Introduction to Algebraic and Abelian Functions is a self-contained presentation of a fundamental subject in algebraic geometry and number theory. For this revised edition, the material on theta functions has been expanded, and the example of the Fermat curves is carried throughout the text. This volume is geared toward a second-year graduate course, but it leads naturally to the study of more advanced books listed in the bibliography.

This essential volume explores the vital role of communication in the aging process and how this varies for different social groups and cultural communities. It reveals how communication can empower people in the process of aging, and that how we communicate about age is critically important to - and is at the heart of - aging successfully. Giles et al. confront the uncertainty and negativity surrounding "aging" - a process with which we all have to cope - by expertly placing communication at the core of the process. They address the need to avoid negative language, discuss the lifespan as an evolving adventure, and introduce a new theory of successful aging - the communication ecology model of successful aging (CEMSA). They explore the research on key topics including: age stereotypes, age identities, and messages of ageism; the role of culture, gender, ethnicity, and being a member of marginalized groups; the ingredients of intergenerational communication; depiction of aging and youth in the media; and how and why talk about death and dying can be instrumental in promoting control over life's demands. Communication for Successful Aging is essential reading for graduate students of psychology, human development, gerontology, and communication, scholars in the social sciences, and all of us concerned with this complex academic and highly personal topic.

William Burnside [1852-1927] was a scholar of international renown, a colourful figure, and a pure mathematician who established abstract algebra as a subject of serious study in Britain. This edition of Collected Papers, enhanced by a series of critical essays, is of major importance to scholars in group theory and the history of mathematics.

This book is dedicated to the structure and combinatorics of classical Hopf algebras. Its main focus is on commutative and cocommutative Hopf algebras, such as algebras of representative functions on groups and enveloping algebras of Lie algebras, as explored in the works of Borel, Cartier, Hopf and others in the 1940s and 50s.The modern and systematic treatment uses the approach of natural operations, illuminating the structure of Hopf algebras by means of their endomorphisms and their combinatorics. Emphasizing notions such as pseudo-coproducts, characteristic endomorphisms, descent algebras and Lie idempotents, the text also covers the important case of enveloping algebras of pre-Lie algebras. A wide range of applications are surveyed, highlighting the main ideas and fundamental results. Suitable as a textbook for masters or doctoral level programs, this book will be of interest to algebraists and anyone working in one of the fields of application of Hopf algebras.

Based on the third International Conference on Symmetries, Differential Equations and Applications (SDEA-III), this proceedings volume highlights recent important advances and trends in the applications of Lie groups, including a broad area of topics in interdisciplinary studies, ranging from mathematical physics to financial mathematics. The selected and peer-reviewed contributions gathered here cover Lie theory and symmetry methods in differential equations, Lie algebras and Lie pseudogroups, super-symmetry and super-integrability, representation theory of Lie algebras, classification problems, conservation laws, and geometrical methods. The SDEA III, held in honour of the Centenary of Noether's Theorem, proven by the prominent German mathematician Emmy Noether, at Istanbul Technical University in August 2017 provided a productive forum for academic researchers, both junior and senior, and students to discuss and share the latest developments in the theory and applications of Lie symmetry groups. This work has an interdisciplinary appeal and will be a valuable read for researchers in mathematics, mechanics, physics, engineering, medicine and finance.

Nowadays algebra is understood basically as the general theory of algebraic oper ations and relations. It is characterised by a considerable intrinsic naturalness of its initial notions and problems, the unity of its methods, and a breadth that far exceeds that of its basic concepts. It is more often that its power begins to be displayed when one moves outside its own limits. This characteristic ability is seen when one investigates not only complete operations, but partial operations. To a considerable extent these are related to algebraic operators and algebraic operations. The tendency to ever greater generality is amongst the reasons that playa role in explaining this development. But other important reasons play an even greater role. Within this same theory of total operations (that is, operations defined everywhere), there persistently arises in its different sections a necessity of examining the emergent feature of various partial operations. It is particularly important that this has been found in those parts of algebra it brings together and other areas of mathematics it interacts with as well as where algebra finds applica tion at the very limits of mathematics. In this connection we mention the theory of the composition of mappings, category theory, the theory of formal languages and the related theory of mathematical linguistics, coding theory, information theory, and algebraic automata theory. In all these areas (as well as in others) from time to time there arises the need to consider one or another partial operation."

