Bellomo, N. / Preziosi, L., Politecnico
Torino, Italy / Romano, A., Universityof Napoli, Italy
1999. Approx. 456 pages. Hardcover
ISBN 3-7643-4007-X
Due in October 1999
"Mechanics and Dynamical Systems with Mathematica"
provides a systematic and unified treatment of mechanics and
dynamical systems,
addressing modeling, qualitative analysis, and simulations of
physical systems using ordinary differential equations.
The scientific computational components are presented using the
software program Mathematica(, both in worked examples and in
the end-of-chapter problems. Special attention is given to
classical mechanics models in light of new computational methods
and concepts from dynamical systems. The book's nine chapters are
organized into three unified parts: mathematical methods for
differential equations; methods of classical mechanics; and
dynamics, stochastic models and discretization of continuous
models.
This book is an essential text for advanced students, graduates
and practitioners in mechanics, scientific computing, physics and
mathematical modeling. It is also suitable as a self-study
resource for professionals and others seeking an understanding of
the subject
from a modeling perspective.
Contents
Models and Differential Equations/ Models and
Mathematical Problems/ Stability and
Perturbation Methods/ Newtonian Dynamics/
Rigid Body Dynamics/ Energy Methods and
Lagrangian Mechanics/ Deterministic and
Stochastic Models in Applied Sciences/
Stability Bifurcations and Chaotic Dynamics/
Discrete Models of Continuos Systems/
Appendix I: Numerical Methods for Ordinary
Differential Equations/ Appendix II:
Kinematics, Applied Forces, Momentum and
Mechanical Energy/ Appendix III: Scientific
Programs
1999. Approx. 112 pages. Softcover
ISBN 3-7643-6194-8
Due in November 1999
Lectures in Mathematics - ETH
There has been fundamental progress in complex differential
geometry in the last two decades. For one, the uniformization
theory of canonical
K?hler metrics has been established in higher dimensions, and
many applications have been found, including the use of
Calabi-Yau spaces in
superstring theory.
The aim of this monograph is to give an essentially
self-contained introduction to the theory of canonical K?hler
metrics on complex
manifolds. It also presents the reader with some advanced topics
in complex differential geometry not easily found elsewhere. The
topics include Calabi-Futaki invariants, extremal K?hler metrics,
the Calabi-Yau theorem on existence of K?hler Ricci-flat
metrics, and recent progress on K?hler-Einstein metrics with
positive scalar curvature. Applications of K?hler-Einstein
metrics to the uniformization theory are alsodiscussed.
Readers with a good general knowledge of differential geometry
and partial differential equations should be able to grasp and
appreciate the materials in this monograph.
Knott, G., Civilized Software Inc., Bethesda, USA
1999. Approx. 240 pages. Hardcover
ISBN 3-7643-4100-9
Due in February 2000
CS
Progress in Computer Science and Applied Logic 18
Spline functions arise in a number of fields: statistics,
computer graphics, programming, computer-aided design
technology, numerical analysis, and other areas of applied
mathematics.
Much work has focused on approximating splines such as B-splines
and Bezier splines. In contrast, this book emphasizes
interpolating
splines. Almost always, the cubic polynomial form is treated in
depth. Interpolating Cubic Splines covers a wide
variety of explicit approaches to designing splines for the
interpolation of points in the plane by curves, and the
interpolation of
points in 3-space by surfaces. These splines include various
estimated-tangent Hermite splines and double-tangent splines, as
well as
classical natural splines and geometrically-continuous splines
such as beta-splines and nu-splines. A variety of special topics
are covered,
including monotonic splines, optimal smoothing splines, basis
representations, and exact energy-minimizing physical splines. An
in-depth review of the differential geometry of curves and a
broad range of exercises, with selected solutions, and complete
computer
programs for several forms of splines and smoothing splines, make
this book useful for a broad audience: students, applied
mathematicians, statisticians, engineers, and practicing
programmers involved in software development in computer
graphics, CAD, and
various engineering applications.
