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Theory and Simulation Methods for Electronic and Phononic Transport in Thermoelectric Materials (SpringerBriefs in Physics)
by Neophytos NeophytouThis book introduces readers to state-of-the-art theoretical and simulation techniques for determining transport in complex band structure materials and nanostructured-geometry materials, linking the techniques developed by the electronic transport community to the materials science community. Starting from the semi-classical Boltzmann Transport Equation method for complex band structure materials, then moving on to Monte Carlo and fully quantum mechanical models for nanostructured materials, the book addresses the theory and computational complexities of each method, as well as their advantages and capabilities. Presented in language that is accessible to junior computational scientists, while including enough detail and depth with regards to numerical implementation to tackle modern research problems, it offers a valuable resource for computational scientists and postgraduate researchers whose work involves the theory and simulation of electro-thermal transport in advanced materials.
Theory and Simulation of Random Phenomena: Mathematical Foundations and Physical Applications (UNITEXT for Physics)
by Ettore Vitali Mario Motta Davide Emilio GalliThe purpose of this book is twofold: first, it sets out to equip the reader with a sound understanding of the foundations of probability theory and stochastic processes, offering step-by-step guidance from basic probability theory to advanced topics, such as stochastic differential equations, which typically are presented in textbooks that require a very strong mathematical background. Second, while leading the reader on this journey, it aims to impart the knowledge needed in order to develop algorithms that simulate realistic physical systems. Connections with several fields of pure and applied physics, from quantum mechanics to econophysics, are provided. Furthermore, the inclusion of fully solved exercises will enable the reader to learn quickly and to explore topics not covered in the main text. The book will appeal especially to graduate students wishing to learn how to simulate physical systems and to deepen their knowledge of the mathematical framework, which has very deep connections with modern quantum field theory.
Theory and Statistical Applications of Stochastic Processes
by Yuliya Mishura Georgiy ShevchenkoThis book is concerned with the theory of stochastic processes and the theoretical aspects of statistics for stochastic processes. It combines classic topics such as construction of stochastic processes, associated filtrations, processes with independent increments, Gaussian processes, martingales, Markov properties, continuity and related properties of trajectories with contemporary subjects: integration with respect to Gaussian processes, Itȏ integration, stochastic analysis, stochastic differential equations, fractional Brownian motion and parameter estimation in diffusion models.
Theory and Synthesis of Linear Passive Time-Invariant Networks
by Dante C. YoulaExploring the overlap of mathematics and engineering network synthesis, this book presents a rigorous treatment of the key principles underpinning linear lumped passive time-invariant networks. Based around a series of lectures given by the author, this thoughtfully written book draws on his wide experience in the field, carefully revealing the essential mathematical structure of network synthesis problems. Topics covered include passive n-ports, broadband matching, the design of passive multiplexes and two-state passive devices. It also includes material not usually found in existing texts, such as the theoretical behavior of transverse electromagnetic (TEM) coupled transmission lines. Introducing fundamental principles in a formal theorem-proof style, illustrated by worked examples, this book is an invaluable resource for graduate students studying linear networks and circuit design, academic researchers, and professional circuit engineers.
Theory and Technology of Roll Stamping
by Vyacheslav Aleksandrovich Golenkov Sergey Yuryevich Radchenko Daniil Olegovich DorokhovThis book gives a complete overview of the roll stamping process of metal forming. This fundamentally new technique features an integrated local loading of the plastic deformation zone of the workpiece, simultaneously combining the die forging operation and local deformation of the deformation zone by rotating rollers or drive rolls. The book presents the basics of the theory behind roll stamping, delivering a complete technical analysis including the key results of mathematical modeling studies and a discussion of methodologies for designing novel roll stamping techniques. The aim of the new metal forming processes proposed in the book is directed toward the production of competitive equipment for fabrication of various mechanical parts having enhanced materials and physical properties in combination with a low cost of production and maintenance. This book is an ideal resource for any student or practicing engineer working with the roll stamping process.
