August 2004, ISBN 0-306-48657-1, Hardbound
Book Series: INTERNATIONAL MATHEMATICAL SERIES : Volume 3
Different Faces of Geometry - edited by the world renowned
geometers S. Donaldson, Ya. Eliashberg, and M. Gromov - presents
the current state, new results, original ideas and open questions
from the following important topics in modern geometry:
Amoebas and Tropical Geometry;
Convex Geometry and Asymptotic Geometric Analysis;
Differential Topology of 4-Manifolds;
3-Dimensional Contact Geometry;
Floer Homology and Low-Dimensional Topology;
Kahler Geometry;
Lagrangian and Special Lagrangian Submanifolds;
Refined Seiberg-Witten Invariants.
These apparently diverse topics have a common feature in that
they are all areas of exciting current activity. The Editors have
attracted an impressive array of leading specialists to author
chapters for this volume: G. Mikhalkin (USA-Canada-Russia), V.D.
Milman (Israel) and A.A. Giannopoulos (Greece), C. LeBrun (USA),
Ko Honda (USA), P. Ozsvath (USA) and Z. Szabo (USA), C. Simpson (France),
D. Joyce (UK) and P. Seidel (USA), and S. Bauer (Germany). "One
can distinguish various themes running through the different
contributions. There is some emphasis on invariants defined by
elliptic equations and their applications in low-dimensional
topology, symplectic and contact geometry (Bauer, Seidel, Ozsvath
and Szabo). These ideas enter, more tangentially, in the articles
of Joyce, Honda and LeBrun. Here and elsewhere, as well as
explaining the rapid advances that have been made, the articles
convey a wonderful sense of the vast areas lying beyond our
current understanding. Simpson's article emphasizes the need for
interesting new constructions (in that case of Kahler and
algebraic manifolds), a point which is also made by Bauer in the
context of 4-manifolds and the "11/8 conjecture".
LeBrun's article gives another perspective on 4-manifold theory,
via Riemannian geometry, and the challenging open questions
involving the geometry of even "well-known" 4-manifolds.
There are also striking contrasts between the articles. The
authors have taken different approaches: for example, the
thoughtful essay of Simpson, the new research results of LeBrun
and the thorough expositions with homework problems of Honda. One
can also ponder the differences in the style of mathematics. In
the articles of Honda, Giannopoulos and Milman, and Mikhalkin,
the "geometry" is present in a very vivid and tangible
way; combining respectively with topology, analysis and algebra.
The papers of Bauer and Seidel, on the other hand, makes the
point that algebraic and algebro-topological abstraction (triangulated
categories, spectra) can play an important role in very
unexpected ways in concrete geometric problems." - From the
Preface by the Editors
Classics in Applied Mathematics 47
Initial-Boundary Value Problems and the Navier-Stokes Equations
gives an introduction to the vast subject of initial and initial-boundary
value problems for PDEs. Applications to parabolic and hyperbolic
systems are emphasized in this text. The Navier-Stokes equations
for compressible and incompressible flows are taken as an example
to illustrate the results.
Researchers and graduate students in applied mathematics and
engineering will find Initial-Boundary Value Problems and the
Navier-Stokes Equations invaluable. The subjects addressed in the
book, such as the well-posedness of initial-boundary value
problems, are of frequent interest when PDEs are used in modeling
or when they are solved numerically. The book explains the
principles of these subjects. The reader will learn what well-posedness
or ill-posedness means and how it can be demonstrated for
concrete problems. There are many new results, in particular on
the Navier-Stokes equations.
When the book was written, the main intent was to write a text on
initial-boundary value problems that was accessible to a rather
wide audience. Therefore, functional analytical prerequisites
were kept to a minimum or were developed in the book. Boundary
conditions are analyzed without first proving trace theorems, and
similar simplications have been used throughout. The direct
approach to the subject still gives a valuable introduction to an
important area of applied analysis.
Audience
This book continues to be useful to researchers and graduate
students in applied math and engineering.
Contents
Preface to the Classics Edition; Errata; Introduction; Chapter 1:
The Navier-Stokes Equations; Chapter 2: Constant-Coefficient
Cauchy Problems; Chapter 3: Linear Variable-Coefficient Cauchy
Problems in 1D; Chapter 4: A Nonlinear Example: Burgers’
Equations; Chapter 5: Nonlinear Systems in One Space Dimension;
Chapter 6: The Cauchy Problem for Systems in Several Dimensions;
Chapter 7: Initial-Boundary Value Problems in One Space
Dimension; Chapter 8: Initial-Boundary Value Problems in Several
Space Dimensions; Chapter 9: The Incompressible Navier-Stokes
Equations: The Spatially Periodic Case; Chapter 10: The
Incompressible Navier-Stokes Equations under Initial and Boundary
Conditions; Appendix 1: Notations and Results from Linear
Algebra; Appendix 2: Interpolation; Appendix 3: Sobolev
Inequalities; Appendix 4: Application of the Arzela-Ascoil
Theorem; References; Author Index; Subject Index.
