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A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses the recent emergence of unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis with potentially significant physical consequences. In addition to prompting a discussion on the role of mathematical methods in the contemporary development of quantum physics, the book features: Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area An overview of recent inventions and advances in understanding functional analytic and algebraic methods for non-selfadjoint operators as well as the use of Krein space theory and perturbation theory Rigorous support of the progress in theoretical physics of non-Hermitian systems in addition to mathematically justified applications in various domains of physics such as nuclear and particle physics and condensed matter physics An ideal reference, Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects is useful for researchers, professionals, and academics in applied mathematics and theoretical and/or applied physics who would like to expand their knowledge of classical applications of quantum tools to address problems in their research. Also a useful resource for recent and related trends, the book is appropriate as a graduate-level and/or PhD-level text for courses on quantum mechanics and mathematical models in physics.
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The main purpose of this book is to introduce the generalized composition operators and the generalized multiplication operators on weighted Hardy spaces . Composition operators have been the subject matter of intensive study over past several decades and they find applications in ergodic theory ,quantum mechanics and other branches of mathematical and physical sciences . The 1st chapter of the book contains introductory material . The compact, Fredholm generalized composition operators are characterized in the second chapter. The Hermitian,Normal ,Quasi normal ,Isometric and co isometric generalized composition operators are presented in the third chapter. It is shown that most of the properties of the generalized multiplication operators differ from the multiplication operators acting on other function spaces .eg:- On most of the function spaces multiplication operators are normal .But this result is not valid incase of generalized multiplication operators on weighted Hardy spaces . In this book some light is thrown on differential and anti-differential operators acting on weighted Hardy spaces .
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The Wave Concept Iterative Procedure (WCIP) method has found an increasing number of users within electromagnetic theory and applications to planar circuits, antennas and diffraction problems. This book introduces in detail this new formulation of integral methods, based on the use of a wave concept with two bounded operators, and applications in a variety of domains in electromagnetics. This approach presents a number of benefits over other integral methods, including overcoming the problem of singularity, and reduced computing time. Through the presentation of mathematical equations to characterize studied structures and explanation of the curves obtained, via validated examples, the authors provide a thorough background to electromagnetism as well as a professional reference to students and researchers.
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Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.
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Presents the theory and methodology for reliability assessments of safety-critical functions through examples from a wide range of applications Reliability of Safety-Critical Systems: Theory and Applications provides a comprehensive introduction to reliability assessments of safety-related systems based on electrical, electronic, and programmable electronic (E/E/PE) technology. With a focus on the design and development phases of safety-critical systems, the book presents theory and methods required to document compliance with IEC 61508 and the associated sector-specific standards. Combining theory and practical applications, Reliability of Safety-Critical Systems: Theory and Applications implements key safety-related strategies and methods to meet quantitative safety integrity requirements. In addition, the book details a variety of reliability analysis methods that are needed during all stages of a safety-critical system, beginning with specification and design and advancing to operations, maintenance, and modification control. The key categories of safety life-cycle phases are featured, including strategies for the allocation of reliability performance requirements; assessment methods in relation to design; and reliability quantification in relation to operation and maintenance. Issues and benefits that arise from complex modern technology developments are featured, as well as: Real-world examples from large industry facilities with major accident potential and products owned by the general public such as cars and tools Plentiful worked examples throughout that provide readers with a deeper understanding of the core concepts and aid in the analysis and solution of common issues when assessing all facets of safety-critical systems Approaches that work on a wide scope of applications and can be applied to the analysis of any safety-critical system A brief appendix of probability theory for reference With an emphasis on how safety-critical functions are introduced into systems and facilities to prevent or mitigate the impact of an accident, this book is an excellent guide for professionals, consultants, and operators of safety-critical systems who carry out practical, risk, and reliability assessments of safety-critical systems. Reliability of Safety-Critical Systems: Theory and Applications is also a useful textbook for courses in reliability assessment of safety-critical systems and reliability engineering at the graduate-level, as well as for consulting companies offering short courses in reliability assessment of safety-critical systems.
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This second edition of Adaptive Filters: Theory and Applications has been updated throughout to reflect the latest developments in this field; notably an increased coverage given to the practical applications of the theory to illustrate the much broader range of adaptive filters applications developed in recent years. The book offers an easy to understand approach to the theory and application of adaptive filters by clearly illustrating how the theory explained in the early chapters of the book is modified for the various applications discussed in detail in later chapters. This integrated approach makes the book a valuable resource for graduate students; and the inclusion of more advanced applications including antenna arrays and wireless communications makes it a suitable technical reference for engineers, practitioners and researchers. Key features: • Offers a thorough treatment of the theory of adaptive signal processing; incorporating new material on transform domain, frequency domain, subband adaptive filters, acoustic echo cancellation and active noise control. • Provides an in-depth study of applications which now includes extensive coverage of OFDM, MIMO and smart antennas. • Contains exercises and computer simulation problems at the end of each chapter. • Includes a new companion website hosting MATLAB® simulation programs which complement the theoretical analyses, enabling the reader to gain an in-depth understanding of the behaviours and properties of the various adaptive algorithms.
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A simplified, yet rigorous treatment of scattering theory methods and their applications Dispersion Decay and Scattering Theory provides thorough, easy-to-understand guidance on the application of scattering theory methods to modern problems in mathematics, quantum physics, and mathematical physics. Introducing spectral methods with applications to dispersion time-decay and scattering theory, this book presents, for the first time, the Agmon-Jensen-Kato spectral theory for the Schr?dinger equation, extending the theory to the Klein-Gordon equation. The dispersion decay plays a crucial role in the modern application to asymptotic stability of solitons of nonlinear Schr?dinger and Klein-Gordon equations. The authors clearly explain the fundamental concepts and formulas of the Schr?dinger operators, discuss the basic properties of the Schr?dinger equation, and offer in-depth coverage of Agmon-Jensen-Kato theory of the dispersion decay in the weighted Sobolev norms. The book also details the application of dispersion decay to scattering and spectral theories, the scattering cross section, and the weighted energy decay for 3D Klein-Gordon and wave equations. Complete streamlined proofs for key areas of the Agmon-Jensen-Kato approach, such as the high-energy decay of the resolvent and the limiting absorption principle are also included. Dispersion Decay and Scattering Theory is a suitable book for courses on scattering theory, partial differential equations, and functional analysis at the graduate level. The book also serves as an excellent resource for researchers, professionals, and academics in the fields of mathematics, mathematical physics, and quantum physics who would like to better understand scattering theory and partial differential equations and gain problem-solving skills in diverse areas, from high-energy physics to wave propagation and hydrodynamics.
