Expected publication date is October 12, 2005
Description
This monograph presents a geometric theory for incompressible
flow and its applications to fluid dynamics. The main objective
is to study the stability and transitions of the structure of
incompressible flows and its applications to fluid dynamics and
geophysical fluid dynamics. The development of the theory and its
applications goes well beyond its original motivation of the
study of oceanic dynamics.
The authors present a substantial advance in the use of geometric
and topological methods to analyze and classify incompressible
fluid flows. The approach introduces genuinely innovative ideas
to the study of the partial differential equations of fluid
dynamics. One particularly useful development is a rigorous
theory for boundary layer separation of incompressible fluids.
The study of incompressible flows has two major interconnected
parts. The first is the development of a global geometric theory
of divergence-free fields on general two-dimensional compact
manifolds. The second is the study of the structure of velocity
fields for two-dimensional incompressible fluid flows governed by
the Navier-Stokes equations or the Euler equations.
Motivated by the study of problems in geophysical fluid dynamics,
the program of research in this book seeks to develop a new
mathematical theory, maintaining close links to physics along the
way. In return, the theory is applied to physical problems, with
more problems yet to be explored.
The material is suitable for researchers and advanced graduate
students interested in nonlinear PDEs and fluid dynamics.
Contents
Introduction
Structure classification of divergence-free vector fields
Structural stability of divergence-free vector fields
Block stability of divergence-free vector fields on manifolds
with nonzero genus
Structural stability of solutions of Navier-Stokes equations
Structural bifurcation for one-parameter family of divergence-free
vector fields
Two examples
Bibliography
Index
Details:
Series: Mathematical Surveys and Monographs,Volume: 119
Publication Year: 2005
ISBN: 0-8218-3693-5
Paging: approximately 288 pp.
Binding: Hardcover
Expected publication date is October 22, 2005
Description
The topic of this book is the study of singular perturbations of
ordinary differential equations, i.e., perturbations that
represent solutions as asymptotic series rather than as analytic
functions in a perturbation parameter. The main method used is
the so-called WKB (Wentzel-Kramers-Brillouin) method, originally
invented for the study of quantum-mechanical systems. The authors
describe in detail the WKB method and its applications to the
study of monodromy problems for Fuchsian differential equations
and to the analysis of Painleve functions. The volume is suitable
for graduate students and researchers interested in differential
equations and special functions.
Contents
Borel resummation
WKB analysis of Schrodinger equations
Applications of WKB analysis to global problems
WKB analysis of the Painleve function
Future directions and projects
Appendix
Bibliography
Index
Details:
Series: Translations of Mathematical Monographs, Volume 227
Subseries: Iwanami Series in Modern Mathematics
Publication Year: 2005
ISBN: 0-8218-3547-5
Paging: approximately 136 pp.
Binding: Hardcover
ISBN 1-58053-642-5
510 pages.
Copyright 2005.
“This is the book colleagues and I wish we had over the last
decade when teaching our graduate cryptography class. Rolf has
done a wonderful job of making so much important information
accessible.”
---From the foreword by Gene Spafford
Whether you’re new to the field or looking to broaden your
knowledge of contemporary cryptography, this comprehensive
resource puts all aspects of this important topic into
perspective. Delivering an accurate introduction to the current
state-of-the-art in modern cryptography, the book offers you a
practical understanding of essential tools and applications to
help you with your daily work. You also find complete coverage of
the underpinnings and basic principles of cryptography to help
you fully master the material.
From mathematical fundamentals and an overview of cryptographic
systems… to details on unkeyed, secret key, and public key
cryptosystems, this authoritative reference gives you solid
working knowledge of the latest and most critical concepts,
techniques, and systems in contemporary cryptography.
Additionally, the book is supported with over 200 equations, more
than 60 illustrations, and numerous time-saving URLs that connect
you to Web sites with related information.
Contents:
Introduction - Cryptology. Cryptographic Systems. Historical
Background Information. Outline of the Book.
Cryptographic Systems - Unkeyed Cryptosystems. Secret Key
Cryptosystems. Public Key Cryptosystems. Final Remarks.
Part I: Mathematical Fundamentals
Discrete Mathematics - Algebraic Basics. Integer Arithmetic.
Modular Arithmetic. Elliptic Curves. Final Remarks.
Probability Theory - Basic Terms and Concepts. Random Variables.
Final Remarks.
Information Theory - Introduction. Entropy. Redundancy. Final
Remarks.
Complexity Theory - Preliminary Remarks. Introduction. Asymptotic
Order Notation. Efficient Computations. Computational Models.
Complexity Classes. Final Remarks
Part II: Unkeyed Cryptosystems
One-Way Functions - Introduction. Conjectured Candidate One-Way
Functions. Integer Factoring Algorithms. Computing Discrete
Logarithms. Hard-Core Predicates. Elliptic Curve Cryptography.
Final Remarks.
Cryptographic Hash Functions - Introduction. Merkle-Damgaard
Construction. Exemplary Cryptographic Hash Functions. Final
Remarks.