Contents
Preface / Mathematical Preliminaries/
Curves/ Surfaces/ Function and Space Curve
Interpolation/ 2-D Function Interpolation/
Spline Curves with Range-Dimension/ Cubic
Polynomial Space Curve Splines/
Double-Tangent Cubic Splines/ Global Cubic
Space Curve Splines/ Smoothing Splines/
Geometrically-Continuous Cubic Splines/
Quadratic Space Curve-Based Cubic Splines/
Cubic Spline Vector Space Basis Functions/
Rational Cubic Splines/ Two Spline Programs/
Tensor Product Surface Splines/
Boundary-Curve Based Surface Splines/
Physical Splines/ References/ Index
Gelfand, I.M., Rutgers University, New Brunswick,
USA
/ Retakh, V.S., Rutgers University, New Brunswick, USA /(Ed.)
1999. Approx. 168 pages. Hardcover
ISBN 3-7643-4013-4
Due in December 1999
Dedicated to the memory of Chih-Han Sah, this volume continues a
long tradition of one of the most influential
mathematical seminars of this century.
A number of topics are covered, including combinatorial geometry,
connections between
logic and geometry, Lie groups, algebras and their
representations. An additional area of
importance is noncommutative algebra andgeometry, and its
relations to modern physics.
Distinguished mathematicians contributing to this work:
T.V. Alekseevskaya / A.V. Borovik / C.-H. Sah / G. Cherlin / J.L.
Dupont / I.M. Gelfand
/ V. Kac / A. Kazarnovsky-Krol / A. Radul / A.L. Rosenberg / N.
White
The Gelfand Mathematical Seminar volumes stimulate the birth of
significant ideas in
contemporary mathematics and remain invaluable reference
material.
Contents
Preface / Matroid Homology / Sporadic
Homogeneous Structures / Three Questions
about Simplices in Spherical and Hyperbolic
3-Space / Poisson Structure for Restricted
Lie Algebras / Noncommutative Smooth
Spaces / A Cycle for Integration Yielding the
Zonal Spherical Function of Type A_n / The
Existence of Fiber Functors
Pittenger, A.O., University of
Maryland, Baltimore, USA
1999. Approx. 152 pages. Hardcover
ISBN 3-7643-4127-0
Due in December 1999
Progress in Computer Science and Applied Logic19
The purpose of this monograph is to provide the mathematically
literate reader with an accessible introduction
to the theory of quantum computing algorithms, one component of a
fascinating and rapidly developing area
which involves topics from physics,mathematics, and computer
science.
The author briefly describes the historical context of quantum
computing and provides the motivation, notation, and assumptions
appropriate for quantum statics, a non-dynamical, finite
dimensional model of quantum mechanics. This model is then used
to define and illustrate quantum logic gates and representative
subroutines required for quantum algorithms. A discussion of the
basic
algorithms of Simon and of Deutsch and Jozsa sets the stage for
the presentation of Grover's search algorithm and Shor's
factoring
algorithm, key algorithms which crystallized interest in the
practicality of quantum computers. A group theoretic abstraction
of
Shor's algorithms completes the discussion of algorithms.
The last third of the book briefly elaborates the need for
error-correction capabilities and then traces the theory of
quantum
error-correcting codes from the earliest examples to an abstract
formulation in Hilbert space.
This text is a good self-contained introductory resource for
newcomers to the field of quantum computing algorithms, as well
as a
useful self-study guide for the more specialized scientist,
mathematician, graduate student, or engineer. Readers interested
in
following the ongoing developments of quantum algorithms will
benefit particularly from this presentation of the notation and
basic theory.