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Mathematics of Bioinformatics: Theory, Methods, and Applications provides a comprehensive format for connecting and integrating information derived from mathematical methods and applying it to the understanding of biological sequences, structures, and networks. Each chapter is divided into a number of sections based on the bioinformatics topics and related mathematical theory and methods. Each topic of the section is comprised of the following three parts: an introduction to the biological problems in bioinformatics; a presentation of relevant topics of mathematical theory and methods to the bioinformatics problems introduced in the first part; an integrative overview that draws the connections and interfaces between bioinformatics problems/issues and mathematical theory/methods/applications.
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A Useful Guide to the Interrelated Areas of Differential Equations, Difference Equations, and Queueing Models Difference and Differential Equations with Applications in Queueing Theory presents the unique connections between the methods and applications of differential equations, difference equations, and Markovian queues. Featuring a comprehensive collection of topics that are used in stochastic processes, particularly in queueing theory, the book thoroughly discusses the relationship to systems of linear differential difference equations. The book demonstrates the applicability that queueing theory has in a variety of fields including telecommunications, traffic engineering, computing, and the design of factories, shops, offices, and hospitals. Along with the needed prerequisite fundamentals in probability, statistics, and Laplace transform, Difference and Differential Equations with Applications in Queueing Theory provides: A discussion on splitting, delayed-service, and delayed feedback for single-server, multiple-server, parallel, and series queue models Applications in queue models whose solutions require differential difference equations and generating function methods Exercises at the end of each chapter along with select answers The book is an excellent resource for researchers and practitioners in applied mathematics, operations research, engineering, and industrial engineering, as well as a useful text for upper-undergraduate and graduate-level courses in applied mathematics, differential and difference equations, queueing theory, probability, and stochastic processes.
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A computational perspective on partial order and lattice theory, focusing on algorithms and their applications This book provides a uniform treatment of the theory and applications of lattice theory. The applications covered include tracking dependency in distributed systems, combinatorics, detecting global predicates in distributed systems, set families, and integer partitions. The book presents algorithmic proofs of theorems whenever possible. These proofs are written in the calculational style advocated by Dijkstra, with arguments explicitly spelled out step by step. The author’s intent is for readers to learn not only the proofs, but the heuristics that guide said proofs. Introduction to Lattice Theory with Computer Science Applications: Examines; posets, Dilworth’s theorem, merging algorithms, lattices, lattice completion, morphisms, modular and distributive lattices, slicing, interval orders, tractable posets, lattice enumeration algorithms, and dimension theory Provides end of chapter exercises to help readers retain newfound knowledge on each subject Includes supplementary material at www.ece.utexas.edu/~garg Introduction to Lattice Theory with Computer Science Applications is written for students of computer science, as well as practicing mathematicians.
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This topical and timely textbook is a collection of problems for students, researchers, and practitioners interested in state-of-the-art material and device applications in quantum mechanics. Most problem are relevant either to a new device or a device concept or to current research topics which could spawn new technology. It deals with the practical aspects of the field, presenting a broad range of essential topics currently at the leading edge of technological innovation. Includes discussion on: Properties of Schroedinger Equation Operators Bound States in Nanostructures Current and Energy Flux Densities in Nanostructures Density of States Transfer and Scattering Matrix Formalisms for Modelling Diffusive Quantum Transport Perturbation Theory, Variational Approach and their Applications to Device Problems Electrons in a Magnetic or Electromagnetic Field and Associated Phenomena Time-dependent Perturbation Theory and its Applications Optical Properties of Nanostructures Problems in Quantum Mechanics: For Material Scientists, Applied Physicists and Device Engineers is an ideal companion to engineering, condensed matter physics or materials science curricula. It appeals to future and present engineers, physicists, and materials scientists, as well as professionals in these fields needing more in-depth understanding of nanotechnology and nanoscience.
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Comprehensive coverage of the basic theoretical concepts and applications of dielectrophoresis from a world-renowned expert. Features hot application topics including: Diagnostics, Cell-based Drug Discovery, Sensors for Biomedical Applications, Characterisation and Sorting of Stem Cells, Separation of Cancer Cells from Blood and Environmental Monitoring Focuses on those aspects of the theory and practice of dielectrophoresis concerned with characterizing and manipulating cells and other bioparticles such as bacteria, viruses, proteins and nucleic acids. Features the relevant chemical and biological concepts for those working in physics and engineering
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This book is an introduction to GIS (Generalized Interval Systems) theory that includes the major results of pitch-class theory. It provides mathematicians with applications of group theory to music and music theorists with the essential connections betw
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Covers the area of lipidomics from fundamentals and theory to applications Presents a balanced discussion of the fundamentals, theory, experimental methods and applications of lipidomics Covers different characterizations of lipids including Glycerophospholipids; Sphingolipids; Glycerolipids and Glycolipids; and Fatty Acids and Modified Fatty Acids Includes a section on quantification of Lipids in Lipidomics such as sample preparation; factors affecting accurate quantification; and data processing and interpretation Details applications of Lipidomics Tools including for Health and Disease; Plant Lipidomics; and Lipidomics on Cellular Membranes
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Fluidics originated as the description of pneumatic and hydraulic control systems, where fluids were employed (instead of electric currents) for signal transfer and processing. Microfluidics and Nanofluidics: Theory and Selected Applications offers an accessible, broad-based coverage of the basics through advanced applications of microfluidics and nanofluidics. It is essential reading for upper-level undergraduates and graduate students in engineering and professionals in industry.
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Describes how to systematically implement various characteristic mode (CM) theories into designs of practical antenna systems This book examines both theoretical developments of characteristic modes (CMs) and practical developments of CM-based methodologies for a variety of critical antenna designs. The book is divided into six chapters. Chapter 1 provides an introduction and discusses the recent advances of the CM theory and its applications in antenna engineering. Chapter 2 describes the formulation of the characteristic mode theory for perfectly electrically conducting (PEC) bodies and discusses its numerical implementations. Chapter 3 presents the CM theory for PEC structures embedded in multilayered medium and its applications. Chapter 4 covers recent advances in CM theory for dielectric bodies and also their applications. Chapter 5 discusses the CM theory for N-port networks and its applications to the design of antenna arrays. Finally, Chapter 6 discusses the design of platform-integrated antenna systems using characteristic modes. This book features the following: Introduces characteristic mode theories for various electromagnetic structures including PEC bodies, structures in multilayered medium, dielectric bodies, and N-port networks Examines CM applications in electrically small antennas, microstrip patch antennas, dielectric resonator antennas, multiport antennas, antenna arrays, and platform mounted antenna systems Discusses numerical algorithms for the implementation of the characteristic mode theories in computer code Characteristic Modes: Theory and Applications in Antenna Engineering will help antenna researchers, engineers, and students find new solutions for their antenna design challenges.
