Operators

Spaces of holomorphic functions have been a prominent theme in analysis since early in the twentieth century. Of interest to complex analysts, functional analysts, operator theorists and systems theorists, their study is now flourishing. This volume, an outgrowth of a 1995 program at the Mathematical Sciences Research Institute, contains expository articles by programme participants. Here researchers and graduate students will encounter Hardy spaces, Bergman spaces, Dirichlet spaces, Hankel and Toeplitz operators, and a sampling of the role these objects play in modern analysis.

This short introduction to microlocal analysis is presented, in the spirit of Hörmander, in the classical framework of partial differential equations. This theory has important applications in areas such as harmonic and complex analysis, and also in theoretical physics. Here Grigis and Sjöstrand emphasise the basic tools, especially the method of stationary phase, and they discuss wavefront sets, elliptic operators, local symplectic geometry, and WKB-constructions. The contents of the book correspond to a graduate course given many times by the authors. It should prove to be useful to mathematicians and theoretical physicists, either to enrich their general knowledge of this area, or as preparation for the current research literature.

Twistor theory has become a diverse subject as it has spread from its origins in theoretical physics to applications in pure mathematics. This 1990 collection of review articles covers the considerable progress made in a wide range of applications such as relativity, integrable systems, differential and integral geometry and representation theory. The articles explore the wealth of geometric ideas which provide the unifying themes in twistor theory, from Penrose's quasi-local mass construction in relativity, to the study of conformally invariant differential operators, using techniques of representation theory.

Numerical Ranges II is a sequel to Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras written by the same authors and published in this series in 1971. The present volume reflects the progress made in the subject, expanding and discussing topics under the general headings of spatial and algebra numerical ranges and further ranges.

The Drive-Inmeaningfully contributes to the complex picture of outdoor cinema that has been central to American culture and to a history of US cinema based on diverse viewing experiences rather than a select number of films.Drive-in cinemas flourished in 1950s America, in some summer weeks to the extent that there were more cinemagoers outdoors than indoors. Often associated with teenagers interested in the drive-in as a ‘passion pit’ or a venue for exploitation films, accounts of the 1950s American drive-in tend to emphasise their popularity with families with young children, downplaying the importance of a film programme apparently limited to old, low-budget or independent films and characterising drive-in operators as industry outsiders. They retain a hold on the popular imagination.The Drive-Inidentifies the mix of generations in the drive-in audience as well as accounts that articulate individual experiences, from the drive-in as a dating venue to a segregated space. Through detai

SPECIAL UPDATED 10th ANNIVERSARY EDITION OF THE MILLION-SELLING POP SCIENCE CLASSICWHAT IF... one man decided to answer all the unanswerable questions, using science. 'Randall Munroe is nerd royalty' BEN GOLDACRE 'Brilliant' ROLLING STONE'Smart answers to silly questions: Munroe reveals all' GUARDIAN'Required reading' NEW YORK TIMESRandall Munroe is the creator of the wildly popular xkcd.com.His readers ask him a lot of strange questions: What would happen if absolutely everyone jumped at the same time? How could we build a Lego bridge between London and New York?What if my DNA vanished?How long could a submarine last in space?What are the odds of meeting my soulmate?In pursuit of answers, Munroe runs computer simulations, pores over stacks of declassified military research memos, solves differential equations and consults everyone from astronauts to nuclear reactor operators. His responses are masterpieces of clarity and hilarity, complemented by comics. (They often predict the comple

While there is a limited data on safety-sensitive professionals, substance use disorders potentially affect pilots and flight attendants at the same rate as the general population - around 15 percent - but due to the high-risk nature of their jobs, aircraft operators are held to a higher standard for substance misuse on the job. To protect the safety of the public and the aviation workforce, the Human Intervention Motivation Study (HIMS) and the Flight Attendant Drug and Alcohol Program (FADAP) were launched to help treat critical aviation workers - pilots and flight attendants, respectively - who misuse substances. In response to a congressional mandate, this new report reviews available evidence on the effectiveness of HIMS and FADAP and offers recommendations for improving these programs.

