This volume goes beyond the understanding of symmetries and exploits them in the study of the behavior of both classical and quantum physical systems. Thus it is important to study the symmetries described by continuous (Lie) groups of transformations. We then discuss how we get operators that form a Lie algebra. Of particular interest to physics is the representation of the elements of the algebra and the group in terms of matrices and, in particular, the irreducible representations. These representations can be identified with physical observables.This leads to the study of the classical Lie algebras, associated with unitary, unimodular, orthogonal and symplectic transformations. We also discuss some special algebras in some detail. The discussion proceeds along the lines of the Cartan-Weyl theory via the root vectors and root diagrams and, in particular, the Dynkin representation of the roots. Thus the representations are expressed in terms of weights, which are generated by the application of the elements of the algebra on uniquely specified highest weight states. Alternatively these representations can be described in terms of tensors labeled by the Young tableaux associated with the discrete symmetry Sn. The connection between the Young tableaux and the Dynkin weights is also discussed. It is also shown that in many physical systems the quantum numbers needed to specify the physical states involve not only the highest symmetry but also a number of sub-symmetries contained in them. This leads to the study of the role of subalgebras and in particular the possible maximal subalgebras. In many applications the physical system can be considered as composed of subsystems obeying a given symmetry. In such cases the reduction of the Kronecker product of irreducible representations of classical and special algebras becomes relevant and is discussed in some detail. The method of obtaining the relevant Clebsch-Gordan (C-G) coefficients for such algebras is discussed and some relevant algorithms are provided. In some simple cases suitable numerical tables of C-G are also included.The above exposition contains many examples, both as illustrations of the main ideas as well as well motivated applications. To this end two appendices of 51 pages - 11 tables in Appendix A, summarizing the material discussed in the main text and 39 tables in Appendix B containing results of more sophisticated examples are supplied. Reference to the tables is given in the main text and a guide to the appropriate section of the main text is given in the tables.

These books grew out of the perception that a number of important conceptual and theoretical advances in research on small group behavior had developed in recent years, but were scattered in rather fragmentary fashion across a diverse literature. Thus, it seemed useful to encourage the formulation of summary accounts. A conference was held in Hamburg with the aim of not only encouraging such developments, but also encouraging the integration of theoretical approaches where possible. These two volumes are the result. Current research on small groups falls roughly into two moderately broad categories, and this classification is reflected in the two books. Volume I addresses theoretical problems associated with the consensual action of task-oriented small groups, whereas Volume II focuses on interpersonal relations and social processes within such groups. The two volumes differ somewhat in that the conceptual work of Volume I tends to address rather strictly defined problems of consensual action, some approaches tending to the axiomatic, whereas the conceptual work described in Volume II is generally less formal and rather general in focus. However, both volumes represent current conceptual work in small group research and can claim to have achieved the original purpose of up-to-date conceptual summaries of progress on new theoretical work.

This book, published in 1976, presents an entirely original approach to the subject of the mind-body problem, examining it in terms of the conceptual links between the physical sciences and the sciences of human behaviour. It is based on the cybernetic concepts of information and feedback and on the related concepts of thermodynamic and communication-theoretic entropy. The foundation of the approach is the theme of continuity between evolution, learning and human consciousness. The author defines life as a process of energy exchange between organism and environment, and evolution as a feedback process maintaining equilibrium between environment and reproductive group. He demonstrates that closely related feedback processes on the levels of the behaving organism and of the organism's nervous system constitute the phenomena of learning and consciousness respectively. He analyses language as an expedient for extending human information-processing and control capacities beyond those provided by one's own nervous system, and shows reason to be a mode of processing information in the form of concepts removed from immediate stimulus control. The last chapter touches on colour vision, pleasure and pain, intentionality, self-awareness and other subjective phenomena. Of special interest to the communication theorist and philosopher, this study is also of interest to psychologists and anyone interested in the connection between the physical and life sciences.