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An accessible and clear introduction to linear algebra with a focus on matrices and engineering applications Providing comprehensive coverage of matrix theory from a geometric and physical perspective, Fundamentals of Matrix Analysis with Applications describes the functionality of matrices and their ability to quantify and analyze many practical applications. Written by a highly qualified author team, the book presents tools for matrix analysis and is illustrated with extensive examples and software implementations. Beginning with a detailed exposition and review of the Gauss elimination method, the authors maintain readers’ interest with refreshing discussions regarding the issues of operation counts, computer speed and precision, complex arithmetic formulations, parameterization of solutions, and the logical traps that dictate strict adherence to Gauss’s instructions. The book heralds matrix formulation both as notational shorthand and as a quantifier of physical operations such as rotations, projections, reflections, and the Gauss reductions. Inverses and eigenvectors are visualized first in an operator context before being addressed computationally. Least squares theory is expounded in all its manifestations including optimization, orthogonality, computational accuracy, and even function theory. Fundamentals of Matrix Analysis with Applications also features: Novel approaches employed to explicate the QR, singular value, Schur, and Jordan decompositions and their applications Coverage of the role of the matrix exponential in the solution of linear systems of differential equations with constant coefficients Chapter-by-chapter summaries, review problems, technical writing exercises, select solutions, and group projects to aid comprehension of the presented concepts Fundamentals of Matrix Analysis with Applications is an excellent textbook for undergraduate courses in linear algebra and matrix theory for students majoring in mathematics, engineering, and science. The book is also an accessible go-to reference for readers seeking clarification of the fine points of kinematics, circuit theory, control theory, computational statistics, and numerical algorithms.
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A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.
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Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics Explores the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. Covers numerous applications of XFEM including fracture mechanics, large deformation, plasticity, multiphase flow, hydraulic fracturing and contact problems Accompanied by a website hosting source code and examples
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This book covers instantaneous power theory as well as the importance of design of shunt, series, and combined shunt-series power active filters and hybrid passive-active power filters Illustrates pioneering applications of the p-q theory to power conditioning, which highlights distinct differences from conventional theories Explores p-q-r theory to give a new method of analyzing the different powers in a three-phase circuit Provides exercises at the end of many chapters that are unique to the second edition
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Master's Thesis from the year 2016 in the subject Mathematics - Algebra, , language: English, abstract: In this thesis, using asymptotic integration, we have investigated the asymptotic of the eigensolutions and the deficiency indices of fourth order differential operators with unbounded coefficients as well as the location of absolutely continuous spectrum of self-adjoint extension operators.We have mainly endeavored to compute eigenvalues of fourth order differential operators when the coefficients are unbounded, determine the deficiency indices of such differential operator and the location of the absolutely continuous spectrum of the self-adjoint extension operator together with their spectral multiplicity. Results obtained for deficiency indices were in the range (2, 2) ≤ defT ≤ (4, 4) under different growth and decay conditions of co-efficients.The concept of unbounded operators provides an abstract framework for dealing with differential operators and unbounded observable such as in quantum mechanics. The theory of unbounded operators was developed by John Von Neumann in the late 1920s and early 1930s in an effort to solve problems related to quantum mechanics and other physical observables. This has provided the background on which other scholars have developed their work in differential operators. Higher order differential operators as defined on Hilbert spaces have received much attention though there still lays the problem of computing the eigenvalues of these ...
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A guide to the growing importance of extreme value risk theory, methods, and applications in the financial sector Presenting a uniquely accessible guide, Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications features a combination of the theory, methods, and applications of extreme value theory (EVT) in finance and a practical understanding of market behavior including both ordinary and extraordinary conditions. Beginning with a fascinating history of EVTs and financial modeling, the handbook introduces the historical implications that resulted in the applications and then clearly examines the fundamental results of EVT in finance. After dealing with these theoretical results, the handbook focuses on the EVT methods critical for data analysis. Finally, the handbook features the practical applications and techniques and how these can be implemented in financial markets. Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications includes: • Over 40 contributions from international experts in the areas of finance, statistics, economics, business, insurance, and risk management • Topical discussions on univariate and multivariate case extremes as well as regulation in financial markets • Extensive references in order to provide readers with resources for further study • Discussions on using R packages to compute the value of risk and related quantities The book is a valuable reference for practitioners in financial markets such as financial institutions, investment funds, and corporate treasuries, financial engineers, quantitative analysts, regulators, risk managers, large-scale consultancy groups, and insurers. Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications is also a useful textbook for postgraduate courses on the methodology of EVTs in finance. François Longin, PhD, is Professor in the Department of Finance at ESSEC Business School, France. He has been working on the applications of extreme value theory to financial markets for many years, and his research has been applied by financial institutions in the risk management area including market, credit, and operational risks. His research works can be found in scientific journals such as The Journal of Finance. Dr. Longin is currently a financial consultant with expertise covering risk management for financial institutions and portfolio management for asset management firms.
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The first book to be published on the Theta method, outlining under what conditions the method outperforms other forecasting methods This book is the first to detail the Theta method of forecasting – one of the most difficult-to-beat forecasting benchmarks, which topped the biggest forecasting competition in the world in 2000: the M3 competition. Written by two of the leading experts in the forecasting field, it illuminates the exact replication of the method and under what conditions the method outperforms other forecasting methods. Recent developments such as multivariate models are also included, as are a series of practical applications in finance, economics, and healthcare. The book also offers practical tools in MS Excel and guidance, as well as provisional access, for the use of R source code and respective packages. Forecasting with the Theta Method: Theory and Applications includes three main parts. The first part, titled Theory, Methods, Models & Applications details the new theory about the method. The second part, Applications & Performance in Forecasting Competitions, describes empirical results and simulations on the method. The last part roadmaps future research and also include contributions from another leading scholar of the method – Dr. Fotios Petropoulos. First ever book to be published on the Theta Method Explores new theory and exact conditions under which methods would outperform most forecasting benchmarks Clearly written with practical applications Employs R – open source code with all included implementations Forecasting with the Theta Method: Theory and Applications is a valuable tool for both academics and practitioners involved in forecasting and respective software development.
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Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.