This book provides an in-depth roadmap for qualitative research methods and data analysis across disciplines using ATLAS.ti. It encompasses and rationalizes key qualitative research concepts and methods with innovative frameworks to enrich the reader’s understanding of qualitative research methods and data analysis. The book contains multiple real-world projects that assist readers in developing conceptual and theoretical knowledge, as well as gaining insights from fieldwork, visualizing data collection, analysis, and methodological interpretations.This easy to use book provides a pragmatic approach to qualitative methods, proficiency in capturing field observations, user-friendly steps to data analysis starting from transcription, preparation of data, reading and identification of quotations, coding, memoing, commenting, code groups, creating smart codes and groups using set, semantic, and proximity operators resulting in generating numerous insightful thematic reports in avariety of

Low-carbon tourism is an emerging issue of tourism industry and academia in recent years. Previous studies have provided us some reasons that tourists participate in low-carbon travel or not, however, these reasons are scattered in literature and not been integrated into the construct of low-carbon travel motivation or low-carbon travel constraint. Meanwhile, previous studies often designed low-carbon package tours through the perspective of operators, few studies have assisted independent tourists on how to save energy and reduce carbon in travel. Therefore, this book is focused into two parts. The purpose of one part is to draw on tourism related literature, to develop and test the Low-Carbon Travel Motivation and Constraint Scales. The purpose of the other part is to draw on tourism related literature, to develop and test the Low-Carbon Travel Behavior Scale.

Navigating Nationalism in Global Enterprise analyzes the role of nationalism in global business strategy, showing how multinationals act not just as drivers of globalization but also as sophisticated operators in a world of nations. Using the case study of German companies in colonial and post-colonial India, Christina Lubinski traces how nationalism's influence on business competitive strategies changed over the twentieth century and across major political turning points, such as two world wars and India's transition to independence. She highlights how national imaginings are both relational because they derive from comparisons with other nations, and historical because they mobilize the past to legitimize future aspirations. Lubinski stresses that learning from the past is how multinationals engage strategically with the content of nationalism – i.e., a nation's history, aspirations, and relationships with other nations. In India, German companies' competitiveness was continuously de

Tracks the evolution of the international cellular industry from the late 1970s to the present.The development of the mobile-phone industry into what we know today required remarkable cooperation between companies, governments, and industrial sectors. Companies developing cellular infrastructure, cellular devices, cellular network services, and eventually software and mobile semiconductors had to cooperate, not simply compete, with each other. In this global history of the mobile-phone industry, Daniel D. Garcia-Swartz and Martin Campbell-Kelly examine its development in the United States, Europe, Japan, and several emerging economies, including China and India. They present the evolution of mobile phones from the perspective of vendors of telephone equipment and network operators, users whose lives have been transformed by mobile phones, and governments that have fostered specific mobile-phone standards. Cellular covers the technical aspects of the cellphone, as well as its social and

Newly available in paperback, title 17 in the bestselling Amazing Machines series is packed full of big, busy bulldozersAmazing Machines: Big Bulldozers follows the animal team as they become bulldozer operators and help out on a busy construction site. Each page is filled with details that machine-mad kids will love.From airplanes to fire engines, the internationally bestselling Amazing Machines series is the perfect way for children to learn about all sorts of vehicles! Each book introduces a new vehicle and the many jobs it can do. Bright, engaging artwork and simple, rhyming text combine to make these fantastic books for young children. Kids will love getting to know the friendly animal characters who feature throughout the series and reading about their fast-paced adventures!

