Methods of Nonlinear Analysis

functions and Hecke L-functions of an imaginary quadratic field，and various problems on elliptic modular forms. As to the values of Dirichlet L-functions， all previous papers and books reiterate a single old result with a single old method. After a review ofelementary Fourier analysis， the author presents completely new results with new methods. though old results will also be proved. No advanced knowledge of number theory is required up to this point. As applications， new formulas for the second factor ofthe class number of a cyclotomic field will be given. The second half of the book assumes familiarity with basic knowledge ofmodular forms. However，all definitions and facts are clearly stated， and precise references are given. The notion ofnearly holomorphic modular forms is introduced and applied to the determination of the critical values of Hecke L-functions of an imaginary quadratic field. Other notable features of the book are： (1) some new results on classical E

Word stress has long presented challenges to phonologists, as they have sought to uncover patterns in its distribution, and devise models to account for its behaviour and formal representation both within single languages and cross-linguistically. In this collection, a team of world-renowned researchers present a variety of viewpoints on the methods and problems involved. Offering fresh perspectives on the topic and its study, this book is specifically concerned with basing theoretical work on broad typological surveys and focuses on the collection, selection and use of data in the analysis of word stress and word rhythm, including their phonetic manifestations. An extensive introduction presents a state-of-the-art review of stress research. The contributors also present StressTyp2, a project in an advanced stage of development, which intends to make publicly available information on word stress in a broad sample of languages and will offer new ways of understanding this key research a

The extent to which language is inseparable from thought has long been a major subject of debate across linguistics, psychology, philosophy and other disciplines. In this study, Wallace Chafe presents a thought-based theory of language that goes beyond traditional views that semantics, syntax, and sounds are sufficient to account for language design. Language begins with thoughts in the mind of a speaker and ends by affecting thoughts in the mind of a listener. This obvious observation is seldom incorporated in descriptions of language design for two major reasons. First, the role of thought is usually usurped by semantics. But semantic structures are imposed on thought by languages and differ from one language to another. Second, thought does not lend itself to familiar methods of linguistic analysis. Chafe suggests ways of describing thoughts, traces the path languages follow from thoughts to sounds, and explores ways in which thoughts are oriented in time, memory, imagination, reali

The extent to which language is inseparable from thought has long been a major subject of debate across linguistics, psychology, philosophy and other disciplines. In this study, Wallace Chafe presents a thought-based theory of language that goes beyond traditional views that semantics, syntax, and sounds are sufficient to account for language design. Language begins with thoughts in the mind of a speaker and ends by affecting thoughts in the mind of a listener. This obvious observation is seldom incorporated in descriptions of language design for two major reasons. First, the role of thought is usually usurped by semantics. But semantic structures are imposed on thought by languages and differ from one language to another. Second, thought does not lend itself to familiar methods of linguistic analysis. Chafe suggests ways of describing thoughts, traces the path languages follow from thoughts to sounds, and explores ways in which thoughts are oriented in time, memory, imagination, reali

The American Novel series provides students of American literature with introductory critical guides to the great works of American fiction by giving details of the novel's composition, publication history and contemporary reception. The group of essays, each specially commissioned from a leading scholar in the field, examines the interpretative methods and prominent ideas on the text. There are also helpful guides to further reading. Specifically designed for undergraduates, the series will be a powerful resource for anyone engaged in the critical analysis of major American novels. This collection of essays on Moby-Dick reconnects Melville's great work with concerns that are central to readers in critical studies. Richard Brodhead introduces the volume with a discussion of the book's unique place in the canon of American literature. He then recounts the novel's history from its mixed reception in the mid-nineteenth century to its prevalent status as a classic. The five essays that fol

The relationship between the police and young people in Australia is a topic of growing concern in Australian society. While people are concerned about juvenile crime, worries have also been expressed about police harassment and violence directed at young people. This book, first published in 1994, provides a sustained analysis of police-youth relations, offering new insights into how young people are policed. Some specific areas addressed include: the legal framework of police-youth interaction in Australia; the rights of young people; the policing of Aboriginal youth; the relationship between the police and young women; and ethnic and community policing, and likely future directions in policy. Written by a team of the leading people in the field this book makes an important contribution to debate on a critical issue. The Police and Young People in Australia shows the implications that contemporary police methods and practices have on the exercise of basic legal rights in Australian s