This Handbook represents the first comprehensive collection of research on communication and people with disabilities. The editors have brought together original contributions focusing on the identity, social, and relationship adjustments faced by people with disabilities and those with whom they relate. Essays report on topics across the communication spectrum--interpersonal and relationship issues, people with disabilities in organizational settings, disability and culture, media and technologies, communication issues as they impact specific types of disabilities--and establish a future agenda for communication and disability research. Each chapter provides a state-of-the-art literature review, practical applications of the material, and keywords and discussion questions to facilitate classroom use. In providing an outlet for current research on communication and disability issues, this unique collection contributes to the lives of people with and without disabilities, helping them to improve their own communication and relationships. Intended for readers in communication, psychology, sociology, rehabilitation, social work, special education, gerontology, and related disciplines, this handbook is certain to augment further theory and research, as well as offer insights for both personal and professional relationships.

The objectives of the volume are to direct the field's attention to the unique value of studying interactions between members of different groups and to offer the most up-to-date summaries of prominent and cutting-edge scholarship on this topic written by leading scholars in the field. A central theme of the volume is that improvement in intergroup relationships will only be possible if social scientists simultaneously take into account both the attitudes, beliefs, emotions, and actions of the different groups that shape the nature of intergroup relations. Understanding how members of different groups interact is critical beyond the value of understanding how majority groups behave and how minority groups respond in isolation. Indeed, as the book exemplifies, groups interpret their interaction differently, experiencing different social realities; approach interactions with different goals; and engage each other with different, and often non-compatible, means or strategies. These different realities, goals, and strategies can produce misunderstanding, suspicion, and conflict even when initial intentions are positive and cooperative. The book will be of interest to professionals and students in social psychology, sociology, social work, education, political science, and conflict management, as well as scholars, students, and practitioners interested in anti-bias education and prejudice reduction techniques and strategies.

The aim of this book is to serve both as an introduction to profinite groups and as a reference for specialists in some areas of the theory. The book is reasonably self-contained. Profinite groups are Galois groups. As such they are of interest in algebraic number theory. Much of recent research on abstract infinite groups is related to profinite groups because residually finite groups are naturally embedded in a profinite group. In addition to basic facts about general profinite groups, the book emphasizes free constructions (particularly free profinite groups and the structure of their subgroups). Homology and cohomology is described with a minimum of prerequisites.

This second edition contains three new appendices dealing with a new characterization of free profinite groups, presentations of pro-p groups and a new conceptually simpler approach to the proof of some classical subgroup theorems. Throughout the text there are additions in the form of new results, improved proofs, typographical corrections, and an enlarged bibliography. The list of open questions has been updated; comments and references have been added about those previously open problems that have been solved after the first edition appeared.

Spaces of constant curvature, i.e. Euclidean space, the sphere, and Loba chevskij space, occupy a special place in geometry. They are most accessible to our geometric intuition, making it possible to develop elementary geometry in a way very similar to that used to create the geometry we learned at school. However, since its basic notions can be interpreted in different ways, this geometry can be applied to objects other than the conventional physical space, the original source of our geometric intuition. Euclidean geometry has for a long time been deeply rooted in the human mind. The same is true of spherical geometry, since a sphere can naturally be embedded into a Euclidean space. Lobachevskij geometry, which in the first fifty years after its discovery had been regarded only as a logically feasible by-product appearing in the investigation of the foundations of geometry, has even now, despite the fact that it has found its use in numerous applications, preserved a kind of exotic and even romantic element. This may probably be explained by the permanent cultural and historical impact which the proof of the independence of the Fifth Postulate had on human thought."

A number of texts have recently become available which provide good general introductions to p-Adic numbers and p-Adic analysis. However, there is at present a gap between such books and the sophisticated applications in the research literature. The aim of this book is to bridge this gulf by providing a collection of intermediate level articles on various applications of p-Adic techniques throughout mathematics. The idea for producing such a volume was suggested by Oxford University Press in connection with a three day meeting `p-Adic Methods and their Applications' held at Manchester University in September 1989 and which have received financial support from the London Mathematical Society. Some of these articles grew out of talks given at this conference, others were written by invitation especially for this volume. All contributions were refereed with a particular view to their suitability for inclusion in such a book.

