This book deals with the characterization of extensions of number fields in terms of the decomposition of prime ideals, and with the group-theoretic questions arising from this number-theoretic problem. One special aspect of this question is the equality of Dedekind zeta functions of different number fields. This is an established problem which was solved for abelian extensions by class field theory, but which was only studied in detail in its general form from around 1970. The basis for the new results was a fruitful exchange between number theory and group theory. Some of the outstanidng results are based on the complete classification of all finite simple groups. This book reports on the great progress achieved in this period. It allows access to the new developments in this part of algebraic number theory and contains a unique blend of number theory and group theory. The results appear for the first time in a monograph and they partially extend the published literature.

In this complete introduction to the theory of finding derivatives of scalar-, vector- and matrix-valued functions with respect to complex matrix variables, Hjorungnes describes an essential set of mathematical tools for solving research problems where unknown parameters are contained in complex-valued matrices. The first book examining complex-valued matrix derivatives from an engineering perspective, it uses numerous practical examples from signal processing and communications to demonstrate how these tools can be used to analyze and optimize the performance of engineering systems. Covering un-patterned and certain patterned matrices, this self-contained and easy-to-follow reference deals with applications in a range of areas including wireless communications, control theory, adaptive filtering, resource management and digital signal processing. Over 80 end-of-chapter exercises are provided, with a complete solutions manual available online.

Linear algebra and matrix theory are among the most important and most frequently applied branches of mathematics. They are especially important in solving engineering and economic models, where either the model is assumed linear, or the nonlinear model is approximated by a linear model, and the resulting linear model is examined.This book is mainly a textbook, that covers a one semester upper division course or a two semester lower division course on the subject.The second edition will be an extended and modernized version of the first edition. We added some new theoretical topics and some new applications from fields other than economics. We also added more difficult exercises at the end of each chapter which require deep understanding of the theoretical issues. We also modernized some proofs in the theoretical discussions which give better overview of the study material. In preparing the manuscript we also corrected the typos and errors, so the second edition will be a corrected, extended and modernized new version of the first edition.

Psychology of Behavioural Interventions and Pandemic Control is a unique text that examines the COVID-19 pandemic in relation to population risk factors and the efficacy of non-pharmaceutical interventions deployed by many governments around the world to bring the pandemic under control. The book presents critical and insightful lessons that can be drawn up to assess governments' performance in relation to the pandemic and to guide the construction of effective measures to put in place in readiness for any future public health crises on this scale. It starts by examining lessons learned from historical pandemics and then turns to early epidemiological modelling that influenced the decision of many governments to implement wide-ranging interventions designed to bring public behaviour under close control. It also examines the findings of research that tried to understand pre-existing population risks factors which had some mediating influences over COVID-19, mortality rates, and the effects of interventions. Early modelling work is critiqued, and the discussion also identifies weaknesses in early modelling research. The author, Barrie Gunter, goes on to consider ways in which multiple disciplines can be triangulated to produce more comprehensive models of risk. He also offers suggestions on how future pandemic-related research might be constructed to deliver more powerful analyses of the effects of interventions and the role played by different population risk factors. This insight might then deliver better policies for pandemic control and for safe release from that control. This is essential reading for students and researchers in psychology, public health and medical sciences. It would also be of interest to policy makers assessing government strategies, responses and performance.

Psychology of Behavioural Interventions and Pandemic Control is a unique text that examines the COVID-19 pandemic in relation to population risk factors and the efficacy of non-pharmaceutical interventions deployed by many governments around the world to bring the pandemic under control. The book presents critical and insightful lessons that can be drawn up to assess governments' performance in relation to the pandemic and to guide the construction of effective measures to put in place in readiness for any future public health crises on this scale. It starts by examining lessons learned from historical pandemics and then turns to early epidemiological modelling that influenced the decision of many governments to implement wide-ranging interventions designed to bring public behaviour under close control. It also examines the findings of research that tried to understand pre-existing population risks factors which had some mediating influences over COVID-19, mortality rates, and the effects of interventions. Early modelling work is critiqued, and the discussion also identifies weaknesses in early modelling research. The author, Barrie Gunter, goes on to consider ways in which multiple disciplines can be triangulated to produce more comprehensive models of risk. He also offers suggestions on how future pandemic-related research might be constructed to deliver more powerful analyses of the effects of interventions and the role played by different population risk factors. This insight might then deliver better policies for pandemic control and for safe release from that control. This is essential reading for students and researchers in psychology, public health and medical sciences. It would also be of interest to policy makers assessing government strategies, responses and performance.

