Methods of Nonlinear Analysis

Philosophy of Mathematics: An Introduction provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era.

Philosophy of Mathematics: An Introduction provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era.

"Harmony is a concept essential to Confucianism and to the way of life of past and present people in East Asia. Integrating methods of textual exegesis, historical investigation, comparative analysis,

Hands-on experts from academia and industry comprehensively describe how to successfully perform all the critical HPLC techniques needed for the analysis of peptides and proteins. The methods range fr

This book presents and explains the methods utilized to apply techniques from big data to massive structural data sets, especially those relating to the generation and analysis of very large networks

A lot of recent developments have been made about adhesively bonded joints modeling using various methods of analysis. The increasing application of adhesives in industry is partly due to the increase

An outstanding panel of hands-on experts and developers of CE equipment describe in step-by-step fashion their best cutting-edge methods for the detection and analysis of DNA mutations and modificatio

This book demonstrates how quantitative methods for text analysis can successfully combine with qualitative methods in the study of different disciplines of the Humanities and Social Sciences (HSS). T

Maoz views the evolution of international relations over the last two centuries as a set of interacting, cooperative and conflicting networks of states. The networks that emerged are the result of national choice processes about forming or breaking ties with other states. States are constantly concerned with their security and survival in an anarchic world. Their security concerns stem from their external environment and their past conflicts. Because many of them cannot ensure their security by their own power, they need allies to balance against a hostile international environment. The alliance choices made by states define the structure of security cooperation networks and spill over into other cooperative networks, including trade and institutions. Maoz tests his theory by applying social networks analysis (SNA) methods to international relations. He offers a novel perspective as a system of interrelated networks that co-evolve and interact with one another.

How do violent jihadists use language to try to persuade people to carry out violent acts? This book analyses over two million words of texts produced by violent jihadists to identify and examine the linguistic strategies employed. Taking a mixed methods approach, the authors combine quantitative methods from corpus linguistics, which allows the identification of frequent words and phrases, alongside close reading of texts via discourse analysis. The analysis compares language use across three sets of texts: those which advocate violence, those which take a hostile but non-violent standpoint, and those which take a moderate perspective, identifying the different uses of language associated with different stages of radicalization. The book also discusses how strategies including use of Arabic, romanisation, formal English, quotation, metaphor, dehumanisation and collectivisation are used to create in- and out-groups and justify violence.

How do violent jihadists use language to try to persuade people to carry out violent acts? This book analyses over two million words of texts produced by violent jihadists to identify and examine the linguistic strategies employed. Taking a mixed methods approach, the authors combine quantitative methods from corpus linguistics, which allows the identification of frequent words and phrases, alongside close reading of texts via discourse analysis. The analysis compares language use across three sets of texts: those which advocate violence, those which take a hostile but non-violent standpoint, and those which take a moderate perspective, identifying the different uses of language associated with different stages of radicalization. The book also discusses how strategies including use of Arabic, romanisation, formal English, quotation, metaphor, dehumanisation and collectivisation are used to create in- and out-groups and justify violence.

Advances in the growth of novel-engineered structures such as sophisticated semiconductor superlattices and heterostructures, as well as new nonlinear optical materials, have opened exciting possibilities for infrared sources, detectors, modulators and novel devices. Brought to maturity, such discrete devices could likely see widespread use in applications as diverse as infrared imaging, chemical sensing, surveillance, short-link and high-bandwidth communications. This book published by MRS, brings together a group of internationally recognized experts in the field to discuss progress in materials, physics, processing and device design and performance. Developments in materials for cooled and uncooled infrared systems based on pyroelectric, micro-bolometric, photovoltaic and photoconductive detectors are emphasized. Progress in compact infrared sources is also highlighted. Topics include: antimonide-related materials - growth, characterization and analysis; antimonide-related devices;

