This monograph brings together my work in mathematical statistics as I have viewed it through the lens of Jordan algebras. Three technical domains are to be seen: applications to random quadratic forms (sums of squares), the investigation of algebraic simplifications of maxi mum likelihood estimation of patterned covariance matrices, and a more wide open mathematical exploration of the algebraic arena from which I have drawn the results used in the statistical problems just mentioned. Chapters 1, 2, and 4 present the statistical outcomes I have developed using the algebraic results that appear, for the most part, in Chapter 3. As a less daunting, yet quite efficient, point of entry into this material, one avoiding most of the abstract algebraic issues, the reader may use the first half of Chapter 4. Here I present a streamlined, but still fully rigorous, definition of a Jordan algebra (as it is used in that chapter) and its essential properties. These facts are then immediately applied to simplifying the M:-step of the EM algorithm for multivariate normal covariance matrix estimation, in the presence of linear constraints, and data missing completely at random. The results presented essentially resolve a practical statistical quest begun by Rubin and Szatrowski [1982], and continued, sometimes implicitly, by many others. After this, one could then return to Chapters 1 and 2 to see how I have attempted to generalize the work of Cochran, Rao, Mitra, and others, on important and useful properties of sums of squares.
Upon his retirement from active service as a Justice of the Supreme Court of Virginia in 2011, Justice Koontz had completed more than four decades of service to citizens of the Commonwealth of Virginia. In order to recognize that service and help preserve Justice Koontz's legacy as one of the outstanding jurists in Virginia and the United States, the Salem/Roanoke County Bar Association instituted this project to collect all of Justice Koontz's published opinions, both from his tenure as a Justice of the Supreme Court and as an inaugural member of the Court of Appeals of Virginia. The second volume to be produced by the Opinions Project includes opinions, concurrences and dissents authored by Justice Koontz during the majority of his second four-year term as Chief Judge of the Court of Appeals. This volume includes the opinions addressing the contempt citations brought against the United Mine Workers during the 1989-1990 Pittston Coal Strike.
Venezuela is located on the northern coast of South America, covering an area of approximately 916,445 square kilometers. The country is known for its vast oil reserves, tropical climate, diverse wildlife, and beautiful landscapes. The population of the country is estimated to be around 28.5 million people, with majority of the population living in the urban areas. The official language spoken in Venezuela is Spanish and the currency is Bolivar. Despite being rich in natural resources, Venezuela has been struggling with political and economic turmoil in recent years. The country has been plagued with hyperinflation, political unrest, and shortages of basic necessities such as food and medicine. The current president, Nicolas Maduro, has been accused of authoritarianism and human rights violations, leading to widespread protests and international criticism. The future of Venezuela remains uncertain as the country continues to grapple with a challenging economic and political situation.
Politics and the Environment has established itself as one of the most comprehensive textbooks in this area. This new edition has been completely revised and updated whilst retaining the features and the theory-to-practice focus which made the first two editions so successful. This text is designed to introduce students to the key concepts and issues which surround environmental problems and their political solutions. The authors investigate the people, movements and organisations that form and implement these policies, and explore the barriers which hinder successful introduction of international environmental politics. The 3rd edition has been expanded to include: The shift in focus in environmental politics from sustainable development to climate change governance An extensive discussion on climate change: including institutional, national and global responses in the aftermath of the Kyoto protocol An increased international focus with more case studies from the UK, Europe, Australia and North America More discussion of global environmental social movements: including the US environmental organisations, in particular the Green Party and the environmental justice groups This textbook is an invaluable and accessible resource for undergraduates studying environmental politics.
Linear algebra and matrix theory are essentially synonymous terms for an area of mathematics that has become one of the most useful and pervasive tools in a wide range of disciplines. It is also a subject of great mathematical beauty. In consequence of both of these facts, linear algebra has increasingly been brought into lower levels of the curriculum, either in conjunction with the calculus or separate from it but at the same level. A large and still growing number of textbooks has been written to satisfy this need, aimed at students at the junior, sophomore, or even freshman levels. Thus, most students now obtaining a bachelor's degree in the sciences or engineering have had some exposure to linear algebra. But rarely, even when solid courses are taken at the junior or senior levels, do these students have an adequate working knowledge of the subject to be useful in graduate work or in research and development activities in government and industry. In particular, most elementary courses stop at the point of canonical forms, so that while the student may have "seen" the Jordan and other canonical forms, there is usually little appreciation of their usefulness. And there is almost never time in the elementary courses to deal with more specialized topics like nonnegative matrices, inertia theorems, and so on. In consequence, many graduate courses in mathematics, applied mathe matics, or applications develop certain parts of matrix theory as needed.
