov, Imperial College, London

The Fourth Janko Group

0-19-852759-4
Publication date: 21 October 2004
Clarendon Press 250 pages, none, 234mm x 156mm
Series: Oxford Mathematical Monographs

An indispensible resource; a unique and essential reference for researchers in the area
Illustrates the amalgam group method

Description

This unique reference illustrates how different methods of finite group theory including representation theory, cohomology theory, combinatorial group theory and local analysis are combined to construct one of the last of the sporadic finite simple groups - the fourth Janko group J 4.

Readership: Graduate students and researchers in pure mathematics, particularly in group theory, geometry and algebra.

Contents

Preface
1 Concrete group theory
2 O 10 + (2) as a prototype
3 Modifying the rank 2 amalgam
4 Pentad group 13+12 . (L 3 (2) x Sym 5)
5 Toward 2 + 1+12 . 3 . Aut (M 22)
6 The 1333-dimensional representation
7 Getting the parabolics together
8 173,067,389-vertex graph triangle
9 History and beyond
Appendices
10 Terminology and notation
11 Matthieu groups and their geometries
References
Index

Jon Williamson, Department of Philosophy, Logic and Scientific Method, London School of Economics, London

Bayesian Nets and Causality:
Philosophical and Computational Foundations

0-19-853079-X
Publication date: October 2004
250 pages, 234mm x 156mm

A major contribution to the study of reasoning
Numerous diagrams
Provides an introduction to central topics in AI and philosophy
Provides new foundations for computational techniques and new algorithms for automated reasoning in AI

Description

'This book is a remarkable piece of work by a very talented author ...' -Don Gillies, Professor of the Philosophy of Science and Mathematics, King's College, London
'Jon Williamson is the ideal person to do this. The book is fluent, interesting, knowledgeable, fair but suitably provocative ...' -Jeff Paris, Professor of Pure Mathematics, Department of Mathematics, University of Manchester
'This book marks an important development ... the whole exposition is something of a tour de force, Williamson's book will come to be recognised as a major contribution ' -Colin Howson, Chair in Philosophy of Science, London School of Economics

Bayesian nets are widely used in artificial intelligence as a calculus for causal reasoning, enabling machines to make predictions, perform diagnoses, take decisions and even to discover causal relationships. This book, aimed at researchers and graduate students in computer science, mathematics and philosophy, brings together two important research topics: how to automate reasoning in artificial intelligence, and the nature of causality and probability in philosophy.

Readership: Researchers and graduate students in computer science, mathematics and philosophy.

Contents

Introduction
Probability
Bayesian Nets
Causal Nets: Foundational Problems
Objective Bayesianism
Two-Stage Bayesian Nets
Causality
Discovering Causal Relationships
Epistemic Causality
Recursive Causality
Logic
Language Change
References
Index

David Christensen, Department of Philosophy, University of Vermont

Putting Logic in its Place

0-19-926325-6
Publication date: November 2004
150 pages, 203mm x 135mm

Description

Does logic help determine whether beliefs are rational? David Christensen argues that it does - but only once we understand beliefs as coming in degrees. Avoiding mathematical technicality, he explains why the degree-of-belief approach offers the key to understanding how logical arguments work. Philosophers working on formal epistemology and logic, as well as those in related areas of cognitive psychology and decision theory, will find much to stimulate them here.

Readership: Scholars and students of philosophy, particularly in formal epistemology and logic; also those in related fields such as cognitive psychology and decision theory

Contents

I Logic and Rational Belief
II Two Models of Belief
III Deductive Constraints: Problem Cases, Possible Solutions
IV Arguments for Deductive Cogency
V Logic, Graded Belief, and Preferences
VI Logic and Idealization

George Karniadakis, Division of Applied Mathematics, Brown University and Spencer Sherwin, Department of Aeronautics, Imperial College London

Spectral/hp element methods for computational fluid dynamics,
Second Edition

0-19-852869-8
Publication date: 17 December 2004
650 pages, More than 200 line drawings, 240mm x 168mm
Series: Numerical Mathematics and Scientific Computation

Completely revised and expanded new edition -- over 50% new material covering the recent and significant progress in multi-domain spectral methods
Broad readership -- in computational fluid mechanics, applied and numerical mathematics, computational mechanics, aerospace and mechanical engineering and climate/ocean modelling
Contains theoretical and implementation material and state-of-the art results
Graded exercises

New to this edition
Coverage of the recent and important developments in discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains and on stabilisation and filtering techniques
Modelling the spectral/hp element applied to less traditional fields, such as seismology, climate modelling and magneto-hydro-dynamics (MHD)


Readership: Students, academics and practitioners in computational fluid mechanics, applied and numerical mathematics, computational mechanics, aerospace and mechanical engineering and climate/ocean modelling.

Contents

Introduction
Fundamental concepts in one dimension
Multi-dimensional expansion bases
Multi-dimensional formulations
Diffusion equation
Advection and advection-diffusion
Non-conforming elements
Algorithms for incompressible flows
Incompressible flow simulations:verification and validation
Hyperbolic conservation laws
Appendices
Jacobi polynomials
Gauss-Type integration
Collocation differentiation
Co discontinuous expansion bases
Characteristic flux decomposition
References
Index