This book studies algebraic representations of graphs in order to investigate combinatorial structures via local symmetries. Topological, combinatorial and algebraic classifications are distinguished by invariants of polynomial type and algorithms are designed to determine all such classifications with complexity analysis. Being a summary of the author's original work on graph embeddings, this book is an essential reference for researchers in graph theory. Contents Abstract Graphs Abstract Maps Duality Orientability Orientable Maps Nonorientable Maps Isomorphisms of Maps Asymmetrization Asymmetrized Petal Bundles Asymmetrized Maps Maps within Symmetry Genus Polynomials Census with Partitions Equations with Partitions Upper Maps of a Graph Genera of a Graph Isogemial Graphs Surface Embeddability

The problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p > 0 is a long standing one. Work on this question has been directed by the Kostrikin Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p > 5 a finite dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p > 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p > 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every simple finite dimensional simple Lie algebra over an algebraically closed field of characteristic p > 3 is of classical, Cartan, or Melikian type. This is the second part of a three-volume book about the classification of the simple Lie algebras over algebraically closed fields of characteristic > 3. The first volume contains the methods, examples and a first classification result. This second volume presents insight in the structure of tori of Hamiltonian and Melikian algebras. Based on sandwich element methods due to A. I. Kostrikin and A. A. Premet and the investigations of filtered and graded Lie algebras, a complete proof for the classification of absolute toral rank 2 simple Lie algebras over algebraically closed fields of characteristic > 3 is given. Contents Tori in Hamiltonian and Melikian algebras 1-sections Sandwich elements and rigid tori Towards graded algebras The toral rank 2 case

This volume contains three invited lectures and sixteen other papers which were pre- sented at the 14th International Conference on Nearrings and Nearfields held in Stellen- bosch, South Africa, July 9-161997. It was also the first nearring conference to be held after the untimely death of James R Clay, who over the years had been an inspiration to many algebraists interested in nearring theory. The occasion was marked by the invitedtalk of Gerhard Betsch, which was devoted to an overview of Clay's contributions to nearring and nearfield theory. This book is affectionately dedicated to the memory of James R Clay. All the papers presented here have been refereed under the supervision of the Editorial Board: Fong Yuen, Carl Maxson, John Meldrum, GUnterPilz, Leon van Wyk and Andries van der Walt. Thanks are due to the referees and to the Editorial Board. A special word of thanks is due to Wen-fong Ke for preparing the final version of the TEX files, and to Fong Yuen for his pains in arranging for the publication of the volume with Kluwer Academic Publishers. Andries van der Walt Stellenbosch, August 1999 COMBINATORIAL ASPECTS OF NEARRING THEORY TO THE MEMORY OF JAMES RAY CLAY GERHARDBETSCH A briefcurriculum vitae ofJames Ray (Jim) Clay Born November5,1938 at Burley (Idaho). Died January 16, 1996 at Tucson (Arizona). Married since 1959 to Carol Cline BURGE, "a truly beautiful daughter of Zion" (Dedication ofJim's 1992 book). Three daughters, ten grand-children.

This book constitutes an elementary introduction to rings and fields, in particular Galois rings and Galois fields, with regard to their application to the theory of quantum information, a field at the crossroads of quantum physics, discrete mathematics and informatics. The existing literature on rings and fields is primarily mathematical. There are a great number of excellent books on the theory of rings and fields written by and for mathematicians, but these can be difficult for physicists and chemists to access. This book offers an introduction to rings and fields with numerous examples. It contains an application to the construction of mutually unbiased bases of pivotal importance in quantum information. It is intended for graduate and undergraduate students and researchers in physics, mathematical physics and quantum chemistry (especially in the domains of advanced quantum mechanics, quantum optics, quantum information theory, classical and quantum computing, and computer engineering). Although the book is not written for mathematicians, given the large number of examples discussed, it may also be of interest to undergraduate students in mathematics.