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Family Theories: Foundations and Applications presents a comprehensive and accessible approach to the most current perspectives in the field of family theory. Integrates classic and contemporary writings on family theories Features compelling case studies drawn from the authors’ experiences working with thousands of students Represents an integrative use of theory, research, and practice Utilizes the metaphor of “developing your theory app” to translate complex academic ideas into accessible, student-friendly language
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A systematic introduction to the theory, development and latest research results of radar data processing technology • Presents both classical theory and development methods of radar data processing • Provides state-of-the-art research results, including data processing for modern style radars, and tracking performance evaluation theory • Includes coverage of performance evaluation, registration algorithm for Radar network, data processing of passive radar, pulse Doppler radar, and phased array radar • Has applications for those engaged in information engineering, radar engineering, electronic countermeasures, infrared techniques, sonar techniques, and military command
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Grothendieck's beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
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The present book highlights developments in varied themes of Information Theory and finds its applications to various disciplines of Mathematics. The main objective is to provide the applications of information theoretic measures to the field of Queueing Theory and will be helpful to Information Theoreticians and Operational Researchers. The book presents new findings which will add to the knowledge of the scientific community for furtherance of research.
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A UNIQUE ENGINEERING AND STATISTICAL APPROACH TO OPTIMAL RESOURCE ALLOCATION Optimal Resource Allocation: With Practical Statistical Applications and Theory features the application of probabilistic and statistical methods used in reliability engineering during the different phases of life cycles of technical systems. Bridging the gap between reliability engineering and applied mathematics, the book outlines different approaches to optimal resource allocation and various applications of models and algorithms for solving real-world problems. In addition, the fundamental background on optimization theory and various illustrative numerical examples are provided. The book also features: An overview of various approaches to optimal resource allocation, from classical Lagrange methods to modern algorithms based on ideas of evolution in biology Numerous exercises and case studies from a variety of areas, including communications, transportation, energy transmission, and counterterrorism protection The applied methods of optimization with various methods of optimal redundancy problem solutions as well as the numerical examples and statistical methods needed to solve the problems Practical thoughts, opinions, and judgments on real-world applications of reliability theory and solves practical problems using mathematical models and algorithms Optimal Resource Allocation is a must-have guide for electrical, mechanical, and reliability engineers dealing with engineering design and optimal reliability problems. In addition, the book is excellent for graduate and PhD-level courses in reliability theory and optimization.
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Comprehensive and up to date coverage of robust control theory and its application • Presented in a well-planned and logical way • Written by a respected leading author, with extensive experience in robust control • Accompanying website provides solutions manual and other supplementary material
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Unsurpassed as a text for upper-division and beginning graduate students, Raman Selden's classic text is the liveliest, most readable and most reliable guide to contemporary literary theory. Includes applications of theory, cross-referenced to Selden's companion volume, Practicing Theory and Reading Literature.
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Develops the theory of jet single-time Lagrange geometry and presents modern-day applications Jet Single-Time Lagrange Geometry and Its Applications guides readers through the advantages of jet single-time Lagrange geometry for geometrical modeling. With comprehensive chapters that outline topics ranging in complexity from basic to advanced, the book explores current and emerging applications across a broad range of fields, including mathematics, theoretical and atmospheric physics, economics, and theoretical biology. The authors begin by presenting basic theoretical concepts that serve as the foundation for understanding how and why the discussed theory works. Subusequent chapters compare the geometrical and physical aspects of jet relativistic time-dependent Lagrange geometry to the classical time-dependent Lagrange geometry. A collection of jet geometrical objects are also examined such as d-tensors, relativistic time-dependent semisprays, harmonic curves, and nonlinear connections. Numerous applications, including the gravitational theory developed by both the Berwald-Moór metric and the Chernov metric, are also presented. Throughout the book, the authors offer numerous examples that illustrate how the theory is put into practice, and they also present numerous applications in which the solutions of first-order ordinary differential equation systems are regarded as harmonic curves on 1-jet spaces. In addition, numerous opportunities are provided for readers to gain skill in applying jet single-time Lagrange geometry to solve a wide range of problems. Extensively classroom-tested to ensure an accessible presentation, Jet Single-Time Lagrange Geometry and Its Applications is an excellent book for courses on differential geometry, relativity theory, and mathematical models at the graduate level. The book also serves as an excellent reference for researchers, professionals, and academics in physics, biology, mathematics, and economics who would like to learn more about model-providing geometric structures.
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The only book to provide a unified view of the interplay between computational number theory and cryptography Computational number theory and modern cryptography are two of the most important and fundamental research fields in information security. In this book, Song Y. Yang combines knowledge of these two critical fields, providing a unified view of the relationships between computational number theory and cryptography. The author takes an innovative approach, presenting mathematical ideas first, thereupon treating cryptography as an immediate application of the mathematical concepts. The book also presents topics from number theory, which are relevant for applications in public-key cryptography, as well as modern topics, such as coding and lattice based cryptography for post-quantum cryptography. The author further covers the current research and applications for common cryptographic algorithms, describing the mathematical problems behind these applications in a manner accessible to computer scientists and engineers. Makes mathematical problems accessible to computer scientists and engineers by showing their immediate application Presents topics from number theory relevant for public-key cryptography applications Covers modern topics such as coding and lattice based cryptography for post-quantum cryptography Starts with the basics, then goes into applications and areas of active research Geared at a global audience; classroom tested in North America, Europe, and Asia Incudes exercises in every chapter Instructor resources available on the book’s Companion Website Computational Number Theory and Modern Cryptography is ideal for graduate and advanced undergraduate students in computer science, communications engineering, cryptography and mathematics. Computer scientists, practicing cryptographers, and other professionals involved in various security schemes will also find this book to be a helpful reference.
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An authoritative and quantitative approach to modern game theory with applications from economics, political science, military science, and finance Mathematical Game Theory combines both the theoretical and mathematical foundations of game theory with a series of complex applications along with topics presented in a logical progression to achieve a unified presentation of research results. This book covers topics such as two-person games in strategic form, zero-sum games, N-person non-cooperative games in strategic form, two-person games in extensive form, parlor and sport games, bargaining theory, best-choice games, cooperative games and dynamic games. Several classical models used in economics are presented which include Cournot, Bertrand, Hotelling, and Stackelberg as well as coverage of modern branches of game theory such as negotiation models, potential games, parlor games, and best choice games. Mathematical Game Theory: • Presents a good balance of both theoretical foundations and complex applications of game theory. • Features an in-depth analysis of parlor and sport games, networking games, and bargaining models. • Provides fundamental results in new branches of game theory, best choice games, network games, and dynamic games. • Presents numerous examples and exercises along with detailed solutions at the end of each chapter. • Is supported by an accompanying website featuring course slides and lecture content. Covering a host of important topics, this book provides a research springboard for graduate students and a reference for researchers who might be working in the areas of applied mathematics, operations research, computer science, or economical cybernetics.
