2015, X, 126 p. 38 illus.
ISBN 978-3-319-08284-4
Introductory book about quantum computing and theory of computing in general
Enables the reader to grasp the concepts without much effort
Includes various Engineering applications of quantum computing
A quantum computer is a computer based on a computational model which uses quantum mechanics, which is a subfield of physics to study phenomena at the micro level. There has been a growing interest on quantum computing in the 1990's, and some quantum computers at the experimental level were recently implemented. Quantum computers enable super-speed computation, and can solve some important problems whose solutions were regarded impossible or intractable with traditional computers.
This book provides a quick introduction to quantum computing for readers who have no backgrounds of both theory of computation and quantum mechanics. gElements of Quantum Computingh presents the history, theories, and engineering applications of quantum computing. The book is suitable to computer scientists, physicist, and software engineers.
Content Level ā Research
Keywords ā Computational Intelligence - Quantum Computer - Quantum Computing - Quantum Mechanics
Related subjects ā Applied & Technical Physics - Artificial Intelligence - Computational Intelligence and Complexity
Introduction.- Models of a Computer.- Quantum Mechanics.- Quantum Computers.- Applications of Quantum Computing.- Future of Quantum Computing.
Series: Springer Undergraduate Mathematics Series
2014, XVII, 204 p. 16 illus. in color.
ISBN 978-1-4471-6526-2
Due: September 14, 2014
Teaches undergraduate students to learn and improve their mathematical writing skills
Contains many exercises and solutions for self-learners
Tried and tested for many years on courses at Queen Mary, University London
This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student.
The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition.
Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150 of them have complete solutions, to facilitate self-study.
Mathematical Writing will be of interest to all mathematics students who want to raise the quality of their coursework, reports, exams, and dissertations.
Content Level ā Lower undergraduate
Keywords ā Elementary Logic - Mathematical Notation - Mathematical Symbols - Mathematical Thesis - Mathematical Writing - Proof Techniques
Related subjects ā Mathematics
Some writing tips.- Essential dictionary I.- Essential dictionary II.- Mathematical sentences.- Describing functions.- Writing well.- Forms of argument.- Induction.- Existence and definitions.- Writing a thesis.
Series: Abel Symposia, Vol. 9
2014, X, 184 p. 17 illus., 15 illus. in color.
Hardcover
ISBN 978-3-319-08556-2
Due: August 31, 2014
Focuses on operator-related function theory and time-frequency analysis, and the profound interplay between them
Collects proceedings of the 2012 Abel Symposium, held at the Norwegian Academy of Science and Letters, Oslo
Benefits scientists working in Harmonic and Complex Analysis, Mathematical Physics and Signal Processing
Presents current state of the art and discusses future research directions
This book collects the proceedings of the 2012 Abel Symposium, held at the Norwegian Academy of Science and Letters, Oslo. The Symposium, and this book, are focused on two important fields of modern mathematical analysis: operator-related function theory and time-frequency analysis; and the profound interplay between them.
Among the original contributions and overview lectures gathered here are a paper presenting multifractal analysis as a bridge between geometric measure theory and signal processing; local and global geometry of Prony systems and Fourier reconstruction of piecewise-smooth functions; Bernstein's problem on weighted polynomial approximation; singular distributions and symmetry of the spectrum; and many others.
Offering a selection of the latest and most exciting results obtained by world-leading researchers, the book will benefit scientists working in Harmonic and Complex Analysis, Mathematical Physics and Signal Processing.
1 P. Abry, S. Jaffard, and H. Wendt: A bridge between geometric measure theory and signal processing: Multifractal analysis.- 2 D. Batenkov and Y. Yomdin: Local and global geometry of Prony systems and Fourier reconstruction of piecewise-smooth functions.- 3 H. Feichtinger: Elements of postmodern harmonic analysis.- 4 G. Kozma and A. Olevskii: Singular distributions and symmetry of the spectrum.- 5 I. Laba: Recent progress on Favard length estimates for planar Cantor sets.- 6 A. Poltoratski: Bernstein's problem on weighted polynomial approximation.- 7 J. Sjostrand: Return to equilibrium, non-self-adjointness and symmetries, recent results with M. Hitrik and F. Herau.- 8 S. Treil: A remark on two weight estimates for positive dyadic operators.
