Rosolino Buccheri, Metod Saniga, William Mark Stuckey

The Nature of Time: Geometry, Physics and Perception

March 2003, ISBN 1-4020-1201-2, Paperback

Book Series: NATO SCIENCE SERIES: II: Mathematics, Physics and Chemistry : Volume 95

This book provides the reader with the most recent scholarly insights into the nature of time - undoubtedly one of the most profound mysteries that science has ever faced. The selected contributions are grouped into four conceptually different yet mutually cohesive chapters, carefully woven into a comprehensive whole that goes well beyond standard treatments. The subjects discussed include the fine structure of psychological time(s) and consciousness, novel algebraic geometrical and number theoretic models of time dimension, different arrows of time, time travel, EPR paradox, quantum non-locality, pregeometry, and a host of relevant epistemological and ontological issues. The book shows that research is becoming necessarily interdisciplinary and does not ignore even such delicate issues as "altered" states of consciousness, religion and metaphysics. Although focused primarily on an academic readership, the treatise can be read with profit by anyone fascinated by the enigma of time.

A coherent, multidisciplinary sampling of the most up-to-date professional research on the nature of time, addressing four major themes: internal times and consciousness, mathematical approaches to the concept of time, the physicist's view of time, and integrative science's views of time. Essential reading for anyone, scientist or layperson, with a serious interest in the topic.

Samuel L. Braunstein, Arun K. Pati

Quantum Information with Continuous Variables

April 2003, ISBN 1-4020-1195-4, Hardbound

Quantum information may sound like science fiction but is, in fact, an active and extremely promising area of research, with a big dream: to build a quantum computer capable of solving problems that a classical computer could not even begin to handle. Research in quantum information science is now at an advanced enough stage for this dream to be credible and well-worth pursuing. It is, at the same time, too early to predict how quantum computers will be built, and what potential technologies will eventually strike gold in their ability to manipulate and process quantum information.

One direction that has reaped many successes in quantum information processing relies on continuous variables. This area is bustling with theoretical and experimental achievements, from continuous-variable teleportation, to in-principle demonstrations of universal computation and efficient error correction. Now the time has come to compile some of the major results into one volume. In this book the leading researchers of the field present up-to-date developments of continuous-variable quantum information. This book is organized to suit many reader levels with introductions to every topic and in-depth discussions of theoretical and experimental results.

Contents

Preface. About the Editors. Part I: Quantum Computing.Part II: Quantum Entanglement. Part III: Part IV: Limits on Quantum Information and Cryptography. Index.

Jonathan S. Golan

Semirings and Affine Equations over Them: Theory and Applications

June 2003, ISBN 1-4020-1358-2, Hardbound

Book Series: MATHEMATICS AND ITS APPLICATIONS : Volume 556

Semiring theory stands with a foot in each of two mathematical domains. The first being abstract algebra and the other the fields of applied mathematics such as optimization theory, the theory of discrete-event dynamical systems, automata theory, and formal language theory, as well as from the allied areas of theoretical computer science and theoretical physics. Most important applications of semiring theory in these areas turn out to revolve around the problem of finding the equalizer of a pair of affine maps between two semimodules. In this volume, we chart the state of the art on solving this problem, and present many specific cases of applications.

This book is essentially the third part of a trilogy, along with Semirings and their Applications, and Power Algebras over Semirings, both written by the same author and published by Kluwer Academic Publishers in 1999. While each book can be read independently of the others, to get the full force of the theory and applications one should have access to all three.

This work will be of interest to academic and industrial researchers and graduate students. The intent of the book is to bring the applications to the attention of the abstract mathematicians and to make the abstract mathematics available to those who are using these tools in an ad-hoc manner without realizing the full force of the theory.

