Basic Methods of Linear Functional Analysis

The book is a benefit for graduate and postgraduate students in the areas of operations research, decision theory, optimization theory, linear algebra, interval analysis and fuzzy sets. The book will

This textbook introduces readers to the basic concepts of quasi-Monte Carlo methods for numerical integration and to the theory behind them. The comprehensive treatment of the subject with detailed ex

Probability theory has been extraordinarily successful at describing a variety of phenomena, from the behaviour of gases to the transmission of messages, and is, besides, a powerful tool with applications throughout mathematics. At its heart are a number of concepts familiar in one guise or another to many: Gauss' bell-shaped curve, the law of averages, and so on, concepts that crop up in so many settings they are in some sense universal. This universality is predicted by probability theory to a remarkable degree. This book explains that theory and investigates its ramifications. Assuming a good working knowledge of basic analysis, real and complex, the author maps out a route from basic probability, via random walks, Brownian motion, the law of large numbers and the central limit theorem, to aspects of ergodic theorems, equilibrium and nonequilibrium statistical mechanics, communication over a noisy channel, and random matrices. Numerous examples and exercises enrich the text.

Probability theory has been extraordinarily successful at describing a variety of phenomena, from the behaviour of gases to the transmission of messages, and is, besides, a powerful tool with applications throughout mathematics. At its heart are a number of concepts familiar in one guise or another to many: Gauss' bell-shaped curve, the law of averages, and so on, concepts that crop up in so many settings they are in some sense universal. This universality is predicted by probability theory to a remarkable degree. This book explains that theory and investigates its ramifications. Assuming a good working knowledge of basic analysis, real and complex, the author maps out a route from basic probability, via random walks, Brownian motion, the law of large numbers and the central limit theorem, to aspects of ergodic theorems, equilibrium and nonequilibrium statistical mechanics, communication over a noisy channel, and random matrices. Numerous examples and exercises enrich the text.

The purpose of A Theory of the Absolute is to sketch a theory of the basic structure of empirical reality, and its relation to the Absolute. It is influenced by the methods of analytic philosophy as w

This book offers a critical and in-depth analysis of access to justice from international and Islamic perspectives. Existing Western models have highlighted the mechanisms by which individuals can access justice; however, access to justice incorporates various conceptions of justice and of its users. This book evaluates the historical development of the justice sector in Iran and discusses issues including the performance of the justice sector, judicial independence, efficiency and accessibility, and normative protection, together with an analysis of barriers. It explores the legal empowerment of users, with a specific focus on women, and presents the findings of a survey study on the perceptions of Iranian women. This study is designed to focus on women's basic legal knowledge, their familiarity with legal procedure, perceptions of cultural barriers, issues that influence their preference for mechanisms of formal or alternative dispute solutions, and their level of satisfaction with t

Serving both as an introduction to the subject and as a reference, this book presents the theory in elegant form and with modern concepts and notation. It covers the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains. The approach is a blend of classical analysis and symmetry group theoretic methods. Finite reflection groups are used to motivate and classify symmetries of weight functions and the associated polynomials. This revised edition has been updated throughout to reflect recent developments in the field. It contains 25% new material, including two brand new chapters on orthogonal polynomials in two variables, which will be especially useful for applications, and orthogonal polynomials on the unit sphere. The most modern and complete treatment of the subject available, it will be useful to a wide audience of mathematicians and applied scientists, including physicists, chemists and engineers.

