A thorough introduction to group theory, this (highly problem-oriented) book goes deeply into the subject to provide a fuller understanding than available anywhere else. The book aims at, not only teaching the material, but also helping to develop the skills needed by a researcher and teacher, possession of which will be highly advantageous in these very competitive times, particularly for those at the early, insecure, stages of their careers. And it is organized and written to serve as a reference to provide a quick introduction giving the essence and vocabulary useful for those who need only some slight knowledge, those just learning, as well as researchers, and especially for the latter it provides a grasp, and often material and perspective, not otherwise available.
The conformal group is the invariance group of geometry (which is not understood), the largest one. Physical applications are implied, as discussed, including reasons for interactions. The group structure as well as those of related groups are analyzed. An inhomogeneous group is a subgroup of a homogeneous one because of nonlinearities of the realization. Conservation of baryons (protons can't decay) is explained and proven. Reasons for various realizations, so matrix elements, of the Lorentz group given. The clearly relevant mass level formula is compared with experimental values. Questions, implications and possibilities, including for differential equations, are raised.
WHY GOD COULD NOT CREATE THE UNIVERSE WITH A DIFFERENT DIMENSION EVEN IF IT WANTED TO or perhaps anything else. Perhaps the universe must be the way it is. It seems that what is omnipotent is mathematics, elementary arithmetic, just counting. Yet even mathematics is not powerful enough to create a universe¿there are just too many conditions, conflicting. Existence is impossible. Beyond that for there to be structure is quite inconceivable. But the universe does exist, there are galaxies, stars, even the possibility of life. That life is possible merely allows it to exist but only with the greatest good fortune does it actually occur. Intelligence is vastly less likely, ability and technology far more improbable. That we are, what we are, seem so strange, inconceivable, that we are left merely with wonder¿and, as we seem unable to realize, the need for the deepest care, responsibility and gratitude. We have been given by the unbelievable benevolence of chance, no life, but life with the most wondrous part of the universe, the ability to think, to know, to create, to wonder¿and thus the demand that we use our most awesome gifts to protect them, to protect and preserve the world in which they exist, and the life, likely so rare if not unique in the universe, which has received these astounding favors of chance, that has been given by nature its most exalted constituents. What we are requires that we enhance what we are, what we are part of, to see, understand and be grateful. An exploration of the precise conditions required for the existence of humans in the universe. ...the author does an admirable job delineating the laws of physics without becoming too bogged down in complicated jargon, and he maintains a sense of wonder about the unique and random nature of the universe. He repeatedly celebrates our highly improbable achievements as a species, marveling at our ability to use the language of abstract mathematics to unravel the mysteries of existence. ... the prevailing tone of the narrative is clear and confident, marked by a meticulous attention to detail. An...often fascinating journey through the history of the universe and mankind. -Kirkus Discoveries
Preface 1 The Physical Meaning of Poincare Massless Representations 1 2 Massless Representations 12 3 Massless Fields are Different 32 4 How to Couple Massless and Massive Matter 56 5 The Behavior of Matter in Fields 73 6 Geometrical Reasons for the Poincare Group 95 7 Description of the Electromagnetic Field 123 8 The Equations Governing Free Gravitation 135 9 How Matter Determines Gravitational Fields 150 10 Nonlinearity and Geometry 165 11 Quantum Gravity 183 References 201 Index 207.
This book is by far the most comprehensive treatment of point and space groups, and their meaning and applications. Its completeness makes it especially useful as a text, since it gives the instructor the flexibility to best fit the class and goals. The instructor, not the author, decides what is in the course. And it is the prime book for reference, as material is much more likely to be found in it than in any other book; it also provides detailed guides to other sources.Much of what is taught is folklore, things everyone knows are true, but (almost?) no one knows why, or has seen proofs, justifications, rationales or explanations. (Why are there 14 Bravais lattices, and why these? Are the reasons geometrical, conventional or both? What determines the Wigner-Seitz cells? How do they affect the number of Bravais lattices? Why are symmetry groups relevant to molecules whose vibrations make them unsymmetrical? And so on). Here these analyses are given, interrelated, and in-depth. The understanding so obtained gives a strong foundation for application and extension. Assumptions and restrictions are not merely made explicit, but also emphasized.In order to provide so much information, details and examples, and ways of helping readers learn and understand, the book contains many topics found nowhere else, or only in obscure articles from the distant past. The treatment is (often completely) different from those elsewhere. At least in the explanations, and usually in many other ways, the book is completely new and fresh. It is designed to inform, educate and make the reader think. It strongly emphasizes understanding.The book can be used at many levels, by many different classes of readers ? from those who merely want brief explanations (perhaps just of terminology), who just want to skim, to those who wish the most thorough understanding.