A unique, much-needed introduction to molecular symmetry and group theory Elements of Molecular Symmetry takes the topic of group theory a step further than most books, presenting a quantum chemistry treatment useful for computational, quantum, physical, and inorganic chemists alike. Clearly explaining how general groups and group algebra describe molecules, Yngve Ahrn first develops the theory, then provides coverage not only for point groups, but also permutation groups, space groups, and Lie groups. With over three decades of teaching experience, Dr. Ahrn brings to the discussion unprecedented depth and clarity, incorporating rigorous topics at a level accessible to anyone with basic knowledge of calculus and algebra. This unique and timely book:
* Extends coverage to molecular orbital theory,
* Utilizes powerful examples to illustrate basic concepts
* Contains introductory material on space groups and continuous groups, including point-group character tables
* Provides a solid background for exploring the theoretical literature

For mathematicians working in group theory, the study of the many infinite-dimensional groups has been carried out in an individual and non-coherent way. For the first time, these apparently disparate groups have been placed together, in order to construct the `big picture'. This book successfully gives an account of this - and shows how such seemingly dissimilar types such as the various groups of operators on Hilbert spaces, or current groups are shown to belong to a bigger entitity. This is a ground-breaking text will be important reading for advanced undergraduate and graduate mathematicians.

Traditional social hypotheses have a built-in tendency to verify themselves and so involuntarily resist attempts at stereotype change or correction. This is the insight demonstrated and discussed as the start point for an alternative approach to the problem of stereotyping and hypothesis testing. Stereotyping as Inductive Hypothesis Testing explicates the proposition that many stereotypes originate not so much in individual brains, but in the stimulus environment that interacts with and constitutes the social individual. This cognitive-ecological approach is then used to analyse the different aspects of language, sign systems and communication that can implicitly govern hypothesis testing procedures and lead to circular or reinforcing outcomes. The authors describe factors in tests such as judgment, memory and expectation and go on to suggest viable ecological learning approaches to them. An original research project based on a classroom situation is used to demonstrate and verify findings. The cognitive-ecological approach is then contextualised in relation to both the traditional approaches it can replace and the contemporary statistical sampling practices it can improve. Written with a profound understanding of the link between theoretical rigour and good empirical research practice this monograph will be invaluable to anyone with an interest in stereotyping or who wishes to enhance the reliability and self-awareness of their research methods.

The 21st-century political landscape has been defined by deep ideological polarization, and as a result scientific inquiry into the psychological mechanisms underlying this divide has taken on increased relevance. The topic is by no means new to social psychology. Classic literature on intergroup conflict shows how pervasive and intractable these group conflicts can be, how readily they can emerge from even minimal group identities, and the hedonic rewards reaped from adopting an "us vs. them" perspective. Indeed, this literature paints a bleak picture for the efficacy of any interventions geared toward reducing intergroup discord. But advances in the psychology of moral judgments and behavior, in particular greater understanding of how moral concerns might inform the creation and stability of political identities, offer new ways forward in understanding partisan divides. This volume brings together leading researchers in moral and political psychology, offering new perspectives on the moral roots of political ideology, and exciting new opportunities for the development of more effective applied interventions.

This volume contains contributions from 24 internationally known scholars covering a broad spectrum of interests in cross-cultural theory and research. This breadth is reflected in the diversity of the topics covered in the volume, which include theoretical approaches to cross-cultural research, the dimensions of national cultures and their measurement, ecological and economic foundations of culture, cognitive, perceptual and emotional manifestations of culture, and bicultural and intercultural processes. In addition to the individual chapters, the volume contains a dialog among 14 experts in the field on a number of issues of concern in cross-cultural research, including the relation of psychological studies of culture to national development and national policies, the relationship between macro structures of a society and shared cognitions, the integration of structural and process models into a coherent theory of culture, how personal experiences and cultural traditions give rise to intra-cultural variation, whether culture can be validly measured by self-reports, the new challenges that confront cultural psychology, and whether psychology should strive to eliminate culture as an explanatory variable.

