This book offers a new look at well-established quantification theory for categorical data, referred to by such names as correspondence analysis, dual scaling, optimal scaling, and homogeneity analysis. These multiple identities are a consequence of its large number of properties that allow one to analyze and visualize the strength of variable association in an optimal solution. The book contains modern quantification theory for analyzing the association between two and more categorical variables in a variety of applicative frameworks. Visualization has attracted much attention over the past decades and given rise to controversial opinions. One may consider variations of plotting systems used in the construction of the classic correspondence plot, the biplot, the Carroll-Green-Schaffer scaling, or a new approach in doubled multidimensional space as presented in the book. There are even arguments for no visualization at all. The purpose of this book therefore is to shed new light on time-honored graphical procedures with critical reviews, new ideas, and future directions as alternatives. This stimulating volume is written with fresh new ideas from the traditional framework and the contemporary points of view. It thus offers readers a deep understanding of the ever-evolving nature of quantification theory and its practice. Part I starts with illustrating contingency table analysis with traditional joint graphical displays (symmetric, non-symmetric) and the CGS scaling and then explores logically correct graphs in doubled Euclidean space for both row and column variables. Part II covers a variety of mathematical approaches to the biplot strategy in graphing a data structure, providing a useful source for this modern approach to graphical display. Part II is also concerned with a number of alternative approaches to the joint graphical display such as bimodal cluster analysis and other statistical problems relevant to quantification theory.

This book is an original-the first-ever treatment of the mathematics of Luck. Setting out from the principle that luck can be measured by the gap between reasonable expectation and eventual realization, the book develops step-by-step a mathematical theory that accommodates the entire range of our pre-systematic understanding of the way in which luck functions in human affairs. In so moving from explanatory exposition to mathematical treatment, the book provides a clear and accessible account of the way in which luck assessment enters into the calculations of rational decision theory.

This book provides a practical guide to the analysis of data from randomized controlled trials (RCT). It gives an answer to the question of how to estimate the intervention effect in an appropriate way. This problem is examined for different RCT designs, such as RCTs with one follow-up measurement, RCTs with more than one follow-up measurement, cluster RCTs, cross-over trials, stepped wedge trials, and N-of-1 trials. The statistical methods are explained in a non-mathematical way and are illustrated by extensive examples. All datasets used in the book are available for download, so readers can reanalyse the examples to gain a better understanding of the methods used. Although most examples are taken from epidemiological and clinical studies, this book is also highly recommended for researchers working in other fields.

This book discusses recent developments in dynamic reliability in multi-state systems (MSS), addressing such important issues as reliability and availability analysis of aging MSS, the impact of initial conditions on MSS reliability and availability, changing importance of components over time in MSS with aging components, and the determination of age-replacement policies. It also describes modifications of traditional methods, such as Markov processes with rewards, as well as a modern mathematical method based on the extended universal generating function technique, the Lz-transform, presenting various successful applications and demonstrating their use in real-world problems. This book provides theoretical insights, information on practical applications, and real-world case studies that are of interest to engineers and industrial managers as well as researchers. It also serves as a textbook or supporting text for graduate and postgraduate courses in industrial, electrical, and mechanical engineering.

Since its inception, fuzzy logic has attracted an incredible amount of interest, and this interest continues to grow at an exponential rate. As such, scientists, researchers, educators and practitioners of fuzzy logic continue to expand on the applicability of what and how fuzzy can be utilised in the real-world. In this book, the authors present key application areas where fuzzy has had significant success. The chapters cover a plethora of application domains, proving credence to the versatility and robustness of a fuzzy approach. A better understanding of fuzzy will ultimately allow for a better appreciation of fuzzy. This book provides the reader with a varied range of examples to illustrate what fuzzy logic can be capable of and how it can be applied. The text will be ideal for individuals new to the notion of fuzzy, as well as for early career academics who wish to further expand on their knowledge of fuzzy applications. The book is also suitable as a supporting text for advanced undergraduate and graduate-level modules on fuzzy logic, soft computing, and applications of AI.

This book describes the unsteady phenomena needed to understand supersonic combustion. Following an initial chapter that introduces readers to the basic concepts in and classical studies on unsteady supersonic combustion, the book highlights recent studies on unsteady phenomena, which offer insights on e.g. interactions between acoustic waves and flames, flow dominating instability, ignition instability, flame flashback, and near-blowout-limit combustion. In turn, the book discusses in detail the fundamental mechanisms of these phenomena, and puts forward practical suggestions for future scramjet design.

