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 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.

10601.49
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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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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

11436.53
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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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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.

9533.46
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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

11126.43
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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.

9381.5
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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.

11440.15
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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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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

12203.55
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The Golden Plate Award has been presented since 1961 by the American Academy of Achievement to approximately 25 guests of honor at the International Achievement Summit.

https://www.achievement.org/our-history/golden-plate-awards/

Sir Fraser Stoddart shared the 2016 Nobel Prize in Chemistry “for the design and synthesis of molecular machines.” Born in Scotland, he has lived in ...

https://www.boundless.com/blog/immigrant-chemists/

Sir Fraser Stoddart shared the 2016 Nobel Prize in Chemistry “for the design and synthesis of molecular machines.” Born in Scotland, he has lived in ...

https://www.boundless.com/blog/immigrant-chemists/

The Prize in Economic Sciences 1972. John R. Hicks “for their pioneering contributions to general economic equilibrium theory and welfare theory”

https://www.nobelprize.org/prizes/lists/nobel-laureates-and-research-affiliations/

Nobelpriset i kemi delas ut årligen av Kungliga Vetenskapsakademin till naturvetare inom kemins olika områden. Det är en av de fem Nobelpriser som etablerades ...

https://sv.wikipedia.org/wiki/Lista_över_nobelpristagare_i_kemi

Emil Fischer: Emil Fischer, German chemist who was awarded the 1902 Nobel Prize for Chemistry in recognition of his investigations of the sugar and purine groups of ...

https://www.britannica.com/biography/Emil-Fischer

Claude-Louis Berthollet: Claude-Louis Berthollet, central French figure in the emergence of chemistry as a modern discipline in the late 18th century. He ...

https://www.britannica.com/biography/Claude-Louis-Berthollet

REPORT Nanobiology Think Tank: Computational and Theoretical Nanoscience is Taking off at the National Cancer Institute I. A. Sidorov and D ...

http://www.aspbs.com/ctn/contents-ctn2006.htm

USC graduate students gain deeper understanding of homelessness. A semesterlong project at USC Annenberg encourages journalism students to challenge misconceptions ...

https://news.usc.edu/

Rudolph Arthur Marcus (born July 21, 1923) is a Canadian-born chemist who received the 1992 Nobel Prize in Chemistry "for his contributions to the theory of electron ...

https://en.wikipedia.org/wiki/Rudolph_A._Marcus

USC graduate students gain deeper understanding of homelessness. A semesterlong project at USC Annenberg encourages journalism students to challenge misconceptions ...

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INDUSTRY RENAISSANCE THE NEW BOOK IS THE EXPERIENCE; ORIGIN OF PLANETS German students' space station experiment seeks to prove planet-formation theory

https://compassmag.3ds.com/

In the context of molecular modelling, a force field (a special case of energy functions or interatomic potentials; not to be confused with force field in classical ...

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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.

10143.45
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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.

7702.74
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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

3581.11
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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.

11440.15
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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

14944.55
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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.

9915.52
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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.

8364.01
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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.

7245.43
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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.

10448.81
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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.

11325.82
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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.

2144.72
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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.

8770.78
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