The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays. Based on the work of speakers and invited participants at the conference "Interactions Between Representation Theory and Algebraic Geometry", held at the University of Chicago, August 21-25, 2017, this volume illustrates the impact of their research and how it has shaped the development of various branches of mathematics through the use of D-modules, the affine Grassmannian, symplectic algebraic geometry, and other topics. All authors have been deeply influenced by their ideas and present here cutting-edge developments on modern topics. Chapters are organized around three distinct themes: Groups, algebras, categories, and representation theory D-modules and perverse sheaves Analogous varieties defined by quivers Representation Theory and Algebraic Geometry will be an ideal resource for researchers who work in the area, particularly those interested in exploring the impact of the Russian school.

Originally published in 1973, this work takes a hard look at the claims made for the small group as a learning medium (lecture, structured discussion, 'sensitivity', training groups etc.). Various theories of group dynamics, leadership function and learning process are looked at critically on the basis of actual research findings. It was intended for students of social psychology and anyone teaching or training to teach at Further Education level at the time, and will still be of interest in its historical context today.

Love and money are important aspects of the everyday lives of couples. This book focuses on the daily routines of disagreement, conflict and joint decisions on these, and other issues such as work, leisure and children, create in the household. Central to the authors' research is a unique diary study of forty couples, who kept a daily record of their joint decisions over the course of a year. The diaries show how challenging, varied and complex the conflicts and decision making of normal everyday life can be and reveal that goals frequently change during the decision-making process with the result that the final outcome often achieves a goal distinct from the original intention. Furthermore, the dynamics of decision making differ according to the problem at stake, the decision-making history of the couple, and the quality of the partnership. The results of the diary study are discussed within the overall context of current research in the field as a whole, including discussion of joint decision-making case studies, close relationships, decision-making research in general and special research methods. Numerous results of psychological, sociological, economic and consumer behaviour studies are summarised and integrated into a model of household decision-making. This book will be primarily of interest to students and researchers in social psychology and economic psychology, but its interdisciplinary and applied nature will also make it of relevance to professionals working in the fields of family therapy and consumer behaviour.

As the first book to examine the psychological motivations underlying people's attitudes, as well as why people form attitudes, this volume presents empirical research describing theoretical perspectives and practical applications. The editors assembled the leaders in the field to examine the topics of attitude function persuasion, individual-differences approaches, and the role of motivation within a variety of psychological disciplines, including social, personality, consumer, and environmental.

Intergroup dialogue is a form of democratic engagement that fosters communication, critical reflection, and collaborative action across social and cultural divides. Engaging social identities is central to this approach. In recent years, intergroup dialogue has emerged as a promising social justice education practice that addresses pressing issues in higher education, school and community settings. This edited volume provides a thoughtful and comprehensive overview of intergroup dialogue spanning conceptual frameworks for practice, and most notably a diverse set of research studies which examine in detail the processes and learning that take place through dialogue. This book addresses questions from the fields of education, social psychology, sociology, and social work, offering specific recommendations and examples related to curriculum and pedagogy. Furthermore, it contributes to an understanding of how to constructively engage students and others in education about difference, identities, and social justice. This book was originally published as a special issue of Equity & Excellence in Education.

A Course in the Theory of Groups is a comprehensive introduction to the theory of groups - finite and infinite, commutative and non-commutative. Presupposing only a basic knowledge of modern algebra, it introduces the reader to the different branches of group theory and to its principal accomplishments. While stressing the unity of group theory, the book also draws attention to connections with other areas of algebra such as ring theory and homological algebra. This new edition has been updated at various points, some proofs have been improved, and lastly about thirty additional exercises are included. There are three main additions to the book. In the chapter on group extensions an exposition of Schreier's concrete approach via factor sets is given before the introduction of covering groups. This seems to be desirable on pedagogical grounds. Then S. Thomas's elegant proof of the automorphism tower theorem is included in the section on complete groups. Finally an elementary counterexample to the Burnside problem due to N.D. Gupta has been added in the chapter on finiteness properties.

