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Basic Real Analysis
Basic Real Analysis and Advanced Real Analysis (available separately or together as a Set) systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.
Basic Algebra
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole.Basic Algebra presents the subject matter in a forward-looking way that takes into account its historical development. It is suitable as a text in a two-semester advanced undergraduate or first-year graduate sequence in algebra, possibly supplemented by some material from Advanced Algebra at the graduate level. It requires of the reader only familiarity with matrix algebra, an understanding of the geometry and reduction of linear equations, and an acquaintance with proofs.
Automorphic Forms and Lie Superalgebras
Most known examples of Lie superalgebras with a related automorphic form such as the Fake Monster Lie algebra whose reflection group is given by the Leech lattice arise from (super)string theory and can be derived from lattice vertex algebras. The No-Ghost Theorem from dual resonance theory and a conjecture of Berger-Li-Sarnak on the eigenvalues of the hyperbolic Laplacian provide strong evidence that they are of rank at most 26.The aim of this book is to give the reader the tools to understand the ongoing classification and construction project of this class of Lie superalgebras and is ideal for a graduate course.
Automatic Differentiation : Applications, Theory, and Implementations
This collection covers the state of the art in automatic differentiation theory and practice. Practitioners and students will learn about advances in automatic differentiation techniques and strategies for the implementation of robust and powerful tools. Computational scientists and engineers will benefit from the discussion of applications, which provide insight into effective strategies for using automatic differentiation for design optimization, sensitivity analysis, and uncertainty quantification.
Atoms, molecules and photons : An introduction to atomic- molecular- and quantum physics
This introduction to Atomic and Molecular Physics explains how our present model of atoms and molecules has been developed over the last two centuries both by many experimental discoveries and, from the theoretical side, by the introduction of quantum physics to the adequate description of micro-particles. It illustrates the wave model of particles by many examples and shows the limits of classical description. The interaction of electromagnetic radiation with atoms and molecules and its potential for spectroscopy is outlined in more detail and in particular lasers as modern spectroscopic tools are discussed more thoroughly. Many examples and problems with solutions are offered to encourage readers to actively engage in experimentation.
Asymptotic Theory of Statistics and Probability
An encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. The book has 34 chapters over a wide range of topics, nearly 600 exercises for practice and instruction, and another 300 worked out examples. It also includes a large compendium of 300 useful inequalities on probability, linear algebra, and analysis that are collected together from numerous sources, as an invaluable reference for researchers in statistics, probability, and mathematics.
Asymptotic Analysis and Boundary Layers
Presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained.
Astrophysics is easy! : An introduction for the amateur astronomer
With some justification, many amateur astronomers believe astrophysics is a very difficult subject, requiring at least degree-level mathematics to understand it properly. This isn’t necessarily the case. Mike Inglis' quantitative approach to the subject explains all aspects of astrophysics in simple terms and cuts through the incomprehensible mathematics with which this fascinating subject is all too often associated. Astrophysics is Easy! begins by looking at the H-R diagram and other basic tools of astrophysics, then ranges across the universe, from a first look at the interstellar medium and nebulae, through the birth, evolution and death of stars, to the physics of galaxies and clusters of galaxies.
Astrophysics : A new approach
For a quantitative understanding of the physics of the universe - from the solar system through the milky way to clusters of galaxies all the way to cosmology - these edited lecture notes are perhaps among the most concise and also among the most critical ones: Astrophysics has not yet stood the redundancy test of laboratory physics, hence should be wary of early interpretations. Special chapters are devoted to magnetic and radiation processes, supernovae, disks, black-hole candidacy, bipolar flows, cosmic rays, gamma-ray bursts, image distortions, and special sources. At the same time, planet earth is viewed as the arena for life, with plants and animals having evolved to homo sapiens during cosmic time. -- This text is unique in covering the basic qualitative and quantitative tools, formulae as well as numbers, needed for the precise interpretation of frontline phenomena in astrophysical research. The author compares mainstream interpretations with new and even controversial ones he wishes to emphasize.
Astronomical image and data analysis
With information and scale as central themes, this comprehensive survey explains how to handle real problems in astronomical data analysis using a modern arsenal of powerful techniques. It treats those innovative methods of image, signal, and data processing that are proving to be both effective and widely relevant. The coverage includes chapters or appendices on: detection and filtering; image compression; multichannel, multiscale, and catalog data analytical methods; wavelets transforms, Picard iteration, and software tools. This second edition of Starck and Murtagh's highly appreciated reference again deals with topics that are at or beyond the state of the art. It presents material which is more algorithmically oriented than most alternatives and broaches new areas like ridgelet and curvelet transforms. Throughout the book various additions and updates have been made.
Assessing and Managing Earthquake Risk : Geo-scientific and Engineering Knowledge for Earthquake Risk Mitigation: developments, tools, techniques
This book points out the need of a multidisciplinary approach in the field of risk assessment and management. It provides an overview of the problems, approaches and common practices directly related to earthquake risk mitigation and, in particular, to the preparation of earthquake emergency plans. Written by a team of specialists from different disciplines, the authors worked together extensively in order to create unity and continuity in the text as a whole. Each topic is illustrated with examples of actual applications taken from the bibliography – including websites with available relevant information. Case studies and information on some relevant international projects are given.
