Indefinites and the Type of Sets

A timely and comprehensive treatment of random field theory with applications across diverse areas of study Level Sets and Extrema of Random Processes and Fields discusses how to understand the properties of the level sets of paths as well as how to compute the probability distribution of its extremal values, which are two general classes of problems that arise in the study of random processes and fields and in related applications. This book provides a unified and accessible approach to these two topics and their relationship to classical theory and Gaussian processes and fields, and the most modern research findings are also discussed. The authors begin with an introduction to the basic concepts of stochastic processes, including a modern review of Gaussian fields and their classical inequalities. Subsequent chapters are devoted to Rice formulas, regularity properties, and recent results on the tails of the distribution of the maximum. Finally, applications of random fields to various areas of mathematics are provided, specifically to systems of random equations and condition numbers of random matrices. Throughout the book, applications are illustrated from various areas of study such as statistics, genomics, and oceanography while other results are relevant to econometrics, engineering, and mathematical physics. The presented material is reinforced by end-of-chapter exercises that range in varying degrees of difficulty. Most fundamental topics are addressed in the book, and an extensive, up-to-date bibliography directs readers to existing literature for further study. Level Sets and Extrema of Random Processes and Fields is an excellent book for courses on probability theory, spatial statistics, Gaussian fields, and probabilistic methods in real computation at the upper-undergraduate and graduate levels. It is also a valuable reference for professionals in mathematics and applied fields such as statistics, engineering, econometrics, mathematical physics, and biology.

A systematic and integrated approach to Cantor Sets and their applications to various branches of mathematics The Elements of Cantor Sets: With Applications features a thorough introduction to Cantor Sets and applies these sets as a bridge between real analysis, probability, topology, and algebra. The author fills a gap in the current literature by providing an introductory and integrated perspective, thereby preparing readers for further study and building a deeper understanding of analysis, topology, set theory, number theory, and algebra. The Elements of Cantor Sets provides coverage of: Basic definitions and background theorems as well as comprehensive mathematical details A biography of Georg Ferdinand Ludwig Philipp Cantor, one of the most significant mathematicians of the last century Chapter coverage of fractals and self-similar sets, sums of Cantor Sets, the role of Cantor Sets in creating pathological functions, p-adic numbers, and several generalizations of Cantor Sets A wide spectrum of topics from measure theory to the Monty Hall Problem An ideal text for courses in real analysis, topology, algebra, and set theory for undergraduate and graduate-level courses within mathematics, computer science, engineering, and physics departments, The Elements of Cantor Sets is also appropriate as a useful reference for researchers and secondary mathematics education majors.

A gentle introduction to the geometry of convex sets in n-dimensional space Geometry of Convex Sets begins with basic definitions of the concepts of vector addition and scalar multiplication and then defines the notion of convexity for subsets of n-dimensional space. Many properties of convex sets can be discovered using just the linear structure. However, for more interesting results, it is necessary to introduce the notion of distance in order to discuss open sets, closed sets, bounded sets, and compact sets. The book illustrates the interplay between these linear and topological concepts, which makes the notion of convexity so interesting. Thoroughly class-tested, the book discusses topology and convexity in the context of normed linear spaces, specifically with a norm topology on an n-dimensional space. Geometry of Convex Sets also features: An introduction to n-dimensional geometry including points; lines; vectors; distance; norms; inner products; orthogonality; convexity; hyperplanes; and linear functionals Coverage of n-dimensional norm topology including interior points and open sets; accumulation points and closed sets; boundary points and closed sets; compact subsets of n-dimensional space; completeness of n-dimensional space; sequences; equivalent norms; distance between sets; and support hyperplanes · Basic properties of convex sets; convex hulls; interior and closure of convex sets; closed convex hulls; accessibility lemma; regularity of convex sets; affine hulls; flats or affine subspaces; affine basis theorem; separation theorems; extreme points of convex sets; supporting hyperplanes and extreme points; existence of extreme points; Krein–Milman theorem; polyhedral sets and polytopes; and Birkhoff’s theorem on doubly stochastic matrices Discussions of Helly’s theorem; the Art Gallery theorem; Vincensini’s problem; Hadwiger’s theorems; theorems of Radon and Caratheodory; Kirchberger’s theorem; Helly-type theorems for circles; covering problems; piercing problems; sets of constant width; Reuleaux triangles; Barbier’s theorem; and Borsuk’s problem Geometry of Convex Sets is a useful textbook for upper-undergraduate level courses in geometry of convex sets and is essential for graduate-level courses in convex analysis. An excellent reference for academics and readers interested in learning the various applications of convex geometry, the book is also appropriate for teachers who would like to convey a better understanding and appreciation of the field to students. I. E. Leonard, PhD, was a contract lecturer in the Department of Mathematical and Statistical Sciences at the University of Alberta. The author of over 15 peer-reviewed journal articles, he is a technical editor for the Canadian Applied Mathematical Quarterly journal. J. E. Lewis, PhD, is Professor Emeritus in the Department of Mathematical Sciences at the University of Alberta. He was the recipient of the Faculty of Science Award for Excellence in Teaching in 2004 as well as the PIMS Education Prize in 2002.

