Alexander V Sergienko Boston University, Massachusetts, USA

Quantum Communications and Cryptography

ISBN: 0849336848
Publication Date: 11/15/2005
Number of Pages: 256

Offers the first comprehensive, in-depth overview of the development and current state of the field
Provides an overview of the history of quantum cryptography as well as future directions
Discusses the basics of quantum logic, entanglement, state sharing, and continuous polarization states
Presents the latest experimental results and theoretical developments together with practical implementations
Considers advanced applications such as free-space quantum cryptography and noise-immune key distribution

All current methods of secure communication such as public-key cryptography can eventually be broken by faster computing. At the interface of physics and computer science lies a powerful solution for secure communications: quantum cryptography. Because eavesdropping changes the physical nature of the information, users in a quantum exchange can easily detect eavesdroppers. This allows for totally secure random key distribution, a central requirement for use of the one-time pad. Since the one-time pad is theoretically proven to be undecipherable, quantum cryptography is the key to perfect secrecy.

Quantum Communications and Cryptography is the first comprehensive review of the past, present, and potential developments in this dynamic field. Leading expert contributors from around the world discuss the scientific foundations, experimental and theoretical developments, and cutting-edge technical and engineering advances in quantum communications and cryptography.

The book describes the engineering principles and practical implementations in a real-world metropolitan network as well as physical principles and experimental results of such technologies as entanglement swapping and quantum teleportation. It also offers the first detailed treatment of quantum information processing with continuous variables. Technologies include both free-space and fiber-based communications systems along with the necessary protocols and information processing approaches.

Bridging the gap between physics and engineering, Quantum Communications and Cryptography supplies a springboard for further developments and breakthroughs in this rapidly growing area.

Table of Contents

A.B. Kharazishvili Tbilisi State University, Georgia

Strange Functions in Real Analysis, Second Edition

Series: Pure and Applied Mathematics Volume: 277

ISBN: 1584885823
Publication Date: 12/21/2005
Number of Pages: 408

Explores strange functions in real analysis and their applications
Includes five new chapters and revised material throughout
Features additional exercises and expanded references
Presents basic set-theoretical concepts as well as basic concepts of general topology and classical descriptive set theory

This book explores strange functions in real analysis and their applications. This book presents basic set-theoretical concepts such as binary relations of special type and the Generalized Continuum Hypothesis. It examines various functions whose constructions need essentially noneffective methods and those whose existence arises from known hypotheses. It also discusses basic concepts of general topology and classical descriptive set theory. This second edition features five new chapters, with revised material throughout the text. It includes additional exercises as well as an expanded reference list. Strange Functions in Real Analysis is a valuable resource for students and mathematicians.

Table of Contents

Introduction: Basic Concepts. Cantor and Peano Type Functions. Functions of First Baire Class (new). Semicontinuous Functions which are not Countably Continuous (new). Singular Monotone Functions. Everywhere Differentiable Nowhere Monotone Functions. Nowhere Approximately Differentiable Functions. Blumberg's Theorem and Sierpinski-Zygmund Function. Lebesgue Nonmeasurable Functions and Functions without the Baire Property. Hamel Basis and Cauchy Functional Equation. Luzin Sets, Sierpinski Sets and their Applications. Absolutely Nonmeasurable Additive Functions (new). Egorov Type Theorems. Sierpinski's Partition of the Euclidean Plane. Bad Functions Defined on Second Category Sets (new). Sup-measurable and Weakly Sup-measurable Functions. Generalized Step-functions and Superposition Operators (new). Ordinary Differential Equations with Bad Right-hand Sides. Nondifferentiable Functions from the Point of View of Category and Measure.

