Capturing the state of the art of the interplay between positivity, noncommutative analysis, and related areas including partial differential equations, harmonic analysis, and operator theory, this volume was initiated on the occasion of the Delft conference in honour of Ben de Pagter's 65th birthday. It will be of interest to researchers in positivity, noncommutative analysis, and related fields. Contributions by Shavkat Ayupov, Amine Ben Amor, Karim Boulabiar, Qingying Bu, Gerard Buskes, Martijn Caspers, Jurie Conradie, Garth Dales, Marcel de Jeu, Peter Dodds, Theresa Dodds, Julio Flores, Jochen Gluck, Jacobus Grobler, Wolter Groenevelt, Markus Haase, Klaas Pieter Hart, Francisco Hernandez, Jamel Jaber, Rien Kaashoek, Turabay Kalandarov, Anke Kalauch, Arkady Kitover, Erik Koelink, Karimbergen Kudaybergenov, Louis Labuschagne, Yongjin Li, Nick Lindemulder, Emiel Lorist, Qi Lu, Miek Messerschmidt, Susumu Okada, Mehmet Orhon, Denis Potapov, Werner Ricker, Stephan Roberts, Pablo Roman, Anton Schep, Claud Steyn, Fedor Sukochev, James Sweeney, Guido Sweers, Pedro Tradacete, Jan Harm van der Walt, Onno van Gaans, Jan van Neerven, Arnoud van Rooij, Freek van Schagen, Dominic Vella, Mark Veraar, Anthony Wickstead, Marten Wortel, Ivan Yaroslavtsev, and Dmitriy Zanin.

Sporadic Groups is the first step in a programme to provide a uniform, self-contained treatment of the foundational material on the sporadic finite simple groups. The classification of the finite simple groups is one of the premier achievements of modern mathematics. The classification demonstrates that each finite simple group is either a finite analogue of a simple Lie group or one of 26 pathological sporadic groups. Sporadic Groups provides for the first time a self-contained treatment of the foundations of the theory of sporadic groups accessible to mathematicians with a basic background in finite groups such as in the author's text Finite Group Theory. Introductory material useful for studying the sporadics, such as a discussion of large extraspecial 2-subgroups and Tits' coset geometries, opens the book. A construction of the Mathieu groups as the automorphism groups of Steiner systems follows. The Golay and Todd modules, and the 2-local geometry for M24 are discussed. This is followed by the standard construction of Conway of the Leech lattice and the Conway group. The Monster is constructed as the automorphism group of the Griess algebra using some of the best features of the approaches of Griess, Conway, and Tits, plus a few new wrinkles. Researchers in finite group theory will find this text invaluable. The subjects treated will interest combinatorists, number theorists, and conformal field theorists.

- Topic has had a huge surge of interest since 2000 due to the greatly increased incidence of social communication disorders - Covers theory and evidence-based practice, making it a rounded and solid resource for students and professionals

- Topic has had a huge surge of interest since 2000 due to the greatly increased incidence of social communication disorders - Covers theory and evidence-based practice, making it a rounded and solid resource for students and professionals

An accessible introduction to the theoretical and computational aspects of linear algebra using MapleTM

Many topics in linear algebra can be computationally intensive, and software programs often serve as important tools for understanding challenging concepts and visualizing the geometric aspects of the subject. Principles of Linear Algebra with Maple uniquely addresses the quickly growing intersection between subject theory and numerical computation, providing all of the commands required to solve complex and computationally challenging linear algebra problems using Maple. The authors supply an informal, accessible, and easy-to-follow treatment of key topics often found in a first course in linear algebra.

Requiring no prior knowledge of the software, the book begins with an introduction to the commands and programming guidelines for working with Maple. Next, the book explores linear systems of equations and matrices, applications of linear systems and matrices, determinants, inverses, and Cramer's rule. Basic linear algebra topics such as vectors, dot product, cross product, and vector projection are explained, as well as the more advanced topics of rotations in space, rolling a circle along a curve, and the TNB Frame. Subsequent chapters feature coverage of linear transformations from Rn to Rm, the geometry of linear and affine transformations, least squares fits and pseudoinverses, and eigenvalues and eigenvectors.

The authors explore several topics that are not often found in introductory linear algebra books, including sensitivity to error and the effects of linear and affine maps on the geometry of objects. The Maple software highlights the topic's visual nature, as the book is complete with numerous graphics in two and three dimensions, animations, symbolic manipulations, numerical computations, and programming. In addition, a related Web site features supplemental material, including Maple code for each chapter's problems, solutions, and color versions of the book's figures.

Extensively class-tested to ensure an accessible presentation, Principles of Linear Algebra with Maple is an excellent book for courses on linear algebra at the undergraduate level. It is also an ideal reference for students and professionals who would like to gain a further understanding of the use of Maple to solve linear algebra problems.