Featuring contributions by distinguished scholars from ten countries, The Wiley Handbook of the History and Philosophy of Criminology provides students, scholars, and criminologists with a truly a global perspective on the theory and practice of criminology throughout the centuries and around the world. In addition to chapters devoted to the key ideas, thinkers, and moments in the intellectual and philosophical history of criminology, it features in-depth coverage of the organizational structure of criminology as an academic discipline world-wide. The first section focuses on key ideas that have shaped the field in the past, are shaping it in the present, and are likely to influence its evolution in the foreseeable future. Beginning with early precursors to criminology’s emergence as a unique discipline, the authors trace the evolution of the field, from the pioneering work of 17th century Italian jurist/philosopher, Cesare Beccaria, up through the latest sociological and biosocial trends. In the second section authors address the structure of criminology as an academic discipline in countries around the globe, including in North America, South America, Europe, East Asia, and Australia. With contributions by leading thinkers whose work has been instrumental in the development of criminology and emerging voices on the cutting edge The Wiley Handbook of the History and Philosophy of Criminology provides valuable insights in the latest research trends in the field world-wide – the ideal reference for criminologists as well as those studying in the field and related social science and humanities disciplines.

This book uses real-world examples to show how individual and collective risks can be blended and treated in a reliable decision-making framework that draws its inspiration from decision theory and market based mechanisms. It then goes into deeper detail by looking at the implications of having to face risks (a) where some kind of probabilistic description is available and (b) where none is available, using the example of insurable risks vs non-insurable risks. Again, by using real-world examples it shows how decision-makers can cope with such situations by a proper understanding and use of modern financial techniques.

This landmark collection presents a wide variety of viewpoints on the value and role of reception theory within the modern discipline of classics. A pioneering collection, looking at the role reception theory plays, or could play, within the modern discipline of classics. Emphasizes theoretical aspects of reception. Written by a wide range of contributors from young scholars to established figures, from Europe, the UK and the USA. Draws on material from many different fields, from translation studies to the visual arts, and from politics to performance. Sets the agenda for classics in the future.

Conservation and the Genetics of Populations gives a comprehensive overview of the essential background, concepts, and tools needed to understand how genetic information can be used to develop conservation plans for species threatened with extinction. Provides a thorough understanding of the genetic basis of biological problems in conservation. Uses a balance of data and theory, and basic and applied research, with examples taken from both the animal and plant kingdoms. An associated website contains example data sets and software programs to illustrate population genetic processes and methods of data analysis. Discussion questions and problems are included at the end of each chapter to aid understanding. Features Guest Boxes written by leading people in the field including James F. Crow, Nancy FitzSimmons, Robert C. Lacy, Michael W. Nachman, Michael E. Soule, Andrea Taylor, Loren H. Rieseberg, R.C. Vrijenhoek, Lisette Waits, Robin S. Waples and Andrew Young. Supplementary information designed to support Conservation and the Genetics of Populations including: Downloadable sample chapter Answers to questions and problems Data sets illustrating problems from the book Data analysis software programs Website links An Instructor manual CD-ROM for this title is available. Please contact our Higher Education team at HigherEducation@wiley.com for more information.