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The technology of acoustical imaging has advanced rapidly over the last sixty years, and now represents a sophisticated technique applied to a wide range of fields including non-destructive testing, medical imaging, underwater imaging and SONAR, and geophysical exploration. Acoustical Imaging: Techniques and Applications for Engineers introduces the basic physics of acoustics and acoustical imaging, before progressing to more advanced topics such as 3D and 4D imaging, elasticity theory, gauge invariance property of acoustic equation of motion and acoustic metamaterials. The author draws together the different technologies in sonar, seismic and ultrasound imaging, highlighting the similarities between topic areas and their common underlying theory. Key features: Comprehensively covers all of the important applications of acoustical imaging. Introduces the gauge invariance property of acoustic equation of motion, with applications in the elastic constants of isotropic solids, time reversal acoustics, negative refraction, double negative acoustical metamaterial and acoustical cloaking. Contains up to date treatments on latest theories of sound propagation in random media, including statistical treatment and chaos theory. Includes a chapter devoted to new acoustics based on metamaterials, a field founded by the author, including a new theory of elasticity and new theory of sound propagation in solids and fluids and tremendous potential in several novel applications. Covers the hot topics on acoustical imaging including time reversal acoustics, negative refraction and acoustical cloaking. Acoustical Imaging: Techniques and Applications for Engineers is a comprehensive reference on acoustical imaging and forms a valuable resource for engineers, researchers, senior undergraduate and graduate students.
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Problems in stochastic homogenization theory typically deal with approximating dierential operators with rapidly oscillatory random coefficients by operators with homogenized deterministic coefficients. Even though the convergence of these operators in multiple scales is well-studied in the existing literature in the form of a Law of Large Numbers, very little is known about their rate of convergence or their large deviations. This work establishes analytic results for the Gaussian correction in homogenization, and large deviation results for homogenization problems in random media. Several special cases are analyzed in detail.
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A guide to the systematic analytical results for ridge, LASSO, preliminary test, and Stein-type estimators with applications Theory of Ridge Regression Estimation with Applications offers a comprehensive guide to the theory and methods of estimation. Ridge regression and LASSO are at the center of all penalty estimators in a range of standard models that are used in many applied statistical analyses. Written by noted experts in the field, the book contains a thorough introduction to penalty and shrinkage estimation and explores the role that ridge, LASSO, and logistic regression play in the computer intensive area of neural network and big data analysis. Designed to be accessible, the book presents detailed coverage of the basic terminology related to various models such as the location and simple linear models, normal and rank theory-based ridge, LASSO, preliminary test and Stein-type estimators.The authors also include problem sets to enhance learning. This book is a volume in the Wiley Series in Probability and Statistics series that provides essential and invaluable reading for all statisticians. This important resource: Offers theoretical coverage and computer-intensive applications of the procedures presented Contains solutions and alternate methods for prediction accuracy and selecting model procedures Presents the first book to focus on ridge regression and unifies past research with current methodology Uses R throughout the text and includes a companion website containing convenient data sets Written for graduate students, practitioners, and researchers in various fields of science, Theory of Ridge Regression Estimation with Applications is an authoritative guide to the theory and methodology of statistical estimation.
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Introduces number operators with a focus on the relationship between quantum mechanics and social science Mathematics is increasingly applied to classical problems in finance, biology, economics, and elsewhere. Quantum Dynamics for Classical Systems describes how quantum tools—the number operator in particular—can be used to create dynamical systems in which the variables are operator-valued functions and whose results explain the presented model. The book presents mathematical results and their applications to concrete systems and discusses the methods used, results obtained, and techniques developed for the proofs of the results. The central ideas of number operators are illuminated while avoiding excessive technicalities that are unnecessary for understanding and learning the various mathematical applications. The presented dynamical systems address a variety of contexts and offer clear analyses and explanations of concluded results. Additional features in Quantum Dynamics for Classical Systems include: Applications across diverse fields including stock markets and population migration as well as a unique quantum perspective on these classes of models Illustrations of the use of creation and annihilation operators for classical problems Examples of the recent increase in research and literature on the many applications of quantum tools in applied mathematics Clarification on numerous misunderstandings and misnomers while shedding light on new approaches in the field Quantum Dynamics for Classical Systems is an ideal reference for researchers, professionals, and academics in applied mathematics, economics, physics, biology, and sociology. The book is also excellent for courses in dynamical systems, quantum mechanics, and mathematical models.
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A comprehensive review of the state of the art in the control of multi-agent systems theory and applications The superiority of multi-agent systems over single agents for the control of unmanned air, water and ground vehicles has been clearly demonstrated in a wide range of application areas. Their large-scale spatial distribution, robustness, high scalability and low cost enable multi-agent systems to achieve tasks that could not successfully be performed by even the most sophisticated single agent systems. Cooperative Control of Multi-Agent Systems: Theory and Applications provides a wide-ranging review of the latest developments in the cooperative control of multi-agent systems theory and applications. The applications described are mainly in the areas of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs). Throughout, the authors link basic theory to multi-agent cooperative control practice – illustrated within the context of highly-realistic scenarios of high-level missions – without losing site of the mathematical background needed to provide performance guarantees under general working conditions. Many of the problems and solutions considered involve combinations of both types of vehicles. Topics explored include target assignment, target tracking, consensus, stochastic game theory-based framework, event-triggered control, topology design and identification, coordination under uncertainty and coverage control. Establishes a bridge between fundamental cooperative control theory and specific problems of interest in a wide range of applications areas Includes example applications from the fields of space exploration, radiation shielding, site clearance, tracking/classification, surveillance, search-and-rescue and more Features detailed presentations of specific algorithms and application frameworks with relevant commercial and military applications Provides a comprehensive look at the latest developments in this rapidly evolving field, while offering informed speculation on future directions for collective control systems The use of multi-agent system technologies in both everyday commercial use and national defense is certain to increase tremendously in the years ahead, making this book a valuable resource for researchers, engineers, and applied mathematicians working in systems and controls, as well as advanced undergraduates and graduate students interested in those areas.
