Hyperidentities are important formulae of second-order logic, and research in hyperidentities paves way for the study of second-order logic and second-order model theory.This book illustrates many important current trends and perspectives for the field of hyperidentities and their applications, of interest to researchers in modern algebra and discrete mathematics. It covers a number of directions, including the characterizations of the Boolean algebra of n-ary Boolean functions and the distributive lattice of n-ary monotone Boolean functions; the classification of hyperidentities of the variety of lattices, the variety of distributive (modular) lattices, the variety of Boolean algebras, and the variety of De Morgan algebras; the characterization of algebras with aforementioned hyperidentities; the functional representations of finitely-generated free algebras of various varieties of lattices and bilattices via generalized Boolean functions (De Morgan functions, quasi-De Morgan functions, super-Boolean functions, super-De Morgan functions, etc); the structural results for De Morgan algebras, Boole-De Morgan algebras, super-Boolean algebras, bilattices, among others.While problems of Boolean functions theory are well known, the present book offers alternative, more general problems, involving the concepts of De Morgan functions, quasi-De Morgan functions, super-Boolean functions, and super-De Morgan functions, etc. In contrast to other generalized Boolean functions discovered and investigated so far, these functions have clearly normal forms. This quality is of crucial importance for their applications in pure and applied mathematics, especially in discrete mathematics, quantum computation, quantum information theory, quantum logic, and the theory of quantum computers.

Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.

This book attempts to 'shake up' the current complacency around therapy and 'mental health' behaviours by putting therapy fully into context using Social Contextual Analysis; showing how changes to our social, discursive, and societal environments, rather than changes to an individual's 'mind', will reduce suffering from the 'mental health' behaviours. Guerin challenges many assumptions about both current therapy and psychology, and offers alternative approaches, synthesized from sociology, social anthropology, sociolinguistics, and elsewhere. The book provides a way of addressing the 'mental health' behaviours including actions, talking, thinking, and emotions, by taking people's external life situations into account, and not relying on an imagined 'internal source'. Guerin describes the broad contexts for current Western therapies, referring to social, discursive, cultural, societal, and economic contexts, and suggests that we need to research the components of therapies and stop treating therapies as units. He reframes different types of therapy away from their abstract jargons, offering an alternative approach grounded in our real social worlds, aligning with new thinking that challenges the traditional methods of therapy, and also providing a better framework for rethinking psychology itself. The book ultimately suggests more emphasis should be put on 'mental health' behaviours as arising from social issues including the modern contexts of extreme capitalism, excessive bureaucracy, weakened discursive communities, and changing forms of social relationships. Practical guidelines are provided for building the reimagined therapies into clinics and institutions where labelling and pathologizing the 'mental health' behaviours will no longer be needed. By putting 'mental health' behaviours and therapy into a naturalistic or ecological social sciences framework, this book will be practical and fascinating reading for professional therapists, counsellors, social workers, and mental health nurses, as well as academics interested in psychology and the social sciences more generally.

This book attempts to 'shake up' the current complacency around therapy and 'mental health' behaviours by putting therapy fully into context using Social Contextual Analysis; showing how changes to our social, discursive, and societal environments, rather than changes to an individual's 'mind', will reduce suffering from the 'mental health' behaviours. Guerin challenges many assumptions about both current therapy and psychology, and offers alternative approaches, synthesized from sociology, social anthropology, sociolinguistics, and elsewhere. The book provides a way of addressing the 'mental health' behaviours including actions, talking, thinking, and emotions, by taking people's external life situations into account, and not relying on an imagined 'internal source'. Guerin describes the broad contexts for current Western therapies, referring to social, discursive, cultural, societal, and economic contexts, and suggests that we need to research the components of therapies and stop treating therapies as units. He reframes different types of therapy away from their abstract jargons, offering an alternative approach grounded in our real social worlds, aligning with new thinking that challenges the traditional methods of therapy, and also providing a better framework for rethinking psychology itself. The book ultimately suggests more emphasis should be put on 'mental health' behaviours as arising from social issues including the modern contexts of extreme capitalism, excessive bureaucracy, weakened discursive communities, and changing forms of social relationships. Practical guidelines are provided for building the reimagined therapies into clinics and institutions where labelling and pathologizing the 'mental health' behaviours will no longer be needed. By putting 'mental health' behaviours and therapy into a naturalistic or ecological social sciences framework, this book will be practical and fascinating reading for professional therapists, counsellors, social workers, and mental health nurses, as well as academics interested in psychology and the social sciences more generally.