The present monograph develops a unified theory of Steinberg groups, independent of matrix representations, based on the theory of Jordan pairs and the theory of 3-graded locally finite root systems. The development of this approach occurs over six chapters, progressing from groups with commutator relations and their Steinberg groups, then on to Jordan pairs, 3-graded locally finite root systems, and groups associated with Jordan pairs graded by root systems, before exploring the volume's main focus: the definition of the Steinberg group of a root graded Jordan pair by a small set of relations, and its central closedness. Several original concepts, such as the notions of Jordan graphs and Weyl elements, provide readers with the necessary tools from combinatorics and group theory. Steinberg Groups for Jordan Pairs is ideal for PhD students and researchers in the fields of elementary groups, Steinberg groups, Jordan algebras, and Jordan pairs. By adopting a unified approach, anybody interested in this area who seeks an alternative to case-by-case arguments and explicit matrix calculations will find this book essential.

This book discusses the origin of graph theory from its humble beginnings in recreational mathematics to its modern setting or modeling communication networks, as is evidenced by the World Wide Web graph used by many Internet search engines. The second edition of the book includes recent developments in the theory of signed adjacency matrices involving the proof of sensitivity conjecture and the theory of Ramanujan graphs. In addition, the book discusses topics such as Pick's theorem on areas of lattice polygons and Graham-Pollak's work on addressing of graphs. The concept of graph is fundamental in mathematics and engineering, as it conveniently encodes diverse relations and facilitates combinatorial analysis of many theoretical and practical problems. The text is ideal for a one-semester course at the advanced undergraduate level or beginning graduate level.

James E. Humphreys is presently Professor of Mathematics at the University of Massachusetts at Amherst. Before this, he held the posts of Assistant Professor of Mathematics at the University of Oregon and Associate Professor of Mathematics at New York University. His main research interests include group theory and Lie algebras. He graduated from Oberlin College in 1961. He did graduate work in philosophy and mathematics at Cornell University and later received hi Ph.D. from Yale University if 1966. In 1972, Springer-Verlag published his first book, "Introduction to Lie Algebras and Representation Theory" (graduate Texts in Mathematics Vol. 9).

Towards Inclusive Societies: Psychological and Sociological Perspectives focuses on the importance of building inclusive societies and communities for global human welfare within psychological, social, political, and cultural realms. It discusses the engagement of psychology and other social science disciplines on the need for building both cultural sensitivity and interdisciplinary dialogue. The volume presents the issues and consequences of globalization and diversity in the social and psychological domains and their role in shaping the physical and mental health of people. It systematically examines the various parameters of inclusivity such as equality, equity, social identity, social stigma, and coexistence of differences in socio-cultural behaviour. The volume focuses on the developments towards building inclusive societies in the South Asian countries including, India, Bangladesh, and Nepal. It also highlights the challenges and possibilities in making social-psychological discourses more inclusive. This book will be of interest to students, teachers, and scholars of psychology, cultural psychology, gender psychology, social psychology, sociology, and political science and social work. It will also be useful for psychologists, sociologists, social scientists, social workers, political scientists, and Gandhian philosophers.

Evolution and the Human-Animal Drive to Conflict examines how fundamental, universal animal drives, such as dominance/prevalence, survival, kinship, and "profit" (greed, advantage, whether of material or social nature), provide the basis for the evolutionary trap that promotes the unstable, conflictive, dominant-prone individual and group human behaviours. Examining this behavioural tension, this book argues that while these innate features set up behaviours that lean towards aggression influenced by social inequalities, the means implemented to defuse them resort to emotional and intellectual strategies that sponsor fanaticism and often reproduce the very same behaviours they intend to defuse. In addressing these concerns, the book argues that we should enhance our resources to promote solidarity, accept cultural differences, deter expansionist and uncontrolled profit drives, and achieve collective access towards knowledge and progress in living conditions. This entails promoting the redistribution of resources and creative labour access and avoiding policies that generate a fragmented world with collective and individual development disparities that invite and encourage dominance behaviours. This resource redistribution asserts that it is necessary to reformulate the global set of human priorities towards increased access to better living conditions, cognitive enhancement, a more amiable interaction with the ecosystem and non-aggressive cultural differences, promote universal access to knowledge, and enhance creativity and cultural convivence. These behavioural changes entail partial derangement of our ancestral animal drives camouflaged under different cultural profiles until the species succeeds in replacing the dominance of basic animal drives with prosocial, collective ones. Though it entails a formidable task of confronting financial, military, and religious powers and cultural inertias – human history is also a challenging, continuous experience in these domains – for the sake of our own self-identity and self-evaluation, we should reject any suggestion of not continuing embracing slowly constructing collective utopias channelled towards improving individual and collective freedom and creativeness. This book will interest academics and students in social, cognitive, and evolutionary psychology, the neurosciences, palaeoanthropology, philosophy, and anthropology.