Table of Contents Preface 1 Foundations 1 2 Why Geometry, so Physics, Require Complex Numbers 25 3 Properties of Statefunctions 38 4 The Foundations of Coherent Superposition 58 5 Geometry, Transformations, Groups and Observers 85 6 The Poincare Group and Its Implications 108 7 The Dimension of Space 122 8 Bosons, Fermions, Spinors and Orthogonal Groups 146 9 The Complete Reasonableness of Quantum Mechanics 159 A: Terminology and Conventions 177 The Einstein Podolsky Rosen Paradox 185 Experimental Meaning of the Concept of Identical Particles 191 Nonexistence of Superselection Rules; Definition of Term "Frame of Reference" 203 Complex Groups, Quantum Mechanics, and the Dimension and Reality of Space 221 The Reality and Dimension of Space and the Complexity of Quantum Mechanics 235 References 255 Index 259.
Table of Contents Preface 1 Foundations 1 2 Why Geometry, so Physics, Require Complex Numbers 25 3 Properties of Statefunctions 38 4 The Foundations of Coherent Superposition 58 5 Geometry, Transformations, Groups and Observers 85 6 The Poincare Group and Its Implications 108 7 The Dimension of Space 122 8 Bosons, Fermions, Spinors and Orthogonal Groups 146 9 The Complete Reasonableness of Quantum Mechanics 159 A: Terminology and Conventions 177 The Einstein Podolsky Rosen Paradox 185 Experimental Meaning of the Concept of Identical Particles 191 Nonexistence of Superselection Rules; Definition of Term "Frame of Reference" 203 Complex Groups, Quantum Mechanics, and the Dimension and Reality of Space 221 The Reality and Dimension of Space and the Complexity of Quantum Mechanics 235 References 255 Index 259.
The conformal group is the invariance group of geometry (which is not understood), the largest one. Physical applications are implied, as discussed, including reasons for interactions. The group structure as well as those of related groups are analyzed. An inhomogeneous group is a subgroup of a homogeneous one because of nonlinearities of the realization. Conservation of baryons (protons can't decay) is explained and proven. Reasons for various realizations, so matrix elements, of the Lorentz group given. The clearly relevant mass level formula is compared with experimental values. Questions, implications and possibilities, including for differential equations, are raised.
A thorough introduction to group theory, this (highly problem-oriented) book goes deeply into the subject to provide a fuller understanding than available anywhere else. The book aims at, not only teaching the material, but also helping to develop the skills needed by a researcher and teacher, possession of which will be highly advantageous in these very competitive times, particularly for those at the early, insecure, stages of their careers. And it is organized and written to serve as a reference to provide a quick introduction giving the essence and vocabulary useful for those who need only some slight knowledge, those just learning, as well as researchers, and especially for the latter it provides a grasp, and often material and perspective, not otherwise available.
This book introduces optimal control problems for large families of deterministic and stochastic systems with discrete or continuous time parameter. These families include most of the systems studied in many disciplines, including Economics, Engineering, Operations Research, and Management Science, among many others. The main objective is to give a concise, systematic, and reasonably self contained presentation of some key topics in optimal control theory. To this end, most of the analyses are based on the dynamic programming (DP) technique. This technique is applicable to almost all control problems that appear in theory and applications. They include, for instance, finite and infinite horizon control problems in which the underlying dynamic system follows either a deterministic or stochastic difference or differential equation. In the infinite horizon case, it also uses DP to study undiscounted problems, such as the ergodic or long-run average cost. After a general introduction to control problems, the book covers the topic dividing into four parts with different dynamical systems: control of discrete-time deterministic systems, discrete-time stochastic systems, ordinary differential equations, and finally a general continuous-time MCP with applications for stochastic differential equations. The first and second part should be accessible to undergraduate students with some knowledge of elementary calculus, linear algebra, and some concepts from probability theory (random variables, expectations, and so forth). Whereas the third and fourth part would be appropriate for advanced undergraduates or graduate students who have a working knowledge of mathematical analysis (derivatives, integrals, ...) and stochastic processes.