Forensic Investigation of Clandestine Laboratories, Second Edition is fully updated to address all aspects of the forensic investigation of clandestine laboratories. While, the first edition focused on the domestic clandestine manufacture of contraband substances, this edition expands the scope to more fully address the clandestine manufacture of explosives that have become a threat that is global in nature. In clandestine laboratory operations, equipment is often simple, household chemical products are utilized, and the education of the operators basic. In fact, most of the time these elements individually are perfectly legal to sell and possess. However, the combination of all these elements is what becomes the scene of illicit activity and a criminal operation. In response to the increase in use of homemade explosive mixtures by terrorists, both domestically and internationally, the section clandestine manufacture of explosives is greatly enhanced. Topics are presented in a manner w

This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling–Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspace form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges–Rovnyak model theory and characteristic operator function for a Hilbert space contraction operator. The chapters that follow generalize the system theory and reproducing kernel techniques to enable an extension of the i

In pioneering work in the 1950s, S. Karlin and J. McGregor showed that probabilistic aspects of certain Markov processes can be studied by analyzing orthogonal eigenfunctions of associated operators. In the decades since, many authors have extended and deepened this surprising connection between orthogonal polynomials and stochastic processes. This book gives a comprehensive analysis of the spectral representation of the most important one-dimensional Markov processes, namely discrete-time birth-death chains, birth-death processes and diffusion processes. It brings together the main results from the extensive literature on the topic with detailed examples and applications. Also featuring an introduction to the basic theory of orthogonal polynomials and a selection of exercises at the end of each chapter, it is suitable for graduate students with a solid background in stochastic processes as well as researchers in orthogonal polynomials and special functions who want to learn about appl

This book provides the first systematic and accessible text for students of hospitality and the culinary arts that directly addresses how more sustainable restaurants and commercial food services can be achieved. Food systems receive growing attention because they link various sustainability dimensions. Restaurants are at the heart of these developments, and their decisions to purchase regional foods, or to prepare menus that are healthier and less environmentally problematic have great influence on food production processes. This book is systematically designed around understanding the inputs and outputs of the commercial kitchen as well as what happens in the restaurant from the perspective of operators, staff and the consumer. The book considers different management approaches and further looks at the role of restaurants, chefs and staff in the wider community and the positive contributions that commercial kitchens can make to promoting sustainable food ways. Case studies from all o

This is a practical guide to IPO a SPAC on Wall St. A Special Purpose Acquisition Company (SPAC) is an empty or almost empty company, with no commercial operations that is formed strictly to raise capital through an Initial Public Offering (IPO) for the purpose of acquiring an existing company. This must-read book shares crucial information about why companies are electing to join the SPAC boom. Companies typically pursue an Initial Public Offering to raise capital, provide shareholder liquidity, create brand awareness, and obtain resources to further expand their business. Increasingly, companies across all sectors are considering mergers with Special Purpose Acquisition Companies, rather than a traditional IPO, to achieve these goals. This trend will likely continue as a growing number of major private equity firms and operators form more SPACs. By merging with a SPAC, firms can access liquidity via the public market.

The interplay of geometry, spectral theory and stochastics has a long and fruitful history, and is the driving force behind many developments in modern mathematics. Bringing together contributions from a 2017 conference at the University of Potsdam, this volume focuses on global effects of local properties. Exploring the similarities and differences between the discrete and the continuous settings is of great interest to both researchers and graduate students in geometric analysis. The range of survey articles presented in this volume give an expository overview of various topics, including curvature, the effects of geometry on the spectrum, geometric group theory, and spectral theory of Laplacian and Schrödinger operators. Also included are shorter articles focusing on specific techniques and problems, allowing the reader to get to the heart of several key topics.

In this primer to the many-body theory of condensed-matter systems, the authors introduce the subject to the non-specialist in a broad, concise, and up-to-date manner. A wide range of topics are covered including the second quantization of operators, coherent states, quantum-mechanical Green's functions, linear response theory, and Feynman diagrammatic perturbation theory. Material is also incorporated from quantum optics, low-dimensional systems such as graphene, and localized excitations in systems with boundaries as in nanoscale materials. Over 100 problems are included at the end of chapters, which are used both to consolidate concepts and to introduce new material. This book is suitable as a teaching tool for graduate courses and is ideal for non-specialist students and researchers working in physics, materials science, chemistry, or applied mathematics who want to use the tools of many-body theory.