Theory, Formulation and Realization of Artifacts Science: 3M&I-Body System (SpringerBriefs in Business)
by Masayuki MatsuiThis book considers and builds on the main propositions regarding body similarity and the principles of nature versus artifacts in science. It also explores the design (matrix) power of the human, Material/Machine, Money & Information (3M&I) body with respect to productivity/gross domestic product (GDP). The book begins in 2009 with Weiner’s cybernetics and describes Matsui’s theory and dynamism concerning the basic equation of W = ZL and artifact formulation using matrix methods, such as Matsui’s matrix equation (Matsui’s ME). In his book Fundamentals and Principles of Artifacts Science: 3M&I-Body System, published by Springer in 2016, the author championed the white-box approach for 3M&I artifacts in contrast to Simon’s artificial approach from 1969. Two principles, the Sandwich (waist) and Balancing theories, and their fundamental problems, were identified. This book now proposes a third principle: the fractal/harmonic-like structure of the cosmos and life types in space and time. The book further elaborates on the complexity of the 3M&I system and management in terms of enterprises, economics, nature, and other applications. Also, the domain of nature versus artifacts is highlighted, demonstrating the possibility of a white-box cybernetics-type robot. This fosters the realization of humanized and harmonic worlds that combine increased happiness and social productivity in an age increasingly dominated by technology.
Theory Informing and Arising from Learning Analytics
by Kathryn Bartimote Sarah K. Howard Dragan GaševićTheory Informing and Arising from Learning Analytics delves into the dynamic intersection of learning theory and educational data analysis within the field of Learning Analytics (LA). This groundbreaking book illuminates how theoretical insights can revolutionize data interpretation, reshape research methodologies, and expand the horizons of human learning and educational theory. Organized into three distinct sections, it offers a comprehensive introduction to the role of theory in LA, features contributions from leading scholars who apply diverse theoretical frameworks to their research, and explores cutting-edge topics where new theories are emerging. A standout feature is the inclusion of three “in conversation” chapters, where expert panels dive into the topics of ethics, self-regulated learning, and qualitative computation, enriched by accompanying podcasts that provide fresh, thought-provoking perspectives. This book is an invaluable resource for researchers, sparking debates on the evolving role of theory in LA and challenging conventional epistemological views. Published by Springer, it is an essential read for both aspiring and seasoned scholars eager to engage with the forefront of LA research.
Theory, Numerics and Applications of Hyperbolic Problems I: Aachen, Germany, August 2016 (Springer Proceedings in Mathematics & Statistics #236)
by Christian Klingenberg Michael WestdickenbergThe first of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.
Theory, Numerics and Applications of Hyperbolic Problems II: Aachen, Germany, August 2016 (Springer Proceedings in Mathematics & Statistics #237)
by Christian Klingenberg Michael WestdickenbergThe second of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.
Theory of Affine Projection Algorithms for Adaptive Filtering
by Kazuhiko OzekiThis book focuses on theoretical aspects of the affine projection algorithm (APA) for adaptive filtering. The APA is a natural generalization of the classical, normalized least-mean-squares (NLMS) algorithm. The book first explains how the APA evolved from the NLMS algorithm, where an affine projection view is emphasized. By looking at those adaptation algorithms from such a geometrical point of view, we can find many of the important properties of the APA, e. g. , the improvement of the convergence rate over the NLMS algorithm especially for correlated input signals. After the birth of the APA in the mid-1980s, similar algorithms were put forward by other researchers independently from different perspectives. This book shows that they are variants of the APA, forming a family of APAs. Then it surveys research on the convergence behavior of the APA, where statistical analyses play important roles. It also reviews developments of techniques to reduce the computational complexity of the APA, which are important for real-time processing. It covers a recent study on the kernel APA, which extends the APA so that it is applicable to identification of not only linear systems but also nonlinear systems. The last chapter gives an overview of current topics on variable parameter APAs. The book is self-contained, and is suitable for graduate students and researchers who are interested in advanced theory of adaptive filtering.