Social psychology and politics are intricately related, and understanding how humans manage power and govern themselves is one of the key issues in psychology. This volume surveys the latest theoretical and empirical work on the social psychology of politics, featuring cutting-edge research from a stellar group of international researchers. It is organized into four main sections that deal with political attitudes and values; political communication and perceptions; social cognitive processes in political decisions; and the politics of intergroup behavior and social identity. The contributions address such exciting questions as how do political attitudes and values develop and change? What role do emotions and moral values play in political behavior? How do political messages and the media influence political perceptions? What are the psychological requirements of effective democratic decision making, and why do democracies sometimes fail? How can intergroup harmony be developed, and what is the role of social identity in political processes? As such, this volume integrates the role of cognitive, affective, social and cultural influences on political perception and behavior, offering an overview of the psychological mechanisms underlying political processes. It provides essential reading for teachers, students, researchers and practitioners in areas related to power, social influence and political behavior.

This book is a study in economic geography, treated historically. Its primary purpose is to describe and explain the industrial geography of London since 1861, using the most recent statistics available for that purpose, noting that this work was originally published in 1962.

This book describes various approaches to the Inverse Galois Problem, a classical unsolved problem of mathematics posed by Hilbert at the beginning of the century. It brings together ideas from group theory, algebraic geometry and number theory, topology, and analysis. Assuming only elementary algebra and complex analysis, the author develops the necessary background from topology, Riemann surface theory and number theory. The first part of the book is quite elementary, and leads up to the basic rigidity criteria for the realization of groups as Galois groups. The second part presents more advanced topics, such as braid group action and moduli spaces for covers of the Riemann sphere, GAR- and GAL- realizations, and patching over complete valued fields. Graduate students and mathematicians from other areas (especially group theory) will find this an excellent introduction to a fascinating field.

From the reviews: ..". The book under review consists of two monographs on geometric aspects of group theory ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ..." Bulletin of the London Mathematical Society, 1996

This volume examines communication processes within the grandmother-mother-daughter relationship, emphasizing an intergenerational perspective. Using observations of and extensive interviews with six sets of middle-income, Caucasian female family members, this book offers a heuristic account of intergenerational mother-daughter relational communication.
Author Michelle Miller-Day integrates and juxtaposes alternative experiences of social interaction, situating readers in the world of grandmothers, mothers, adult daughters, and granddaughters as they experience, describe, and analyze their family communication. Miller-Day incorporates aged mothers and younger mid-life mothers and their adult daughters into the research to illustrate how this type of maternal relationship is experienced at different points in a woman's life. With the inclusion of three generations of women, Miller-Day offers multigenerational perspectives on family, and examines them for patterns of maternal interaction, providing symbolic links across generational boundaries.
"Communication Among Grandmothers, Mothers, and Adult Daughters "enables readers to understand more completely the richly textured nature of maternal relationships. It will be an invaluable resource for scholars and researchers in the areas of communication and relationships, including family communication, intergenerational communication, women's studies, family studies, interpersonal communication, and relationships, as well as social workers, psychologists, and counselors, who strive to understand family communication processes and their dynamics across generational lines.

Originally published in 1988, the purpose of this book was to explore the interrelations among communication, social cognition and affect. The contributors, selected by the editors, were some of the best known in their fields and they significantly added to the knowledge of this interdisciplinary domain at the time. In late April 1986 the authors met at a conference centre at the University of Kentucky. They presented first drafts of their chapters and exchanged ideas. Out of these interactions came this book, which has a broad interest across several areas of psychology and communication. While answering a number of questions, the authors also posed others for future examination.