Contents

Preface. Introduction. 1 : Semirings. 2: Partially-Ordered Semirings. 3: Complete Semirings. 4: Residuated Semirings. 5: Matrix Semirings. 6: Symmetric Extension of a Semiring. 7: Semimodules. 8: Homomorphisms between Semimodules. 9: Affine Maps between Semimodules. 10: Partially-ordered Semimodules. 11: Eigenelements. 12: Permanents and Determinants. Bibliography. Index of Applications. Index of Terminology.

M. Konstantinov, University of Architecture, Sofia, Bulgaria
D. Wei Gu, University of Leicester, Department of Engineering, Leicester, UK
V. Mehrmann, Institut fur Mathematik, Berlin, Germany
P. Petkov, Technical University of Sofia, Department of Systems and Control, Bulgaria

Perturbation Theory for Matrix Equations

Included in series
Studies in Computational Mathematics, 9

Description

The book is devoted to the perturbation analysis of matrix equations. The importance of perturbation analysis is that it gives a way to estimate the influence of measurement and/or parametric errors in mathematical models together with the rounding errors done in the computational process. The perturbation bounds may further be incorporated in accuracy estimates for the solution computed in finite arithmetic. This is necessary for the development of reliable computational methods, algorithms and software from the viewpoint of modern numerical analysis.

In this book a general perturbation theory for matrix algebraic equations is presented. Local and non-local perturbation bounds are derived for general types of matrix equations as well as for the most important equations arising in linear algebra and control theory. A large number of examples, tables and figures is included in order to illustrate the perturbation techniques and bounds.

Contents

1 Introduction.
2 Perturbation problems.
3 Problems with explicit solutions.
4 Problems with implicit solutions.
5 Lyapunov majorants.
6 Singular problems.
7 Perturbation bounds.
8 General Sylvester equations.
9 Specific Sylvester equations.
10 General Lyapunov equations.
11 Lyapunov equations in control theory.
12 General quadratic equations.
13 Continuous-time Riccati equations.
14 Coupled Riccati equations.
15 General fractional-afine equations.
16 Symmetric fractional-afine equations.
A Elements of algebra and analysis.
B Unitary and orthogonal decompositions.
C Kronecker product of matrices.
D Fixed point principles.
E Sylvester operators.
F Lyapunov operators.
G Lyapunov-like operators.
H Notation.
References.
Index.

Year 2003, Hardbound
ISBN: 0-444-51315-9
428 pages

OMAR PORDAVI

RECENT RESEARCH ON PURE AND APPLIED ALGEBRA

- 2003
ISBN:1-59033-578-3

Summary:

This new volume gathers results in pure and applied algebra from researchers around the globe. The selection of these papers was carried out under the auspices of a special editorial board.

Table of Contents:

Preface; Structure and Commutativity of Associative Rings (Mohammad Ashraf, King Abdulaziz University, Saudi Arabia); On Commutativity of Rings with Constraints on a Subset (Mohammad Ashraf); Galois Module Theory Over a Discrete Valuation Ring (Robert Underwood, Auburn University Montgomery, USA); Exchange Rings with Stable Range Conditions (Huanyin Chen, Hunan Normal University, P.R. China); Integral Representation of the Generalized Inverse and its Applications (Yimin Wei, Fudan University, Shanghai); Coherent Vectors as Eigenvectors of a Backwardshift on a Deformed Hilbert Space (P.K. Das, Indian Statistical Institute, Calcutta); Theoretical and Numerical Considerations about Pade Approximants for the Matrix Logarithm (J.R. Cardoso, Instituto Superior de Engenharia de Coimbra and F. Silva Leite, Universidade de Coimbra, Portugal); Factroizations of Cuchy-Vandermonde Matrices with One Multiple Pole (J.J. Martinez, Universidad de Alcala and J.M. Pena, Universidad de Zaragoza, Spain); On Maximal Subgroups of Sylow Subgroups of Finite Groups (M. Assad, Cairo University, Egypt); A Note on the Brauer Quotients of a Crossed Burnside Functor (Fumihito Oda, Toyama National College of Technology, Japan); Index.