This is the first volume of the two-volume book on linear algebra, in the University of Tokyo (UTokyo) Engineering Course.The objective of this volume is to present, from the engineering viewpoint, the standard mathematical results in linear algebra such as those on systems of equations and eigenvalue problems. In addition to giving mathematical theorems and formulas, it explains how the mathematical concepts such as rank, eigenvalues, and singular values are linked to engineering applications and numerical computations.In particular, the following four aspects are emphasized.

Originally published in 1981, this volume presents papers from the first Ontario Symposium on Personality and Social Psychology held at the University of Western Ontario from August 25-27, 1978. The general theme of the symposium was social cognition. The chapters have been grouped into two major parts. Chapters 1-5 focus on the implications of cognitive structures for social cognition, with particular emphasis on the nature of social schemata and the organization of social information. Chapters 6-11 focus on the consequences for social cognition of various cognitive processes and mechanisms, including verbal and nonverbal communicative processes, category accessibility, salience and selective attention, hypothesis-testing, and self-centered biases. Chapter 12 comments on the general perspectives taken in the previous chapters and suggests some additional directions for future consideration. Today it can be read and enjoyed in its historical context.

Elliptic operators arise naturally in several different mathematical settings, notably in the representation theory of Lie groups, the study of evolution equations, and the examination of Riemannian manifolds. This book develops the basic theory of elliptic operators on Lie groups and thereby extends the conventional theory of parabolic evolution equations to a natural non-commutative context. In order to achieve this goal, the author presents a synthesis of ideas from partial differential equations, harmonic analysis, functional analysis, and the theory of Lie groups. He begins by discussing the abstract theory of general operators with complex coefficients before concentrating on the central case of second-order operators with real coefficients. A full discussion of second-order subellilptic operators is also given. Prerequisites are a familiarity with basic semigroup theory, the elementary theory of Lie groups, and a firm grounding in functional analysis as might be gained from the first year of a graduate course.

- well organized and comprehensive three-part structure - features impressive roster of well-known contributors

- well organized and comprehensive three-part structure - features impressive roster of well-known contributors

This book developed from a course given by the author to undergraduate and postgraduate students. It takes up Matrix Theory, Antenna Theory, and Probability Theory in detail. The first chapter on matrix theory discusses in reasonable depth the theory of Lie Algebras leading upto Cartan's Classification Theory. It also discusses some basic elements of Functional Analysis and Operator Theory in infinite dimensional Banach and Hilbert spaces. The second chapter discusses Basic Probability Theory and the topics discussed find applications to Stochastic Filtering Theory for differential equations driven by white Gaussian noise. The third chapter is on Antenna Theory with a focus on Modern Quantum Antenna Theory. The book will be a valuable resource to students and early career researchers in the field of Mathametical Physics.

This is a collection of papers dedicated to Leonid Kantorovich and his work. Kantorovich was a Russian mathematician and economist who published in the three areas covered in this book: functional analysis, optimization, and mathematical economics. Kantorovich is credited as being amongst the first inventors of linear programming, the primary technique of optimization. Linear programming consists of creating a matrix of parameters relevant to a system and maximizing the unknown variables using those constraints. Kantorovich then applied this theory to optimal macroeconomic planning in a socialist economy, for which he received the Nobel prize. The present book is dedicated to the memory of Kantorovich, who died in 1986, but is more than a Festschrift. It contains original contributions from several researchers in the USSR never before seen in the US, which enhances the value of the volume. It is organized in a logical sequence from the mathematics to the applications of the theories to concrete problems.

This contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Algebraic Combinatorics, Hyperplane Arrangements, Homological Algebra, and String Theory. The book aims to showcase the area, especially for the benefit of junior mathematicians and researchers who are new to the field; it will aid them in broadening their background and to gain a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.

This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.

Bringing together trust research, rhetoric, ethnomethodology and conversation analysis, this book formulates an analytical program for conceptualizing and defining trustworthiness as an empirical research object in social interaction. Revisiting Trustworthiness in Social Interaction examines trustworthiness as a relational and dynamic concept. It reviews sociological and rhetorical approaches to the study of trustworthiness and respecifies it as an interactional phenomenon displayed, tested and negotiated by participants in social interaction. It identifies four participant orientations of trustworthiness that may be foregrounded in peoples' dynamic identity projects, and it defines the phenomena 'character-bound displays' and 'sequential negotiation of character', both indicative of participants' orientation to trustworthiness. In this way, the book turns the theoretical concept of trustworthiness into an empirical object of interaction analysis, pointing to a vast number of interactional indicators, which allow interaction analysts to explore if and how interactants orient to trustworthiness in an encounter. Exemplary cases from both mundane and institutional encounters are analyzed using ethnomethodological multimodal conversation analysis showing how trustworthiness is done, challenges, achived, negotiated and lost in interaction. The intended audiences are scholars of conversation analysis, ethnomethodology, rhetoric and the social sciences, especially communication, organizational and leadership studies, and their students.

The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.