Presenting diverse perspectives from eminent scholars and contemporary researchers, The Handbook of Impression Formation contextualizes current and future areas of research in the social psychology of impression formation within a rich historic framework. Affirming that impression formation is at the core of human experience, chapters explore how and why people form snap judgments about others and when those impressions update. They examine the processes through which people infer the reasons for the events they encounter, allowing people to plan for appropriate behavioral responses to social contexts. The research reviewed is informed by the foundational theory of unconscious automatic processes involved in making judgements of other people, pioneered by Professor Jim Uleman who contributes a chapter that suggests important new directions, and concludes the volume by reflecting on the state of the field more broadly. The book explores how certain attributes stimulate categorization, examining current issues around implicit bias, stereotypes, and social media. Chapters cover a range of approaches, featuring personal narratives, presentation of new data and discoveries, comprehensive literature reviews, and contemplations on where the field must go and what questions require focus for progress to be made, calling for even the most advanced scholars to contribute more to the collective investigation of impression formation. This fascinating work provides a solid foundation from which all researchers can build a new and unique program of research, and arms the reader with the intellectual tools they need to chart new theoretical territory and discover aspects of the human experience we have yet to even wonder about. It is essential reading for students and academics in social psychology, and the social sciences more broadly.

Psychology of Prejudice and Discrimination provides a comprehensive and compelling overview of what psychological theory and research have to say about the nature, causes, and reduction of prejudice and discrimination. It balances a detailed discussion of theories and selected research with applied examples that ensure the material is relevant to students. This edition has been thoroughly revised and updated and addresses several interlocking themes. It first looks at the nature of prejudice and discrimination, followed by a discussion of research methods. Next come the psychological underpinnings of prejudice: the nature of stereotypes, the conditions under which stereotypes influence responses to other people, contemporary theories of prejudice, and how individuals' values and belief systems are related to prejudice. Explored next are the development of prejudice in children and the social context of prejudice. The theme of discrimination is developed via discussions of the nature of discrimination, the experience of discrimination, and specific forms of discrimination, including gender, gender identity, sexual orientation, age, ability, and appearance. The concluding theme is the reduction of prejudice. The book is accompanied by a comprehensive website featuring an Instructor Manual that contains activities and tools to help with teaching a prejudice and discrimination course; PowerPoint slides for every chapter; and a Test Bank with short answer and multiple-choice exam questions for every chapter. This book is an essential companion for all students of prejudice and discrimination, including those in psychology, education, social work, business, communication studies, ethnic studies, and other disciplines. In addition to courses on prejudice and discrimination, this book will also appeal to those studying racism and diversity.

Based on extensive analysis of real-time, authentic crisis encounters collected in the UK and US, Crisis Talk: Negotiating with Individuals in Crisis sheds light on the relatively hidden world of communication between people in crisis and the professionals whose job it is to help them. The crisis situations explored in this book involve police hostage and crisis negotiators and emergency dispatchers interacting with individuals in crisis who threaten suicide or self-harm. The practitioners face various communicative challenges in these encounters, including managing strong emotions, resistance, hostility, and unresponsiveness. Using conversation analysis, Crisis Talk presents evidence on how practitioners deal with the interactional challenge of negotiating with people in crisis and how what they say shapes outcomes. Each chapter includes recommendations based on the detailed analysis of numerous cases of actual negotiation. Crisis Talk shows readers how every turn taken by negotiators can exacerbate or solve the communicative challenges created by crisis situations, making it a unique and invaluable text for academics in psychology, sociology, linguistic sciences, and related fields, as well as for practitioners engaging in crisis negotiation training or fieldwork.