Theory of Agglomerative Hierarchical Clustering (Behaviormetrics: Quantitative Approaches to Human Behavior #15)
by Sadaaki MiyamotoThis book discusses recent theoretical developments in agglomerative hierarchical clustering. The general understanding of agglomerative hierarchical clustering is that its theory was completed long ago and there is no room for further methodological studies, at least in its fundamental structure. This book has been planned counter to that view: it will show that there are possibilities for further theoretical studies and they will be not only for methodological interests but also for usefulness in real applications. When compared with traditional textbooks, the present book has several notable features. First, standard linkage methods and agglomerative procedure are described by a general algorithm in which dendrogram output is expressed by a recursive subprogram. That subprogram describes an abstract tree structure, which is used for a two-stage linkage method for a greater number of objects. A fundamental theorem for single linkage using a fuzzy graph is proved, which uncovers several theoretical features of single linkage. Other theoretical properties such as dendrogram reversals are discussed. New methods using positive-definite kernels are considered, and some properties of the Ward method using kernels are studied. Overall, theoretical features are discussed, but the results are useful as well for application-oriented users of agglomerative clustering.
The Theory of Algebraic Numbers (Dover Books on Mathematics #9)
by Harry Pollard Harold G. DiamondAn excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture. 1975 edition. References. List of Symbols. Index.
Theory of Algebraic Surfaces (SpringerBriefs in Mathematics)
by Kunihiko KodairaThis is an English translation of the book in Japanese, published as the volume 20 in the series of Seminar Notes from The University of Tokyo that grew out of a course of lectures by Professor Kunihiko Kodaira in 1967. It serves as an almost self-contained introduction to the theory of complex algebraic surfaces, including concise proofs of Gorenstein's theorem for curves on a surface and Noether's formula for the arithmetic genus. It also discusses the behavior of the pluri-canonical maps of surfaces of general type as a practical application of the general theory. The book is aimed at graduate students and also at anyone interested in algebraic surfaces, and readers are expected to have only a basic knowledge of complex manifolds as a prerequisite.
Theory of Approximation (Dover Books on Mathematics)
by N. I. AchieserA pioneer of many modern developments in approximation theory, N. I. Achieser designed this graduate-level text from the standpoint of functional analysis. The first two chapters address approximation problems in linear normalized spaces and the ideas of P. L. Tchebysheff. Chapter III examines the elements of harmonic analysis, and Chapter IV, integral transcendental functions of the exponential type. The final two chapters explore the best harmonic approximation of functions and Wiener's theorem on approximation. Professor Achieser concludes this exemplary text with an extensive section of problems and applications (elementary extremal problems, Szego's theorem, the Carathéodory-Fejér problem, and more).
Theory of Besov Spaces (Developments in Mathematics #56)
by Yoshihiro SawanoThis is a self-contained textbook of the theory of Besov spaces and Triebel–Lizorkin spaces oriented toward applications to partial differential equations and problems of harmonic analysis. These include a priori estimates of elliptic differential equations, the T1 theorem, pseudo-differential operators, the generator of semi-group and spaces on domains, and the Kato problem. Various function spaces are introduced to overcome the shortcomings of Besov spaces and Triebel–Lizorkin spaces as well. The only prior knowledge required of readers is familiarity with integration theory and some elementary functional analysis.Illustrations are included to show the complicated way in which spaces are defined. Owing to that complexity, many definitions are required. The necessary terminology is provided at the outset, and the theory of distributions, L^p spaces, the Hardy–Littlewood maximal operator, and the singular integral operators are called upon. One of the highlights is that the proof of the Sobolev embedding theorem is extremely simple. There are two types for each function space: a homogeneous one and an inhomogeneous one. The theory of function spaces, which readers usually learn in a standard course, can be readily applied to the inhomogeneous one. However, that theory is not sufficient for a homogeneous space; it needs to be reinforced with some knowledge of the theory of distributions. This topic, however subtle, is also covered within this volume. Additionally, related function spaces—Hardy spaces, bounded mean oscillation spaces, and Hölder continuous spaces—are defined and discussed, and it is shown that they are special cases of Besov spaces and Triebel–Lizorkin spaces.
