How can social bonds in society be strengthened? How do we learn and develop prosocial behaviour?
This comprehensive textbook provides up-to-date coverage of the social phenomenon of prosocial behaviour, incorporating all the major developments in the fields of developmental and social psychology. The first section identifies different forms of prosocial behaviour, including estimates of prevalence in everyday situations and the controversy between biological and cultural perspectives as explanatory models of prosocial behaviour. The second and third sections focus on learning and development, with emphasis on social learning, responsibility, empathy and guilt. The fourth section explores the prevalence of prosocial behaviour, in particular the situational and personality factors which inhibit urgently needed prosocial behaviour. The final section is devoted to practical applications, such as how to increase the likelihood that people will work as volunteers in community organisations and how to heighten the willingness to offer first aid.
This book will be an invaluable resource for both undergraduate and postgraduate students of social psychology and sociology, as well as anyone with an interest in social services and voluntary organisations.

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Social influence processes play a key role in human behavior. Arguably our extraordinary evolutionary success has much to do with our subtle and highly developed ability to interact with and influence each other. In this volume, leading international researchers review and integrate contemporary theory and research on the many ways people influence each other, considering both explicit, direct, and implicit, indirect influence strategies. Three sections examine fundamental processes and theory in social influence research, the role of cognitive processes and strategies in social influence phenomena, and the operation of social influence mechanisms in group settings. By applying the latest research to a wide range of interpersonal phenomena, this volume greatly advances our understanding of social influence mechanisms in strategic social interaction, and should be of interest to all students, researchers and practitioners interested in the dynamics of everyday interpersonal behavior.

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Mathematical Methods in Practice Advisory Editors Bruno Brosowski UniversitAt Frankfurt Germany Gary F. Roach University of Strathclyde UK Volume 3 Applied Nonlinear Semigroups A. Belleni-Morante University of Florence, Italy A. C. McBride University of Strathclyde, UK In many disciplines such as physics, chemistry, biology, meteorology, electronics and economics, it is increasingly necessary to develop mathematical models that describe how the state of a system evolves with time. A useful way of studying such a model is to recast the appropriate evolution equation as an Abstract Cauchy Problem (ACP), which can then be analysed via the powerful theory of semigroups of operators. The user-friendly presentation in the book is centred on Abstract Cauchy Problems which model various processes such as particle transport, diffusion and combustion, all of which are examples of systems which evolve with time. The authors provide an introduction to the requisite concepts from functional analysis before moving on to the theory of semigroups of linear operators and their application to linear ACPs. These ideas are then applied to semilinear problems and fully nonlinear problems and it is shown how results from the linear theory can be extended. Finally, a variety of applications of practical interest are included. By leading a non-expert to the solutions of problems involving evolution equations via the theory of semigroups of operators, both linear and nonlinear, the book provides an accessible introduction to the treatment of the subject. The reader is assumed to have a basic knowledge of real analysis and vector spaces. M.Sc. and graduate students of functional analysis, applied mathematics, physics and engineering will find this an invaluable introduction to the subject.

This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hypersurfaces follows with results that are proved in the context of Lie sphere geometry as well as those that are obtained using standard methods of submanifold theory. Next comes a thorough treatment of the theory of real hypersurfaces in complex space forms. A central focus is a complete proof of the classification of Hopf hypersurfaces with constant principal curvatures due to Kimura and Berndt. The book concludes with the basic theory of real hypersurfaces in quaternionic space forms, including statements of the major classification results and directions for further research.

This monograph is concerned with the interplay between the theory of operator semigroups and spectral theory. The basics on operator semigroups are concisely covered in this self-contained text. Part I deals with the Hille--Yosida and Lumer--Phillips characterizations of semigroup generators, the Trotter--Kato approximation theorem, Kato 's unified treatment of the exponential formula and the Trotter product formula, the Hille--Phillips perturbation theorem, and Stone 's representation of unitary semigroups. Part II explores generalizations of spectral theory 's connection to operator semigroups.