Series: Fields Institute Communications, Vol. 72
2014, VIII, 231 p. 5 illus., 3 illus. in color.
Hardcover
Information
ISBN 978-1-4939-1254-4
Due: September 14, 2014
Contains a comprehensive treatment of the status of the corona problem
Treats both the history and context of the corona problem
Features many new results about the corona problem
The purpose of the corona workshop was to consider the corona problem in both one and several complex variables, both in the context of function theory and harmonic analysis as well as the context of operator theory and functional analysis. It was held in June 2012 at the Fields Institute in Toronto, and attended by about fifty mathematicians. This volume validates and commemorates the workshop, and records some of the ideas that were developed within.
The corona problem dates back to 1941. It has exerted a powerful influence over mathematical analysis for nearly 75 years. There is material to help bring people up to speed in the latest ideas of the subject, as well as historical material to provide background. Particularly noteworthy is a history of the corona problem, authored by the five organizers, that provides a unique glimpse at how the problem and its many different solutions have developed.
There has never been a meeting of this kind, and there has never been a volume of this kind. Mathematicians?both veterans and newcomers?will benefit from reading this book. This volume makes a unique contribution to the analysis literature and will be a valuable part of the canon for many years to come.
The History of the Corona Problem (R.G. Douglas, S.G. Krantz, E.T. Sawyer, S. Treil, B.D. Wick).- Corona Problem for H^\infty on Riemann Surfaces (A. Brudnyi).- Connections of the Corona Problem with Operator Theory and Complex Geometry (R.G. Douglas).- On the Maximal Ideal Space of a Sarason-Type Algebra on the Unit Ball (J. Eschmeier).- A Subalgebra of the Hardy Algebra Relevant in Control Theory and its Algebraic-Analytic Properties (M. Frentz, A. Sasane).- The Corona Problem in Several Complex Variables (S.G. Krantz).- Corona-Type Theorems and Division in Some Function Algebras on Planar Domains (R. Mortini, R. Rupp).- The Ring of Real-Valued Multivariate Polynomials: An Analyst's Perspective (R. Mortini, R. Rupp).- Structure in the Spectra of Some Multiplier Algebras (R. Rochberg).- Corona Solutions Depending Smoothly on Corona Data (S. Treil, B.D. Wick).- On the Taylor Spectrum of M-Tuples of Analytic Toeplitz Operators on the Polydisk (T.T. Trent).
Series: Springer Proceedings in Mathematics & Statistics, Vol. 94
2014, XX, 240 p. 10 illus., 8 illus. in color.
Hardcover
ISBN 978-3-319-08250-9
Due: September 14, 2014
Presents new research findings in the area of difference and differential equations
Addresses applications as well as theoretical perspectives
Of interest to a broad readership of researchers in applied mathematics
Delay differential and difference equations serve as models for a range of processes in biology, physics, engineering, and control theory. In this volume, the participants of the International Conference on Delay Differential and Difference Equations and Applications, Balatonfured, Hungary, July 15-19, 2013 present recent research in this quickly-evolving field. The papers relate to the existence, asymptotic, and oscillatory properties of the solutions; stability theory; numerical approximations; and applications to real world phenomena using deterministic and stochastic discrete and continuous dynamical systems.
On Necessary and Sufficient Conditions for Preserving Convergence Rates to Equilibrium in Deterministically and Stochastically Perturbed Differential Equations with Regularly Varying Nonlinearity.- Comparison Theorems for Second Order Functional Differential Equations.- Analysis of Qualitative Dynamic Properties of Positive Polynomial Systems using Transformations.- Almost Oscillatory Solutions of Second Order Difference Equations of Neutral Type.- Uniform Weak Disconjugacy and Principal Solutions for Linear Hamiltonian Systems.- Stability Criteria for Delay Differential Equations.- Analyticity of Solutions of a Differential Equation with a Threshold Delay.- Application of Advanced Integro-Differential Equations in Insurance Mathematics and Process Engineering.- Stability and Control of Systems with Propagation.- Discrete Ito Formula for Delay Stochastic Difference Equations with Multiple Noises.- On Semilinear Hyperbolic Functional Equations.- A Fast Parallel Algorithm for Delay Partial Differential Equations Modeling the Cell Cycle in Cell Lines Derived from Human Tumors.