This book is by far the most comprehensive treatment of point and space groups, and their meaning and applications. Its completeness makes it especially useful as a text, since it gives the instructor the flexibility to best fit the class and goals. The instructor, not the author, decides what is in the course. And it is the prime book for reference, as material is much more likely to be found in it than in any other book; it also provides detailed guides to other sources.Much of what is taught is folklore, things everyone knows are true, but (almost?) no one knows why, or has seen proofs, justifications, rationales or explanations. (Why are there 14 Bravais lattices, and why these? Are the reasons geometrical, conventional or both? What determines the Wigner-Seitz cells? How do they affect the number of Bravais lattices? Why are symmetry groups relevant to molecules whose vibrations make them unsymmetrical? And so on). Here these analyses are given, interrelated, and in-depth. The understanding so obtained gives a strong foundation for application and extension. Assumptions and restrictions are not merely made explicit, but also emphasized.In order to provide so much information, details and examples, and ways of helping readers learn and understand, the book contains many topics found nowhere else, or only in obscure articles from the distant past. The treatment is (often completely) different from those elsewhere. At least in the explanations, and usually in many other ways, the book is completely new and fresh. It is designed to inform, educate and make the reader think. It strongly emphasizes understanding.The book can be used at many levels, by many different classes of readers ? from those who merely want brief explanations (perhaps just of terminology), who just want to skim, to those who wish the most thorough understanding.
This collection of articles is edited by Hal Varian, Dean of the School of Information Management and Systems, University of California, Berkeley. It provides a high quality and practical selection of contributed articles that impart the expertise of an international contingent of Mathematica users from the economic, financial, investments, quantitative business and operations research communities.
Deficit thinking is a pseudoscience founded on racial and class bias. It "blames the victim" for school failure instead of examining how schools are structured to prevent poor students and students of color from learning. Dismantling Contemporary Deficit Thinking provides comprehensive critiques and anti-deficit thinking alternatives to this oppressive theory by framing the linkages between prevailing theoretical perspectives and contemporary practices within the complex historical development of deficit thinking. Dismantling Contemporary Deficit Thinking examines the ongoing social construction of deficit thinking in three aspects of current discourse – the genetic pathology model, the culture of poverty model, and the "at-risk" model in which poor students, students of color, and their families are pathologized and marginalized. Richard R. Valencia challenges these three contemporary components of the deficit thinking theory by providing incisive critiques and discussing competing explanations for the pervasive school failure of many students in the nation’s public schools. Valencia also discusses a number of proactive, anti-deficit thinking suggestions from the fields of teacher education, educational leadership, and educational ethnography that are intended to provide a more equitable and democratic schooling for all students.
Why is it so difficult to design and implement fundamental educational reform in large city schools in spite of broad popular support for change? How does the politics of race complicate the challenge of building and sustaining coalitions for improving urban schools? These questions have provoked a great deal of theorizing, but this is the first book to explore the issues on the basis of extensive, solid evidence. Here a group of political scientists examines education reform in Atlanta, Baltimore, Detroit, and Washington, D.C., where local governmental authority has passed from white to black leaders. The authors show that black administrative control of big-city school systems has not translated into broad improvements in the quality of public education within black-led cities. Race can be crucial, however, in fostering the broad civic involvement perhaps most needed for school reform. In each city examined, reform efforts often arise but collapse, partly because leaders are unable to craft effective political coalitions that would commit community resources to a concrete policy agenda. What undermines the leadership, according to the authors, is the complex role of race in each city. First, public authority does not guarantee access to private resources, usually still controlled by white economic elites. Second, local authorities must interact with external actors, at the state and national levels, who remain predominantly white. Finally, issues of race divide the African American community itself and often place limits on what leaders can and cannot do. Filled with insightful explanations together with recommendations for policy change, this book is an important component of the debate now being waged among researchers, education activists, and the community as a whole.