Measuring Behaviour is the established go-to text for anyone interested in scientific methods for studying the behaviour of animals or humans. It is widely used by students, teachers and researchers in a variety of fields, including biology, psychology, the social sciences and medicine. This new fourth edition has been completely rewritten and reorganised to reflect major developments in how behavioural studies are conducted. It includes new sections on the replication crisis, covering Open Science initiatives such as preregistration, as well as fully up-to-date information on the use of remote sensors, big data and artificial intelligence in capturing and analysing behaviour. The sections on the analysis and interpretation of data have been rewritten to align with current practices, with advice on avoiding common pitfalls. Although fully revised and revamped, this new edition retains the simplicity, clarity and conciseness that have made Measuring Behaviour a classic since the first e

Measuring Behaviour is the established go-to text for anyone interested in scientific methods for studying the behaviour of animals or humans. It is widely used by students, teachers and researchers in a variety of fields, including biology, psychology, the social sciences and medicine. This new fourth edition has been completely rewritten and reorganised to reflect major developments in how behavioural studies are conducted. It includes new sections on the replication crisis, covering Open Science initiatives such as preregistration, as well as fully up-to-date information on the use of remote sensors, big data and artificial intelligence in capturing and analysing behaviour. The sections on the analysis and interpretation of data have been rewritten to align with current practices, with advice on avoiding common pitfalls. Although fully revised and revamped, this new edition retains the simplicity, clarity and conciseness that have made Measuring Behaviour a classic since the first e

Actuaries have access to a wealth of individual data in pension and insurance portfolios, but rarely use its full potential. This book will pave the way, from methods using aggregate counts to modern developments in survival analysis. Based on the fundamental concept of the hazard rate, Part I shows how and why to build statistical models, based on data at the level of the individual persons in a pension scheme or life insurance portfolio. Extensive use is made of the R statistics package. Smooth models, including regression and spline models in one and two dimensions, are covered in depth in Part II. Finally, Part III uses multiple-state models to extend survival models beyond the simple life/death setting, and includes a brief introduction to the modern counting process approach. Practising actuaries will find this book indispensable, and students will find it helpful when preparing for their professional examinations.

It is widely accepted among conservation biologists that genetics is, more than ever, an essential and efficient tool for wild and captive population management and reserve design. However, a true synergy between population genetics and conservation biology is lacking. Following the first International Workshop on Population Genetics for Animal Conservation in 2003 at the Centro di Ecologia Alpina, Trento, Italy (recently incorporated into the Edmund Mach Foundation), the scientific committee felt that, given the global urgency of animal conservation, it was imperative that discussions at the conference were made accessible to graduate students and wildlife managers. This book integrates 'the analytical methods approach' with the 'real problems approach' in conservation genetics. Each chapter is an exhaustive review of one area of expertise, and a special effort has been made to explain the statistical tools available for the analysis of molecular data as clearly as possible. The resul

It is widely accepted among conservation biologists that genetics is, more than ever, an essential and efficient tool for wild and captive population management and reserve design. However, a true synergy between population genetics and conservation biology is lacking. Following the first International Workshop on Population Genetics for Animal Conservation in 2003 at the Centro di Ecologia Alpina, Trento, Italy (recently incorporated into the Edmund Mach Foundation), the scientific committee felt that, given the global urgency of animal conservation, it was imperative that discussions at the conference were made accessible to graduate students and wildlife managers. This book integrates 'the analytical methods approach' with the 'real problems approach' in conservation genetics. Each chapter is an exhaustive review of one area of expertise, and a special effort has been made to explain the statistical tools available for the analysis of molecular data as clearly as possible. The resul

This text is geared toward students who have an undergraduate degree or extensive coursework in engineering or the physical sciences and who wish to develop their understanding of the essential topics of applied mathematics. The methods covered in the chapters form the core of analysis in engineering and the physical sciences. Readers will learn the solutions, techniques, and approaches that they will use as academic researchers or industrial R&D specialists. For example, they will be able to understand the fundamentals behind the various scientific software packages that are used to solve technical problems (such as the equations describing the solid mechanics of complex structures or the fluid mechanics of short-term weather prediction and long-term climate change), which is crucial to working with such codes successfully. Detailed and numerous worked problems help to ensure a clear and well-paced introduction to applied mathematics. Computational challenge problems at the end of eac