This monograph introduces and explores the notions of a commutator equation and the equationally-defined commutator from the perspective of abstract algebraic logic. An account of the commutator operation associated with equational deductive systems is presented, with an emphasis placed on logical aspects of the commutator for equational systems determined by quasivarieties of algebras. The author discusses the general properties of the equationally-defined commutator, various centralization relations for relative congruences, the additivity and correspondence properties of the equationally-defined commutator and its behavior in finitely generated quasivarieties. Presenting new and original research not yet considered in the mathematical literature, The Equationally-Defined Commutator will be of interest to professional algebraists and logicians, as well as graduate students and other researchers interested in problems of modern algebraic logic.

This book explores the classical and beautiful character theory of finite groups. It does it by using some rudiments of the language of categories. Originally emerging from two courses offered at Peking University (PKU), primarily for third-year students, it is now better suited for graduate courses, and provides broader coverage than books that focus almost exclusively on groups. The book presents the basic tools, notions and theorems of character theory (including a new treatment of the control of fusion and isometries), and introduces readers to the categorical language at several levels. It includes and proves the major results on characteristic zero representations without any assumptions about the base field. The book includes a dedicated chapter on graded representations and applications of polynomial invariants of finite groups, and its closing chapter addresses the more recent notion of the Drinfeld double of a finite group and the corresponding representation of GL_2(Z).

In the 1960s divorce was increasing around the world and marriage conciliation services were a necessary development to deal with those who wanted to seek help for their problems. Originally published in 1968, the purpose of this title was to give some account of the widely differing types of marital conciliation services operating in Britain and also some other parts of the world at the time. The author, who was based at the National Marriage Guidance Council of Great Britain, first outlines the British services, then presents comparative studies of the services overseas in Australia, New Zealand, Scandinavia and Finland and the United States and Canada. Today it can be read and enjoyed in its historical context.

Few Americans escape the experience of divorce, either first-hand or through the dissolutions of marriages of friends or relatives. According to the author, mediation offers a good alternative to the strictly adversarial divorce process that was so prevalent before such programs began to emerge. Originally published in 1991, this book was unique at the time in that it not only explores the role of communication in divorce mediation, but it also presents original research to support its claims. A series of empirical studies, it points readers to a more focused set of recommendations about communication than the typical practitioner's "How-to" books. A simulation exercise is also included, so that readers can apply the concepts described and see the results. The main goal of this text is to provide mediators with a language for understanding their own and their disputants' communication patterns, strategies, and tactics - a shortcoming of most other books on this topic when first published.

This edited collection covers the role of the process observer - a position that enhances the effectiveness of group functioning by observing the process, summarizing the behavior of the group so that the group can learn and, if needed, improve its functioning. There is little guidance on best practices for this role, and in most settings, process observers are forced to rely on whatever previous training they have received in group work to fulfil their role. The first of its kind, this book offers a wealth of resources for the role of group process observer organized in a systematic way. Each contributor focuses on a specific aspect of group process observation, identifying what is currently known on the topic, suggesting best practices, and providing the reader with tools, structures, and guidelines for effective process observation. Students and educators of group work courses will find this book integral as it covers the existing gap in literature on group process observation.

This edited collection covers the role of the process observer - a position that enhances the effectiveness of group functioning by observing the process, summarizing the behavior of the group so that the group can learn and, if needed, improve its functioning. There is little guidance on best practices for this role, and in most settings, process observers are forced to rely on whatever previous training they have received in group work to fulfil their role. The first of its kind, this book offers a wealth of resources for the role of group process observer organized in a systematic way. Each contributor focuses on a specific aspect of group process observation, identifying what is currently known on the topic, suggesting best practices, and providing the reader with tools, structures, and guidelines for effective process observation. Students and educators of group work courses will find this book integral as it covers the existing gap in literature on group process observation.