Random Bit Generators - Introduction. Realizations and
Implementations. Statistical Randomness Testing. Final Remarks.
Part III: Secret Key Crytosystems
Symmetric Encryption Systems - Introduction. Block Ciphers.
Stream Ciphers. Perfectly Secure Encryption. Final Remarks.
Message Authentication Codes - Introduction. Computationally
Secure MACs. Information-Theoretically Secure MACs. Final Remarks.
Pseudo-Random Bit Generators - Introduction. Cryptographically
Secure PRBGs. Final Remarks.
Pseudo-Random Functions - Introduction. Constructions. Random
Oracle Model. Final Remarks.
Part IV: Public Key Cryptosystems
Asymmetric Encryption Systems - Introcution. Merkle’s Puzzles.
RSA. Rabin. ElGamal. Identity-Based Encryption. Probabilistic
Encryption. Optimal Asymmetric Encryption Padding. Final Remarks.
Digital Signature Systems - Introduction. RSA. ElGamal. Schnorr.
DSA. One-Time Signature Systems. Provably Secure Digital
Signature Systems. Digital Signatures for Streams. Variations.
Final Remarks.
Key Establishment - Introduction. Key Distribution Protocols. Key
Agreement Protocols. Quantum Key Exchange. Final Remarks.
Entity Authentication - Introduction. Authentication Technologies.
Zero-Knowledge Authentication Protocols. Final Remarks.
Secure Multi-Party Computation.
Part V: Epilogue
Key Management - Introduction. Key Generation and Distribution.
Key Storage. Key Destruction. Final Remarks.
Conclusions.
Rolf Oppliger is the founder and owner of eSECURITY Technologies,
works for the Swiss federal administration, and teaches at the
University of Zurich. He is also the author of Security
Technologies for the World Wide Web, Second Edition, Internet and
Intranet Security, Second Edition and Secure Messaging with PGP
and S/MIME (Artech House, 2003, 2002, 2001) among other titles.
Dr. Oppliger received his M.Sc. and Ph.D. in Computer Science
from the University of Berne, Switzerland, and the Venia Legendi
in Computer Science from the University of Zurich, Switzerland.
Series: Progress in Nonlinear Differential Equations and Their
Applications, Vol. 63
2005, Approx. 455 p., Hardcover
ISBN: 3-7643-7249-4
About this book
This volume contains contributions by former students and
collaborators of Haim Brezis given in honor of his 60th
anniversary at a conference in Gaeta. H. Brezis has made
significant contributions in the fields of partial differential
equations and functional analysis. He is an inspiring teacher and
counselor of many mathematicians in the front ranks. The
collection of papers presented here grew out from his deep
insight of analysis. In addition it reflects Brezis's elegant way
of creative thinking.
Table of contents
Preface.- 37 contributions by experts in the field.
Series: Progress in Nonlinear Differential Equations and Their
Applications, Vol. 64
2005, Approx. 580 p., Hardcover
ISBN: 3-7643-7266-4
About this book
The book offers an overview of some of the most important
developments in the field of nonlinear analysis, including
- bifurcation theory
- dynamical properties of parabolic semiflows
- fluid dynamics, and
- degenerate parabolic problems.
Written for:
Graduate and postgraduate students, researchers
Keywords:
Calculus of variations
Functional analysis
Navier-Stokes equations
Numerical analysis
Partial differential equations
Table of contents
Preface.- 32 contributions by experts in the field.
*
Series: Advanced Courses in Mathematics - CRM Barcelona
2005, Approx. 280 p., Softcover
ISBN: 3-7643-7294-X
About this textbook
The aim of this text is to treat selected topics of the subject
of contemporary cryptology, structured in five quite independent
but related themes: Efficient distributed computation modulo a
shared secret, multiparty computation, modern cryptography,
provable security for public key schemes, and efficient and
secure public-key cryptosystems.
Table of contents
Efficient Distributed Computation Modulo a Shared Secret (D.
Catalano).- Multiparty Computation, an Introduction (R. Cramer
and I. Damgard).- Foundations of Modern Cryptography (G. Di
Crescenso).- Provable Security for Public Key Schemes (D.
Pointcheval).- Efficient and Secure Public-Key Cryptosystems (T.
Takagi).
2005, Approx. 160 p. 20 illus., Hardcover
ISBN: 0-8176-4387-7
About this book
This monograph examines and develops the Global Smoothness
Preservation Property (GSPP) and the Shape Preservation Property
(SPP) in the field of interpolation of functions. The study is
developed for the univariate and bivariate cases using well-known
classical interpolation operators of Lagrange, Grunwald, Hermite-Fejer
and Shepard type. One of the first books on the subject, it
presents interesting new results alongwith an excellent survey of
past research.
Table of contents
Introduction.- Global Smoothness Preservation, Univariate Case.-
Partial Shape Preservation, Univariate Case.- Global Smoothness
Preservation, Bivariate Case.- Partial Shape Preservation,
Bivariate Case.- Appendix: Graphs of Shepard Surfaces.-
Bibliography Index.