Industrial mathematics is evolving into an important branch of
mathematics. Mathematicians, in Italy in particular, are becoming
increasingly aware of this new trend and are engaged in bridging
the gap between highly specialized mathematical research and the
emerging demand for innovation from industry. In this respect,
the contributions in this volume provide both R&D workers in
industry with a general view of existing skills, and academics
with state-of-the-art applications of mathematics to real-world
problems, which may also be incorporated in advanced courses.
Contents:
New Perspectives on Mathematical Modeling of Semiconductors (G Al・et
al.)
Undesirable Growth, Oscillations and Indeterminacy in an Economy
with Private Substitutes for Environmental Goods (A Antoci et al.)
Aerodynamic Effects in Proximity to High-Speed Trains (R Balli et
al.)
Active Infrared Thermography in Nondestructive Evaluation (P
Bison et al.)
Admission Control Algorithms Based on Self-Similar Traffic
Modeling for IP Networks (F Chiti et al.)
Discontinuity Surfaces for a Class of Isotropic Elastic Materials
(D De Tommasi et al.)
Semi-explicit Time-Stepping Methods for Dynamical Systems with
Complementary Constraints (L Lopez et al.)
An Evolution Model for the Delamination of Thin Films:
Theoretical and Numerical Aspects (F Pistella et al.)
Entropy Function in Heterogeneous and Anisotropic Nonlinear
Ferroelastic Crystals (L Restuccia & M Francaviglia)
An Almost-Robust a Posteriori Estimator for the One-Dimensional
Advection-Diffusion-Reaction Problem (G Sangalli)
An Application of Lattice Boltzmann Model to Open Systems (F Tosi)
Dimension Reduction Problems for Non-Simple Grade Two Materials (E
Zappale)
and other papers
Readership: Researchers in mathematical modeling, numerical and
computational mathematics.
608pp Pub. date: Jun 2005
ISBN 981-256-368-7
This book arises out of the need for Quantum Mechanics (QM) to
be part of the common education of mathematics students. Rather
than starting from the Dirac?Von Neumann axioms, the book offers
a short presentation of the mathematical structure of QM using
the C*-algebraic structure of the observable based on the
operational definition of measurements and the duality between
states and observables. The description of states and observables
as Hilbert space vectors and operators is then derived from the
GNS and Gelfand?Naimark Theorems.
For finite degrees of freedom, the Weyl algebra codifies the
experimental limitations on the measurements of position and
momentum (Heisenberg uncertainty relations) and Schroedinger QM
follows from the von Neumann uniqueness theorem.
The existence problem of the dynamics is related to the self-adjointness
of the differential operator describing the Hamiltonian and
solved by the Rellich?Kato theorems. Examples are discussed which
include the explanation of the discreteness of the atomic spectra.
Because of the increasing interest in the relation between QM and
stochastic processes, a final chapter is devoted to the
functional integral approach (Feynman?Kac formula), the
formulation in terms of ground state correlations (Wightman
functions) and their analytic continuation to imaginary time (Euclidean
QM). The quantum particle on a circle as an example of the
interplay between topology and functional integral is also
discussed in detail.
Contents:
Mathematical Description of a Physical System
Mathematical Description of a Quantum System
The Quantum Particle
Quantum Dynamics
The Schroedinger Equation
Examples
Quantum Mechanics and Stochastic Processes
Readership: Academics, mathematicians, advanced undergraduate and
graduate students in mathematics and mathematical physics.
160pp Pub. date: Scheduled Winter 2005
ISBN 981-256-431-4
This volume provides a concise introduction to the methodology
of nonstandard finite difference (NSFD) schemes construction and
shows how they can be applied to the numerical integration of
differential equations occurring in the natural, biomedical, and
engineering sciences. These methods had their genesis in the work
of Mickens in the 1990's and are now beginning to be widely
studied and applied by other researchers. The importance of the
book derives from its clear and direct explanation of NSFD in the
introductory chapter along with a broad discussion of the future
directions needed to advance the topic.