June 2004 / Approx. 420 pages / Softcover / ISBN 0-89871-565-2
2004, XXIII, 427 p. 213 illus., Hardcover
ISBN: 3-540-00935-3
About this book
For the first time in book form, this comprehensive and
systematic monograph presents the methods for the reversible
synthesis of logic functions and circuits. This methodology
offers designers the capability to solve major problems in system
design now and in the future, such as the high rate of power
consumption, and the emergence of quantum effects for highly
dense ICs. The challenge addressed here is to design reliable
systems that consume as little power as possible and in which the
signals are processed and transmitted at very high speeds with
very high signal integrity. Researchers in academia or industry
and graduate students, who work in logic synthesis, computer
design, computer-aided design tools, and low power VLSI circuit
design, will find this book a valuable resource.
Keywords:
Computer Design
Logic Synthesis
Quantum Computing
Reversible Logic
Three Dimensional Circuits
Volume package: Computer Graphics & Geometric Modelling
2004, Approx. 912 p. 7 tabs. With CD-ROM., Hardcover
ISBN: 1-85233-818-0
About this textbook
Possibly the most comprehensive overview of computer graphics as
seen in the context of geometric modelling, this two volume work
covers implementation and theory in a thorough and systematic
fashion. Computer Graphics and Geometric Modelling:
Implementation and Algorithms, covers the computer graphics part
of the field of geometric modelling and includes all the standard
computer graphics topics. The first part deals with basic
concepts and algorithms and the main steps involved in displaying
photorealistic images on a computer. The second part covers
curves and surfaces and a number of more advanced geometric
modelling topics including intersection algorithms, distance
algorithms, polygonizing curves and surfaces, trimmed surfaces,
implicit curves and surfaces, offset curves and surfaces,
curvature, geodesics, blending etc. The third part touches on
some aspects of computational geometry and a few special topics
such as interval analysis and finite element methods. The volume
includes two companion programs.
Table of contents
Introduction Raster Algorithms Clipping Transformations and the
Graphics Pipeline Approaches to Geometric Modelling Basic
Geometric Modeling Tools Visible Surface Algorithms Colour
Illumination and Shading Rendering Techniques Curves in Computer
Graphics Surfaces in Computer Graphics Intersection Algorithms
Global Geometric Modelling Topics Local Geometric Modelling
Topics Intrinsic Geometric Modelling Computational Geometry
Topics Interval Analysis The Finite Element Method Quaternions
Digital Image Processing Topics Chaos and Fractals Appendices:
Notation Abstract Program Syntax IGES GM - AS Geometric Modelling
Program - on CD SPACE - A Manifold Exploration Program - on CD
Series: Monographs in Computer Science
2004, Approx. 340 p. 30 illus., Hardcover
ISBN: 0-387-95569-0
Due: July 2004
About this book
New discoveries about algorithms are leading scientists beyond
the Church-Turing Thesis, which governs the "algorithmic
universe" and asserts the conventionality of recursive
algorithms. A new paradigm for computation, the super-recursive
algorithm, offers promising prospects for algorithms of much
greater computing power and efficiency. Super-Recursive
Algorithms provides an accessible, focused examination of the
theory of super-recursive algorithms and its ramifications for
the computer industry, networks, artificial intelligence,
embedded systems, and the Internet. The book demonstrates how
these algorithms are more appropriate as mathematical models for
modern computers, and how these algorithms present a better
framework for computing methods in such areas as numerical
analysis, array searching, and controlling and monitoring systems.
Problems of software development, parallel and distributed
processing, pervasive and emerging computation, computer
architecture, machine learning, brain modeling, knowledge
discovery, and intelligent systems are addressed. Topics and
Features: * Encompasses and systematizes all main classes of
super-recursive algorithms and the theory behind them * Describes
the strengthening link between the theory of super-recursive
algorithms and actual algorithms close to practical realization *
Examines the theory’s basis as a foundation for advancements in
computing, information science, and related technologies *
Highlights how super-recursive algorithms pave the way for more
advanced design, utilization, and maintenance of computers *
Possesses a comprehensive bibliography and index This clear
exposition, motivated by numerous examples and illustrations,
serves to develop a new paradigm for complex, high-performance
computing based on both partial recursive functions and more
inclusive recursive algorithms. Researchers and advanced students
interested in theory of computation and algorithms will find the
book an essential resource for an important new class of
algorithms.
Table of contents
* Introduction * Recursive algorithms * Subrecursive algorithms *
Super-recursive algorithms: Problems of computability * Super-recursive
algorithms: Problems of efficiency * Conclusion