The subject of one of the great advertising campaigns of the early 20th century, the "Somewhere West of Laramie" ads, Jordan is a well-remembered marque despite its brief duration. Edward Stanlaw "Ned" Jordan was born November 21, 1882, in Merrill, Wisconsin, and worked as a journalist before finding work in the automobile industry. A pioneer of automobile advertising and sales who got his start with Thomas B. Jeffery and Company in 1907, he founded the Jordan Motor Car Company with fellow Jeffery employees Russell S. Begg as experimental engineer and Paul Zens as purchasing agent in 1916. This book is both a biography of Ned Jordan and a history of his company and its vehicles from its beginning in 1916 to its end on April 1, 1932, when non-payment of franchise taxes forced its dissolution. Jordan's first models were four- and seven-passenger custom-type touring cars, but it would become famous for the Sport Marine, the Playboy, the Little Tomboy, and the Little Custom Jordan. Spectacularly illustrated.
Fundamental to the study of any mathematical structure is an understanding of its symmetries. In the class of Banach spaces, this leads naturally to a study of isometries-the linear transformations that preserve distances. In his foundational treatise, Banach showed that every linear isometry on the space of continuous functions on a compact metric
Mathematica by Example, Fifth Edition is an essential desk reference for the beginning Mathematica user, providing step-by-step instructions on achieving results from this powerful software tool. The book fully accounts for the dramatic changes to functionality and visualization capabilities in the most recent version of Mathematica (10.4). It accommodates the full array of new extensions in the types of data and problems that Mathematica can immediately handle, including cloud services and systems, geographic and geometric computation, dynamic visualization, interactive applications and other improvements. It is an ideal text for scientific students, researchers and aspiring programmers seeking further understanding of Mathematica. Written by seasoned practitioners with a view to practical implementation and problem-solving, the book's pedagogy is delivered clearly and without jargon using representative biological, physical and engineering problems. Code is provided on an ancillary website to support the use of Mathematica across diverse applications. - Provides a clear organization, integrated topic coverage, and accessible exposition for novices - Includes step-by-step instructions for the most popular implementations - Contains new applications, exercises and examples from a variety of fields, including biology, physics and engineering - Supported by a website providing Mathematica code derived from examples in the book
The theory of the Lebesgue integral is a main pillar in the foundation of modern analysis and its applications, including probability theory. This volume shows how and why the Lebesgue integral is such a universal and powerful concept. The lines of development of the theory are made clear by the order in which the main theorems are presented. Frequent references to earlier theorems made in the proofs emphasize the interdependence of the theorems and help to show how the various definitions and theorems fit together. Counterexamples are included to show why a hypothesis in a theorem cannot be dropped. The book is based upon a course on real analysis which the author has taught. It is particularly suitable for a one-year course at the graduate level. Precise statements and complete proofs are given for every theorem, with no obscurity left. For this reason the book is also suitable for self-study. Request Inspection Copy
This is the most thorough treatment of normal forms currently existing in book form. There is a substantial gap between elementary treatments in textbooks and advanced research papers on normal forms. This book develops all the necessary theory 'from scratch' in just the form that is needed for the application to normal forms, with as little unnecessary terminology as possible.
Thoroughly updated, featuring new material on important topics such as hyperbolic geometry in higher dimensions and generalizations of hyperbolicity Includes full solutions for all exercises Successful first edition sold over 800 copies in North America
This book presents a unified treatise of the theory of measure and integration. In the setting of a general measure space, every concept is defined precisely and every theorem is presented with a clear and complete proof with all the relevant details. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped. The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading but also to delineate the structure of the theory. The precision and clarity of presentation make the book an ideal textbook for a graduate course in real analysis while the wealth of topics treated also make the book a valuable reference work for mathematicians.The book is also very helpful to graduate students in statistics and electrical engineering, two disciplines that apply measure theory.
This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material. Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a year-long course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable.