Social influence processes play a key role in human behaviour. Arguably our extraordinary evolutionary success has much to do with our subtle and highly developed ability to interact with and influence each other. In this volume, leading international researchers review and integrate contemporary theory and research on the many ways people influence each other, considering both explicit, direct and implicit, indirect influence strategies. Three sections examine fundamental processes and theory in social influence research, the role of cognitive processes and strategies in social influence phenomena, and the operation of social influence mechanisms in group settings. By applying the latest research to a wide range of interpersonal phenomena, this volume greatly advances our understanding of social influence mechanisms in strategic social interaction, and will be valuable to all students, researchers and practitioners interested in the dynamics of everyday interpersonal behaviour.

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David Riesman’s The Lonely Crowd: A Study in the Changing American Character is one of the best-known books in the history of sociology – holding a mirror up to contemporary America and showing the nation its own character as it had never seen it before.

Its success is a testament to Riesman’s mastery of one key critical thinking skill: interpretation. In critical thinking, interpretation focuses on understanding the meaning of evidence, and is frequently characterized by laying down clear definitions, and clarifying ideas and categories for the reader. All these processes are on full display in The Lonely Crowd – which, rather than seeking to challenge accepted wisdom or generate new ideas, provides incisive interpretations and definitions of ideas and data from a variety of sources.

Above all, Riesman’s book is a work of categorization – a form of interpretation that can be vital to building and communicating systematic arguments. With the aid of his two co-authors (Nathan Glazer and Reuel Denney), he defined three cultural types that formed a perfect pattern for understanding mid-century American society and the changes it was undergoing. The clarity of the book’s definitions tapped directly into the zeitgeist of the 1950s, powering it to best-seller status and an audience that extended far beyond academia.

This book gathers research papers and surveys on the latest advances in Schubert Calculus, presented at the International Festival in Schubert Calculus, held in Guangzhou, China on November 6-10, 2017. With roots in enumerative geometry and Hilbert's 15th problem, modern Schubert Calculus studies classical and quantum intersection rings on spaces with symmetries, such as flag manifolds. The presence of symmetries leads to particularly rich structures, and it connects Schubert Calculus to many branches of mathematics, including algebraic geometry, combinatorics, representation theory, and theoretical physics. For instance, the study of the quantum cohomology ring of a Grassmann manifold combines all these areas in an organic way. The book is useful for researchers and graduate students interested in Schubert Calculus, and more generally in the study of flag manifolds in relation to algebraic geometry, combinatorics, representation theory and mathematical physics.

This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2019. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field. The topics covered in this volume from the workshop represent the most modern trends in the field : Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

This innovative book examines radicalization from new psychological perspectives by examining the different typologies of radicalizing individuals, what makes individuals resilient against radicalization, and events that can trigger individuals to radicalize or to deradicalize. What is radicalization? Which psychological processes or events in a person's life play a role in radicalization? What determines whether a personal is resilient against radicalization, and is deradicalization something that we can achieve? This book goes beyond previous publications on this topic by identifying concrete key events in the process of radicalization, providing a useful theoretical framework that summarizes the current state-of-the-art research on radicalization and deradicalization. A model is presented in which a distinction is made between different levels of radicalization and deradicalization, with key underlying psychological needs discussed: the need for identity, justice, significance, and sensation. The authors also describe what makes people resilient against messages from "the outside world" when they belong to an extremist group and discuss observable events which may "trigger" a person to radicalize (further) or to deradicalize. Including real-world examples and clear guidelines for interventions aimed at prevention of radicalization and stimulation of deradicalization, this is essential reading for policy makers, researchers, practitioners, and students interested in this crucial societal issue.

A series of three symposia took place on the topic of trace formulas, each with an accompanying proceedings volume. The present volume is the third and final in this series and focuses on relative trace formulas in relation to special values of L-functions, integral representations, arithmetic cycles, theta correspondence and branching laws. The first volume focused on Arthur's trace formula, and the second volume focused on methods from algebraic geometry and representation theory. The three proceedings volumes have provided a snapshot of some of the current research, in the hope of stimulating further research on these topics. The collegial format of the symposia allowed a homogeneous set of experts to isolate key difficulties going forward and to collectively assess the feasibility of diverse approaches.

This textbook provides an introduction to representations of general -algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers. The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of -algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded -algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensatze, induced representations, well-behaved representations and representations on rigged modules. Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.