The Bellman function, a powerful tool originating in control theory, can be used successfully in a large class of difficult harmonic analysis problems and has produced some notable results over the last thirty years. This book by two leading experts is the first devoted to the Bellman function method and its applications to various topics in probability and harmonic analysis. Beginning with basic concepts, the theory is introduced step-by-step starting with many examples of gradually increasing sophistication, culminating with Calderón–Zygmund operators and end-point estimates. All necessary techniques are explained in generality, making this book accessible to readers without specialized training in non-linear PDEs or stochastic optimal control. Graduate students and researchers in harmonic analysis, PDEs, functional analysis, and probability will find this to be an incisive reference, and can use it as the basis of a graduate course.

Wigner's theorem is a fundamental part of the mathematical formulation of quantum mechanics. The theorem characterizes unitary and anti-unitary operators as symmetries of quantum mechanical systems, and is a key result when relating preserver problems to quantum mechanics. At the heart of this book is a geometric approach to Wigner-type theorems, unifying both classical and more recent results. Readers are initiated in a wide range of topics from geometric transformations of Grassmannians to lattices of closed subspaces, before moving on to a discussion of applications. An introduction to all the key aspects of the basic theory is included as are plenty of examples, making this book a useful resource for beginning graduate students and non-experts, as well as a helpful reference for specialist researchers.

Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. This first volume covers a wide range of areas related to integrable systems, often emphasizing the deep connections with algebraic geometry. Common themes include theta functions and Abelian varieties, Lax equations, integrable hierarchies, Hamiltonian flows and difference operators. These powerful tools are applied to spinning top,

This concise text was created as a workbook for learning to use vector calculus in practical calculations and derivations. Its only prerequisite is a familiarity with one-dimensional differential and integral calculus. Though it often makes use of physical examples, knowledge of physics itself is not required to study the mathematics of vector calculus. The approach is suitable for advanced undergraduates and graduate students in mathematics, physics, and other areas of science.The two-part treatment opens with a brief text that develops vector calculus from the very beginning and then addresses some more detailed applications. Topics include vector differential operators, vector identities, integral theorems, Dirac delta function, Green's functions, general coordinate systems, and dyadics. The second part consists of answered problems, all closely related to the development of vector calculus in the text. Those who study this book and work out the problems will find that rather than m

In recent years, the study of formal semantics and formal pragmatics has grown tremendously, showing that core aspects of language meaning can be explained by a few principles. These principles are grounded in the logic that is behind - and tightly intertwined with - the grammar of human language. In this book, some of the most prominent figures in linguistics, including Noam Chomsky and Barbara H. Partee, offer new insights into the nature of linguistic meaning and pave the way for the further development of formal semantics and formal pragmatics. Each chapter investigates various dimensions in which the logical nature of human language manifests itself within a language and/or across languages. Phenomena like bare plurals, free choice items, scalar implicatures, intervention effects, and logical operators are investigated in depth and at times cross-linguistically and/or experimentally. This volume will be of interest to scholars working within the fields of semantics, pragmatics, la

Covering the latest in marine surveying technology, this Reeds Professional handbook is aimed at students of marine surveying, professional marine surveyors, boatyard operators, and technically-minded boat owners.Reeds Marine Surveying covers the latest marine surveying technology, including analysis of the mechanical behaviour of materials, failure analysis, stress concentration, fatigue and fracture, corrosion, wood-damaging organisms, polymer chemistry, and the composition and characteristics of common plastics, metal, alloys and composite materials.This new edition expands its scope to include coverage of surveying topics relevant to ships and class surveying and includes more examples of common problems and the practical elements of surveying, as well as be updated throughout in line with technological developments, guidelines and best practice. Reeds Marine Surveying has been in print for nearly twenty years and excellently serves the community of marine surveyors by providing te