This detailed and up-to-date guide to modern MOS structures describes important tools, cutting-edge models, novel phenomena and current challenges in measuring and improving the control of future MOS systems for transistor channels. Building up from basic electrostatics, it introduces the ideal MOS system, physical and electrical properties of high-k oxides, their dielectric constants, and energy offsets to semiconductors and metals, before moving on to electrical and physical characterization methods for high-k dielectric materials. Finally, real MOS systems are introduced: high-k dielectrics and interlayers, the influence of phonon dynamics, interface states and bulk traps, effective metal work functions, gate leakage phenomena and high mobility channel materials. Abstract concepts are supported by practical examples and critical comparison, encouraging an intuitive understanding of the principles at work, and presented alongside recent theoretical and experimental results, making th

Using a wide range of professional genres such as research papers, business reports, performance commentaries, guidebooks and legal documents, this study focuses on the discourse of professional writing, employing analytic paradigms from systemic-functional linguistics, pragmatics, text analysis, sociology and anthropological linguistics. Kenneth Kong argues that while professions use different sets of practices, their use of language displays many universals. This is demonstrated through the analysis of data from a broad cross-section of professional settings such as medicine, law, business, mass media and engineering. This examination of professional discourse, and its important role in society, will be of interest to researchers in applied linguistics, to professionals who want to understand the role of language in their work, and to teachers of English for specific purposes.

The majority of empirical research in economics ignores the potential benefits of nonparametric methods, while the majority of advances in nonparametric theory ignore the problems faced in applied econometrics. This book helps bridge this gap between applied economists and theoretical nonparametric econometricians. It discusses in depth, and in terms that someone with only one year of graduate econometrics can understand, basic to advanced nonparametric methods. The analysis starts with density estimation and motivates the procedures through methods that should be familiar to the reader. It then moves on to kernel regression, estimation with discrete data, and advanced methods such as estimation with panel data and instrumental variables models. The book pays close attention to the issues that arise with programming, computing speed, and application. In each chapter, the methods discussed are applied to actual data, paying attention to presentation of results and potential pitfalls.

Emphasizing practical understanding over the technicalities of specific algorithms, this elegant textbook is an accessible introduction to the field of optimization, focusing on powerful and reliable convex optimization techniques. Students and practitioners will learn how to recognize, simplify, model and solve optimization problems - and apply these principles to their own projects. A clear and self-contained introduction to linear algebra demonstrates core mathematical concepts in a way that is easy to follow, and helps students to understand their practical relevance. Requiring only a basic understanding of geometry, calculus, probability and statistics, and striking a careful balance between accessibility and rigor, it enables students to quickly understand the material, without being overwhelmed by complex mathematics. Accompanied by numerous end-of-chapter problems, an online solutions manual for instructors, and relevant examples from diverse fields including engineering, data

The majority of empirical research in economics ignores the potential benefits of nonparametric methods, while the majority of advances in nonparametric theory ignore the problems faced in applied econometrics. This book helps bridge this gap between applied economists and theoretical nonparametric econometricians. It discusses in depth, and in terms that someone with only one year of graduate econometrics can understand, basic to advanced nonparametric methods. The analysis starts with density estimation and motivates the procedures through methods that should be familiar to the reader. It then moves on to kernel regression, estimation with discrete data, and advanced methods such as estimation with panel data and instrumental variables models. The book pays close attention to the issues that arise with programming, computing speed, and application. In each chapter, the methods discussed are applied to actual data, paying attention to presentation of results and potential pitfalls.

Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics. Noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more algebraic viewpoint, as it addresses quantization as a deformation of Poisson structures. This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics. The chapters include presentations of previously

Taking more of a qualitative rather than computational approach, this text presents the techniques required to undertake basic modeling of biological systems through the development and analysis of dy

This book deals with the application of wavelet and spectral methods for the analysis of nonlinear and dynamic processes in economics and finance. It reflects some of the latest developments in the ar

A careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book. It focuses on the interrelationship between three subjects in analysis: Markov proce

Economists increasingly recognise that engagement with social ontology – the study of the basic subject matter and constitution of social reality - can facilitate more relevant analysis. This growing

This work is the third of an encyclopedic four- volume set describing the basic physiology and the chemical sensitivity of chronic degenerative diseases and methods for diagnosis and reversal of chron

Economists increasingly recognise that engagement with social ontology – the study of the basic subject matter and constitution of social reality - can facilitate more relevant analysis. This growing

