John A. Kalman (U of Auckland)

Automated Reasoning with OTTER

with foreword by Larry Wos (Argonne) 552 pages 10x7 inches w/ CDROM
Feb 2001 Hardcover
ISBN 1-58949-004-5

Description:
Automating reasoning has been described as ``one of the most exciting and potentially fruitful areas of research that there has ever been.'' This book provides you with the means: a powerful reasoning program called Otter, currently in use to answer diverse and deep questions in mathematics and logic. The volume presents an intriguing and thorough treatment of automated reasoning and Otter -- through numerous examples, exercises, and challenging questions. No background is needed. The early chapters lead you through Otter's fundamental operations and show you how to present questions and problems to Otter, beginning with simple puzzles. Numerous input files and proofs are provided, so you can experiment and play with problems. Gradually, more challenging applications are introduced, and more powerful strategies discussed -- strategies that are crucial to Otter's power and impressive list of successes.

Contents:
Chs. 1-5 give an introduction to logic, automated reasoning, and Otter. The approach is based on examples, including "the wolf, the goat, and the cabbages", and includes numerous exercises that lead you gently from the simple to the complex. Included in these chapters is a discussion of the language for conveying a problem to Otter, the means for drawing conclusions, and mechanisms for controlling the program's attack.
Chs. 6-9 provide a fuller treatment of such concepts as substitution, hyperresolution, and proof by contradiction. These chapters are for readers who have "some acquaintance" with first-order logic. The fine detail is complemented nicely by illustrations and case studies, as well as cryptarithmetic puzzles and puzzles on "truth-tellers and liars" and "knights and knaves" -- all of which can be translated into clauses and solved by running Otter.
Ch. 10 shows how, with the help of more sophisticated techniques, the class of reasoning problems that Otter can attack can be greatly extended. In particular, this chapter focuses on propositional connectives such as "not", "or", and "and", and discusses the notion of "logical equivalence." The chapter ends with a helpful section on how Otter can be used to translate formulas into clause automatically.
The remaining chapters are concerned mainly with logical problems whose solution requires reasoning about equality. One simple example is the following: Suppose we know that (a) if two persons x and y are acquainted, then x is also acquainted with y's spouse, and (b) Dick's spouse is acquainted with Eve's spouse. The problem is to show that (c) Dick is acquainted with Eve. Implicit in this problem is the idea that (d) if x and y are acquainted, then y and x are acquainted, and (e) the spouse of the spouse of x is x. To use the hypothesis (e), reasoning about equality is needed. Otter provides special facilities for investigating such problems.


Dmitry I. Kamenev & Gennady P. Berman (Los Alamos)

Quantum Chaos: A Harmonic Oscillator in Monochromatic Wave

160 pages, 9x6 inches
March 2001 Hardcover
ISBN 1-58949-001-0

Description:
This book, for the first time, presents a review on transition from regular dynamics to quantum chaos in a quantum degenerate system -- a harmonic oscillator perturbed by a monochromatic wave. The model, being one of the simplest dynamical systems, exhibits the fundamental properties of nonlinearity, quantum instability and chaos. And, more importantly, it describes practical systems such as an ion in a linear ion trap interacting with laser radiation, an electron in magnetic field interacting with a plasma wave, an acoustic quantum cyclotron resonance in metals, and a two-dimensional electron gas in semiconductor heterostructures. This book explains in details how the transition to quantum chaos occurs and how the theoretical predictions can be tested in experiments. The book is useful to students and scientists who are interested to understand the nature of quantum instabilities and chaos in dynamic systems and their applications in technological problems.