Contents
Preface / Acknowledgements / 1. Quantum
Statics / 2. Basics of Quantum Computation /
3. Quantum Algorithms / 4. Quantum
Error-Correcting Codes / Afterword /
References / Index
Features
* clear and concise exposition
* minimal prerequisites
* detailed overview of the historical context of quantum
computing
* discussion of the most recent developments, including the
factoring algorithm of Shor and the somewhat different technique
of Grover
* interesting applications to a number of areas from encryption
systems to databaseresearch
Nagasawa, M., University of Zurich, Switzerland
1999. Approx. 618 pages. Hardcover
ISBN 3-7643-6208-1
Due in December 1999
Monographs in Mathematics94
Stochastic Processes in Quantum Physics addresses the question
"What is the mathematics needed for
describing the movement of quantum particlwhile sample paths of a
non-relativistic quantum particles",
and shows that it is the theory of stochastic (in particular
Markov) processes and that a relativistic
quantum particle has pure-jump sample paths while sample paths of
a non-relativistic quantum particle are
continuous.
Together with known techniques, some new stochastic methods are
applied in solving the equation of motion and the equation of
dynamics of relativistic quantum particles.
The problem of the origin of universes is discussed as an
application of the theory.
The text is almost self-contained and requires only an elementary
knowledge of probability theory at the graduate level, and some
selected chapters can be used as (sub-)textbooks for advanced
courses on stochastic processes, quantum theory and
theoretical chemistry.
Havin, V.P., St. PetersburgUniversity, Russia
/ Nikolski, N.K.,Universit? de Bordeaux, Franc (Ed.)
1999. Approx. 400 pages. Hardcover
ISBN 3-7643-6214-6
Due in December 1999
Operator Theory: Advances and Applications 113
This volume is devoted to some topical problems and various
applications of operator theory and its interplay with
modern complex analysis. It consists of 30 carefully selected
surveys and research papers.
The main subjects of the volume include: ? free interpolation by
analytic functions in its development from the pathbreaking works
by
L. Carleson up to the most recent achievements and in its
connections with the theory of singular integral operators and
Carleson-type embedding theorems, moment problems etc.
? Sz?kefalvi-Nagy-Foias model spaces studied from the point of
view of holomorphic spaces ? holomorphic spaces (Hardy, Bergman,
H?lder, and Sobolev spaces) ? analytic functions smooth up to the
boundary with their subtle properties related
to the Nevanlinna-Smirnov factorization, division and
multiplication, and zero sets ? a new approach to weighted
inequalities for
singular integrals based on the Bellman function in optimization
theory; ? the uncertainty principle in harmonic
analysis and, in particular, a complete version of Turan's lemma
on trigonometric sums ? Hankel operators and stationary Gaussian
processes ? Fourier multipliers, and spectral analysis of some
differential operators.
These themes are united by the "operator theoretic
ideology" and systematic use of modern function theoretical
techniques.
The book is dedicated to the memory of S. A. Vinogradov. It
contains a bibliographical note (with a lively portrait) of S. A.
Vinogradov, a
detailed survey of his mathematical achievements, and a complete
list of publications, as well as the translations of two
of Vinogradov's surveys whose Russian originals are now hardly
accessible.
Ram'rez de Arellano, E. / Shapiro,M.V. / Tovar,
L.M. / Vasilevski, N.L.,
IPN, Mexico City, Mexico (Ed.)
1999. Approx. 296 pages. Hardcover
ISBN 3-7643-6228-6
Due in December 1999
Operator Theory: Advances and Applications 114
This volume is a collection of up-to-date research and expository
papers on different aspects of complex
analysis, including relations to operator theory and hypercomplex
analysis.
The articles cover many important and essential subjects, such as
the Schrodinger equation, subelliptic operators, Lie algebras
and superalgebras, Toeplitz and Hankel operators, reproducing
kernels and Qp spaces, among others.
Most of the papers were presented at the International Symposium
on Complex Analysis and Related Topics held in Cuernavaca
(Morelos), Mexico, in November 1996, which was attended by
approximately 50 experts in the field. The book can be used as a
reference
work on recent research in the subjects covered.
It is one of the few books stressing the relation between
operator theory and complex and hypercomplex analyses.
The book is addressed to researchers and postgraduate students in
the fields named here and in related ones.