In the structural design of airframes and buildings, probability-based procedures are used to mitigate the risk of failure as well as produce cost-effective designs. This book introduces the subject of probabilistic analysis to structural and fire protection engineers and can also be used as a reference to guide those applying this technology. In addition to providing an understanding of how fire affects structures and how to optimize the performance of structural framing systems, Probability-Based Structural Fire Load provides guidance for design professionals and is a resource for educators. The goal of this book is to bridge the gap between prescriptive and probability-based performance design methods and to simplify very complex and comprehensive computer analyses to the point that stochastic structural fire loads have a simple, approximate analytical expression that can be used in structural analysis and design on a day-to-day basis. Numerous practical examples are presented in st

This timely book by internationally regarded scholar of ethics and social/political philosophy, Michael Boylan, focuses on the history, application and significance of human rights in the West and China. Boylan engages the key current philosophical debates prevalent in human rights discourse today and draws them together to argue for the existence of natural, universal human rights. Arguing against the grain of mainstream philosophical beliefs, Boylan asserts that there is continuity between human rights and natural law and that human beings require basic, essential goods for minimum action. These include food, clean water and sanitation, clothing, shelter and protection from bodily harm, including basic healthcare. The achievement of this goal, Boylan demonstrates, will require significant resource allocation and creative methods of implementation involving public and private institutions. Combining technical argument with four fictional narratives about human rights, the book invites

What happens in our brain when we make a decision? What triggers a neuron to send out a signal? What is the neural code? This textbook for advanced undergraduate and beginning graduate students provides a thorough and up-to-date introduction to the fields of computational and theoretical neuroscience. It covers classical topics, including the Hodgkin–Huxley equations and Hopfield model, as well as modern developments in the field such as generalized linear models and decision theory. Concepts are introduced using clear step-by-step explanations suitable for readers with only a basic knowledge of differential equations and probabilities, and are richly illustrated by figures and worked-out examples. End-of-chapter summaries and classroom-tested exercises make the book ideal for courses or for self-study. The authors also give pointers to the literature and an extensive bibliography, which will prove invaluable to readers interested in further study.

Optimization is an essential technique for solving problems in areas as diverse as accounting, computer science and engineering. Assuming only basic linear algebra and with a clear focus on the fundamental concepts, this textbook is the perfect starting point for first- and second-year undergraduate students from a wide range of backgrounds and with varying levels of ability. Modern, real-world examples motivate the theory throughout. The authors keep the text as concise and focused as possible, with more advanced material treated separately or in starred exercises. Chapters are self-contained so that instructors and students can adapt the material to suit their own needs and a wide selection of over 140 exercises gives readers the opportunity to try out the skills they gain in each section. Solutions are available for instructors. The book also provides suggestions for further reading to help students take the next step to more advanced material.

Recent experimental advances in the control of quantum superconducting circuits, nano-mechanical resonators and photonic crystals has meant that quantum measurement theory is now an indispensable part of the modelling and design of experimental technologies. This book, aimed at graduate students and researchers in physics, gives a thorough introduction to the basic theory of quantum measurement and many of its important modern applications. Measurement and control is explicitly treated in superconducting circuits and optical and opto-mechanical systems, and methods for deriving the Hamiltonians of superconducting circuits are introduced in detail. Further applications covered include feedback control, metrology, open systems and thermal environments, Maxwell's demon, and the quantum-to-classical transition.

Dependability metrics are omnipresent in every engineering field, from simple ones through to more complex measures combining performance and dependability aspects of systems. This book presents the mathematical basis of the analysis of these metrics in the most used framework, Markov models, describing both basic results and specialised techniques. The authors first present both discrete and continuous time Markov chains before focusing on dependability measures, which necessitate the study of Markov chains on a subset of states representing different user satisfaction levels for the modelled system. Topics covered include Markovian state lumping, analysis of sojourns on subset of states of Markov chains, analysis of most dependability metrics, fundamentals of performability analysis, and bounding and simulation techniques designed to evaluate dependability measures. The book is of interest to graduate students and researchers in all areas of engineering where the concepts of lifetime