This book addresses the issue of designing the microstructure of fiber composite materials in order to obtain optimum performance. Besides the systematic treatment of conventional continuous and discontinuous fiber composites, the book also presents the state-of-the-art of the development of textile structural composites as well as the nonlinear elastic finite deformation theory of flexible composites. The author's experience during twenty years of research and teaching on composite materials is reflected in the broad spectrum of topics covered, including laminated composites, statistical strength theories of continuous fiber composites, short fiber composites, hybrid composites, two- and three-dimensional textile structural composites and flexible composites. This book provides the first comprehensive analysis and modeling of the thermo-mechanical behavior of fiber composites with these distinct microstructures. Overall, the inter-relationships among the processing, microstructures an

This book addresses the issue of designing the microstructure of fiber composite materials in order to obtain optimum performance. Besides the systematic treatment of conventional continuous and discontinuous fiber composites, the book also presents the state-of-the-art of the development of textile structural composites as well as the nonlinear elastic finite deformation theory of flexible composites. The author's experience during twenty years of research and teaching on composite materials is reflected in the broad spectrum of topics covered, including laminated composites, statistical strength theories of continuous fiber composites, short fiber composites, hybrid composites, two- and three-dimensional textile structural composites and flexible composites. This book provides the first comprehensive analysis and modeling of the thermo-mechanical behavior of fiber composites with these distinct microstructures. Overall, the inter-relationships among the processing, microstructures an

This book is dedicated to the mathematical study of two-dimensional statistical hydrodynamics and turbulence, described by the 2D Navier–Stokes system with a random force. The authors' main goal is to justify the statistical properties of a fluid's velocity field u(t,x) that physicists assume in their work. They rigorously prove that u(t,x) converges, as time grows, to a statistical equilibrium, independent of initial data. They use this to study ergodic properties of u(t,x) – proving, in particular, that observables f(u(t,.)) satisfy the strong law of large numbers and central limit theorem. They also discuss the inviscid limit when viscosity goes to zero, normalising the force so that the energy of solutions stays constant, while their Reynolds numbers grow to infinity. They show that then the statistical equilibria converge to invariant measures of the 2D Euler equation and study these measures. The methods apply to other nonlinear PDEs perturbed by random forces.

Stylistics has become the most common name for a discipline which at various times has been termed 'literary linguistics', 'rhetoric', 'poetics', 'literary philology' and 'close textual reading'. This Handbook is the definitive account of the field, drawing on linguistics and related subject areas such as psychology, sociology, anthropology, educational pedagogy, computational methods, literary criticism and critical theory. Placing stylistics in its intellectual and international context, each chapter includes a detailed illustrative example and case study of stylistic practice, with arguments and methods open to examination, replication and constructive critical discussion. As an accessible guide to the theory and practice of stylistics, it will equip the reader with a clear understanding of the ethos and principles of the discipline, as well as with the capacity and confidence to engage in stylistic analysis.

The first book on the topic, and written by the founder of the technique, this comprehensive resource provides a detailed overview of sum-frequency spectroscopy, its fundamental principles, and the wide range of applications for surfaces, interfaces, and bulk. Beginning with an overview of the historical context, and introductions to the basic theory of nonlinear optics and surface sum-frequency generation, topics covered include discussion of different experimental arrangements adopted by researchers, notes on proper data analysis, an up-to-date survey commenting on the wide range of successful applications of the tool, and a valuable insight into current unsolved problems and potential areas to be explored in the future. With the addition of chapter appendices that offer the opportunity for more in-depth theoretical discussion, this is an essential resource that integrates all aspects of the subject and is ideal for anyone using, or interested in using, sum-frequency spectroscopy.

This book examines qualitative and quantitative methods for nonlinear differential equations and treats integrability and nonintegrability theory. Starting from the idea of a constant of motion for si

Toru Takemitsu (1930–1996) was the best-known Japanese composer of his generation, bringing aspects of Eastern and Western traditions together, yet he remained something of an elusive figure. The composer's own commentaries about his music, poetic and philosophical in tone, have tended to deepen the mystery and much writing on Takemitsu to date has adopted a similar attitude, leaving many questions about his compositional methods unanswered. This book is the first complete study of the composer's work to appear in English. It is also the first book in this language to offer an in-depth analysis of his music. Takemitsu's works are increasingly popular with Western audiences and Peter Burt attempts for the first time to shed light on the hitherto rather secretive world of his working methods, as well as place him in context as heir to the rich tradition of Japanese composition in the twentieth century.

