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.
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
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
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)
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