How did the first female voters cast their ballots? For almost 100 years, answers to this question have eluded scholars. Counting Women's Ballots employs new data and novel methods to provide insights into whether, how, and with what consequences women voted in the elections after suffrage. The analysis covers a larger and more diverse set of places, over a longer period of time, than has previously been possible. J. Kevin Corder and Christina Wolbrecht find that the extent to which women voted and which parties they supported varied considerably across time and place, challenging attempts to describe female voters in terms of simple generalizations. Many women adapted quickly to their new right; others did not. In some cases, women reinforced existing partisan advantages; in others, they contributed to dramatic political realignment. Counting Women's Ballots improves our understanding of the largest expansion of the American electorate during a transformative period of American histor

How did the first female voters cast their ballots? For almost 100 years, answers to this question have eluded scholars. Counting Women's Ballots employs new data and novel methods to provide insights into whether, how, and with what consequences women voted in the elections after suffrage. The analysis covers a larger and more diverse set of places, over a longer period of time, than has previously been possible. J. Kevin Corder and Christina Wolbrecht find that the extent to which women voted and which parties they supported varied considerably across time and place, challenging attempts to describe female voters in terms of simple generalizations. Many women adapted quickly to their new right; others did not. In some cases, women reinforced existing partisan advantages; in others, they contributed to dramatic political realignment. Counting Women's Ballots improves our understanding of the largest expansion of the American electorate during a transformative period of American histor

This volume collects seven of Marc Nerlove's previously published, classic essays on panel data econometrics written over the past thirty-five years, together with a cogent essay on the history of the subject, which began with George Biddell Airey's monograph published in 1861. Since Professor Nerlove's 1966 Econometrica paper with Pietro Balestra, panel data and methods of econometric analysis appropriate to such data have become increasingly important in the discipline. The principal factors in the research environment affecting the future course of panel data econometrics are the phenomenal growth in the computational power available to the individual researcher at his or her desktop and the ready availability of data sets, both large and small, via the Internet. The best way to formulate statistical models for inference is motivated and shaped by substantive problems and understanding of the processes generating the data at hand to resolve them. The essays illustrate both the role

This volume collects seven of Marc Nerlove's previously published, classic essays on panel data econometrics written over the past thirty-five years, together with a cogent essay on the history of the subject, which began with George Biddell Airey's monograph published in 1861. Since Professor Nerlove's 1966 Econometrica paper with Pietro Balestra, panel data and methods of econometric analysis appropriate to such data have become increasingly important in the discipline. The principal factors in the research environment affecting the future course of panel data econometrics are the phenomenal growth in the computational power available to the individual researcher at his or her desktop and the ready availability of data sets, both large and small, via the Internet. The best way to formulate statistical models for inference is motivated and shaped by substantive problems and understanding of the processes generating the data at hand to resolve them. The essays illustrate both the role

The authors describe here a framework in which the type notation of functional languages is extended to include a notation for binding times (that is run-time and compile-time) that distinguishes between them. Consequently the ability to specify code and verify program correctness can be improved. Two developments are needed, the first of which introduces the binding time distinction into the lambda calculus, in a manner analogous with the introduction of types into the untyped lambda calculus. Methods are also presented for introducing combinators for run-time. The second concerns the interpretation of the resulting language, which is known as the mixed lambda-calculus and combinatory logic. The notion of 'parametrized semantics' is used to describe code generation and abstract interpretation. The code generation is for a simple abstract machine designed for the purpose; it is close to the categorical abstract machine. The abstract interpretation focuses on a strictness analysis that

The authors describe here a framework in which the type notation of functional languages is extended to include a notation for binding times (that is run-time and compile-time) that distinguishes between them. Consequently the ability to specify code and verify program correctness can be improved. Two developments are needed, the first of which introduces the binding time distinction into the lambda calculus, in a manner analogous with the introduction of types into the untyped lambda calculus. Methods are also presented for introducing combinators for run-time. The second concerns the interpretation of the resulting language, which is known as the mixed lambda-calculus and combinatory logic. The notion of 'parametrized semantics' is used to describe code generation and abstract interpretation. The code generation is for a simple abstract machine designed for the purpose; it is close to the categorical abstract machine. The abstract interpretation focuses on a strictness analysis that