This book provides a systematic, rigorous and self-contained treatment of positive dynamical systems. A dynamical system is positive when all relevant variables of a system are nonnegative in a natural way. This is in biology, demography or economics, where the levels of populations or prices of goods are positive. The principle also finds application in electrical engineering, physics and computer sciences. "The author has greatly expanded the field of positive systems in surprising ways." - Prof. Dr. David G. Luenberger, Stanford University(USA)

Loop groups, the simplest class of infinite dimensional Lie groups, have recently been the subject of intense study. This book gives a complete and self-contained account of what is known about them from a geometrical and analytical point of view, drawing together the many branches of mathematics from which current theory developed--algebra, geometry, analysis, combinatorics, and the mathematics of quantum field theory. The authors discuss Loop groups' applications to simple particle physics and explain how the mathematics used in connection with Loop groups is itself interesting and valuable, thereby making this work accessible to mathematicians in many fields.

Features Written to be self-contained. Ideal as a primary textbook for an undergraduate course in linear algebra. Applications of the general theory which are of interest to disciplines outside of mathematics, such as engineering.

Features Written to be self-contained. Ideal as a primary textbook for an undergraduate course in linear algebra. Applications of the general theory which are of interest to disciplines outside of mathematics, such as engineering.

This work deals with the matrix methods of continuous signal and image processing according to which strip-transformation is used. The authors suggest ways to solve a problem of evaluating potential noise immunity and synthesis of an optimal filter for the case of pulse noises, of applying the two-dimensional strip-transformation for storage and noise immune transmission of images. The strip-transformation of images is illustrated by examples and classes of images invariant relative to symmetrical orthogonal transformations. The monograph is intended for scientists and specialists whose activities are connected with computer signals and images processing, instrumentation and metrology. It can also be used by undergraduates, as well as by post-graduates for studying computer methods of signal and image processing.

Primarily concerned with the study of cohomology theories of general topological spaces with "general coefficient systems", the parts of sheaf theory covered here are those areas important to algebraic topology. Among the many innovations in this book, the concept of the "tautness" of a subspace is introduced and exploited; the fact that sheaf theoretic cohomology satisfies the homotopy property is proved for general topological spaces; and relative cohomology is introduced into sheaf theory. A list of exercises at the end of each chapter helps students to learn the material, and solutions to many of the exercises are given in an appendix. This new edition of a classic has been substantially rewritten and now includes some 80 additional examples and further explanatory material, as well as new sections on Cech cohomology, the Oliver transfer, intersection theory, generalised manifolds, locally homogeneous spaces, homological fibrations and p- adic transformation groups. Readers should have a thorough background in elementary homological algebra and in algebraic topology.

This new text offers a student-centered approach. It presents groups first approach, offers flexibility, and is aimed at both a one- and two-semester course. The primary difference from key competitors is level and organization. There are many AA texts, offering a wide-range of levels, and this text is written to the precise middle of the market. Abstract Algebra is taught at every four-year university and college throughout the world. It is a course typically required of mathematics majors, yet also of those planning on becoming teachers. The groups-first approach is the most popular.