Aspects of Mathematical Finance
Considering the stupendous gain in importance, in the banking and insurance industries since the early 1990’s, of mathematical methodology, especially probabilistic methodology, it was a very natural idea for the French "Académie des Sciences" to propose a series of public lectures, accessible to an educated audience, to promote a wider understanding for some of the fundamental ideas, techniques and new tools of the financial industries. These lectures were given at the "Académie des Sciences" in Paris by internationally renowned experts in mathematical finance, and later written up for this volume which develops, in simple yet rigorous terms, some challenging topics such as risk measures, the notion of arbitrage, dynamic models involving fundamental stochastic processes like Brownian motion and Lévy processes.
Aspects of Brownian motion
Stochastic calculus and excursion theory are very efficient tools to obtain either exact or asymptotic results about Brownian motion and related processes. The emphasis of this book is on special classes of such Brownian functionals as: - Gaussian subspaces of the Gaussian space of Brownian motion; - Brownian quadratic funtionals; - Brownian local times, - Exponential functionals of Brownian motion with drift; - Winding number of one or several Brownian motions around one or several points or a straight line, or curves; - Time spent by Brownian motion below a multiple of its one-sided supremum.
Argumentation Methods for Artificial Intelligence in Law
In this book, Walton presents his perspective on argumentation methods for artificial intelligence and law. … the different tools are combined in a way that makes them potentially useful for understanding legal reasoning. … this book offers a valuable perspective on the current state and future research directions of argumentation methods for artificial intelligence and law." (Jelle van Veenen, Artificial Intelligence and Law,
Approximation of Additive Convolution-Like Operators : Real C*-Algebra Approach
Various aspects of numerical analysis for equations arising in boundary integral equation methods have been the subject of several books published in the last 15 years [95, 102, 183, 196, 198]. Prominent examples include various classes of o- dimensional singular integral equations or equations related to single and double layer potentials. Usually, a mathematically rigorous foundation and error analysis for the approximate solution of such equations is by no means an easy task. One reason is the fact that boundary integral operators generally are neither integral operatorsof the formidentity plus compact operatornor identity plus an operator with a small norm. Consequently, existing standard theories for the numerical analysis of Fredholm integral equations of the second kind are not applicable. In the last 15 years it became clear that the Banach algebra technique is a powerful tool to analyze the stability problem for relevant approximation methods [102, 103, 183, 189]. The starting point for this approach is the observation that the ? stability problem is an invertibility problem in a certain BanachorC -algebra. As a rule, this algebra is very complicated – and one has to ?nd relevant subalgebras to use such tools as local principles and representation theory.
Applied Quantitative Finance
Applied Quantitative Finance (2nd edition) provides a comprehensive and state-of-the-art treatment of cutting-edge topics and methods. It provides solutions to and presents theoretical developments in many practical problems such as risk management, pricing of credit derivatives, quantification of volatility and copula modelling. The synthesis of theory and practice supported by computational tools is reflected in the selection of topics as well as in a finely tuned balance of scientific contributions on practical implementation and theoretical concepts. This linkage between theory and practice offers theoreticians insights into considerations of applicability and, vice versa, provides practitioners comfortable access to new techniques in quantitative finance.
Applied Physics of Carbon Nanotubes : Fundamentals of Theory, Optics and Transport Devices
The book describes the state-of-the-art in fundamental, applied and device physics of nanotubes, including fabrication, manipulation and characterization for device applications; optics of nanotubes; transport and electromechanical devices and fundamentals of theory for applications. This information is critical to the field of nanoscience since nanotubes have the potential to become a very significant electronic material for decades to come. The book will benefit all all readers interested in the application of nanotubes, either in their theoretical foundations or in newly developed characterization tools that may enable practical device fabrication.
Applied Multivariate Statistical Analysis
This book presents the tools and concepts of multivariate data analysis in a way that is understandable for non-mathematicians and practitioners who face statistical data analysis.
Applied computational materials modeling : Theory, simulation and experiment
this book provides the average person working in the materials field with a more balanced perspective of the role that computational modeling can play in every day research and development efforts. This is done by presenting a series of examples of the successful application of various computational modeling procedures (everything from first principles to quantum approximate to CALPHAD methods) to real life surface and bulk alloy problems.This book should have a large appeal in the materials community, both for experimentalists who would greatly benefit from adding computational methods to their everyday research regimes, as well as for those scientists/engineers familiar with a particular computational method who would like to add complementary techniques to their arsenal of research and development tools
ANEMONA : A Mulit-agent Methodology for Holonic Manufacturing Systems
ANEMONA is a multi-agent system (MAS) methodology for holonic manufacturing system (HMS) analysis and design, based on HMS requirements. The development process of ANEMONA provides clear and HMS-specific modeling guidelines for HMS designers, and complete development phases for the HMS life cycle.