Understand the fundamental theory and practical design aspects of green and soft wireless communications networks with this expert text. It provides comprehensive and unified coverage of 5G physical layer design, as well as design of the higher and radio access layers and the core network, drawing on viewpoints from both academia and industry. Get to grips with the theory through authoritative discussion of information-theoretical results, and learn about fundamental green design trade-offs, software-defined network architectures, and energy efficient radio resource management strategies. Applications of wireless big data and artificial intelligence to wireless network design are included, providing an excellent design reference, and real-world examples of employment in software-defined 5G networks and energy saving solutions from wireless communications companies and cellular operators help to connect theory with practice. This is an essential text for graduate students, professionals

An introduction to how the mathematical tools from quantum field theory can be applied to economics and finance, providing a wide range of quantum mathematical techniques for designing financial instruments. The ideas of Lagrangians, Hamiltonians, state spaces, operators and Feynman path integrals are demonstrated to be the mathematical underpinning of quantum field theory, and which are employed to formulate a comprehensive mathematical theory of asset pricing as well as of interest rates, which are validated by empirical evidence. Numerical algorithms and simulations are applied to the study of asset pricing models as well as of nonlinear interest rates. A range of economic and financial topics are shown to have quantum mechanical formulations, including options, coupon bonds, nonlinear interest rates, risky bonds and the microeconomic action functional. This is an invaluable resource for experts in quantitative finance and in mathematics who have no specialist knowledge of quantum f

This is Volume 2 of a two-volume book that provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. The two-volume book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. Volume 2 features critical results, which are proven carefully and in detail, including automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics. Volume 1 features discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem. With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automo

This is Volume 1 of a two-volume book that provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. The two-volume book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. Volume 1 features critical results, which are proven carefully and in detail, including discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem. Volume 2 features automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics. With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automo

Wick ordering of creation and annihilation operators is of fundamental importance for computing averages and correlations in quantum field theory and, by extension, in the Hudson–Parthasarathy theory of quantum stochastic processes, quantum mechanics, stochastic processes, and probability. This book develops the unified combinatorial framework behind these examples, starting with the simplest mathematically, and working up to the Fock space setting for quantum fields. Emphasizing ideas from combinatorics such as the role of lattice of partitions for multiple stochastic integrals by Wallstrom–Rota and combinatorial species by Joyal, it presents insights coming from quantum probability. It also introduces a 'field calculus' which acts as a succinct alternative to standard Feynman diagrams and formulates quantum field theory (cumulant moments, Dyson–Schwinger equation, tree expansions, 1-particle irreducibility) in this language. Featuring many worked examples, the book is aimed at mathem

This book develops and simplifies the concept of quantum mechanics based on the postulates of quantum mechanics. The text discusses the technique of disentangling the exponential of a sum of operators, closed under the operation of commutation, as the product of exponentials to simplify calculations of harmonic oscillator and angular momentum. Based on its singularity structure, the Schrödinger equation for various continuous potentials is solved in terms of the hypergeometric or the confluent hypergeometric functions. The forms of the potentials for which the one-dimensional Schrödinger equation is exactly solvable are derived in detail. The problem of identifying the states of two-level systems which have no classical analogy is addressed by going beyond Bell-like inequalities and separability. The measures of quantumness of mutual information in two two-level systems is also covered in detail.