Linear algebra is one of the most important branches of mathematics - important because of its many applications to other areas of mathematics, and important because it contains a wealth of ideas and results which are basic to pure mathematics. This book gives an introduction to linear algebra, and develops and proves its fundamental properties and theorems taking a pure mathematical approach - linear algebra contains some fine pure mathematics. Its main topics include: vector spaces and algebras, dimension, linear maps, direct sums, and (briefly) exact sequences; matrices and their connections with linear maps, determinants (properties proved using some elementary group theory), and linear equations; Cayley-Hamilton and Jordan theorems leading to the spectrum of a linear map - this provides a geometric-type description of these maps; Hermitian and inner product spaces introducing some metric properties (distance, perpendicularity etc.) into the theory, also unitary and orthogonal maps and matrices; applications to finite fields, mathematical coding theory, finite matrix groups, the geometry of quadratic forms, quaternions and Cayley numbers, and some basic group representation theory; and, a large number of examples, exercises and problems are provided. It gives answers and/or sketch solutions to all of the problems in an appendix -some of these are theoretical and some numerical, both types are important. No particular computer algebra package is discussed but a number of the exercises are intended to be solved using one of these packages chosen by the reader. The approach is pure-mathematical, and the intended readership is undergraduate mathematicians, also anyone who requires a more than basic understanding of the subject. This book will be most useful for a 'second course' in linear algebra, that is for students that have seen some elementary matrix algebra. But as all terms are defined from scratch, this book can be used for a 'first course' for more advanced students.

Everyday Applications of Psychological Science explores several core areas of psychology, showing readers how to apply these principles to everyday situations in order to better their understanding of human behavior and improve their quality of life. The authors of this book, who are award-winning educators of psychology, have culled and collated the best practical research-based advice that psychological science can offer in an easy-to-read and digestible format. Lively and peppered with anecdotes, this book explores topical areas normally found in introductory psychology books but do so in a way that makes psychological science practical, accessible, and relevant to our readers. In Everyday Applications of Psychological Science, the best science that psychology has to offer is translated into life hacks that are applicable to improving readers' physical health, mental health, psychological wealth, relationships, and happiness. Everyday Applications of Psychological Science is vital reading for those interested in learning more about the field of psychology more generally and how aspects of it can be applied to daily life. Our approach may be of particular interest to current and prospective undergraduate students of psychology and those interested in learning more about mental health issues.

This book explores welfare politics, unemployment, and interventions in relation to the labour market from a critical psychological perspective. Using critical fieldwork and theory, the author explores the administration of the unemployed, and the drive to increase labour market participation through strategies of activation. There is a strong and coherent conceptual and theoretical framing for this work, with a critical perspective (essentially, question everything) taking centre stage. It will give an overall coherence in addressing the topic. The theoretical framing is cogent and, in combination with the critical perspective, works well for integrating the material and delivering a fresh approach to this topic. Psychology, Punitive Activation and Welfare will appeal to students engaging with critical psychology, unemployment or policy, by providing a distinct application of theoretical and methodological tools to think differently about the relationship between labour market non/participation, human misery, psychology, and frontline enactment of policy and research.

This book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level.It treats set theory, group theory, ring and ideal theory, and field theory (including Galois theory), and culminates with a treatment of Dedekind rings, including rings of algebraic integers.In addition to treating standard topics, it contains material not often dealt with in books at this level. It provides a fresh perspective on the subjects it covers, with, in particular, distinctive treatments of factorization theory in integral domains and of Galois theory.As an introduction, it presupposes no prior knowledge of abstract algebra, but provides a well-motivated, clear, and rigorous treatment of the subject, illustrated by many examples. Written with an eye toward number theory, it contains numerous applications to number theory (including proofs of Fermat's theorem on sums of two squares and of the Law of Quadratic Reciprocity) and serves as an excellent basis for further study in algebra in general and number theory in particular.Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students' knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further.

This is the first monograph devoted to clean ring and matrix theory. It aims to study a theory of expressing an element in a ring as the sum of some special ones, such as idempotents, units, nilpotents, tripotents, involutions, etc. A matrix over such rings is thereby expressed as the sum of some special matrices. Also another topics on the behaviors of topological properties and *-properties of such rings are investigated.The book is based on the results of various published papers, particularly, by the authors'. It is accessible for students familiar with general abstract algebra, while the topics are interesting for researchers in the field of ring, matrix and operator theory.