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Professors Wen and Huang present current developments in tribology research along with tribology fundamentals and applications, including lubrication theory, lubrication design, friction mechanism, wear mechanism, friction control, and their applications. In addition to classical tribology, Wen and Huang cover the research areas of the modern tribology, as well as the regularities and characteristics of tribological phenomena in practice. Furthermore, the authors present the basic theory, numerical analysis methods, and experimental measuring techniques of tribology as well as their applications in engineering. Provides a systematic presentation of tribology fundamentals and their applications Discusses the current states and development trends in tribology research Applies the applications to modern day engineering Computer programs available for download from the book’s companion site Principles of Tribology is aimed at postgraduates and senior-level undergraduates studying tribology, and can be used for courses covering theory and applications. Tribology professionals and students specializing in allied areas of mechanical engineering and materials science will also find the book to be a helpful reference or introduction to the topic. Companion website for the book: www.wiley.com/go/wen/tribology
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Mathematical Morphology allows for the analysis and processing of geometrical structures using techniques based on the fields of set theory, lattice theory, topology, and random functions. It is the basis of morphological image processing, and finds applications in fields including digital image processing (DSP), as well as areas for graphs, surface meshes, solids, and other spatial structures. This book presents an up-to-date treatment of mathematical morphology, based on the three pillars that made it an important field of theoretical work and practical application: a solid theoretical foundation, a large body of applications and an efficient implementation. The book is divided into five parts and includes 20 chapters. The five parts are structured as follows: Part I sets out the fundamental aspects of the discipline, starting with a general introduction, followed by two more theory-focused chapters, one addressing its mathematical structure and including an updated formalism, which is the result of several decades of work. Part II extends this formalism to some non-deterministic aspects of the theory, in particular detailing links with other disciplines such as stereology, geostatistics and fuzzy logic. Part III addresses the theory of morphological filtering and segmentation, featuring modern connected approaches, from both theoretical and practical aspects. Part IV features practical aspects of mathematical morphology, in particular how to deal with color and multivariate data, links to discrete geometry and topology, and some algorithmic aspects; without which applications would be impossible. Part V showcases all the previously noted fields of work through a sample of interesting, representative and varied applications.
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Project Report from the year 2014 in the subject Communications - Multimedia, Internet, New Technologies, , language: English, abstract: Thanks to the advances in telecommunications and mobile computing, smartphoneshave emerged as a vital tool for enhanced communication, connectivity andproductivity. With the increased penetration of smartphones and mobileapplications, Over-The-Top (OTT) mobile messaging applications now constitute asignificant threat to mobile network operators' SMS-messaging revenues. Theliterature available today shows that OTT applications like WhatsApp, Viber,Facebook Chat, Skype, etc will cost $54 billion lost in revenue to mobile networkoperators. As a result, it becomes critical for mobile network operators to put in placeeffective strategies that will slow the impact of OTT apps.This research investigates the pro-active measures that mobile operators have takenin developing countries to address this challenge and also measures theeffectiveness of these measures in their respective markets.Data was collected through questionnaires from over 400 pre-paid subscribers inAccra. The findings of the research show that OTT apps are changing the behaviourof smartphone users regarding text messaging. The research revealed that morethan half smartphone users send less than 5 SMS messages a day. However, withthe introduction of "bundles" by mobile operators in Ghana as a strategy to generatea sustainable average revenue per user seems to be working. ...
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This book serves as a comprehensive source of asymptotic results for econometric models with deterministic exogenous regressors. Such regressors include linear (more generally, piece-wise polynomial) trends, seasonally oscillating functions, and slowly varying functions including logarithmic trends, as well as some specifications of spatial matrices in the theory of spatial models. The book begins with central limit theorems (CLTs) for weighted sums of short memory linear processes. This part contains the analysis of certain operators in Lp spaces and their employment in the derivation of CLTs. The applications of CLTs are to the asymptotic distribution of various estimators for several econometric models. Among the models discussed are static linear models with slowly varying regressors, spatial models, time series autoregressions, and two nonlinear models (binary logit model and nonlinear model whose linearization contains slowly varying regressors). The estimation procedures include ordinary and nonlinear least squares, maximum likelihood, and method of moments. Additional topical coverage includes an introduction to operators, probabilities, and linear models; Lp-approximable sequences of vectors; convergence of linear and quadratic forms; regressions with slowly varying regressors; spatial models; convergence; nonlinear models; and tools for vector autoregressions.
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This combined survey of operant and classical conditioning provides professional and academic readers with an up-to-date, inclusive account of a core field of psychology research, with in-depth coverage of the basic theory, its applications, and current topics including behavioral economics. Provides comprehensive coverage of operant and classical conditioning, relevant fundamental theory, and applications including the latest techniques Features chapters by leading researchers, professionals, and academicians Reviews a range of core literature on conditioning Covers cutting-edge topics such as behavioral economics
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This book naturally follows on from Volume I, developing the mathematical foundations and physical applications of the relatively new subject known as Unity Root Matrix Theory (URMT).The mathematical advances extend URMT's new method of arbitrary vector embedding to two arbitrary vectors, in three or more dimensions, by way of a complete reformulation of URMT in terms of projection operators and exterior products. The similarity of the resulting matrix forms to those used in quaternions, rotations and electromagnetism enables URMT to extend its physical applications to angular dynamics and the electromagnetic plane wave. In particular, URMT's inherently discrete nature results in a treatment of quantised particle spin.Armed with a common mathematical formulation of physical applications as an eigenvector solution to a matrix operator, all generated in a language more recognisable to conventional mathematical physics, the path is now clear for closer future development of URMT to existing, and highly successful, physical theories.
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Plates: Theories and Applications provides a comprehensive introduction to plate structures, covering classical theory and applications. It considers plate structures in several forms, starting from the simple uniform, thin, homogeneous metallic structure to more efficient and durable alternatives involving features such as variable-thickness, lamination, sandwich construction, fiber reinforcement, functional gradation, and moderately-thick to very-thick geometry. Different theoretical models are then discussed for analysis and design purposes starting from the classical thin plate theory to alternatives obtained by incorporation of appropriate complicating effects or by using fundamentally different assumptions. Plates: Theories and Applications alsocovers the latest developments on the topic.
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Modern Vibrational Spectroscopy and Micro-Spectroscopy: Theory, Instrumentation and Biomedical Applications unites the theory and background of conventional vibrational spectroscopy with the principles of microspectroscopy. It starts with basic theory as it applies to small molecules and then expands it to include the large biomolecules which are the main topic of the book with an emphasis on practical experiments, results analysis and medical and diagnostic applications. This book is unique in that it addresses both the parent spectroscopy and the microspectroscopic aspects in one volume. Part I covers the basic theory, principles and instrumentation of classical vibrational, infrared and Raman spectroscopy. It is aimed at researchers with a background in chemistry and physics, and is presented at the level suitable for first year graduate students. The latter half of Part I is devoted to more novel subjects in vibrational spectroscopy, such as resonance and non-linear Raman effects, vibrational optical activity, time resolved spectroscopy and computational methods. Thus, Part 1 represents a short course into modern vibrational spectroscopy. Part II is devoted in its entirety to applications of vibrational spectroscopic techniques to biophysical and bio-structural research, and the more recent extension of vibrational spectroscopy to microscopic data acquisition. Vibrational microscopy (or microspectroscopy) has opened entirely new avenues toward applications in the biomedical sciences, and has created new research fields collectively referred to as Spectral Cytopathology (SCP) and Spectral Histopathology (SHP). In order to fully exploit the information contained in the micro-spectral datasets, methods of multivariate analysis need to be employed. These methods, along with representative results of both SCP and SHP are presented and discussed in detail in Part II.