This book presents to a lucid, theoretical vision of what a lean company should look like, as well as the organizing principles that are its reason for existence and the rational for the activities that go on inside it. It's among the first (if not the first) lean manufacturing guide to address all facets of your company from top management to customer service (and not to mention the assembly line). The Lean Company: Making the Right Choices is ideal for production management, industrial and manufacturing engineering students. The authors draw from the highly-respected Lean Aerospace Initiative (LAI) developed by MIT, which they had helped advance. It features a thorough treatment of 'the big picture,' a means to justify lean investments, and the operational strategies modern companies must employ as they compete in the modern world. It takes a broad look at change, the way employees respond to change, and some of the techniques managers can use to minimize change's adverse effects.
A continuation of the authors' previous book, Isometries on Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two covers much of the work that has been done on characterizing isometries on various Banach spaces. Picking up where the first volume left off, the book begins with a chapter on the Banach-Stone property.
These notes are based on lectures given at the University of Virginia over the past twenty years. They may be viewed as a course in function theory for nonspecialists. Chapters 1-6 give the function-theoretic background to Hardy Classes and Operator Theory, Oxford Mathematical Monographs, Oxford University Press, New York, 1985. These chapters were written first, and they were origi nally intended to be a part of that book. Half-plane function theory continues to be useful for applications and is a focal point in our account (Chapters 5 and 6). The theory of Hardy and Nevanlinna classes is derived from proper ties of harmonic majorants of subharmonic functions (Chapters 3 and 4). A selfcontained treatment of harmonic and subharmonic functions is included (Chapters 1 and 2). Chapters 7-9 present concepts from the theory of univalent functions and Loewner families leading to proofs of the Bieberbach, Robertson, and Milin conjectures. Their purpose is to make the work of de Branges accessible to students of operator theory. These chapters are by the second author. There is a high degree of independence in the chapters, allowing the material to be used in a variety of ways. For example, Chapters 5-6 can be studied alone by readers familiar with function theory on the unit disk. Chapters 7-9 have been used as the basis for a one-semester topics course.
A history of the settlement and development of the townships of Brushy Lake and Hickory Ridge and of the emergence of the town of Hickory ridge, all located within the state of Arkansas. The time span covered begins with the discovery of America and comes forth to about the year 2000. It includes such events as DeSoto's trek through the area, transfer of ownership via the Louisiana Purchase, regional exploration and surveying, territorial politics and gaining the status of statehood. Following the time of the Civil War, the narrative focuses more on the development of Cross County, the two townships of Brushy Lake and Hickory Ridge and, finally, on the town of hickory Ridge. A history of some of the region's schools, churches, and cemeteries is included as well as several maps, some as early as 1819, a full record of Cross County post offices, Peace Court Records from the early part of the 20th century, and many random photographs.
Research topics in the book include complex dynamics, minimal surfaces, fluid flows, harmonic, conformal, and polygonal mappings, and discrete complex analysis via circle packing. The nature of this book is different from many mathematics texts: the focus is on student-driven and technology-enhanced investigation. Interlaced in the reading for each chapter are examples, exercises, explorations, and projects, nearly all linked explicitly with computer applets for visualization and hands-on manipulation.
Maple by Example, Third Edition, is a reference/text for beginning and experienced students, professional engineers, and other Maple users. This new edition has been updated to be compatible with the most recent release of the Maple software. Coverage includes built-in Maple commands used in courses and practices that involve calculus, linear algebra, business mathematics, ordinary and partial differential equations, numerical methods, graphics and more. Updated coverage of Maple features and functions Backwards compatible for all versions New applications from a variety of fields, including biology, physics and engineering Expanded topics with many additional examples
This is one of the most important baseball books to be published in a long time, taking a comprehensive look at black participation in the national pastime from 1858 through 1900. It provides team rosters and team histories, player biographies, a list of umpires and games they officiated and information on team managers and team secretaries. Well known organizations like the Washington's Mutuals, Philadelphia Pythians, Chicago Uniques, St. Louis Black Stockings, Cuban Giants and Chicago Unions are documented, as well as lesser known teams like the Wilmington Mutuals, Newton Black Stockings, San Francisco Enterprise, Dallas Black Stockings, Galveston Flyaways, Louisville Brotherhoods and Helena Pastimes. Player biographies trace their connections between teams across the country. Essays frame the biographies, discussing the social and cultural events that shaped black baseball. Waiters and barbers formed the earliest organized clubs and developed local, regional and national circuits. Some players belonged to both white and colored clubs, and some umpires officiated colored, white and interracial matches. High schools nurtured young players and transformed them into powerhouse teams, like Cincinnati's Vigilant Base Ball Club. A special essay covers visual representations of black baseball and the artists who created them, including colored artists of color who were also baseballists.