This book discusses basic topics in the spectral theory of dynamical systems. It also includes two advanced theorems, one by H. Helson and W. Parry, and another by B. Host. Moreover, Ornstein's family of mixing rank-one automorphisms is given with construction and proof. Systems of imprimitivity and their relevance to ergodic theory are also examined. Baire category theorems of ergodic theory, scattered in literature, are discussed in a unified way in the book. Riesz products are introduced and applied to describe the spectral types and eigenvalues of rank-one automorphisms. Lastly, the second edition includes a new chapter "Calculus of Generalized Riesz Products", which discusses the recent work connecting generalized Riesz products, Hardy classes, Banach's problem of simple Lebesgue spectrum in ergodic theory and flat polynomials.

This volume provides an accessible and coherent introduction to some of the scientific progress on functional equations on groups in the last two decades. It presents the latest methods of treating the topic and contains new and transparent proofs. Its scope extends from the classical functional equations on the real line to those on groups, in particular, non-abelian groups. This volume presents, in careful detail, a number of illustrative examples like the cosine equation on the Heisenberg group and on the group SL(2, ). Some of the examples are not even seen in existing monographs. Thus, it is an essential source of reference for further investigations.

This book addresses the nature of the chemical bond in inorganic and coordination compounds. In particular, it explains how general symmetry rules can describe chemical bond of simple inorganic molecules. Since the complexity of studying even simple molecules requires approximate methods, this book introduces a quantum mechanical treatment taking into account the geometric peculiarities of the chemical compound. In the case of inorganic molecules, a convenient approximation comes from symmetry, which constrains both the electronic energies and the chemical bonds. The book also gives special emphasis on symmetry rules and compares the use of symmetry operators with that of Hamiltonian operators. Where possible, the reactivity of molecules is also rationalized in terms of these symmetry properties. As practical examples, electronic spectroscopy and magnetism give experimental confirmation of the predicted electronic energy levels. Adapted from university lecture course notes, this book is the ideal companion for any inorganic chemistry course dealing with group theory.

Occasioned by the international conference "Rings and Factorizations" held in February 2018 at University of Graz, Austria, this volume represents a wide range of research trends in the theory of commutative and non-commutative rings and their modules, including multiplicative ideal theory, Dedekind and Krull rings and their generalizations, rings of integer valued-polynomials, topological aspects of ring theory, factorization theory in rings and semigroups and direct-sum decompositions of modules. The volume will be of interest to researchers seeking to extend or utilize work in these areas as well as graduate students wishing to find entryways into active areas of current research in algebra. A novel aspect of the volume is an emphasis on how diverse types of algebraic structures and contexts (rings, modules, semigroups, categories) may be treated with overlapping and reinforcing approaches.

This book offers an introduction to the theory of groupoids and their representations encompassing the standard theory of groups. Using a categorical language, developed from simple examples, the theory of finite groupoids is shown to knit neatly with that of groups and their structure as well as that of their representations is described. The book comprises numerous examples and applications, including well-known games and puzzles, databases and physics applications. Key concepts have been presented using only basic notions so that it can be used both by students and researchers interested in the subject. Category theory is the natural language that is being used to develop the theory of groupoids. However, categorical presentations of mathematical subjects tend to become highly abstract very fast and out of reach of many potential users. To avoid this, foundations of the theory, starting with simple examples, have been developed and used to study the structure of finite groups and groupoids. The appropriate language and notions from category theory have been developed for students of mathematics and theoretical physics. The book presents the theory on the same level as the ordinary and elementary theories of finite groups and their representations, and provides a unified picture of the same. The structure of the algebra of finite groupoids is analysed, along with the classical theory of characters of their representations. Unnecessary complications in the formal presentation of the subject are avoided. The book offers an introduction to the language of category theory in the concrete setting of finite sets. It also shows how this perspective provides a common ground for various problems and applications, ranging from combinatorics, the topology of graphs, structure of databases and quantum physics.