Starting with the Schur-Zassenhaus theorem, this monograph documents a wide variety of results concerning complementation of normal subgroups in finite groups. The contents cover a wide range of material from reduction theorems and subgroups in the derived and lower nilpotent series to abelian normal subgroups and formations. Contents Prerequisites The Schur-Zassenhaus theorem: A bit of history and motivation Abelian and minimal normal subgroups Reduction theorems Subgroups in the chief series, derived series, and lower nilpotent series Normal subgroups with abelian sylow subgroups The formation generation Groups with specific classes of subgroups complemented

Contemporary politics is mass-communication politics. Politicians are not only seen and heard, they are seen and heard in close-up through television appearances, speeches, interviews, and on social media. In this book, the authors analyse the ways in which politicians communicate with each other, the media, and the electorate; they also discuss the implications of contemporary political discourse on the democratic process as a whole. Politicians in interviews are typically castigated for their evasiveness. However, microanalytic research shows that there is more to political discourse than this apparent ambiguity. This book reveals how equivocation, interruptions, and personal antagonism can offer valuable insights into a politician's communicative style. The authors review their empirical research not only on political interviews, but also on speeches, parliamentary debates, and political journalism. Further insights include how political speakers interact with their audiences, how party leaders engage in adversarial discourse at PMQs, and how the spoken messages of politicians can be affected by modern journalistic editing techniques. Thereby, this research generates greater awareness of communicative practices in a diverse range of political contexts. While the interviews and parliamentary debates analysed pertain to UK politics, the speeches also draw on the USA, and European and Far Eastern nations. This engaging book is a fascinating resource for students and academics in psychology, politics, communication, and other related disciplines such as sociology and linguistics. The research is also extremely relevant to policy makers and practitioners in politics and political journalism.

Contemporary politics is mass-communication politics. Politicians are not only seen and heard, they are seen and heard in close-up through television appearances, speeches, interviews, and on social media. In this book, the authors analyse the ways in which politicians communicate with each other, the media, and the electorate; they also discuss the implications of contemporary political discourse on the democratic process as a whole. Politicians in interviews are typically castigated for their evasiveness. However, microanalytic research shows that there is more to political discourse than this apparent ambiguity. This book reveals how equivocation, interruptions, and personal antagonism can offer valuable insights into a politician's communicative style. The authors review their empirical research not only on political interviews, but also on speeches, parliamentary debates, and political journalism. Further insights include how political speakers interact with their audiences, how party leaders engage in adversarial discourse at PMQs, and how the spoken messages of politicians can be affected by modern journalistic editing techniques. Thereby, this research generates greater awareness of communicative practices in a diverse range of political contexts. While the interviews and parliamentary debates analysed pertain to UK politics, the speeches also draw on the USA, and European and Far Eastern nations. This engaging book is a fascinating resource for students and academics in psychology, politics, communication, and other related disciplines such as sociology and linguistics. The research is also extremely relevant to policy makers and practitioners in politics and political journalism.

This book explores the role of listening in community engagement and peace building efforts, bridging academic research in communication and practical applications for individual and social change. For all their differences, community engagement and peacebuilding efforts share much in common: the need to establish and agree on achievable and measurable goals, the importance of trust, and the need for conflict management, to name but a few. This book presents listening-considered as a multi-disciplinary concept related to but distinct from civility, civic participation, and other social processes-as a primary mechanism for accomplishing these tasks. Individual chapters explore these themes in an array of international contexts, examining topics such as conflict resolution, restorative justice, environmental justice, migrants and refugees, and trauma-informed peacebuilding. The book includes contemporary literature reviews and theoretical insights covering the role of listening as related to individual, social, and governmental efforts to better engage communities and build, maintain, or establish peace in an increasingly divided world. This collection provides invaluable insight to researchers, students, educators, and practitioners in intercultural and international communication, conflict management, peacebuilding, community engagement, and international studies.

