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This book is an introduction to the study of methods of obtaining generating functions. It is an expository work at the level of the beginning graduate student. The first part of Chapter I gives the reader the necessary definitions and basic concepts. The fundamental method of direct summation is explained and illustrated. The second part of Chapter I deals with the methods developed by Rainville. These methods are based principally on inventive manipulation of power series. Weisner's group-theoretic method is explained in detail in Chapter II and is further illustrated in Chapter III. When this method is applicable, it yields a set of at least three generating functions. In Chapter II for the Laguerre polynomials six generating functions were found. Truesdell's method is studied in Chapter IV. For a given set of functions {fez, an the success of this method depends on the existence of certain transformations. If fez, a) can be transformed into F(z, a) such that a a-; F(z, a)=F(z, a+ 1), or if fez, a) can be transformed into G(z, a) such that a a-; G(z, a)=G(z, a-I), then from each transformed function a generating function can be obtained. Truesdell's method for obtaining the transformed functions does not require any ingenuity on the user's part. Truesdell has shown how these simple results may be exploited to generate more complicated results by means of specified, systematic, and general processes. His method of obtaining generating functions is only one of these results.
"As expected, this book is complex but it is also engaging, thought-provoking, and exciting because it helps nurses and other readers think deeply about meeting the needs of patients at their most vulnerable moments. Score: 94, 4 Stars--Doody's Medical Reviews Callista Roy, one of nursingís leading theorists and creator of the widely used Roy Adaptation Model of Nursing, presents a unique pathway for developing knowledge for nursing practice. Her book distills the most relevant information from 200 published research studies to provide a roadmap for progressing from nursing research to middle-range theory to optimum practice regimens. It is based on tested knowledge, clear evidence, and refined caring perspectives. Step by step, the text identifies and critiques research suited for developing cumulative knowledge for practice and uses the research to develop middle-range theories that apply across all health care settings. It then presents the evidence for practice for each middle range theory, refocuses EBP within nursing knowledge and within defined levels of readiness for practice, and recommends changes for practice based on evidence. Grounded in the Roy Adaptation Model of Nursing, the book provides a single conceptual basis for synthesis of research into middle range theories for use across all patient populations. It clarifies ways to select research from one conceptual basis to build middle-range theories, how to classify evidence for practice by levels of readiness, and recommend research-based changes in practice. The text includes quantitative and qualitative research designs and offers instruments to measure major concepts for implementation. Also included are plentiful examples, tables that display values across studies, definitions of major terms and concepts, and diagrams of concepts. Supplementing the text is a faculty guide for using the text to teach critical thinking at multiple graduate levels and videos illuminating each section of the book. Key Features: Explains clearly how middle-range theories grow from research Designed for implementation in practice Uses Royís five core ìadaptationî contexts as organizing themes: coping, changing life events, loss, chronic health condition, and traumatic events Constitutes a seminal work from a pre-eminent nursing theorist and educator Includes faculty guide and videos elucidating each section of the book
In combinatorics, one often considers the process of enumerating objects of a certain nature, which results in a sequence of positive integers. With each such sequence, one can associate a generating function, whose properties tell us a lot about the nature of the objects being enumerated. Nowadays, the language of generating functions is the main language of enumerative combinatorics. This book is based on the course given by the author at the College of Mathematics of the Independent University of Moscow. It starts with definitions, simple properties, and numerous examples of generating functions. It then discusses various topics, such as formal grammars, generating functions in several variables, partitions and decompositions, and the exclusion-inclusion principle. In the final chapter, the author describes applications of generating functions to enumeration of trees, plane graphs, and graphs embedded in two-dimensional surfaces. Throughout the book, the reader is motivated by interesting examples rather than by general theories. It also contains a lot of exercises to help the reader master the material. Little beyond the standard calculus course is necessary to understand the book. It can serve as a text for a one-semester undergraduate course in combinatorics.
Should transhuman and posthuman persons ever be brought into existence? And if so, could they be generated in a good and loving way? This study explores how society may respond to the actual generation of new kinds of persons from ethical, philosophical, and theological perspectives. Contributors to this volume address a number of essential questions, including the ethical ramifications of generating new life, the relationships that generators may have with their creations, and how these creations may consider their generation. This collection's interdisciplinary approach traverses the philosophical writings of Aristotle, Aquinas, Kant, Nietzsche, and Heidegger, alongside theological considerations from Jewish, Christian, and Islamic traditions. It invites academics, faith leaders, policy makers, and stakeholders to think through the ethical gamut of generating posthuman and transhuman persons.
The challenge of how to ensure that working families see their living standards improve over time is central in rich countries. Many argue that conditions are stagnating for many, driving political polarization and threatening social stability. Generating Prosperity for Working Families in Affluent Countries investigates how common such a "squeeze" on middle-income earners has actually been, and what forces underlie it in terms of globalization, technology, and government policies. Generating Prosperity for Working Families in Affluent Countries presents the findings of a comprehensive analysis of performance in improving living standards across the wealthy nations of the OECD. It relates performance to overall economic growth, exploring why these often diverge substantially, and to the different models of capitalism or economic growth embedded in each country. Going beyond income, other indicators and aspects of living standards are also incorporated including non-monetary indicators of deprivation and financial strain, wealth and its distribution, and intergenerational mobility. Through looking across this broad canvas, this book teases out how ordinary households have fared in recent decades in these critically important respects, and how that should inform the quest for inclusive growth and prosperity.
Explore core concepts, theories and formulations of phase-only Fresnel holograms, which paves the way for 3-D holographic display system.