Contents:
Applications of Mickens Discretizations to Boundary Value
Problems of Bratu, Gelfand and Others (R Buckmire)
Nonstandard Finite Difference Time Domain Algorithms for
Computational Electromagnetics: Applications to Current Topics in
Optics and Photonics (J B Cole)
Reliable Finite Difference Schemes with Applications in
Mathematical Ecology (D T Dimitrov et al.)
Application of the Nonstandard Finite Difference Method in Non-Smooth
Mechanics (Y Dumont)
Finite Difference Schemes on Unbounded Domains (M Ehrhardt)
Dynamically-Consistent Nonstandard Finite Difference Methods for
Epidemic Models (A Gumel & K C Patidar)
Nonstandard Finite Difference Methods and Biological Models (S R-J
Jang)
Contribution to the Theory of Nonstandard Finite Difference
Methods and Applications to Singular Perturbation Problems (J M-S
Lubuma & K C Patidar)
Nonstandard Discretization Methods on Lotka坊olterra
Differential Equations (L-I W Roeger)
Readership: Applied mathematicians, and researchers in numerical
& computational mathematics and analysis &
differentialequations. Usable as a secondary text to a standard
undergraduate orgraduate course on numerical methods for
differential equations.
660pp (approx.) Pub. date: Scheduled Winter 2005
ISBN 981-256-404-7
The aim of this book is to provide a comprehensive
introduction to cryptography without using complex mathematical
constructions. The themes are conveyed in a form that only
requires a basic knowledge of mathematics, but the methods are
described in sufficient detail to enable their computer
implementation.
The book describes the main techniques and facilities of
contemporary cryptography, proving key results along the way. The
contents of the first five chapters can be used for one-semester
course.
Contents:
Public Key Cryptosystems
Solving Discrete Logarithm Problem
Digital Signatures
Cryptographic Protocols
Elliptic Curve Cryptosystems
Theoretical Security of Cryptosystems
Modern Secret-Key Ciphers
Random Numbers in Cryptography
Readership: Academics, IT specialists and graduate students
interested in cryptography algorithms.
208pp Pub. date: Sept 2005
ISBN 981-256-405-5
This is the first book on analytic hyperbolic geometry, fully analogous to analytic Euclidean geometry. Analytic hyperbolic geometry regulates relativistic mechanics just as analytic Euclidean geometry regulates classical mechanics. The book presents a novel gyrovector space approach to analytic hyperbolic geometry, fully analogous to the well-known vector space approach to Euclidean geometry. A gyrovector is a hyperbolic vector. Gyrovectors are equivalence classes of directed gyrosegments that add according to the gyroparallelogram law just as vectors are equivalence classes of directed segments that add according to the parallelogram law. In the resulting “gyrolanguage” of the book one attaches the prefix “gyro” to a classical term to mean the analogous term in hyperbolic geometry. The prefix stems from Thomas gyration, which is the mathematical abstraction of the relativistic effect known as Thomas precession. Gyrolanguage turns out to be the language one needs to articulate novel analogies that the classical and the modern in this book share.
The scope of analytic hyperbolic geometry that the book presents
is cross-disciplinary, involving nonassociative algebra, geometry
and physics. As such, it is naturally compatible with the special
theory of relativity and, particularly, with the nonassociativity
of Einstein velocity addition law. Along with analogies with
classical results that the book emphasizes, there are remarkable
disanalogies as well. Thus, for instance, unlike Euclidean
triangles, the sides of a hyperbolic triangle are uniquely
determined by its hyperbolic angles. Elegant formulas for
calculating the hyperbolic side-lengths of a hyperbolic triangle
in terms of its hyperbolic angles are presented in the book.
The book begins with the definition of gyrogroups, which is fully
analogous to the definition of groups. Gyrogroups, both
gyrocommutative and nongyrocommutative, abound in group theory.