Marwan Moubachir INRIA-Project OPALE, Sophia Antipolis, France
Jean-Paul Zolesio INRIA , Sophia Antipolis, France

Moving Shape Analysis and Control: Applications to Fluid Structure Interactions

Series: Pure and Applied Mathematics Volume: 278

ISBN: 1584886110
Publication Date: 1/6/2006
Number of Pages: 344

Provides various tools to handle moving domains on the level of definition, computation, optimization, and control
Addresses real-world engineering problems with applications
Emphasizes the eularian approach using evolution and derivation tools for controlling fluids and systems
Includes new chapters devoted to fluid control described using Navier-Stokes equations
Features new approaches to deal with boundary control fluid-structure interaction systems

Moving Shape Analysis & Control: Applications to Fluid Structure Interactions provides a mathematical analysis of problems related to the evolution of domains. This book addresses real-world engineering, with applications to such situations as free surface flows, phase changes, fracture and contact problems, and fluid interaction problems in industrial settings such as civil transport vehicles. It emphasizes the eularian approach using evolution and derivation tools for controlling fluids and systems. It also includes chapters devoted to fluid control described using Navier-Stokes equations and features new approaches to deal with boundary control fluid-structure interaction systems.

Table of Contents

Introduction. An introductory example: the inverse Stefan problem. Weak evolution of sets and tube derivatives. Shape differential equation and level set formulation. Dynamical shape control of the Navier-Strokes equations. Tube derivative in a lagrangian setting. Sensitivity analysis for a simple fluid-solid interaction system. Sensitivity analysis for a general fluid-structure interaction system. A Functional spaces and regulatity of domains. B Distribution spaces. C The Fourier Transform. D Sobolev spaces.

Roland Glowinski Univ of Houston
Jean-Paul Zolesio INRIA , Sophia Antipolis, France

Free and Moving Boundaries: Analysis, Simulation and Control

Series: Lecture Notes in Pure and Applied Mathematics

ISBN: 1584886064
Publication Date: 4/15/2006
Number of Pages: 300

Emphasizes numerical and theoretical control of moving boundaries
Explores the problems of optimal control theory applied to partial differential equations arising from continuum mechanics
Addresses boundary variation and control, dynamical control of geometry, optimization, and inverse problems
Features contributions from leading experts

Featuring contributions presented at an important international conference, Free and Moving Boundaries: Analysis, Simulation, and Control emphasizes numerical and theoretical control of moving boundaries in fluid structure couple systems, arteries, shape stabilization level methods, family of moving geometries, and boundary control. This book explores the problems of optimal control theory applied to partial differential equations arising from continuum mechanics. It also specifically addresses the topics of boundary variation and control, dynamical control of geometry, optimization, and inverse problems arising in such areas as biomathematics and controlling fluid-structure devices.

Leandro Pardo University of Madrid, Spain

Statistical Inference Based on Divergence Measures

Series: Statistics: A Series of Textbooks and Monographs Volume: 185

ISBN: 1584886005
Publication Date: 10/5/2005
Number of Pages: 512

Presents alternative procedures to classical problems of statistical inference, such as estimation and testing
Introduces and compares minimum divergence estimators as well as divergence test statistics
Covers the classical maximum likelihood estimator, chi-square test statistics, and the likelihood ratio test
Includes over 120 exercises with solutions

Organized in systematic way, Statistical Inference Based on Divergence Measures presents classical problems of statistical inference, such as estimation and hypothesis testing, on the basis of measures of entropy and divergence with applications to multinomial and generation populations. On the basis of divergence measures, this book introduces minimum divergence estimators as well as divergence test statistics and compares them to the classical maximum likelihood estimator, chi-square test statistics, and the likelihood ratio test in different statistical problems. The text includes over 120 exercises with solutions, making it ideal for students with a basic knowledge of statistical methods.

Table of Contents

Divergence Measures: Definition and Properties. Entropy as a Measure of Diversity: Sampling Distributions. Goodness of Fit Based on f-Divergence Statistics: Simple Null Hypothesis. Optimality of f-Divergence Test Statistics in Goodness-of-Fit. Minimum f-Divergence Estimators. Goodness-of-Fit based on f-Divergence Statistics: Composite Null Hypothesis. Testing Loglinear Models using f-Divergence Test Statistics. f-Divergence Measures in Contingency Tables. Testing in General Populations. References.