This book presents a systematic treatment of the Rademacher system, one of the most important unifying concepts in mathematics, and includes a number of recent important and beautiful results related to the Rademacher functions. The book discusses the relationship between the properties of the Rademacher system and geometry of some function spaces. It consists of three parts, in which this system is considered respectively in Lp-spaces, in general symmetric spaces and in certain classes of non-symmetric spaces (BMO, Paley, Cesaro, Morrey). The presentation is clear and transparent, providing all main results with detailed proofs. Moreover, literary and historical comments are given at the end of each chapter. This book will be suitable for graduate students and researchers interested in functional analysis, theory of functions and geometry of Banach spaces.

Detailed Description

This book presents the theory and methods of flexible and generalized uncertainty optimization. Particularly, it describes the theory of generalized uncertainty in the context of optimization modeling. The book starts with an overview of flexible and generalized uncertainty optimization. It covers uncertainties that are both associated with lack of information and are more general than stochastic theory, where well-defined distributions are assumed. Starting from families of distributions that are enclosed by upper and lower functions, the book presents construction methods for obtaining flexible and generalized uncertainty input data that can be used in a flexible and generalized uncertainty optimization model. It then describes the development of the associated optimization model in detail. Written for graduate students and professionals in the broad field of optimization and operations research, this second edition has been revised and extended to include more worked examples and a section on interval multi-objective mini-max regret theory along with its solution method.

This book focuses on a selection of special topics, with emphasis on past and present research of the authors on "canonical" Riemannian metrics on smooth manifolds. On the backdrop of the fundamental contributions given by many experts in the field, the volume offers a self-contained view of the wide class of "Curvature Conditions" and "Critical Metrics" of suitable Riemannian functionals. The authors describe the classical examples and the relevant generalizations. This monograph is the winner of the 2020 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.

Considering that the motion of strings with finitely many masses on them is described by difference equations, this book presents the spectral theory of such problems on finite graphs of strings. The direct problem of finding the eigenvalues as well as the inverse problem of finding strings with a prescribed spectrum are considered. This monograph gives a comprehensive and self-contained account on the subject, thereby also generalizing known results. The interplay between the representation of rational functions and their zeros and poles is at the center of the methods used. The book also unravels connections between finite dimensional and infinite dimensional spectral problems on graphs, and between self-adjoint and non-self-adjoint finite-dimensional problems. This book is addressed to researchers in spectral theory of differential and difference equations as well as physicists and engineers who may apply the presented results and methods to their research.

This book gathers contributions from the 15th ICOLD Benchmark Workshop on Numerical Analysis of Dams. The workshop provided an opportunity for engineers, researchers and operators to present and exchange their experiences and the latest advances in numerical modelling in the context of the design, performance and monitoring of dams. Covering various aspects of computer analysis tools and safety assessment criteria, and their development over recent decades, the book is a valuable reference resource for those in the engineering community involved in the safety, planning, design, construction, operation and maintenance of dams.

This handbook is focused on the analytical dimension in researching international entrepreneurship. It offers a diverse collection of chapters focused on qualitative and quantitative methods that are being practised and can be used by future researchers in the field of international entrepreneurship. The qualitative cluster covers articles, conceptual and empirical chapters as well as literature reviews, whereas the quantitative cluster analyses international entrepreneurship through a broad range of statistical methods such as regressions, panel data, structural equation modelling as well as decision-making and optimisation models in certain and uncertain circumstances. This book is essential reading for researchers, scholars and practitioners who want to learn and implement new methods in analysing entrepreneurial opportunities across national borders.

This book shows how information theory, probability, statistics, mathematics and personal computers can be applied to the exploration of numbers and proportions in music. It brings the methods of scientific and quantitative thinking to questions like: What are the ways of encoding a message in music and how can we be sure of the correct decoding? How do claims of names hidden in the notes of a score stand up to scientific analysis? How many ways are there of obtaining proportions and are they due to chance? After thoroughly exploring the ways of encoding information in music, the ambiguities of numerical alphabets and the words to be found "hidden" in a score, the book presents a novel way of exploring the proportions in a composition with a purpose-built computer program and gives example results from the application of the techniques. These include information theory, combinatorics, probability, hypothesis testing, Monte Carlo simulation and Bayesian networks, presented in an easily understandable form including their development from ancient history through the life and times of J. S. Bach, making connections between science, philosophy, art, architecture, particle physics, calculating machines and artificial intelligence. For the practitioner the book points out the pitfalls of various psychological fallacies and biases and includes succinct points of guidance for anyone involved in this type of research. This book will be useful to anyone who intends to use a scientific approach to the humanities, particularly music, and will appeal to anyone who is interested in the intersection between the arts and science.With a foreword by Ruth Tatlow (Uppsala University), award winning author of Bach's Numbers: Compositional Proportion and Significance and Bach and the Riddle of the Number Alphabet."With this study Alan Shepherd opens a much-needed examination of the wide range of mathematical claims that have been made about J. S. Bach's music, offering both tools and methodological cautions with the potential to help clarify old problems." Daniel R. Melamed, Professor of Music in Musicology, Indiana University