This book gives a new interpretation of the reception of the new world by the old. It is the first in-depth study of the pre-Enlightenment methods by which Europeans attempted to describe and classify the American Indian and his society. Between 1512 and 1724 a simple determinist view of human society was replaced by a more sophisticated relativist approach. Anthony Pagden uses new methods of technical analysis, already developed in philosophy and anthropology, to examine four groups of writers who analysed Indian culture: the sixteenth-century theologian, Francisco de Vitoria, and his followers; the 'champion of the Indians' Bartolomé de Las Casas; and the Jesuit historians José de Acosta and Joseph François Lafitau. Dr Pagden explains the sources for their theories and how these conditioned their observations. He also examines for the first time the key terms in each writer's vocabulary - words such as 'barbarian' and 'civil' - and the assumptions that lay beneath them.

Combining the methods of the modern philosopher with those of the historian of ideas, Knud Haakonssen presents an interpretation of the philosophy of law which Adam Smith developed out of - and partly in response to - David Hume's theory of justice. While acknowledging that the influences on Smith were many and various, Dr Haakonssen suggests that the decisive philosophical one was Hume's analysis of justice in A Treatise of Human Nature and the second Enquiry. He therefore begins with a thorough investigation of Hume, from which he goes on to show the philosophical originality of Smith's new form of natural jurisprudence. At the same time, he provides an over all reading of Smith's social and political thought, demonstrating clearly the exact links between the moral theory of The Theory of Moral Sentiments, the Lectures on Jurisprudence, and the sociohistorical theory of The Wealth of Nations. This is the first full analysis of Adam Smith's jurisprudence; it emphasizes its normative a

This book provides definitions and mathematical derivations of fundamental relationships of tensor analysis encountered in nonlinear continuum mechanics and continuum physics, with a focus on finite d

This book deals with the application of fractal and nonlinear time-series analysis to seismicity and earthquakes within the framework of earthquake prediction research. Emphasis is on theoretical foun

Using autoethnographic and autopoetic methods based on analysis of his own experiences of growing up black in Louisiana and then working his way through the "White Ivory Tower," Alexander (communicati

In recent years the development of new classification and regression algorithms based on deep learning has led to a revolution in the fields of artificial intelligence, machine learning, and data analysis. The development of a theoretical foundation to guarantee the success of these algorithms constitutes one of the most active and exciting research topics in applied mathematics. This book presents the current mathematical understanding of deep learning methods from the point of view of the leading experts in the field. It serves as both a starting point for researchers and graduate students in mathematics trying to get into the field, as well as an invaluable reference for future research.

Using Bishop's work on constructive analysis as a framework, this monograph gives a systematic, detailed and general constructive theory of probability theory and stochastic processes. It is the first extended account of this theory: almost all of the constructive existence and continuity theorems that permeate the book are original. It also contains results and methods hitherto unknown in the constructive and nonconstructive settings. The text features logic only in the common sense and, beyond a certain mathematical maturity, requires no prior training in either constructive mathematics or probability theory. It will thus be accessible and of interest, both to probabilists interested in the foundations of their speciality and to constructive mathematicians who wish to see Bishop's theory applied to a particular field.

Social movements have attracted much attention in recent years, both from scholars and among the wider public. This book examines the consequences of social movements, covering such issues as the impact of social movements on the life course of participants and the population in general, on political elites and markets, and on political parties and processes of social movement institutionalization. The volume makes a significant contribution to research on social movement outcomes in three ways: theoretically, by showing the importance of hitherto undervalued topics in the study of social movements outcomes; methodologically, by expanding the scientific boundaries of this research field through an interdisciplinary approach and new methods of analysis; and empirically, by providing new evidence about social movement outcomes from Europe and the United States.

Social movements have attracted much attention in recent years, both from scholars and among the wider public. This book examines the consequences of social movements, covering such issues as the impact of social movements on the life course of participants and the population in general, on political elites and markets, and on political parties and processes of social movement institutionalization. The volume makes a significant contribution to research on social movement outcomes in three ways: theoretically, by showing the importance of hitherto undervalued topics in the study of social movements outcomes; methodologically, by expanding the scientific boundaries of this research field through an interdisciplinary approach and new methods of analysis; and empirically, by providing new evidence about social movement outcomes from Europe and the United States.