Exact Finite-Difference Schemes is a first overview of the topic also describing the state-of-the-art in this field of numerical analysis. Construction of exact difference schemes for various parabolic and elliptic partial differential equations are discussed, including vibrations and transport problems. After this, applications are discussed, such as the discretisation of ODEs and PDEs and numerical methods for stochastic differential equations. Contents: Basic notation Preliminary results Hyperbolic equations Parabolic equations Use of exact difference schemes to construct NSFD discretizations of differential equations Exact and truncated difference schemes for boundary-value problem Exact difference schemes for stochastic differential equations Numerical blow-up time Bibliography

Descriptor linear systems theory is an important part in the general field of control systems theory, and has attracted much attention in the last two decades. In spite of the fact that descriptor linear systems theory has been a topic very rich in content, there have been only a few books on this topic. This book provides a systematic introduction to the theory of continuous-time descriptor linear systems and aims to provide a relatively systematic introduction to the basic results in descriptor linear systems theory. The clear representation of materials and a large number of examples make this book easy to understand by a large audience. General readers will find in this book a comprehensive introduction to the theory of descriptive linear systems. Researchers will find a comprehensive description of the most recent results in this theory and students will find a good introduction to some important problems in linear systems theory.

This monograph provides a modern introduction to the theory of quantales. First coined by C.J. Mulvey in 1986, quantales have since developed into a significant topic at the crossroads of algebra and logic, of notable interest to theoretical computer science. This book recasts the subject within the powerful framework of categorical algebra, showcasing its versatility through applications to C*- and MV-algebras, fuzzy sets and automata. With exercises and historical remarks at the end of each chapter, this self-contained book provides readers with a valuable source of references and hints for future research. This book will appeal to researchers across mathematics and computer science with an interest in category theory, lattice theory, and many-valued logic.

Based on extensive analysis of real-time, authentic crisis encounters collected in the UK and US, Crisis Talk: Negotiating with Individuals in Crisis sheds light on the relatively hidden world of communication between people in crisis and the professionals whose job it is to help them. The crisis situations explored in this book involve police hostage and crisis negotiators and emergency dispatchers interacting with individuals in crisis who threaten suicide or self-harm. The practitioners face various communicative challenges in these encounters, including managing strong emotions, resistance, hostility, and unresponsiveness. Using conversation analysis, Crisis Talk presents evidence on how practitioners deal with the interactional challenge of negotiating with people in crisis and how what they say shapes outcomes. Each chapter includes recommendations based on the detailed analysis of numerous cases of actual negotiation. Crisis Talk shows readers how every turn taken by negotiators can exacerbate or solve the communicative challenges created by crisis situations, making it a unique and invaluable text for academics in psychology, sociology, linguistic sciences, and related fields, as well as for practitioners engaging in crisis negotiation training or fieldwork.

This book is mainly intended for first-year University students who undertake a basic abstract algebra course, as well as instructors. It contains the basic notions of abstract algebra through solved exercises as well as a 'True or False' section in each chapter. Each chapter also contains an essential background section, which makes the book easier to use.

This edited volume brings together the latest research in understanding the nature, origins, and evolution of human sociability, one of the most intriguing aspects of human psychology. Sociability-our sophisticated ability to interact with others, imagine, plan, and execute interdependent behaviours-lies at the heart of our evolutionary success, and is the most important prerequisite for the development of increasingly elaborate civilizations. With contributions from internationally renowned researchers in areas of social psychology as well as anthropology and evolutionary psychology, this book demonstrates the role of social psychology in explaining how human sociability evolved, how it shapes our mental and emotional lives, and how it influences both large-scale civilizational practices and intimate interpersonal relations. Chapters cover the core psychological characteristics that shape human sociability, including such phenomena as the role of information exchange, affective processes, social norms, power relations, personal relationships, attachment patterns, personality characteristics, and evolutionary pressures. Featuring a wide variety of empirical and theoretical backgrounds, the book will be of interest to students and researchers in all areas of the social sciences, as well as practitioners and applied professionals who deal with issues related to sociability in their daily lives.