The Theory of Collusion and Competition Policy
by Joseph E. HarringtonA review of the theoretical research on unlawful collusion, focusing on the impact and optimal design of competition law and enforcement. Collusion occurs when firms in a market coordinate their behavior for the purpose of producing a supracompetitive outcome. The literature on the theory of collusion is deep and broad but most of that work does not take account of the possible illegality of collusion. Recently, there has been a growing body of research that explicitly focuses on collusion that runs afoul of competition law and thereby makes firms potentially liable for penalties. This book, by an expert on the subject, reviews the theoretical research on unlawful collusion, with a focus on two issues: the impact of competition law and enforcement on whether, how long, and how much firms collude; and the optimal design of competition law and enforcement.The book begins by discussing general issues that arise when models of collusion take into account competition law and enforcement. It goes on to consider game-theoretic models that encompass the probability of detection and penalties incurred when convicted, and examines how these policy instruments affect the frequency of cartels, cartel duration, cartel participation, and collusive prices. The book then considers the design of competition law and enforcement, examining such topics as the formula for penalties and leniency programs. The book concludes with suggested future lines of inquiry into illegal collusion.
Theory of Computation
by George TourlakisLearn the skills and acquire the intuition to assess the theoretical limitations of computer programming Offering an accessible approach to the topic, Theory of Computation focuses on the metatheory of computing and the theoretical boundaries between what various computational models can do and not do--from the most general model, the URM (Unbounded Register Machines), to the finite automaton. A wealth of programming-like examples and easy-to-follow explanations build the general theory gradually, which guides readers through the modeling and mathematical analysis of computational phenomena and provides insights on what makes things tick and also what restrains the ability of computational processes. Recognizing the importance of acquired practical experience, the book begins with the metatheory of general purpose computer programs, using URMs as a straightforward, technology-independent model of modern high-level programming languages while also exploring the restrictions of the URM language. Once readers gain an understanding of computability theory--including the primitive recursive functions--the author presents automata and languages, covering the regular and context-free languages as well as the machines that recognize these languages. Several advanced topics such as reducibilities, the recursion theorem, complexity theory, and Cook's theorem are also discussed. Features of the book include: A review of basic discrete mathematics, covering logic and induction while omitting specialized combinatorial topics A thorough development of the modeling and mathematical analysis of computational phenomena, providing a solid foundation of un-computability The connection between un-computability and un-provability: Gödel's first incompleteness theorem The book provides numerous examples of specific URMs as well as other programming languages including Loop Programs, FA (Deterministic Finite Automata), NFA (Nondeterministic Finite Automata), and PDA (Pushdown Automata). Exercises at the end of each chapter allow readers to test their comprehension of the presented material, and an extensive bibliography suggests resources for further study. Assuming only a basic understanding of general computer programming and discrete mathematics, Theory of Computation serves as a valuable book for courses on theory of computation at the upper-undergraduate level. The book also serves as an excellent resource for programmers and computing professionals wishing to understand the theoretical limitations of their craft.
Theory of Computational Complexity
by Ding-Zhu Du Ker-I KoPraise for the First Edition "...complete, up-to-date coverage of computational complexity theory...the book promises to become the standard reference on computational complexity." -Zentralblatt MATH A thorough revision based on advances in the field of computational complexity and readers' feedback, the Second Edition of Theory of Computational Complexity presents updates to the principles and applications essential to understanding modern computational complexity theory. The new edition continues to serve as a comprehensive resource on the use of software and computational approaches for solving algorithmic problems and the related difficulties that can be encountered. Maintaining extensive and detailed coverage, Theory of Computational Complexity, Second Edition, examines the theory and methods behind complexity theory, such as computational models, decision tree complexity, circuit complexity, and probabilistic complexity. The Second Edition also features recent developments on areas such as NP-completeness theory, as well as: A new combinatorial proof of the PCP theorem based on the notion of expander graphs, a research area in the field of computer science Additional exercises at varying levels of difficulty to further test comprehension of the presented material End-of-chapter literature reviews that summarize each topic and offer additional sources for further study Theory of Computational Complexity, Second Edition, is an excellent textbook for courses on computational theory and complexity at the graduate level. The book is also a useful reference for practitioners in the fields of computer science, engineering, and mathematics who utilize state-of-the-art software and computational methods to conduct research. A thorough revision based on advances in the field of computational complexity and readers' feedback, the Second Edition of Theory of Computational Complexity presents updates to the principles and applications essential to understanding modern computational complexity theory. The new edition continues to serve as a comprehensive resource on the use of software and computational approaches for solving algorithmic problems and the related difficulties that can be encountered. Maintaining extensive and detailed coverage, Theory of Computational Complexity, Second Edition, examines the theory and methods behind complexity theory, such as computational models, decision tree complexity, circuit complexity, and probabilistic complexity. The Second Edition also features recent devnd complexity at the graduate level. The book is also a useful reference for practitioners in the fields of computer science, engineering, and mathematics who utilize state-of-the-art software and computational methods to conduct research.