From the elegance of the Black-Scholes equation to the complexity of multi-factor interest rate models and hybrid derivatives, this book is your comprehensive guide to quantitative finance, complete with 15+ advanced C++ projects using QuantLib and Boost.You'll move seamlessly from mathematical foundations to real-world implementation, building a professional-grade toolkit for pricing, risk analysis, and calibration. Inside, you will learn core option pricing methods, master single-and multi-factor interest rate models, and construct and calibrate trees and lattices for advanced derivatives. You will also explore cutting edge products: exotic multi-asset options, hybrid derivatives, credit instruments, and cross-currency swaps.Packed with practical source code, step-by-step calibrations, and performance-tuned Boost integration, this book bridges the gap between academic finance and production-grade quant development. Whether you're a quant developer, financial engineer, or an advanced

Do you have a biological question that could be readily answered by computational techniques, but little experience in programming? Do you want to learn more about the core techniques used in computational biology and bioinformatics? Written in an accessible style, this guide provides a foundation for both newcomers to computer programming and those interested in learning more about computational biology. The chapters guide the reader through: a complete beginners' course to programming in Python, with an introduction to computing jargon; descriptions of core bioinformatics methods with working Python examples; scientific computing techniques, including image analysis, statistics and machine learning. This book also functions as a language reference written in straightforward English, covering the most common Python language elements and a glossary of computing and biological terms. This title will teach undergraduates, postgraduates and professionals working in the life sciences how t

Measurement in Fluid Mechanics is an introductory general reference in experimental fluid mechanics, describing both classical and more modern methods for flow visualization and for measuring flow rate, pressure, velocity, temperature, concentration, and wall shear stress. Particularly suitable as a textbook for graduate and advanced undergraduate courses, Measurement in Fluid Mechanics is also a valuable tool for practising engineers and applied scientists. This book is written by a single author, in a consistent and straightforward style, with plenty of clear illustrations, an extensive bibliography, and over 100 suggested exercises. Measurement in Fluid Mechanics also features extensive background materials in system response, measurement uncertainty, signal analysis, optics, fluid mechanical apparatus, and laboratory practices, which shield the reader from having to consult with a large number of primary references. Whether for instructional or reference purposes, this book is a va

Measurement in Fluid Mechanics is an introductory general reference in experimental fluid mechanics, describing both classical and more modern methods for flow visualization and for measuring flow rate, pressure, velocity, temperature, concentration, and wall shear stress. Particularly suitable as a textbook for graduate and advanced undergraduate courses, Measurement in Fluid Mechanics is also a valuable tool for practising engineers and applied scientists. This book is written by a single author, in a consistent and straightforward style, with plenty of clear illustrations, an extensive bibliography, and over 100 suggested exercises. Measurement in Fluid Mechanics also features extensive background materials in system response, measurement uncertainty, signal analysis, optics, fluid mechanical apparatus, and laboratory practices, which shield the reader from having to consult with a large number of primary references. Whether for instructional or reference purposes, this book is a va

The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and influence. 'Data science' and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? How does it all fit together? Now in paperback and fortified with exercises, this book delivers a concentrated course in modern statistical thinking. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov Chain Monte Carlo, inference after model selection, and dozens more. The distinctly modern approach integrates methodology and algorithms with statistical inference. Each chapter ends with class-tested exercises, and the book concludes wit

This comprehensive guide to Bayesian methods in astronomy enables hands-on work by supplying complete R, JAGS, Python, and Stan code, to use directly or to adapt. It begins by examining the normal model from both frequentist and Bayesian perspectives and then progresses to a full range of Bayesian generalized linear and mixed or hierarchical models, as well as additional types of models such as ABC and INLA. The book provides code that is largely unavailable elsewhere and includes details on interpreting and evaluating Bayesian models. Initial discussions offer models in synthetic form so that readers can easily adapt them to their own data; later the models are applied to real astronomical data. The consistent focus is on hands-on modeling, analysis of data, and interpretations that address scientific questions. A must-have for astronomers, its concrete approach will also be attractive to researchers in the sciences more generally.