This book takes a deep dive into several key linear algebra subjects as they apply to data analytics and data mining. The book offers a case study approach where each case will be grounded in a real-world application. This text is meant to be used for a second course in applications of Linear Algebra to Data Analytics, with a supplemental chapter on Decision Trees and their applications in regression analysis. The text can be considered in two different but overlapping general data analytics categories, clustering and interpolation. Knowledge of mathematical techniques related to data analytics, and exposure to interpretation of results within a data analytics context, are particularly valuable for students studying undergraduate mathematics. Each chapter of this text takes the reader through several relevant and case studies using real world data. All data sets, as well as Python and R syntax are provided to the reader through links to Github documentation. Following each chapter is a short exercise set in which students are encouraged to use technology to apply their expanding knowledge of linear algebra as it is applied to data analytics. A basic knowledge of the concepts in a first Linear Algebra course are assumed; however, an overview of key concepts are presented in the Introduction and as needed throughout the text.

Edward Conze's The Psychology of Mass Propaganda presents a commentary on the psychology of propaganda and the rise of fascism in Europe in the 1930s. Completed in 1939, during the period of Conze's own inflection from Marxist philosophy to Buddhist studies, the original manuscript was never published and is now in print for the first time. Presenting a unique historical perspective, while also appealing to an acutely topical interest in the conditions under which autocracy and fascism arise, the book examines the psychology of mass propaganda through copious contemporary and historical examples. Conze focuses especially on recent news articles and the statements of the propagandists of many of the governments that would go on to participate in the Second World War, including Germany, Italy, the USSR, USA and UK, all of which he interprets through the lens of recent psychological and historical research. The book has been edited and includes a new introduction by Richard N. Levine and Nathan H. Levine, also featuring a foreword by American legal scholar Laurence H. Tribe, and an afterword by actor, director, writer, and Buddhist priest Peter Coyote. This is a fascinating opportunity for scholars across several disciplines, including political scientists and psychologists, historians and sociologists, to access one of Conze's previously unpublished works. It will also be of importance to those interested in Conze's work on Buddhist philosophy, and in the psychology of propaganda more broadly.

With applications in quantum field theory, general relativity and elementary particle physics, this four-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This third volume covers supersymmetry, including detailed coverage of conformal supersymmetry in four and some higher dimensions, furthermore quantum superalgebras are also considered. Contents Lie superalgebras Conformal supersymmetry in 4D Examples of conformal supersymmetry for D > 4 Quantum superalgebras

Shows readers how empathy facilitates better communication. Author has years of teaching and consulting experience that has refined his approach to the subject.

Shows readers how empathy facilitates better communication. Author has years of teaching and consulting experience that has refined his approach to the subject.

Optimal feedback control arises in different areas such as aerospace engineering, chemical processing, resource economics, etc. In this context, the application of dynamic programming techniques leads to the solution of fully nonlinear Hamilton-Jacobi-Bellman equations. This book presents the state of the art in the numerical approximation of Hamilton-Jacobi-Bellman equations, including post-processing of Galerkin methods, high-order methods, boundary treatment in semi-Lagrangian schemes, reduced basis methods, comparison principles for viscosity solutions, max-plus methods, and the numerical approximation of Monge-Ampere equations. This book also features applications in the simulation of adaptive controllers and the control of nonlinear delay differential equations. Contents From a monotone probabilistic scheme to a probabilistic max-plus algorithm for solving Hamilton-Jacobi-Bellman equations Improving policies for Hamilton-Jacobi-Bellman equations by postprocessing Viability approach to simulation of an adaptive controller Galerkin approximations for the optimal control of nonlinear delay differential equations Efficient higher order time discretization schemes for Hamilton-Jacobi-Bellman equations based on diagonally implicit symplectic Runge-Kutta methods Numerical solution of the simple Monge-Ampere equation with nonconvex Dirichlet data on nonconvex domains On the notion of boundary conditions in comparison principles for viscosity solutions Boundary mesh refinement for semi-Lagrangian schemes A reduced basis method for the Hamilton-Jacobi-Bellman equation within the European Union Emission Trading Scheme