Aimed at students taking laboratory courses in experimental optics, this book introduces readers to optical instruments and their uses. The book explains the basic operation of lenses, mirrors, telescopes in the laboratory and under field conditions, how to use optical instruments to their maximum potential and how to keep them in working order. It gives an account of the laws of geometrical optics which govern the design, layout and working of optical instruments. The book describes the interactions of polarised light with matter and the instruments and devices derived from this, and discusses the choice of spectrometers and detectors for various spectral regions, with particular attention to CCD cameras. The emphasis throughout is on description, with mathematical precision confined to the appendices, which explain the ray transfer matrix and outline the Seidel theory of optical aberrations. The appendices also introduce Fourier methods in optics and Fourier transform infra-red spect

What happens in our brain when we make a decision? What triggers a neuron to send out a signal? What is the neural code? This textbook for advanced undergraduate and beginning graduate students provides a thorough and up-to-date introduction to the fields of computational and theoretical neuroscience. It covers classical topics, including the Hodgkin–Huxley equations and Hopfield model, as well as modern developments in the field such as generalized linear models and decision theory. Concepts are introduced using clear step-by-step explanations suitable for readers with only a basic knowledge of differential equations and probabilities, and are richly illustrated by figures and worked-out examples. End-of-chapter summaries and classroom-tested exercises make the book ideal for courses or for self-study. The authors also give pointers to the literature and an extensive bibliography, which will prove invaluable to readers interested in further study.

Aimed at students taking laboratory courses in experimental optics, this book introduces readers to optical instruments and their uses. The book explains the basic operation of lenses, mirrors, telescopes in the laboratory and under field conditions, how to use optical instruments to their maximum potential and how to keep them in working order. It gives an account of the laws of geometrical optics which govern the design, layout and working of optical instruments. The book describes the interactions of polarised light with matter and the instruments and devices derived from this, and discusses the choice of spectrometers and detectors for various spectral regions, with particular attention to CCD cameras. The emphasis throughout is on description, with mathematical precision confined to the appendices, which explain the ray transfer matrix and outline the Seidel theory of optical aberrations. The appendices also introduce Fourier methods in optics and Fourier transform infra-red spect

Optimization is an essential technique for solving problems in areas as diverse as accounting, computer science and engineering. Assuming only basic linear algebra and with a clear focus on the fundamental concepts, this textbook is the perfect starting point for first- and second-year undergraduate students from a wide range of backgrounds and with varying levels of ability. Modern, real-world examples motivate the theory throughout. The authors keep the text as concise and focused as possible, with more advanced material treated separately or in starred exercises. Chapters are self-contained so that instructors and students can adapt the material to suit their own needs and a wide selection of over 140 exercises gives readers the opportunity to try out the skills they gain in each section. Solutions are available for instructors. The book also provides suggestions for further reading to help students take the next step to more advanced material.

This timely book by internationally regarded scholar of ethics and social/political philosophy, Michael Boylan, focuses on the history, application and significance of human rights in the West and China. Boylan engages the key current philosophical debates prevalent in human rights discourse today and draws them together to argue for the existence of natural, universal human rights. Arguing against the grain of mainstream philosophical beliefs, Boylan asserts that there is continuity between human rights and natural law and that human beings require basic, essential goods for minimum action. These include food, clean water and sanitation, clothing, shelter and protection from bodily harm, including basic healthcare. The achievement of this goal, Boylan demonstrates, will require significant resource allocation and creative methods of implementation involving public and private institutions. Combining technical argument with four fictional narratives about human rights, the book invites

This tutorial-style book reviews experimental approaches for the analysis of solid mechanics based on interference-optical methods, including coherent-optical techniques and photoelastic methods. Suit

This book is devoted to the analysis of approximate solution techniques for differential equations, based on classical orthogonal polynomials. These techniques are popularly known as spectral methods.