This volume combines an introduction to central collineations with an introduction to projective geometry, set in its historical context and aiming to provide the reader with a general history through the middle of the nineteenth century. Topics covered include but are not limited to: The Projective Plane and Central Collineations The Geometry of Euclid's Elements Conic Sections in Early Modern Europe Applications of Conics in History With rare exception, the only prior knowledge required is a background in high school geometry. As a proof-based treatment, this monograph will be of interest to those who enjoy logical thinking, and could also be used in a geometry course that emphasizes projective geometry.

This authoritative text presents the classical theory of functions of a single complex variable in complete mathematical and historical detail. Requiring only minimal, undergraduate-level prerequisites, it covers the fundamental areas of the subject with depth, precision, and rigor. Standard and novel proofs are explored in unusual detail, and exercises - many with helpful hints - provide ample opportunities for practice and a deeper understanding of the material. In addition to the mathematical theory, the author also explores how key ideas in complex analysis have evolved over many centuries, allowing readers to acquire an extensive view of the subject's development. Historical notes are incorporated throughout, and a bibliography containing more than 2,000 entries provides an exhaustive list of both important and overlooked works. Classical Analysis in the Complex Plane will be a definitive reference for both graduate students and experienced mathematicians alike, as well as an exemplary resource for anyone doing scholarly work in complex analysis. The author's expansive knowledge of and passion for the material is evident on every page, as is his desire to impart a lasting appreciation for the subject. "I can honestly say that Robert Burckel's book has profoundly influenced my view of the subject of complex analysis. It has given me a sense of the historical flow of ideas, and has acquainted me with byways and ancillary results that I never would have encountered in the ordinary course of my work. The care exercised in each of his proofs is a model of clarity in mathematical writing...Anyone in the field should have this book on [their bookshelves] as a resource and an inspiration."- From the Foreword by Steven G. Krantz

This book examines the current state of the field of mathematics pre-service teacher education through the theme of borders. Borders are ubiquitous; they can be used to define, classify, organize, make sense of, and/or group. There are many ways that the concept of a border illuminates the field of mathematics pre-service teacher education. Consequently, there are a multitude of responses to these borders: researchers and practitioners question, challenge, cross, blur, and erase them. Chapters include the following topics: explorations of mathematics across topics (e.g., geometry, algebra, probability) and with other disciplines (e.g., science, the arts, social sciences); challenging gender, cultural, and racial borders; exploring the structure and curriculum of teacher education programs; spaces inhabited by teacher education programs (e.g., university, community); and international collaborations and programs to promote cross-cultural sharing and learning. The book targets a readership of researchers and graduate students in integrated education studies, teacher education, practitioners of mathematics education, curriculum developers, and educational administrators and policy makers.

This book is the first systematic treatment of this area so far scattered in a vast number of articles. As in classical topology, concrete problems require restricting the (generalized point-free) spaces by various conditions playing the roles of classical separation axioms. These are typically formulated in the language of points; but in the point-free context one has either suitable translations, parallels, or satisfactory replacements. The interrelations of separation type conditions, their merits, advantages and disadvantages, and consequences are discussed. Highlights of the book include a treatment of the merits and consequences of subfitness, various approaches to the Hausdorff's axiom, and normality type axioms. Global treatment of the separation conditions put them in a new perspective, and, a.o., gave some of them unexpected importance. The text contains a lot of quite recent results; the reader will see the directions the area is taking, and may find inspiration for her/his further work. The book will be of use for researchers already active in the area, but also for those interested in this growing field (sometimes even penetrating into some parts of theoretical computer science), for graduate and PhD students, and others. For the reader's convenience, the text is supplemented with an Appendix containing necessary background on posets, frames and locales.

This is a companion textbook for an introductory course in physics. It aims to link the theories and models that students learn in class with practical problem-solving techniques. In other words, it should address the common complaint that 'I understand the concepts but I can't do the homework or tests'. The fundamentals of introductory physics courses are addressed in simple and concise terms, with emphasis on how the fundamental concepts and equations should be used to solve physics problems.