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Differential Game Theory with Applications to Missiles and Autonomous Systems explains the use of differential game theory in autonomous guidance and control systems. The book begins with an introduction to the basic principles before considering optimum control and game theory. Two-party and multi-party game theory and guidance are then covered and, finally, the theory is demonstrated through simulation examples and models and the simulation results are discussed. Recent developments in the area of guidance and autonomous systems are also presented. Key features: Presents new developments and how they relate to established control systems knowledge. Demonstrates the theory through simulation examples and models. Covers two-party and multi-party game theory and guidance. Accompanied by a website hosting MATLAB® code. The book is essential reading for researchers and practitioners in the aerospace and defence industries as well as graduate students in aerospace engineering.
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Premises, formulation, consequences and applications of a hypothesis (principle) of uncertain future are reviewed. The hypothesis can be used in economics, especially in utility theory, and in forecasting.
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During the last two decades, remarkable and often spectacular progress has been made in the methodological and instrumental aspects of x–ray absorption and emission spectroscopy. This progress includes considerable technological improvements in the design and production of detectors especially with the development and expansion of large-scale synchrotron reactors All this has resulted in improved analytical performance and new applications, as well as in the perspective of a dramatic enhancement in the potential of x–ray based analysis techniques for the near future. This comprehensive two-volume treatise features articles that explain the phenomena and describe examples of X–ray absorption and emission applications in several fields, including chemistry, biochemistry, catalysis, amorphous and liquid systems, synchrotron radiation, and surface phenomena. Contributors explain the underlying theory, how to set up X–ray absorption experiments, and how to analyze the details of the resulting spectra. X-Ray Absorption and X-ray Emission Spectroscopy: Theory and Applications: Combines the theory, instrumentation and applications of x-ray absorption and emission spectroscopies which offer unique diagnostics to study almost any object in the Universe. Is the go-to reference book in the subject for all researchers across multi-disciplines since intense beams from modern sources have revolutionized x-ray science in recent years Is relevant to students, postdocurates and researchers working on x-rays and related synchrotron sources and applications in materials, physics, medicine, environment/geology, and biomedical materials
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Structural Health Monitoring (SHM) is the interdisciplinary engineering field devoted to the monitoring and assessment of structural health and integrity. SHM technology integrates non-destructive evaluation techniques using remote sensing and smart materials to create smart self-monitoring structures characterized by increased reliability and long life. Its applications are primarily systems with critical demands concerning performance where classical onsite assessment is both difficult and expensive. Advanced Structural Damage Detection: From Theory to Engineering Applications is written by academic experts in the field and provides students, engineers and other technical specialists with a comprehensive review of recent developments in various monitoring techniques and their applications to SHM. Contributing to an area which is the subject of intensive research and development, this book offers both theoretical principles and feasibility studies for a number of SHM techniques. Key features: Takes a multidisciplinary approach and provides a comprehensive review of main SHM techniques Presents real case studies and practical application of techniques for damage detection in different types of structures Presents a number of new/novel data processing algorithms Demonstrates real operating prototypes Advanced Structural Damage Detection: From Theory to Engineering Applications is a comprehensive reference for researchers and engineers and is a useful source of information for graduate students in mechanical and civil engineering
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The golden standard evaluation reference text Now in its second edition, Evaluation Theory, Models, and Applications is the vital text on evaluation models, perfect for classroom use as a textbook, and as a professional evaluation reference. The book begins with an overview of the evaluation field and program evaluation standards, and proceeds to cover the most widely used evaluation approaches. With new evaluation designs and the inclusion of the latest literature from the field, this Second Edition is an essential update for professionals and students who want to stay current. Understanding and choosing evaluation approaches is critical to many professions, and Evaluation Theory, Models, and Applications, Second Edition is the benchmark evaluation guide. Authors Daniel L. Stufflebeam and Chris L. S. Coryn, widely considered experts in the evaluation field, introduce and describe 23 program evaluation approaches, including, new to this edition, transformative evaluation, participatory evaluation, consumer feedback, and meta-analysis. Evaluation Theory, Models, and Applications, Second Edition facilitates the process of planning, conducting, and assessing program evaluations. The highlighted evaluation approaches include: Experimental and quasi-experimental design evaluations Daniel L. Stufflebeam's CIPP Model Michael Scriven's Consumer-Oriented Evaluation Michael Patton's Utilization-Focused Evaluation Robert Stake's Responsive/Stakeholder-Centered Evaluation Case Study Evaluation Key readings listed at the end of each chapter direct readers to the most important references for each topic. Learning objectives, review questions, student exercises, and instructor support materials complete the collection of tools. Choosing from evaluation approaches can be an overwhelming process, but Evaluation Theory, Models, and Applications, Second Edition updates the core evaluation concepts with the latest research, making this complex field accessible in just one book.
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A highly successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced prerequisite knowledge and concepts in either area. Elementary Number Theory with Programming features comprehensive coverage of the methodology and applications of the most well-known theorems, problems, and concepts in number theory. Using standard mathematical applications within the programming field, the book presents modular arithmetic and prime decomposition, which are the basis of the public-private key system of cryptography. In addition, the book includes: Numerous examples, exercises, and research challenges in each chapter to encourage readers to work through the discussed concepts and ideas Select solutions to the chapter exercises in an appendix Plentiful sample computer programs to aid comprehension of the presented material for readers who have either never done any programming or need to improve their existing skill set A related website with links to select exercises An Instructor’s Solutions Manual available on a companion website Elementary Number Theory with Programming is a useful textbook for undergraduate and graduate-level students majoring in mathematics or computer science, as well as an excellent supplement for teachers and students who would like to better understand and appreciate number theory and computer programming. The book is also an ideal reference for computer scientists, programmers, and researchers interested in the mathematical applications of programming.
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A comprehensive overview of current empirical valence bond (EVB) theory and applications, one of the most powerful tools for studying chemical processes in the condensed phase and in enzymes. Discusses the application of EVB models to a broad range of molecular systems of chemical and biological interest, including reaction dynamics, design of artificial catalysts, and the study of complex biological problems Edited by a rising star in the field of computational enzymology Foreword by Nobel laureate Arieh Warshel, who first developed the EVB approach
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This book develops several aspects of the theory of distributions on manifolds. Beginning with a section on prerequisites, it shortly outlines the most important concepts needed from the fields of functional analysis, differential geometry and distribution theory, thus enabling students with basic knowledge in these fields to follow the main body of the book. The second chapter then deals with the kernel theorem by Laurent Schwartz, stating that all linear and continuous operators from the space of test functions on one manifold into the space of distributions on another manifold can be given by a kernel distribution on the product space. After proving this theorem, regular and regularising kernel operators are examined as special cases of kernel operators that allow an extension of the kernel map to distribution spaces. The last chapter then moves on to microlocal analysis on manifolds, where first of all an intrinsic, coordinate-invariant definition of the wave front set for distributions on a manifold is developed. Ultimately, the thesis returns to regular kernel operators and investigates their microlocal properties.