Contents:
Ch.1 Introduction
Ch.2 Classical Resonance Perturbation Theory
Ch.3 Stability of the Classical Ground State
Ch.4 Dynamics of an Ion in a Linear Ion Trap
Ch.5 Quantum Resonance Cells
Ch.6 Symmetry of the Quasienergy States
Ch.7 Tunneling Between Resonance Cells
Ch.8 Weak Quantum Chaos
Ch.9 Quantum Chaos of an Ion in a Linear Trap
Ch.10 Dynamics of the Monochromatically Perturbed Oscillator as a Solid-state Problem of Electron Localization
Ch.11 Stability of the Quantum Ground State
Ch.12 Conclusion


Kenneth Kuttler

Basic Analysis

556 pages, 10x7 inches
Nov 2001 Hardcover
ISBN 1-58949-019-3

Description:
This is a book on basic analysis and related topics. It presents the most important theorems in measure and integration, an introduction to functional analysis, the big advanced calculus theorems about the Frechet derivative including the implicit function theorem, and other topics including fixed point theorems and applications, the Brouwer degree, and an introduction to the generalized Riemann integral. Although there are some abstract topics, the emphasis is on analysis which takes place in the context of n dimensional Euclidean space.

The book is directed to advanced undergraduates and beginning graduate students in math and physical science who are interested in analysis and is self contained for this audience. It could be used as a textbook for a two semester course.

Contents:
Preface
1. Basic set theory
2. Linear algebra
3. General topology
4. Spaces of continuous functions
5. Abstract measure and integration
6. The construction of measures
7. Lebesgue measure
8. Product measure
9. Fourier series
10. The Frechet derivative
11. Change of variables for C^1 maps
12. The L^p spaces
13. Fourier transforms
14. Banach spaces
15. Hilbert spaces
16. Brouwer degree
17. Differential forms
18. Representation theorems
19. Weak derivatives
20. Fundamental theorem of calculus
App. A The Hausdorff maximal theorem
App. B The generalized Riemann integral


ed. Robert Clark (U of New South Wales)

Experimental Implementation of Quantum Computation (IQC'01)

372 pages, 10x7 inches
Dec 2001 Hardcover
ISBN 1-58949-013-4

Description:

The volume presents reports of the latest developments in the experimental implementation of quantum computer proposals worldwide. It also includes theoretical investigations relevant to the various computer architectures, implementation strategies and computer operation. The reports provide a framework that sets out both the challenges of the various experimental proposals together with progress that has been made in overcoming these challenges.

Invited Contributors
David Awschalom (UCSB)
Hans Bachor (Australian National University)
Crispin Barnes (University of Cambridge)
Rainer Blatt (University of Innsbruck)
Sam Braunstein (University of Wales)
Isaac Chuang (IBM Almaden)
Ivan Deutsch (University of New Mexico)
David DiVincenzo (IBM T.J. Watson)
Jon Dowling (Caltech)
Mark Dykman (Michigan State University)
Andrew Dzurak (University of New South Wales)
Chris Hammel (Los Alamos National Laboratory)
Yoshiro Hirayama (NTT Basic Research Laboratories)
Xuedong Hu (University of Maryland)
Bill Huber (NIST)
Richard Hughes (Los Alamos National Laboratory)
Poul Jessen (University of Arizona)
David Kielpinski (NIST)
Tom King (UCSB)
Paul Kwiat (Los Alamos National Laboratory)
Daniel Loss (University of Basel)
Hideo Mabuchi (California Institute of Technology)
Gerard Milburn (University of Queensland)
Don Parkin (Los Alamos National Laboratory)
Keith Schwab (Maryland)
Selim Shahriar (MIT)
David Lucas (University of Oxford)
Yasuo Takahashi (NTT Basic Research Laboratories)
Jaw-shen Tsai (NEC Fundamental Research)
John Tucker (University of Illinois)
Birgitta Whaley (UC Berkeley)
Kang Wang (UCLA)
Stan Williams (Hewlett Packard Laboratories, Palo Alto)
Yoshi Yamamoto (Stanford University)


ed. Miao Li & Yong-Shi Wu

Physics in Noncommutative World I: Field Theories

608 pages, 10x7 inches
July 2002 Hardcover
ISBN 1-58949-021-5

Description:

Recent years have witnessed increasing interests in physics in noncommutative space, and noncommutative space-time. The notion of quantized space-time and that of noncommuting guiding-center coordinates in the lowest Landau level have existed for quite a while. Lately since the discovery of noncommutative field theories in matrix models that describe string theory nonperturbatively, noncommutative Yang-Mills and its cousins have been explored extensively in hundreds of papers in the literature. One expects that a large part of efforts in string theory will continue to be directed in this direction. Also, many common physical features have been found in string theoretical systems and quantum Hall systems in condensed matter. The goal of this reprint collection is to serve young students and interested researchers with readily available sources of original ideas and useful techniques, and to help to promote communications among different disciplines. The book includes eight chapters, each starting with a brief introduction.