An Invitation to Representation Theory offers an introduction to groups and their representations, suitable for undergraduates. In this book, the ubiquitous symmetric group and its natural action on polynomials are used as a gateway to representation theory. The subject of representation theory is one of the most connected in mathematics, with applications to group theory, geometry, number theory and combinatorics, as well as physics and chemistry. It can however be daunting for beginners and inaccessible to undergraduates. The symmetric group and its natural action on polynomial spaces provide a rich yet accessible model to study, serving as a prototype for other groups and their representations. This book uses this key example to motivate the subject, developing the notions of groups and group representations concurrently. With prerequisites limited to a solid grounding in linear algebra, this book can serve as a first introduction to representation theory at the undergraduate level, for instance in a topics class or a reading course. A substantial amount of content is presented in over 250 exercises with complete solutions, making it well-suited for guided study.
James Tobin, 1981 Nobel laureate in economics, was the outstanding monetary economist among American Keynesian economists. This book, the first written about James Tobin, examines his leading role as a Keynesian macroeconomist and monetary economist, and considers the continuing relevance of his ideas.
Incredible Consequences of Brain Injury: The Ways your Brain can Break explains the acquired brain disorders that can suddenly change a person’s life. Underlining the intricate workings of the human brain and the amazing things it does every day, this book examines what happens when the brain stops functioning as it should. Through the use of case studies and historical examples, this concentrated collection of different neuropsychological conditions provides the reader a glimpse into the lived experiences of each disorder. Each chapter is firmly rooted in relevant neuropsychological literature combined with easy-to-understand explanations and guided reflection. In its essence, this book is a celebration of the human brain and the myriad factors that make it up, serving to maintain hope in recovering from brain conditions, and to marvel at the intricate workings of the brain. This valuable compendium is essential for anyone who wants to learn more about how the brain functions and dysfunctions and will be equally useful for students, instructors, and healthcare workers. It will further be of use to individuals with brain conditions and their dear ones and for the individuals who are interested in learning more about the human brain.
Originally published in 1984, Douglas A. Bohi and Michael A. Toman have produced a convenient reference source about disparate elements in the theory of nonrenewable resource supply and about general issues that arise when applying dynamic economic analysis. The authors emphasise the inherently dynamic nature of resource supply decisions, the effects of resource depletion on costs and behaviour, and the influence of uncertainty about costs, prices, and reserves. This title will be useful to students interested in environmental studies and economics, practitioners, and others who need to know more about complex interactions of economic forces and the resource base.
Special purpose jurisdictions, such as school districts, water districts, and transit authorities, constitute the most common form of local government in the United States today. This book offers the first political theory of special purpose jurisdictions and provides extensive empirical analyses of the politics and finances of these often overlooked but increasingly influential governments.
The Mechanics of Solder Alloy Interconnects is a resource to be used in developing a solder joint reliability assessment. Each chapter is written to be used as a stand-alone resource for a particular aspect of materials and modeling issues. With this gained understanding, the reader in search of a solution to a solder joint reliability problem knows where in the materials and modeling communities to go for the appropriate answer.
Written by clinicians, for clinicians, Cardiovascular Medicine and Surgery offers a comprehensive, authoritative, and multidisciplinary approach to this rapidly evolving field. Covering every area relevant to the daily practice of cardiovascular medicine, this new and innovative reference text, led by Drs. Debabrata Mukherjee and Richard A. Lange, brings together a stellar team of cardiovascular specialists from leading medical centers worldwide who focus on cutting-edge strategies for the clinical and surgical management of patients. Both medicine and surgery are highlighted in chapters along with follow-up care and changing technology to equip the clinician for optimal patient care. Highly structured and templated chapters cover pathogenesis, diagnosis, management, special considerations/limitations, follow-up care, and on-going and future research.
Written by Ved P. Gandhi, Liam P. Ebrill, George A. Mackenzie, Luis Mañas-Antón, Jitendra R. Modi, Somchai Richupan, Fernando Sanchez-Ugarte, and Parthasarathi Shome, this book contains 12 articles. It examines the relevance to developing countries of the tax policy recommendations of supply-side economists and attempts to delineate policy guidelines to ensure that fiscal management enhances rather than inhibits growth and efficiency in the wider economy.
Psychology in Action, 12e is a comprehensive introductory Psychology product that fosters active learning and provides a wealth of tools that empower students to master and make connections between the key concepts. Students will leave the classroom with a solid foundation in basic psychology that will serve them in their daily lives no matter what their chosen field of study and career path.
Thank you for visiting our website. Would you like to provide feedback on how we could improve your experience?
This site does not use any third party cookies with one exception — it uses cookies from Google to deliver its services and to analyze traffic.Learn More.