Evolution and the Human-Animal Drive to Conflict examines how fundamental, universal animal drives, such as dominance/prevalence, survival, kinship, and "profit" (greed, advantage, whether of material or social nature), provide the basis for 'the evolutionary trap' that promotes the unstable, conflictive, dominant-prone individual and group human behaviours. Examining this behavioural tension, the book argues that while these innate features set up behaviours that lean towards aggression influenced by social inequalities, the means implemented to defuse them resort to emotional and intellectual strategies that sponsor fanaticism and often reproduce the very same behaviours they intend to defuse. In addressing these concerns, the book argues that we should enhance our resources to promote solidarity, accept cultural differences, deter expansionist and uncontrolled profit drives, and achieve collective access towards knowledge and progress in living conditions. This entails promoting the redistribution of resources and creative labour access and avoiding policies that generate a fragmented world with collective and individual development disparities that invite and encourage dominance behaviours.This resource redistribution asserts that it is necessary to reformulate the global set of human priorities towards increased access to better living conditions, cognitive enhancement, a more amiable interaction with the ecosystem and non-aggressive cultural differences, promote universal access to knowledge and enhance creativity and cultural convivence. These behavioural changes entail partial derangement of our ancestral animal drives camouflaged under different cultural profiles until the species succeeds in replacing the dominance of basic animal drives with prosocial, collective ones. Though it entails a formidable task of confronting financial, military, and religious powers and cultural inertias - human history is also a challenging, continuous experience in these domains - for the sake of our own self-identity and self-evaluation we should reject any suggestion of not continuing embracing slowly constructing collective utopias channelled towards improving individual and collective freedom and creativeness. This book will interest academics and students in social, cognitive, and evolutionary psychology, the neurosciences, paleoanthropology, philosophy, and anthropology.

Insecurity is an inevitable part of being human. Although life is insecure for every organism, humans alone are burdened by knowing that this is so. This ground-breaking volume features contributions by leading international researchers exploring the social psychology of insecurity, and how existential, metaphysical and social uncertainty influence human social behaviour. Chapters in the book investigate the psychological origins of insecurity, evolutionary theorizing about the functions of insecurity, the motivational strategies people adopt to manage insecurity, self-regulation strategies, the role of insecurity in the formation and maintenance of social relationships, and the influence of insecurity and uncertainty on the organization of larger social systems and public affairs. The chapters also discuss how insecurity influences many areas of contemporary social life, highlighting the applied implications of this line of research. Topics covered include the role of insecurity in social communication, social judgments, decision making, group identification, morality, interpersonal behaviour, relationships, attitudes and many applied aspects of social life and politics where understanding the psychology of insecurity is of critical importance. This accessible and engaging book will be of interest to students, researchers and practitioners as a textbook or reference book in behavioral and social science fields, as well as to a broad spectrum of intelligent lay audience seeking to understand one of the most intriguing issues that shapes human social life.

Insecurity is an inevitable part of being human. Although life is insecure for every organism, humans alone are burdened by knowing that this is so. This ground-breaking volume features contributions by leading international researchers exploring the social psychology of insecurity, and how existential, metaphysical and social uncertainty influence human social behaviour. Chapters in the book investigate the psychological origins of insecurity, evolutionary theorizing about the functions of insecurity, the motivational strategies people adopt to manage insecurity, self-regulation strategies, the role of insecurity in the formation and maintenance of social relationships, and the influence of insecurity and uncertainty on the organization of larger social systems and public affairs. The chapters also discuss how insecurity influences many areas of contemporary social life, highlighting the applied implications of this line of research. Topics covered include the role of insecurity in social communication, social judgments, decision making, group identification, morality, interpersonal behaviour, relationships, attitudes and many applied aspects of social life and politics where understanding the psychology of insecurity is of critical importance. This accessible and engaging book will be of interest to students, researchers and practitioners as a textbook or reference book in behavioral and social science fields, as well as to a broad spectrum of intelligent lay audience seeking to understand one of the most intriguing issues that shapes human social life.

This book gathers together selected contributions presented at the 3rd Moroccan Andalusian Meeting on Algebras and their Applications, held in Chefchaouen, Morocco, April 12-14, 2018, and which reflects the mathematical collaboration between south European and north African countries, mainly France, Spain, Morocco, Tunisia and Senegal. The book is divided in three parts and features contributions from the following fields: algebraic and analytic methods in associative and non-associative structures; homological and categorical methods in algebra; and history of mathematics. Covering topics such as rings and algebras, representation theory, number theory, operator algebras, category theory, group theory and information theory, it opens up new avenues of study for graduate students and young researchers. The findings presented also appeal to anyone interested in the fields of algebra and mathematical analysis.