This textbook explains the basic ideas of subjective probability and shows how subjective probabilities must obey the usual rules of probability to ensure coherency. It defines the likelihood function, prior distributions and posterior distributions. It explains how posterior distributions are the basis for inference and explores their basic properties. Various methods of specifying prior distributions are considered, with special emphasis on subject-matter considerations and exchange ability. The regression model is examined to show how analytical methods may fail in the derivation of marginal posterior distributions. The remainder of the book is concerned with applications of the theory to important models that are used in economics, political science, biostatistics and other applied fields. New to the second edition is a chapter on semiparametric regression and new sections on the ordinal probit, item response, factor analysis, ARCH-GARCH and stochastic volatility models. The new ed

This book examines the recent evolution of the Mediterranean Welfare regime, and how the economic crisis may be contributing to redefine its basic traits. Moving from the macro comparative analysis of

In recent years the interaction between dynamical systems theory and non-equilibrium statistical mechanics has been enormous. The discovery of fluctuation theorems as a fundamental structure common to almost all non-equilibrium systems, and the connections with the free energy calculation methods of Jarzynski and Crooks, have excited both theorists and experimentalists. This graduate-level book charts the development and theoretical analysis of molecular dynamics as applied to equilibrium and non-equilibrium systems. Designed for both researchers in the field and graduate students of physics, it connects molecular dynamics simulation with the mathematical theory to understand non-equilibrium steady states. It also provides a link between the atomic, nano, and macro worlds. The book ends with an introduction to the use of non-equilibrium statistical mechanics to justify a thermodynamic treatment of non-equilibrium steady states, and gives a direction to further avenues of exploration.

This book offers for the first time a conceptual history of compromise. Alin Fumurescu combines contextual historical analysis of daily parlance and a survey of the usage of the word from the end of the sixteenth century to the beginning of the eighteenth century in both French and English with an analysis of canonical texts in the history of political thought. This book fills a significant gap in the literature about compromise and demonstrates the connection between different understandings of compromise and corresponding differences in understandings of political representation. In addition, Fumurescu addresses two controversial contemporary debates about when compromise is beneficial and when it should be avoided at all costs. A better understanding of the genealogy of compromise offers new venues for rethinking basic assumptions regarding political representation and the relationship between individuals and politics.

This book is a thorough introduction to the formal foundations and practical applications of Bayesian networks. It provides an extensive discussion of techniques for building Bayesian networks that model real-world situations, including techniques for synthesizing models from design, learning models from data, and debugging models using sensitivity analysis. It also treats exact and approximate inference algorithms at both theoretical and practical levels. The treatment of exact algorithms covers the main inference paradigms based on elimination and conditioning and includes advanced methods for compiling Bayesian networks, time-space tradeoffs, and exploiting local structure of massively connected networks. The treatment of approximate algorithms covers the main inference paradigms based on sampling and optimization and includes influential algorithms such as importance sampling, MCMC, and belief propagation. The author assumes very little background on the covered subjects, supplying

This popular text explains the basic models of insurance processes. It also presents mathematical frameworks and methods used in actuarial modeling. Along with significantly editing and revamping all

This book offers a concise, but highly useful introduction to the basic concepts, techniques, and new applications of Atomic Absorption Spectroscopy (AAS). This well-established materials analysis tec

The theory of optimal transportation has its origins in the eighteenth century when the problem of transporting resources at a minimal cost was first formalised. Through subsequent developments, particularly in recent decades, it has become a powerful modern theory. This book contains the proceedings of the summer school 'Optimal Transportation: Theory and Applications' held at the Fourier Institute in Grenoble. The event brought together mathematicians from pure and applied mathematics, astrophysics, economics and computer science. Part I of this book is devoted to introductory lecture notes accessible to graduate students, while Part II contains research papers. Together, they represent a valuable resource on both fundamental and advanced aspects of optimal transportation, its applications, and its interactions with analysis, geometry, PDE and probability, urban planning and economics. Topics covered include Ricci flow, the Euler equations, functional inequalities, curvature-dimensio