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2012 Reprint of 1955 Edition. Exact facsimile of the original edition, not reproduced with Optical Recognition Software. A stochastic process is one in which the probabilities of a set of events keep changing with time. Bush and Mosteller make use of the mathematical techniques developed for the study of such processes in building a theory of learning and then apply the theory to explain the results of several learning experiments. Contents: Part I: The mathematical system and the general model -- 1. The basic model -- 2. Stimulus sampling and conditioning -- 3. Sequences of events -- 4. Distributions of response probabilities -- 5. The equal alpha condition -- 6. Approximate methods -- 7. Operators with limits zero and unity -- 8. Commuting operators -- Part II: Applications -- 9. Identification and estimation -- 10. Free-recall verbal learning -- 11. Avoidance training -- 12. An experiment on imitation -- 13. Symmetric choice problems -- 14. Runway experiments -- 15. Evaluations.
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Filling the gap for a systematic, authoritative, and up-to-date review of this cutting-edge technique, this book covers both low and high frequency EPR, emphasizing the importance of adopting the multifrequency approach to study paramagnetic systems in full detail by using the EPR method. In so doing, it discusses not only the underlying theory and applications, but also all recent advances – with a final section devoted to future perspectives.
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Spend your study time wisely As you advance from student to apprentice to journeyman status, you log a lot of study hours. Make the most of those hours with this fully updated, sharply focused self-study course. It contains everything you need to know about electrical theory and applications, clearly defined and logically organized, with illustrations for clarity and review questions at the end of each chapter to help you test your knowledge. * Understand electron theory and how electricity affects matter * Recognize applications for both alternating and direct current * Comprehend Ohm's Law and the laws governing magnetic circuits * Learn from detailed drawings and diagrams * Explore trigonometry and alternative methods of calculation * Identify instruments and measurements used in electrical applications * Apply proper grounding and ground testing, insulation testing, and power factor correction
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The origins and significance of electron density in the chemical, biological, and materials sciences Electron density is one of the fundamental concepts underlying modern chemistry and one of the key determinants of molecular structure and stability. It is also the basic variable of density functional theory, which has made possible, in recent years, the application of the mathematical theory of quantum physics to chemical and biological systems. With an equal emphasis on computational and philosophical questions, A Matter of Density: Exploring the Electron Density Concept in the Chemical, Biological, and Materials Sciences addresses the foundations, analysis, and applications of this pivotal chemical concept. The first part of the book presents a coherent and logically connected treatment of the theoretical foundations of the electron density concept. Discussion includes the use of probabilities in statistical physics; the origins of quantum mechanics; the philosophical questions at the heart of quantum theory, like quantum entanglement; and methods for the experimental determination of electron density distributions. The remainder of the book deals with applications of the electron density concept in the chemical, biological, and materials sciences. Contributors offer insights on how a deep understanding of the origins of chemical reactivity can be gleaned from the concepts of density functional theory. Also discussed are the applications of electron density in molecular similarity analysis and electron density-derived molecular descriptors, such as electrostatic potentials and local ionization energies. This section concludes with some applications of modern density functional theory to surfaces and interfaces. An essential reference for students as well as quantum and computational chemists, physical chemists, and physicists, this book offers an unparalleled look at the development of the concept of electron density from its inception to its role in density functional theory, which led to the 1998 Nobel Prize in Chemistry.
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The theory of logical consequence is central in modern logic and its applications. However, it is mostly dispersed in an abundance of often difficultly accessible papers, and rarely treated with applications in mind. This book collects the most fundamental aspects of this theory and offers the reader the basics of its applications in computer science, artificial intelligence, and cognitive science, to name but the most important fields where this notion finds its many applications. Both deductive and non-deductive consequence are discussed. The starting point is classical deductive consequence: classical logic is the reference system, and the non-classical deductive systems are seen as extensions, deviations, or variations thereof. The discussion of non-classical deductive consequence focuses on many-valued, intuitionistic, modal, paraconsistent, and substructural logical consequences. The topic of non-deductive consequence is elaborated on from the viewpoints of abductive, inductive, and probabilistic logics. All in all, the major contemporary (classes of) logical systems are here discussed. The approach is mathematical in essence, and the mathematical background, mainly founded on order relations, is treated thoroughly and in an accessible way for the non-mathematician. Presents the theory and methodology for reliability assessments of safety-critical functions through examples from a wide range of applications Reliability of Safety-Critical Systems: Theory and Applications provides a comprehensive introduction to reliability assessments of safety-related systems based on electrical, electronic, and programmable electronic (E/E/PE) technology. With a focus on the design and development phases of safety-critical systems, the book presents theory and methods required to document compliance with IEC 61508 and the associated sector-specific standards. Combining theory and practical applications, Reliability of Safety-Critical Systems: Theory and Applications implements key safety-related strategies and methods to meet quantitative safety integrity requirements. In addition, the book details a variety of reliability analysis methods that are needed during all stages of a safety-critical system, beginning with specification and design and advancing to operations, maintenance, and modification control. The key categories of safety life-cycle phases are featured, including strategies for the allocation of reliability performance requirements; assessment methods in relation to design; and reliability quantification in relation to operation and maintenance. Issues and benefits that arise from complex modern technology developments are featured, as well as: Real-world examples from large industry facilities with major accident potential and products owned by the general public such as cars and tools Plentiful worked examples throughout that provide readers with a deeper understanding of the core concepts and aid in the analysis and solution of common issues when assessing all facets of safety-critical systems Approaches that work on a wide scope of applications and can be applied to the analysis of any safety-critical system A brief appendix of probability theory for reference With an emphasis on how safety-critical functions are introduced into systems and facilities to prevent or mitigate the impact of an accident, this book is an excellent guide for professionals, consultants, and operators of safety-critical systems who carry out practical, risk, and reliability assessments of safety-critical systems. Reliability of Safety-Critical Systems: Theory and Applications is also a useful textbook for courses in reliability assessment of safety-critical systems and reliability engineering at the graduate-level, as well as for consulting companies offering short courses in reliability assessment of safety-critical systems.