The Langlands Programme is one of the most important areas in modern pure mathematics. The importance of this volume lies in its potential to recast many aspects of the programme in an entirely new context. For example, the morphisms in the monomial category of a locally p-adic Lie group have a distributional description, due to Bruhat in his thesis. Admissible representations in the programme are often treated via convolution algebras of distributions and representations of Hecke algebras. The monomial embedding, introduced in this book, elegantly fits together these two uses of distribution theory. The author follows up this application by giving the monomial category treatment of the Bernstein Centre, classified by Deligne-Bernstein-Zelevinsky.This book gives a new categorical setting in which to approach well-known topics. Therefore, the context used to explain examples is often the more generally accessible case of representations of finite general linear groups. For example, Galois base-change and epsilon factors for locally p-adic Lie groups are illustrated by the analogous Shintani descent and Kondo-Gauss sums, respectively. General linear groups of local fields are emphasized. However, since the philosophy of this book is essentially that of homotopy theory and algebraic topology, it includes a short appendix showing how the buildings of Bruhat-Tits, sufficient for the general linear group, may be generalised to the tom Dieck spaces (now known as the Baum-Connes spaces) when G is a locally p-adic Lie group.The purpose of this monograph is to describe a functorial embedding of the category of admissible k-representations of a locally profinite topological group G into the derived category of the additive category of the admissible k-monomial module category. Experts in the Langlands Programme may be interested to learn that when G is a locally p-adic Lie group, the monomial category is closely related to the category of topological modules over a sort of enlarged Hecke algebra with generators corresponding to characters on compact open modulo the centre subgroups of G. Having set up this functorial embedding, how the ingredients of the celebrated Langlands Programme adapt to the context of the derived monomial module category is examined. These include automorphic representations, epsilon factors and L-functions, modular forms, Weil-Deligne representations, Galois base change and Hecke operators.

Written by an algebraic topologist motivated by his own desire to learn, this book represents the compilation of results in the theory of polynomial invariants of finite groups. As well as covering invariant theory, the book also introduces some of the basic concepts behind ideal theory and homological algebra in a liberating context, and discusses the mutual impact of invariant theory and algebraic topology. Along the way, the author also examines such topics as the Hilbert-Noether finiteness theorems, methods for constructing invariants, the Poincare series, localization and use of gradings, and the Hilbert Syzygy theorem. Larry Smith includes numerous examples and illustrates the theorems by applying them to concrete cases.

Provides a thorough discussion of the orderability of a group. The book details the major developments in the theory of lattice-ordered groups, delineating standard approaches to structural and permutation representations. A radically new presentation of the theory of varieties of lattice-ordered groups is offered.;This work is intended for pure and applied mathematicians and algebraists interested in topics such as group, order, number and lattice theory, universal algebra, and representation theory; and upper-level undergraduate and graduate students in these disciplines.;College or university bookstores may order five or more copies at a special student price which is available from Marcel Dekker Inc, upon request.

This book offers a biographical account of Henri Tajfel, one of the most influential European social psychologists of the twentieth century, offering unique insights into his ground-breaking work in the areas of social perception, social identity and intergroup relations. The author, Rupert Brown, paints a vivid and personal portrait of Tajfel's life, his academic career and its significance to social psychology, and the key ideas he developed. It traces Tajfel's life from his birth in Poland just after the end of World War I, his time as a prisoner-of-war in World War II, his work with Jewish orphans and other displaced persons after that war, and thence to his short but glittering academic career as a social psychologist. Based on a range of sources including interviews, archival material, correspondence, photographs, and scholarly output, Brown expertly weaves together Tajfel's personal narrative with his evolving intellectual interests and major scientific discoveries. Following a chronological structure with each chapter dedicated to a significant transition period in Tajfel's life, the book ends with an appraisal of two of his principal posthumous legacies: the European Association of Social Psychology, a project always close to Tajfel's heart and for which he worked tirelessly; and the 'social identity approach' to social psychology initiated by Tajfel over forty years ago and now one of the discipline's most important perspectives. This is fascinating reading for students, established scholars, and anyone interested in social psychology and the life and lasting contribution of this celebrated scholar.