This textbook is intended to introduce advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations.Topics covered include computer arithmetic, error analysis, solution of systems of linear equations, least squares problems, eigenvalue problems, nonlinear equations, optimization, polynomial interpolation and approximation, numerical differentiation and integration, ordinary differential equations, and partial differential equations. For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the Python programming language.This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra.
The study of matroids is a branch of discrete mathematics with basic links to graphs, lattices, codes, transversals, and projective geometries. Matroids are of fundamental importance in combinatorial optimization and their applications extend into electrical engineering and statics. This incisive survey of matroid theory falls into two parts: the first part provides a comprehensive introduction to the basics of matroid theory while the second treats more advanced topics. The book contains over five hundred exercises and includes, for the first time in one place, short proofs for most of the subjects' major theorems. The final chapter lists sixty unsolved problems and details progress towards their solutions.
An up-to-date version of the complete, self-contained introduction to matrix analysis theory and practice Providing accessible and in-depth coverage of the most common matrix methods now used in statistical applications, Matrix Analysis for Statistics, Third Edition features an easy-to-follow theorem/proof format. Featuring smooth transitions between topical coverage, the author carefully justifies the step-by-step process of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors; the Moore-Penrose inverse; matrix differentiation; and the distribution of quadratic forms. An ideal introduction to matrix analysis theory and practice, Matrix Analysis for Statistics, Third Edition features: • New chapter or section coverage on inequalities, oblique projections, and antieigenvalues and antieigenvectors • Additional problems and chapter-end practice exercises at the end of each chapter • Extensive examples that are familiar and easy to understand • Self-contained chapters for flexibility in topic choice • Applications of matrix methods in least squares regression and the analyses of mean vectors and covariance matrices Matrix Analysis for Statistics, Third Edition is an ideal textbook for upper-undergraduate and graduate-level courses on matrix methods, multivariate analysis, and linear models. The book is also an excellent reference for research professionals in applied statistics. James R. Schott, PhD, is Professor in the Department of Statistics at the University of Central Florida. He has published numerous journal articles in the area of multivariate analysis. Dr. Schott’s research interests include multivariate analysis, analysis of covariance and correlation matrices, and dimensionality reduction techniques.
With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. The book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.
Basic Analysis II: A Modern Calculus in Many Variables focuses on differentiation in Rn and important concepts about mappings from Rn to Rm, such as the inverse and implicit function theorem and change of variable formulae for multidimensional integration. These topics converge nicely with many other important applied and theoretical areas which are no longer covered in mathematical science curricula. Although it follows on from the preceding volume, this is a self-contained book, accessible to undergraduates with a minimal grounding in analysis. Features Can be used as a traditional textbook as well as for self-study Suitable for undergraduates in mathematics and associated disciplines Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
Jordan is a small country located in the Middle East, bordered by Saudi Arabia to the south and east, Iraq to the north-east, Syria to the north and Israel to the west. It has a population of around 10 million people, with the majority being Muslim. Jordan is known for its rich history and culture, with evidence of human habitation dating back to the Paleolithic era. Jordan has a diverse economy, with industries including agriculture, tourism, and mining. The capital city, Amman, is home to many international businesses and serves as a hub for the country's economy. Jordan is also home to several important historical sites, such as Petra, a city carved into rock and considered a UNESCO World Heritage Site, and the Dead Sea, known for its salt content and therapeutic properties. Despite its location in a region that has been marked by conflict, Jordan has been able to maintain stability and remains a popular destination for travelers.
This volume consists of the proofs of 391 problems in Real Analysis: Theory of Measure and Integration (3rd Edition).Most of the problems in Real Analysis are not mere applications of theorems proved in the book but rather extensions of the proven theorems or related theorems. Proving these problems tests the depth of understanding of the theorems in the main text.This volume will be especially helpful to those who read Real Analysis in self-study and have no easy access to an instructor or an advisor.
This will help us customize your experience to showcase the most relevant content to your age group
Please select from below
Login
Not registered?
Sign up
Already registered?
Success – Your message will goes here
We'd love to hear from you!
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.