Making a substantiated choice of the most efficient statistical test is one of the basic problems of statistics. Asymptotic efficiency is an indispensable technique for comparing and ordering statistical tests in large samples. It is especially useful in nonparametric statistics where it is usually necessary to rely on heuristic tests. This monograph presents a unified treatment of the analysis and calculation of the asymptotic efficiencies of nonparametric tests. Powerful new methods are developed to evaluate explicitly different kinds of efficiencies. Of particular interest is the description of domains of the Bahadur local optimality and related characterisation problems based on recent research by the author. Other Russian results are also published here for the first time in English. Researchers, professionals and students in statistics will find this book invaluable.

Making a substantiated choice of the most efficient statistical test is one of the basic problems of statistics. Asymptotic efficiency is an indispensable technique for comparing and ordering statistical tests in large samples. It is especially useful in nonparametric statistics where it is usually necessary to rely on heuristic tests. This monograph presents a unified treatment of the analysis and calculation of the asymptotic efficiencies of nonparametric tests. Powerful new methods are developed to evaluate explicitly different kinds of efficiencies. Of particular interest is the description of domains of the Bahadur local optimality and related characterisation problems based on recent research by the author. Other Russian results are also published here for the first time in English. Researchers, professionals and students in statistics will find this book invaluable.

This is a fully revised and expanded edition of a very successful and widely used book. It describes the physical basis of all the principal, and most of the more specialised, techniques currently employed in the study of well-characterised solid surfaces. The coverage of each technique, illustrated with selected examples, is underpinned by discussion of the relevant physical principles, and the complementary aspects of the various methods are also described. Throughout, the emphasis is on understanding the concepts involved, rather than on an exhaustive review of applications. The book will be of great use to final year undergraduate and postgraduate students in physics, chemistry and materials science. It will also be valuable to established researchers in any area of surface science concerned with the acquisition and analysis of experimental data.

Maoz views the evolution of international relations over the last two centuries as a set of interacting, cooperative and conflicting networks of states. The networks that emerged are the result of national choice processes about forming or breaking ties with other states. States are constantly concerned with their security and survival in an anarchic world. Their security concerns stem from their external environment and their past conflicts. Because many of them cannot ensure their security by their own power, they need allies to balance against a hostile international environment. The alliance choices made by states define the structure of security cooperation networks and spill over into other cooperative networks, including trade and institutions. Maoz tests his theory by applying social networks analysis (SNA) methods to international relations. He offers a novel perspective as a system of interrelated networks that co-evolve and interact with one another.

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

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

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

The first treatment of advanced knowledge of electrical sneak circuits and its analysis method in power electronics The work on sneak circuit and its analysis methods for power converters contributes

This is the 2005 second edition of a highly successful and well-respected textbook on the numerical techniques used to solve partial differential equations arising from mathematical models in science, engineering and other fields. The authors maintain an emphasis on finite difference methods for simple but representative examples of parabolic, hyperbolic and elliptic equations from the first edition. However this is augmented by new sections on finite volume methods, modified equation analysis, symplectic integration schemes, convection-diffusion problems, multigrid, and conjugate gradient methods; and several sections, including that on the energy method of analysis, have been extensively rewritten to reflect modern developments. Already an excellent choice for students and teachers in mathematics, engineering and computer science departments, the revised text includes more latest theoretical and industrial developments.

Clifton (theology, Alphacrucis College, Sydney, Australia) applies academic methods of analysis to the movement in which he is a member, teacher, and ordained minister. He explores Pentecostal ecclesi

This book presents a description and analysis of sociolinguistics written from a demographer’s perspective. It synthesizes the data on the materials, methods, and issues of this interdisciplinary fie

This introductory text covers basic electronics and the behavior of passive components, circuit analysis and systematic troubleshooting. The analytical methods used are strongly based on Ohm's and Ki