When the State Meets the Street probes the complex moral lives of street-level bureaucrats: the frontline social and welfare workers, police officers, and educators who represent government’s human face to ordinary citizens. Too often dismissed as soulless operators, these workers wield a significant margin of discretion and make decisions that profoundly affect people’s lives. Combining insights from political theory with his own ethnographic fieldwork as a receptionist in an urban antipoverty agency, Bernardo Zacka shows us firsthand the predicament in which these public servants are entangled.Public policy consists of rules and regulations, but its implementation depends on how street-level bureaucrats interpret them and exercise discretionary judgment. These workers are expected to act as sensible moral agents in a working environment that is notoriously challenging and that conspires against them. Confronted by the pressures of everyday work, they often and unknowingly settle for

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the first publication in the Perspectives in Logic series, Pour-El and Richards present the first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning. The book focuses on the computability or noncomputability of standard processes in analysis and physics. Topics include classical analysis, Hilbert and Banach spaces, bounded and unbounded linear operators, eigenvalues, eigenvectors, and equations of mathematical physics. The work is self-contained, and although it is intended primarily for logicians and analysts, it should also be of interest to researchers and graduate students in physics and computer science.

This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels, and VIEs with non-compact operators. It will act as a 'stepping stone' to the literature on the advanced theory of VIEs, bringing the reader to the current state of the art in the theory. Each chapter contains a large number of exercises, extending from routine problems illustrating or complementing the theory to challenging open research problems. The increasingly important role of VIEs in the mathematical modelling of phenomena where memory effects play a key role is illustrated with some 30 concrete examples, and the notes at the end of each chapter feature complementary references as a guide to further reading.

An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research ac

A careful and accessible exposition of a functional analytic approach to initial boundary value problems for semilinear parabolic differential equations, with a focus on the relationship between analytic semigroups and initial boundary value problems. This semigroup approach is distinguished by the extensive use of the ideas and techniques characteristic of the recent developments in the theory of pseudo-differential operators, one of the most influential works in the modern history of analysis. Complete with ample illustrations and additional references, this new edition offers both streamlined analysis and better coverage of important examples and applications. A powerful method for the study of elliptic boundary value problems, capable of further extensive development, is provided for advanced undergraduates or beginning graduate students, as well as mathematicians with an interest in functional analysis and partial differential equations.

Providing in-depth coverage, this book covers the fundamentals of computation and programming in C language. Essential concepts including operators and expressions, input and output statements, loop statements, arrays, pointers, functions, strings and preprocessors are described in a lucid manner. A unique approach - 'Learn by quiz' - features questions based on confidence-based learning methodology. It helps the reader to identify the right answer with adequate explanation and reasoning as to why the other options are incorrect. Computer programs and review questions are interspersed throughout the text. The book is appropriate for undergraduate students of engineering, computer science and information technology. It can be used for self-study and assists in the understanding of theoretical concepts and their applications.

Coal has been fundamental for the development of industrial and transport technologies since the nineteenth century. Globalisation, including colonialism, would not have been possible without coal-based energy and thus the exploitation of coal in every part of the world. But coal mining is a labour-intensive activity and mine operators had to find, mobilise and direct workers to these sites to enable exploitation. The recruitment of miners often targeted groups with a perceived inferior status. This turned coal mining communities into dense social spheres characterised by the intricate dynamics of ethnic identifications, interracial relations and class formation. The twelve articles presented in this volume cover cases from Africa, Asia, the Americas, Turkey, the Soviet Union and Western Europe, as well as a broad range of topics, from segregation, forced labour and subcontracting, to labour struggles, discrimination, ethnic paternalism and sports.

This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, includi

Reproducing kernel Hilbert spaces have developed into an important tool in many areas, especially statistics and machine learning, and they play a valuable role in complex analysis, probability, group representation theory, and the theory of integral operators. This unique text offers a unified overview of the topic, providing detailed examples of applications, as well as covering the fundamental underlying theory, including chapters on interpolation and approximation, Cholesky and Schur operations on kernels, and vector-valued spaces. Self-contained and accessibly written, with exercises at the end of each chapter, this unrivalled treatment of the topic serves as an ideal introduction for graduate students across mathematics, computer science, and engineering, as well as a useful reference for researchers working in functional analysis or its applications.