An accessible, clearly organized survey of the basic topics of measure theory for students and researchers in mathematics, statistics, and physics In order to fully understand and appreciate advanced probability, analysis, and advanced mathematical statistics, a rudimentary knowledge of measure theory and like subjects must first be obtained. The Theory of Measures and Integration illuminates the fundamental ideas of the subject-fascinating in their own right-for both students and researchers, providing a useful theoretical background as well as a solid foundation for further inquiry. Eric Vestrup's patient and measured text presents the major results of classical measure and integration theory in a clear and rigorous fashion. Besides offering the mainstream fare, the author also offers detailed discussions of extensions, the structure of Borel and Lebesgue sets, set-theoretic considerations, the Riesz representation theorem, and the Hardy-Littlewood theorem, among other topics, employing a clear presentation style that is both evenly paced and user-friendly. Chapters include: * Measurable Functions * The Lp Spaces * The Radon-Nikodym Theorem * Products of Two Measure Spaces * Arbitrary Products of Measure Spaces Sections conclude with exercises that range in difficulty between easy «finger exercises»and substantial and independent points of interest. These more difficult exercises are accompanied by detailed hints and outlines. They demonstrate optional side paths in the subject as well as alternative ways of presenting the mainstream topics. In writing his proofs and notation, Vestrup targets the person who wants all of the details shown up front. Ideal for graduate students in mathematics, statistics, and physics, as well as strong undergraduates in these disciplines and practicing researchers, The Theory of Measures and Integration proves both an able primary text for a real analysis sequence with a focus on measure theory and a helpful background text for advanced courses in probability and statistics.

Innovation is the life blood of practically every organization. Innovation drives growth, development, and prosperity for many organizations and geographical areas. Sometimes, innovation thrives within a certain geographical location or in certain organizations that are known for their innovative approaches. This outstanding new volume will demonstrate how to measure the success of innovation in all types of organizations. In the last decade, there have been tremendous investments in creativity and innovations sponsored by companies, cities, states, countries, universities, NGO’s, and even non-profits. With the magnitude of emphasis on creativity and innovation, the sponsors and key stakeholders will demand to know the value of these programs. The Value of Innovation: Measuring the Impact and ROI in Creativity and Innovation Programs will show step-by-step how to measure the impact and the ROI of innovation and creativity programs. The process collects six types of data: reaction, learning, application, impact, ROI, and intangibles. Data are collected analyzed and reported using a systematic, logic model. Conservative standards create results that are both CEO and CFO friendly. This proven process has been used now in 5000 organizations and this new book adapts the method directly to this critical area of innovation, showing examples and case studies.

Written by an experienced and well-respected physician and professor, this new volume, building on the previous volume, Ultrasonic Topographical and Pathotopographical Anatomy, also available from Wiley-Scrivener, presents the ultrasonic topographical and pathotopographical anatomy of the head and neck, offering further detail into these important areas for use by medical professionals. This atlas of topographic and pathotopographic human anatomy is a fundamental and practically important book designed for doctors of all specializations and students of medical schools. Here you can find almost everything that is connected with the topographic and pathotopographic human anatomy, including original graphs of logical structures of topographic anatomy and development of congenital abnormalities, topography of different areas in layers, pathotopography, computer and magnetic resonance imaging (MRI) of topographic and pathotopographic anatomy. Also you can find here new theoretical and practical sections of topographic anatomy developed by the author himself which are published for the first time. They are practically important for mastering the technique of operative interventions and denying possibility of iatrogenic complications during operations. This important new volume will be valuable to physicians, junior physicians, medical residents, lecturers in medicine, and medical students alike, either as a textbook or as a reference. It is a must-have for any physician’s library.