This book studies the struggle to enforce international human rights law in federal courts. In 1980, a federal appeals court ruled that a Paraguayan family could sue a Paraguayan official under the Alien Tort Statute – a dormant provision of the 1789 Judiciary Act – for torture committed in Paraguay. Since then, courts have been wrestling with this step toward a universal approach to human rights law. Davis examines attempts by human rights groups to use the law to enforce human rights norms. He explains the separation of powers issues arising when victims sue the United States or when the United States intervenes to urge dismissal of a claim and analyses the controversies arising from attempts to hold foreign nations, foreign officials, and corporations liable under international human rights law. While Davis's analysis is driven by social science methods, its foundation is the dramatic human story from which these cases arise.

This book studies the struggle to enforce international human rights law in federal courts. In 1980, a federal appeals court ruled that a Paraguayan family could sue a Paraguayan official under the Alien Tort Statute – a dormant provision of the 1789 Judiciary Act – for torture committed in Paraguay. Since then, courts have been wrestling with this step toward a universal approach to human rights law. Davis examines attempts by human rights groups to use the law to enforce human rights norms. He explains the separation of powers issues arising when victims sue the United States or when the United States intervenes to urge dismissal of a claim and analyses the controversies arising from attempts to hold foreign nations, foreign officials, and corporations liable under international human rights law. While Davis's analysis is driven by social science methods, its foundation is the dramatic human story from which these cases arise.

Where did SARS come from? Have we inherited genes from Neanderthals? How do plants use their internal clock? The genomic revolution in biology enables us to answer such questions. But the revolution would have been impossible without the support of powerful computational and statistical methods that enable us to exploit genomic data. Many universities are introducing courses to train the next generation of bioinformaticians: biologists fluent in mathematics and computer science, and data analysts familiar with biology. This readable and entertaining book, based on successful taught courses, provides a roadmap to navigate entry to this field. It guides the reader through key achievements of bioinformatics, using a hands-on approach. Statistical sequence analysis, sequence alignment, hidden Markov models, gene and motif finding and more, are introduced in a rigorous yet accessible way. A companion website provides the reader with Matlab-related software tools for reproducing the steps de

This refreshing, introductory textbook covers both standard techniques for solving ordinary differential equations, as well as introducing students to qualitative methods such as phase-plane analysis. The presentation is concise, informal yet rigorous; it can be used either for 1-term or 1-semester courses. Topics such as Euler's method, difference equations, the dynamics of the logistic map, and the Lorenz equations, demonstrate the vitality of the subject, and provide pointers to further study. The author also encourages a graphical approach to the equations and their solutions, and to that end the book is profusely illustrated. The files to produce the figures using MATLAB are all provided in an accompanying website. Numerous worked examples provide motivation for and illustration of key ideas and show how to make the transition from theory to practice. Exercises are also provided to test and extend understanding: solutions for these are available for teachers.

This book is concerned with partial differential equations applied to fluids problems in science and engineering and is designed for two potential audiences. First, this book can function as a text for a course in mathematical methods in fluid mechanics in non-mathematics departments or in mathematics service courses. The authors have taught both. Second, this book is designed to help provide serious readers of journals (professionals, researchers, and graduate students) in analytical science and engineering with tools to explore and extend the missing steps in an analysis. The topics chosen for the book are those that the authors have found to be of considerable use in their own research careers. These topics are applicable in many areas, such as aeronautics and astronautics; biomechanics; chemical, civil, and mechanical engineering; fluid mechanics; and geophysical flows. Continuum ideas arise in other contexts, and the techniques included have applications there as well.

This book is concerned with partial differential equations applied to fluids problems in science and engineering and is designed for two potential audiences. First, this book can function as a text for a course in mathematical methods in fluid mechanics in non-mathematics departments or in mathematics service courses. The authors have taught both. Second, this book is designed to help provide serious readers of journals (professionals, researchers, and graduate students) in analytical science and engineering with tools to explore and extend the missing steps in an analysis. The topics chosen for the book are those that the authors have found to be of considerable use in their own research careers. These topics are applicable in many areas, such as aeronautics and astronautics; biomechanics; chemical, civil, and mechanical engineering; fluid mechanics; and geophysical flows. Continuum ideas arise in other contexts, and the techniques included have applications there as well.