This proceedings volume gathers selected, peer-reviewed works presented at the Polynomial Rings and Affine Algebraic Geometry Conference, which was held at Tokyo Metropolitan University on February 12-16, 2018. Readers will find some of the latest research conducted by an international group of experts on affine and projective algebraic geometry. The topics covered include group actions and linearization, automorphism groups and their structure as infinite-dimensional varieties, invariant theory, the Cancellation Problem, the Embedding Problem, Mathieu spaces and the Jacobian Conjecture, the Dolgachev-Weisfeiler Conjecture, classification of curves and surfaces, real forms of complex varieties, and questions of rationality, unirationality, and birationality. These papers will be of interest to all researchers and graduate students working in the fields of affine and projective algebraic geometry, as well as on certain aspects of commutative algebra, Lie theory, symplectic geometry and Stein manifolds.

Youth in Superdiverse Societies brings together theoretical, methodological and international approaches to the study of globalization, diversity, and acculturation in adolescence. It examines vital issues including migration, integration, cultural identities, ethnic minorities, and the interplay of ethnic and cultural diversity with experiences of growing up as an adolescent. This important volume focuses on understanding the experiences and consequences of multicultural societies and offers valuable new insights in the field of intergroup relations and the complexity of growingly heterogeneous societies. The book comprises four sections. The first includes fresh theoretical perspectives for studying youth development in multicultural societies, exploring topics such as superdiversity, globalization, bicultural identity development, polyculturalism, the interplay of acculturation and development, as well as developmental-ecological approaches. The second section highlights innovative methods in studying multicultural societies. It contains innovative dynamic concepts (e.g., experience-based sampling), methods for studying the nested structure of acculturative contexts, and suggestions for cross-comparative research to differentiate universal and context-specific processes. The third section examines social relations and social networks in diverse societies and features developmentally crucial contexts (e.g., family, peers, schools) and contributions on interethnic interactions in real-life contexts. The final section presents applications in natural settings and includes contributions on participatory action research and teachers dealings' with ethnic diversity. Each chapter provides a thorough overview of current research trends and findings, followed by detailed recommendations for future research, suggesting how the approaches can be cited, applied and improved. Youth in Superdiverse Societies is valuable reading for students studying adolescent acculturation and development in psychology, sociology, education, anthropology, linguistics and political science. It will also be of interest to scholars and researchers in social and developmental psychology, and related disciplines, as well as professionals in the field of migration.

This book offers a biographical account of Henri Tajfel, one of the most influential European social psychologists of the twentieth century, offering unique insights into his ground-breaking work in the areas of social perception, social identity and intergroup relations. The author, Rupert Brown, paints a vivid and personal portrait of Tajfel's life, his academic career and its significance to social psychology, and the key ideas he developed. It traces Tajfel's life from his birth in Poland just after the end of World War I, his time as a prisoner-of-war in World War II, his work with Jewish orphans and other displaced persons after that war, and thence to his short but glittering academic career as a social psychologist. Based on a range of sources including interviews, archival material, correspondence, photographs, and scholarly output, Brown expertly weaves together Tajfel's personal narrative with his evolving intellectual interests and major scientific discoveries. Following a chronological structure with each chapter dedicated to a significant transition period in Tajfel's life, the book ends with an appraisal of two of his principal posthumous legacies: the European Association of Social Psychology, a project always close to Tajfel's heart and for which he worked tirelessly; and the 'social identity approach' to social psychology initiated by Tajfel over forty years ago and now one of the discipline's most important perspectives. This is fascinating reading for students, established scholars, and anyone interested in social psychology and the life and lasting contribution of this celebrated scholar.

This book provides an understandable review of SU(3) representations, SU(3) Wigner-Racah algebra and the SU(3) SO(3) integrity basis operators, which are often considered to be difficult and are avoided by most nuclear physicists. Explaining group algebras that apply to specific physical systems and discussing their physical applications, the book is a useful resource for researchers in nuclear physics. At the same time it helps experimentalists to interpret data on rotational nuclei by using SU(3) symmetry that appears in a variety of nuclear models, such as the shell model, pseudo-SU(3) model, proxy-SU(3) model, symplectic Sp(6, R) model, various interacting boson models, various interacting boson-fermion models, and cluster models. In addition to presenting the results from all these models, the book also describes a variety of statistical results that follow from the SU(3) symmetry.