This textbook gives a detailed and comprehensive presentation of linear algebra based on an axiomatic treatment of linear spaces. For this fourth edition some new material has been added to the text, for instance, the intrinsic treatment of the classical adjoint of a linear transformation in Chapter IV, as well as the discussion of quaternions and the classifica tion of associative division algebras in Chapter VII. Chapters XII and XIII have been substantially rewritten for the sake of clarity, but the contents remain basically the same as before. Finally, a number of problems covering new topics-e.g. complex structures, Caylay numbers and symplectic spaces - have been added. I should like to thank Mr. M. L. Johnson who made many useful suggestions for the problems in the third edition. I am also grateful to my colleague S. Halperin who assisted in the revision of Chapters XII and XIII and to Mr. F. Gomez who helped to prepare the subject index. Finally, I have to express my deep gratitude to my colleague J. R. Van stone who worked closely with me in the preparation of all the revisions and additions and who generously helped with the proof reading."

Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest.
In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc.
The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published.
A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed.
- Thorough and practical source for information
- Provides in-depth coverage of new topics in algebra
- Includes references to relevant articles, books and lecture notes

This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads of commutative algebra, algebraic geometry, representation theory, and combinatorics. Therefore, this text uniquely presents an exciting playing field for graduate students and researchers in mathematics, physics, and computer science, to expand their knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for the Grassmannian varieties and their Schubert subvarieties are introduced and the text presents some important applications of SMT including the Cohen-Macaulay property, normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. This text would serve well as a reference book for a graduate work on Grassmannian varieties and would be an excellent supplementary text for several courses including those in geometry of spherical varieties, Schubert varieties, advanced topics in geometric and differential topology, representation theory of compact and reductive groups, Lie theory, toric varieties, geometric representation theory, and singularity theory. The reader should have some familiarity with commutative algebra and algebraic geometry.

Vamik Volkan examines the impact of past and present historical events, cultural elements, political movements and their mental images on the psyche of individuals. Beginning with the history of the debates concerning the relevance of external events to the human psyche, Volkan moves on to look at the spread of psychoanalysis worldwide and the need to become familiar with the cultural, historical, and political issues when working abroad. The remaining chapters follow the story of a successful businessman who calls himself a 'Muslim Armenian'. His psychological journey clearly illustrates how ghosts from the past can remain alive and active in our lives, and how a clear understanding of his people's history and culture allowed the analyst to understand some important causes of his symptoms and personality characteristics. By presenting a total case report, Volkan illustrates the methods applied to improve the analysand's psychological health. By presenting a case from the viewpoint of a psychoanalytic supervisor, including the supervisor's reactions to the individual being analysed, he has exposed another rich topic to consideration. With this book, Vamik Volkan has given us much to reflect upon.

Brings needed focus diversity and inclusion to the discipline of family communication. Suitable for advanced courses in family communication and family studies.

For courses in Differential Equations and Linear Algebra. The right balance between concepts, visualisation, applications, and skills Differential Equations and Linear Algebra provides the conceptual development and geometric visualisation of a modern differential equations and linear algebra course that is essential to science and engineering students. It balances traditional manual methods with the new, computer-based methods that illuminate qualitative phenomena - a comprehensive approach that makes accessible a wider range of more realistic applications. The book combines core topics in elementary differential equations with concepts and methods of elementary linear algebra. It starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout.

Brings needed focus diversity and inclusion to the discipline of family communication. Suitable for advanced courses in family communication and family studies.

This book examines the phenomenon of silence in relation to human behaviour from multiple perspectives, drawing on psychological and cultural-philosophical ideas to create new, surprising connections between silence, quiet and rest. Silence and being quiet are present in everyday life and in politics, but why do we talk about it so rarely? Silence can be cathartic and peaceful, but equally oppressive and unbearable. In the form of communication, we keep secrets to protect ourselves and others, but on the other hand subjects can be silenced with dictatorial posturing - a communicative display of power - and something can be literally 'hushed up' that needs to be disclosed. In unique and engaging style, Theodor Itten explores the multi-layered internal conversation on silence in relation to the self and emotions, demonstrating why it is sometimes necessary in our modern society. Describing and analyzing human behaviour in relation to silence, the book also draws on psychoanalytic ideas by outlining the power of silence in processing our emotions and relationships and hiding innermost feelings. With rich narrative signposts providing thought-provoking and amusing insights, and interpersonal communication examined in relation to everyday life, this is fascinating reading for students and academics in psychology, philosophy, cultural studies, and related areas.

The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In this monograph, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science.