This is the first book to systematically investigate the texts in the Hebrew Bible in which a character expresses a wish to die. Contrary to previous scholarship on these texts that assumed these death wishes were simply a desire to escape suffering, Hanne Løland Levinson employs narrative criticism and conversation analysis, together with diachronic methods, to carefully hear each death-wish text in its literary context. She demonstrates that death wishes embody powerful, multi-faceted rhetorical strategies. Grouping the death-wish texts into four main rhetorical strategies of negotiation, expression of despair and anger, longing to undo one's existence, and wishing for a different reality, Løland Levinson portrays the complex reasons why characters in the Hebrew Bible wish for death. She concludes that the death wishes navigate the tension between longing for death and fighting for survival - a tension that many live with also today as they attempt to claim agency and autonomy in lif

What is a focus group? Why do we use them? When should we use them? When should we not? Focus Groups for the Social Science Researcher provides a step-by-step guide to undertaking focus groups, whether as a stand-alone method or alongside other qualitative or quantitative methods. It recognizes the challenges that focus groups encounter and provides tips to address them. The book highlights three unique, inter-related characteristics of focus groups. First, they are inherently social in form. Second, the data emerge organically through conversation; they are emic in nature. Finally, focus groups generate data at three levels of analysis: the individual, group, and interactive level. The book builds from these three characteristics to explain when focus groups can usefully be employed in different research designs. This is an essential text for students and researchers looking for a concise and accessible introduction to this important approach to data collection.

What is a focus group? Why do we use them? When should we use them? When should we not? Focus Groups for the Social Science Researcher provides a step-by-step guide to undertaking focus groups, whether as a stand-alone method or alongside other qualitative or quantitative methods. It recognizes the challenges that focus groups encounter and provides tips to address them. The book highlights three unique, inter-related characteristics of focus groups. First, they are inherently social in form. Second, the data emerge organically through conversation; they are emic in nature. Finally, focus groups generate data at three levels of analysis: the individual, group, and interactive level. The book builds from these three characteristics to explain when focus groups can usefully be employed in different research designs. This is an essential text for students and researchers looking for a concise and accessible introduction to this important approach to data collection.

What is knowledge and how is it represented? This book focuses on the idea of formalising knowledge as relations, interpreting knowledge represented in databases or logic programs as relational data and discovering new knowledge by identifying hidden and defining new relations. After a brief introduction to representational issues, the author develops a relational language for abstract machine learning problems. He then uses this language to discuss traditional methods such as clustering and decision tree induction, before moving onto two previously underestimated topics that are just coming to the fore: rough set data analysis and inductive logic programming. Its clear and precise presentation is ideal for undergraduate computer science students. The book will also interest those who study artificial intelligence or machine learning at the graduate level. Exercises are provided and each concept is introduced using the same example domain, making it easier to compare the individual pro

What is knowledge and how is it represented? This book focuses on the idea of formalising knowledge as relations, interpreting knowledge represented in databases or logic programs as relational data and discovering new knowledge by identifying hidden and defining new relations. After a brief introduction to representational issues, the author develops a relational language for abstract machine learning problems. He then uses this language to discuss traditional methods such as clustering and decision tree induction, before moving onto two previously underestimated topics that are just coming to the fore: rough set data analysis and inductive logic programming. Its clear and precise presentation is ideal for undergraduate computer science students. The book will also interest those who study artificial intelligence or machine learning at the graduate level. Exercises are provided and each concept is introduced using the same example domain, making it easier to compare the individual pro

Cluster analysis comprises a range of methods of classifying multivariate data into subgroups, and these techniques are widely applicable. The 4th edition of Cluster Analysis updates the successful 3

Now in its fourth edition, Behavioral Research and Analysis: An Introduction to Statistics within the Context of Experimental Design presents an overview of statistical methods within the context of e

This monograph is a technical explication of the relationships between data-gathering methods and reporting methods in large-scale educational assessments, with the focus on marketbasket' reporting. C