Theory of Control Systems Described by Differential Inclusions
by Zhengzhi Han Xiushan Cai Jun HuangThis book provides a brief introduction to the theory of finitedimensional differential inclusions, and deals in depth with control of threekinds of differential inclusion systems. The authors introduce the algebraicdecomposition of convex processes, the stabilization of polytopic systems, andobservations of Luré systems. They also introduce the elemental theory offinite dimensional differential inclusions, and the properties and designs ofthe control systems described by differential inclusions. Addressing thematerial with clarity and simplicity, the book includes recent researchachievements and spans all concepts, concluding with a critical mathematicalframework. This book is intended for researchers, teachers and postgraduatestudents in the area of automatic control engineering.
Theory Of Difference Equations Numerical Methods And Applications: Numerical Methods And Applications
by V. Lakshmikantham V. Trigiante"Provides a clear and comprehensive overview of the fundamental theories, numerical methods, and iterative processes encountered in difference calculus. Explores classical problems such as orthological polynomials, the Euclidean algorithm, roots of polynomials, and well-conditioning."
The Theory of Difference Schemes
by Alexander A. SamarskiiThe Theory of Difference Schemes emphasizes solutions to boundary value problems through multiple difference schemes. It addresses the construction of approximate numerical methods and computer algorithms for solving mathematical physics problems. The book also develops mathematical models for obtaining desired solutions in minimal time using direct or iterative difference equations. Mathematical Reviews said it is "well-written [and] an excellent book, with a wealth of mathematical material and techniques."
Theory of Differential Equations in Engineering and Mechanics
by Kam Tim ChauThis gives comprehensive coverage of the essential differential equations students they are likely to encounter in solving engineering and mechanics problems across the field -- alongside a more advance volume on applications. This first volume covers a very broad range of theories related to solving differential equations, mathematical preliminaries, ODE (n-th order and system of 1st order ODE in matrix form), PDE (1st order, 2nd, and higher order including wave, diffusion, potential, biharmonic equations and more). Plus more advanced topics such as Green’s function method, integral and integro-differential equations, asymptotic expansion and perturbation, calculus of variations, variational and related methods, finite difference and numerical methods. All readers who are concerned with and interested in engineering mechanics problems, climate change, and nanotechnology will find topics covered in these books providing valuable information and mathematics background for their multi-disciplinary research and education.
Theory of Digital Automata
by Oleksandr Petrov Mykola Karpinskyy Bohdan Borowik Valery LahnoThis book serves a dual purpose: firstly to combine the treatment of circuits and digital electronics, and secondly, to establish a strong connection with the contemporary world of digital systems. The need for this approach arises from the observation that introducing digital electronics through a course in traditional circuit analysis is fast becoming obsolete. Our world has gone digital. Automata theory helps with the design of digital circuits such as parts of computers, telephone systems and control systems. A complete perspective is emphasized, because even the most elegant computer architecture will not function without adequate supporting circuits. The focus is on explaining the real-world implementation of complete digital systems. In doing so, the reader is prepared to immediately begin design and implementation work. This work serves as a bridge to take readers from the theoretical world to the everyday design world where solutions must be complete to be successful.
Theory of Distributions (Chapman & Hall/CRC Pure and Applied Mathematics)
by M.A. Al-GwaizA textbook for a graduate course in the theory of distributions and related topics, for students of applied mathematics or theoretical physics. Introduces the theory, explicates mathematical structures and the Hilbert-space aspects, and presents applications to typical boundary problems. Annotation
Theory of Distributions
by Svetlin G. GeorgievThis book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This book, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.