This ground-breaking volume presents a unique contribution to the development of social and political psychology both in Turkey and globally, providing a complex analysis of intergroup relations in the diverse Turkish context. Turkey is home to a huge variety of social, ethnic and religious groups and hosts the largest number of refugees in the world. This diversity creates a unique opportunity to understand how powerful forces of ethnicity, migration and political ideology shape intergroup processes and intergroup relations. Bringing together novel research findings, the international collection of authors explore everything from disability, age and gender, Kurdish and Armenian relations as "traditional minorities", the recent emergence of a "new minority" of Syrian refugees and Turkey's complex political history. The theories and paradigms considered in the book - social identity, intergroup contact, integrated threat, social representations - are leading approaches in social and political psychology, but the research presented tests these approaches in the context of a very diverse and dynamic non-WEIRD (Western, Educated, Industrialized, Rich and Democratic) society, with the goal of contributing toward the development of a more intercultural and democratic social and political psychology. Bringing together cutting-edge research and providing important insights into the psychological underpinnings of a singular societal situation from a variety of perspectives, this book is essential reading for students studying the psychology, politics and social science of intergroup relations, as well as practitioners interested in conflict resolution.

This ground-breaking volume presents a unique contribution to the development of social and political psychology both in Turkey and globally, providing a complex analysis of intergroup relations in the diverse Turkish context. Turkey is home to a huge variety of social, ethnic and religious groups and hosts the largest number of refugees in the world. This diversity creates a unique opportunity to understand how powerful forces of ethnicity, migration and political ideology shape intergroup processes and intergroup relations. Bringing together novel research findings, the international collection of authors explore everything from disability, age and gender, Kurdish and Armenian relations as "traditional minorities", the recent emergence of a "new minority" of Syrian refugees and Turkey's complex political history. The theories and paradigms considered in the book - social identity, intergroup contact, integrated threat, social representations - are leading approaches in social and political psychology, but the research presented tests these approaches in the context of a very diverse and dynamic non-WEIRD (Western, Educated, Industrialized, Rich and Democratic) society, with the goal of contributing toward the development of a more intercultural and democratic social and political psychology. Bringing together cutting-edge research and providing important insights into the psychological underpinnings of a singular societal situation from a variety of perspectives, this book is essential reading for students studying the psychology, politics and social science of intergroup relations, as well as practitioners interested in conflict resolution.

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.

New to the Fourth Edition Reorganised and revised chapter seven and thirteen New exercises and examples Expanded, updated references Further historical material on figures besides Galois: Omar Khayyam, Vandermonde, Ruffini, and Abel A new final chapter discussing other directions in which Galois Theory has developed: the inverse Galois problem, differential Galois theory, and a (very) brief introduction to p-adic Galois representations.

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 self-containedtext is an excellent introductionto Lie groups and their actions on manifolds. Theauthors start withan elementarydiscussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay between differential geometry and Lie theory. Special emphasis is placed on homogeneous spaces and invariant geometric structures. The last section of the book is dedicated to the structure theory of Lie groups. Particularly, they focus on maximal compact subgroups, dense subgroups, complex structures, and linearity.

This text is accessible to a broad range of mathematicians and graduate students; it will be useful both as a graduate textbook and as a research reference."

An encompassing socio-historical survey of the political and sociological nature of groups, communities and societies. A transdisciplinary study of crowds, masses and groups as historical, sociological, psychological and psychosocial phenomena. A unique combination of sociology, psychoanalysis and group analysis in the study of social formations. An inquiry into the enigma of crowds and mass psychology with the history of group analytic and group relations' advances in England, especially the study of large groups in the research on group processes. A comprehensive presentation of the social unconscious theory in association with the study of large groups and the Incohesion theory as new group analytic tools for understanding contemporary crowds and masses. In today's world, flooded by social conflicts and polarizations and the mass impact of social media, this book enables the reader to map out the field of the unconscious life of crowds illuminating the darkness of twenty-first century collective movements.

Working out solutions to polynomial equations is a mathematical problem that dates from antiquity. Galois developed a theory in which the obstacle to solving a polynomial equation is an associated collection of symmetries. Obtaining a root requires "breaking" that symmetry. When the degree of an equation is at least five, Galois Theory established that there is no formula for the solutions like those found in lower degree cases. However, this negative result doesn't mean that the practice of equation-solving ends. In a recent breakthrough, Doyle and McMullen devised a solution to the fifth-degree equation that uses geometry, algebra, and dynamics to exploit icosahedral symmetry. Polynomials, Dynamics, and Choice: The Price We Pay for Symmetry is organized in two parts, the first of which develops an account of polynomial symmetry that relies on considerations of algebra and geometry. The second explores beyond polynomials to spaces consisting of choices ranging from mundane decisions to evolutionary algorithms that search for optimal outcomes. The two algorithms in Part I provide frameworks that capture structural issues that can arise in deliberative settings. While decision-making has been approached in mathematical terms, the novelty here is in the use of equation-solving algorithms to illuminate such problems. Features Treats the topic-familiar to many-of solving polynomial equations in a way that's dramatically different from what they saw in school Accessible to a general audience with limited mathematical background Abundant diagrams and graphics.