Goong Chen / David A Church / Marlan O Scully / Texas A&M University, College Station, USA
Berthold-Georg Englert / National University of Singapore, Singapore
Carsten Henkel / Institut fur Physik, Universitat Potsdam, Germany
Bernd Rohwedder / Buenos Aires, Argentina

Principles, Designs and Analysis of Quantum Computing Devices

Series: Applied Mathematics and Nonlinear Science

ISBN: 1584886811
Publication Date: 8/15/2006
Number of Pages: 352

Presents in an accessible, tutorial style the analysis, modeling, and design of major types of quantum computing devices
Bridges theory and experiment in an important and rapidly growing area of interest
Addresses several types of quantum devices including ion traps, cavity QED, quantum dots, and NMR
Includes a full chapter on linear optics computers that emphasizes both classical and quantum electrodynamics
Covers such topics as two-level atoms and imperfect quantum operations

The design and construction of the quantum computer is a major goal of scientists in the 21st century, and rapid progress continues in the theory, design, and fabrication of quantum computing devices. Beginning with a concise introduction to quantum computations and written in a tutorial style, this book presents the analysis, modeling, and design of major types of quantum computing devices, including ion traps, cavity quantum electrodynamics, linear optics, quantum dots and quantum computing gates, and nuclear magnetic resonance. Additional coverage includes two-level atoms and imperfect quantum operations. The presentation includes illustrations, circuits, and diagrams that facilitate understanding.

Table of Contents

Introduction to Quantum Computation. Two-Level Atoms and Cavity QED. Imperfect Quantum Operations. Ion Traps. Quantum Dots Quantum Computing Gates. Linear Optics Computers. Nuclear Magnetic Resonance (Optical and Tentative).

Robert Carlson University of Colorado, Colorado Springs, USA

A Concrete Introduction to Real Analysis

Series: Pure and Applied Mathematics Volume: 280
ISBN: 1584886544
Publication Date: 6/2/2006
Number of Pages: 304

Introduces themes of estimation, approximation, and convergence through concrete problems from calculus
Includes exercises, ranging from simple to challenging, as well as a solutions manual
Supports an optional one-semester introduction to analysis, allowing stronger students to join in the second semester
Contains several auxiliary topics such as formal logic, infinite products, continued fractions, and rearrangement of series
Presents conceptual underpinnings of calculus without unnecessary abstraction

Drawing from the history of mathematics and practical applications, A Concrete Introduction to Real Analysis uses problems emerging from calculus to introduce themes of estimation, approximation, and convergence. Avoiding unnecessary abstractions to provide an accessible presentation of material, this book covers discrete calculus, selected area computations, Taylor's theorem, infinite sequences and series, limits, continuity and differentiability of functions, the Riemann integral, and much more. It contains a large collection of examples and exercises, ranging from simple problems that allow students to check their understanding to challenging problems that develop new material.

Table of Contents

Discrete Calculus. Selected Area Computations. Limits and Taylor's Theorem. Infinite Series. A Bit of Logic. Real Numbers. Functions. Integrals. More Integrals.

Luca Lorenzi / University of Parma, Italy
Marcello Bertoldi / Banca Intesa, Milano, Italy

Analytical Methods for Markov Semigroups

Series: Pure and Applied Mathematics
ISBN: 1584886595
Publication Date: 7/26/2006
Number of Pages: 550

Collects, unifies, and updates most of the results available only as research papers in the mathematical literature
Contains Schauder's estimates for non-homogeneous elliptic and parabolic problems and for degenerate elliptic operators modeled on Ornstein-Uhlenbeck
Analyzes Markov semigroups in spaces of bounded and continuous functions and in relevant Lp spaces
Includes analysis of Markov semigroups associated with elliptic operators with unbounded coefficients in unbounded domains
Features nondegenerate and degenerate Ornstein-Uhlenbeck operators in bounded and continuous functions and Lp spaces related to its Gaussian invariant measure

Analytical Methods for Markov Semigroups provides comprehensive results on Markov semigroups associated with elliptic operators with unbounded coefficients. With Schauder's estimates for non-homogeneous elliptic and parabolic problems and for a class of degenerate elliptic operators modeled on the Ornstein-Uhlenbeck operator, the authors thoroughly analyze Markov semigroups in spaces of bounded and continuous functions and in Lp spaces as well as Markov semigroups associated with elliptic operators with unbounded coefficients in unbounded domains. They also describe the spectrum and domain of the Ornstein-Uhlenbeck operator in Lp spaces related to the Lebesgue measure and to the invariant measure.

Table of Contents

Markov Semigroups in RN. Markov Semigroups in Unbounded Open Sets. A Class of Markov Semigroups in RN associated with Degenerate Elliptic Operators.

John Dauns / Tulane University, New Orleans, Louisiana, USA
Yiqiang Zhou / Memorial University of Newfoundland, St. John's, Canada

Classes of Modules

Series: Pure and Applied Mathematics Volume: 281

ISBN: 1584886609
Publication Date: 6/14/2006
Number of Pages: 232

Explores the themes of a natural class and a type submodule and how they structure much of ring and module theory
Gives tools, new methods, and new concepts to advance ring and module theory
Compiles previously scattered material with improved and extended results as well as simplified proofs
Provides self-contained, accessible material for students and readers with some knowledge of basic ring theory

Developing the type dimension of a module, Classes of Modules demonstrates that in the next generation of ring and module theory, it will be very important to work with natural classes and type submodules. This book presents the concepts of a natural class and a type submodule, exploring how they enter into much of ring and module theory. It carefully develops the foundations of the subject and the advanced theorems. Self-contained, accessible, and well-suited for those with some background in basic ring and module theory, this text compiles material that was previously scattered throughout the literature, along with improved and extended results as well as simplified proofs.

Table of Contents

Preliminary Background. Important Module Classes and Constructions. Finiteness Conditions. Type Theory of Modules: Dimension. Type Theory of Modules: Decompositions. Lattices of Module Classes.

M.A. Al-Gawaiz / King Saud University, Riyadh, Saudi Arabia
S.A. Elsanousi / King Saud University, Riyadh, Saudi Arabia

Elements of Real Analysis

Series: Pure and Applied Mathematics

ISBN: 1584886617
Publication Date: 8/1/2006
Number of Pages: 420

Presents material for a course on real analysis, aimed at undergraduate students with some knowledge of calculus
Covers the real number system, sequences, and series
Explores functions, limits, continuity, and differentiability
Includes integration theory, both Riemann and Lebesgue
Begins with basic axioms of the real number system and gradually builds the basic core of real analysis

Requiring only basic knowledge of elementary calculus, this book presents the necessary material for a first course in real analysis. It covers three groups of main topics: the real number system, sequences, and series; functions, limits, continuity, and differentiability; and integration, including Riemann integrals. It also contains two chapters on Lebesgue integrals, a topic not usually covered at this level. It begins with the basic axioms of the real number system and gradually builds the basic core of real analysis. Developed by experts who teach such courses, this text is ideal for undergraduate students in mathematics and related disciplines such as engineering, statistics, computer science, and physics.