Readership: graduate students, professors, and researchers in theoretical physics, mathematical physics and theoretical high energy physics and condensed matter theory.

Table of Contents:

0. Foreword

1. Early Papers
H.S. Snyder: Quantized Space-time
C.N. Yang: On Quantized Space-time
J.E. Moyal: Quantum Mechanics as a Statistical Theory

2. A Quick Math Guide
A. Connes: C* Algebra and Differential Geometry
A. Connes and M.A. Rieffel: Yang-Mills for Noncommutative Two-tori
J. Wess and B. Zumino: Covariant Differential Calculus on the Quantum Hyperplane
J. Madore: The Fuzzy Sphere

3. Noncommutative Geometry and Quantum Hall Systems
S.M. Girvin and T. Jach: Formalism for the Quantum Hall Effect: Hilbert Space of Analytic Functions
V. Pasquier and F.D.M. Haldane: A Dipole Interpretation of the nu =1/2 State
N. Read: Lowest-Landau-level Theory of the Quantum Hall Effect: the Fermi-liquid-like State

4. Noncommutative Field Theory in Matrix Mode
M. Li: Strings from IIB Matrices
A. Connes, M. R. Douglas and A. Schwarz: Noncommutative Geometry and Matrix Theory: Compactification on Tori
P. M. Ho and Y. S. Wu: Noncommutative Gauge Theories in Matrix Theory
H. Aoki, N. Ishibashi, S. Iso, H. Kawai, Y. Kitazawa, and T. Tada: Noncommutative Yang-Mills in IIB Matrix Model
N. Ishibashi, S. Iso, H. Kawai, and Y. Kitazawa: Wilson Loops in Noncommutative Yang Mills
D. Kabat and W. Taylor: Spherical Membranes in Matrix Theory

5. Noncommutative Geometry from String Theory
E. Witten: Bound States of Strings and p-Branes
P. M. Ho and Y. S. Wu: Noncommutative Geometry and D-Branes
M. R. Douglas and C. Hull: D-branes and the Noncommutative Torus
C. S. Chu and P. M. Ho: Noncommutative Open String and D-brane
V. Schomerus: D-branes and Deformation Quantization
N. Seiberg and E. Witten: String Theory and Noncommutative Geometry

6. Quantum Effects in NCFT
T. Filk: Divergencies in a Field Theory on Quantum Space
D. Bigatti and L. Susskind: Magnetic Fields, Branes and Noncommutative Geometry
S. Minwalla, M. Van Raamsdonk, N. Seiberg: Noncommutative Perturbative Dynamics
A. Armoni: Comments on Perturbative Dynamics of Non-Commutative Yang-Mills Theory

7. Instantons and Solitons in NCFT
N. Nekrasov and A. Schwarz: Instantons on Noncommutative R4, and (2,0) Superconformal Six Dimensional Theory
R. Gopakumar, S. Minwalla, and A. Strominger: Noncommutative Solitons
J. A. Harvey, P. Kraus, F. Larsen, and E. J. Martinec: D-branes and Strings as Non-commutative Solitons
D. Gross and N. Nekrasov: Monopoles and Strings in Noncommutative Gauge Theory

8. Gravity Dual of Noncommutative Gauge Theories
J. M. Maldacena and J. G. Russo: Large N Limit of Non-Commutative Gauge Theories
M. Li and Y. S. Wu: Holography and Noncommutative Yang-Mills
S. R. Das and S. J. Rey: Open Wilson Lines in Noncommutative Gauge Theory and Tomography of Holographic Dual Supergravity