Surprisingly, the seemingly structureless Einstein velocity
addition of special relativity turns out to be a gyrocommutative
gyrogroup operation. Introducing scalar multiplication, some
gyrocommutative gyrogroups of gyrovectors become gyrovector
spaces. The latter, in turn, form the setting for analytic
hyperbolic geometry just as vector spaces form the setting for
analytic Euclidean geometry. By hybrid techniques of differential
geometry and gyrovector spaces, it is shown that Einstein (Mobius)
gyrovector spaces form the setting for Beltrami?Klein (Poincare)
ball models of hyperbolic geometry. Finally, novel applications
of Mobius gyrovector spaces in quantum computation, and of
Einstein gyrovector spaces in special relativity, are presented.
Readership: Undergraduates, graduate students, researchers and
academics in geometry, algebra, mathematical physics, theoretical
physics and astronomy.
484pp Pub. date: Sept 2005
ISBN 981-256-457-8
Markov Chain Monte Carlo (MCMC) originated in statistical
physics, but has spilled over into various application areas,
leading to a corresponding variety of techniques and methods.
That variety stimulates new ideas and developments from many
different places, and there is much to be gained from cross-fertilization.
This book presents five expository essays by leaders in the
field, drawing from perspectives in physics, statistics and
genetics, and showing how different aspects of MCMC come to the
fore in different contexts. The essays derive from tutorial
lectures at an interdisciplinary program at the Institute for
Mathematical Sciences, Singapore, which exploited the exciting
ways in which MCMC spreads across different disciplines.
Contents:
Introduction to Markov Chain Monte Carlo Simulations and their
Statistical Analysis (B A Berg)
An Introduction to Monte Carlo Methods in Statistical Physics (D
P Landau)
Notes on Perfect Simulation (W S Kendall)
Sequential Monte Carlo Methods and Their Applications (R Chen)
Markov Chain Monte Carlo in the Analysis of Genetic Data on
Pedigrees (E A Thompson)
Readership: Academic researchers in physics, statistics and
bioinformatics.
250pp (approx.) Pub. date: Scheduled Winter 2005
ISBN 981-256-427-6
From the Foreword by Professor Leonidas J. Guibas
"Geometry, graphics, and vision all deal in some form with
the shape of objects, their motions, as well as the transport of
light and its interactions with objects. This book clearly shows
how much they have in common and the kinds of synergies that
occur when a common core of material is presented in a way that
both serves and is enriched by all three disciplines. This book
truly establishes bridges where they make the most impact: early
on in a student's education. The book can also benefit graduate
students and researchers across all parts of computer science
that deal with modeling or interacting with the physical world.
The material is methodically organized, the exposition is
rigorous yet well-motivated with plenty of instructive examples."
Visual Computing: Geometry, Graphics, and Vision is a concise
introduction to common notions, methodologies, data structures,
and algorithmic techniques arising in the mature fields of
computer graphics, vision, and computational geometry. The
central goal of the book is to provide a global and unified view
of the rich interdisciplinary visual computing field. The book is
written for undergraduate students and game development and
graphics professionals. Lecturers in computer graphics and vision
will also find it complementary and valuable. The book aims at
broadening and fostering readers? knowledge of essential 3D
techniques by providing a sizeable overall picture and describing
essential concepts. Throughout the book, appropriate real world
applications are covered to illustrate uses and generate interest
in adjacent fields. The book also provides concise C++ code for
common tasks that will be of interest to a broad audience of
practitioners.
KEY FEATURES
Provides a concise text and professional reference on the cross-disciplinary
field of visual computing
Complements traditional textbooks in computer graphics/geometry/vision
Provides concise C++ code for common tasks that will appeal to a
broad audience of practitioners
Includes a color insert to illustrate principles covered
Includes a companion Web site with additional information,
details, and code from the book
AUTHOR BIO
Frank Nielsen (Japan) is a technical director and researcher at
Sony Computer Science Laboratories Inc., and has written
extensively on graphic design and programming in several journals
including Transactions on Graphics, Computational Geometry:
Theory and Applications, Transactions on Pattern Analysis, and
Machine Intelligence. His writings have also appeared in numerous
conference papers. Nielsen has also taught in France at ESSI and
ISIA (Ecole des Mines de Paris). He holds a Ph.D. degree in
Computer Science from the University of Nice (France).
ISBN 1-58450-427-7
PUB DATE August 2005
FORMAT Cloth - 560 pages