On Beatty Sets And Some Generalisations Thereof
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| Author | : Marc Technau |
| Publisher | : BoD – Books on Demand |
| Total Pages | : 106 |
| Release | : 2018-08-24 |
| Genre | : Mathematics |
| ISBN | : 3958260888 |
Beatty sets (also called Beatty sequences) have appeared as early as 1772 in the astronomical studies of Johann III Bernoulli as a tool for easing manual calculations and - as Elwin Bruno Christoffel pointed out in 1888 - lend themselves to exposing intricate properties of the real irrationals. Since then, numerous researchers have explored a multitude of arithmetic properties of Beatty sets; the interrelation between Beatty sets and modular inversion, as well as Beatty sets and the set of rational primes, being the central topic of this book. The inquiry into the relation to rational primes is complemented by considering a natural generalisation to imaginary quadratic number fields.
| Author | : Prapanpong Pongsriiam |
| Publisher | : American Mathematical Society |
| Total Pages | : 402 |
| Release | : 2023-06-02 |
| Genre | : Mathematics |
| ISBN | : 1470464446 |
This new edition of Analytic Number Theory for Beginners presents a friendly introduction to analytic number theory for both advanced undergraduate and beginning graduate students, and offers a comfortable transition between the two levels. The text starts with a review of elementary number theory and continues on to present less commonly covered topics such as multiplicative functions, the floor function, the use of big $O$, little $o$, and Vinogradov notation, as well as summation formulas. Standard advanced topics follow, such as the Dirichlet $L$-function, Dirichlet's Theorem for primes in arithmetic progressions, the Riemann Zeta function, the Prime Number Theorem, and, new in this second edition, sieve methods and additive number theory. The book is self-contained and easy to follow. Each chapter provides examples and exercises of varying difficulty and ends with a section of notes which include a chapter summary, open questions, historical background, and resources for further study. Since many topics in this book are not typically covered at such an accessible level, Analytic Number Theory for Beginners is likely to fill an important niche in today's selection of titles in this field.
| Author | : Urban Larsson |
| Publisher | : Cambridge University Press |
| Total Pages | : 499 |
| Release | : 2019-05-09 |
| Genre | : Computers |
| ISBN | : 1108485804 |
Surveys the state-of-the-art in combinatorial game theory, that is games not involving chance or hidden information.
| Author | : Steven French |
| Publisher | : OUP Oxford |
| Total Pages | : 413 |
| Release | : 2014-01-30 |
| Genre | : Philosophy |
| ISBN | : 0191507725 |
In The Structure of the World, Steven French articulates and defends the bold claim that there are no objects. At the most fundamental level, modern physics presents us with a world of structures and making sense of that view is the central aim of the increasingly widespread position known as structural realism. Drawing on contemporary work in metaphysics and philosophy of science, as well as the 'forgotten' history of structural realism itself, French attempts to further ground and develop this position. He argues that structural realism offers the best way of balancing our need to accommodate the results of modern science with our desire to arrive at an appropriately informed understanding of the world that science presents to us. Covering not only the realism-antirealism debate, the nature of representation, and the relationship between metaphysics and science, The Structure of the World defends a form of eliminativism about objects that sets laws and symmetry principles at the heart of ontology. In place of a world of microscopic objects banging into one another and governed by the laws of physics, it offers a world of laws and symmetries, on which determinate physical properties are dependent. In presenting this account, French also tackles the distinction between mathematical and physical structures, the nature of laws, and causality in the context of modern physics, and he concludes by exploring the extent to which structural realism can be extended into chemistry and biology.
| Author | : Edward W. Said |
| Publisher | : Vintage |
| Total Pages | : 434 |
| Release | : 2014-10-01 |
| Genre | : Social Science |
| ISBN | : 0804153868 |
A groundbreaking critique of the West's historical, cultural, and political perceptions of the East that is—three decades after its first publication—one of the most important books written about our divided world. "Intellectual history on a high order ... and very exciting." —The New York Times In this wide-ranging, intellectually vigorous study, Said traces the origins of "orientalism" to the centuries-long period during which Europe dominated the Middle and Near East and, from its position of power, defined "the orient" simply as "other than" the occident. This entrenched view continues to dominate western ideas and, because it does not allow the East to represent itself, prevents true understanding.
| Author | : Jerald L. Ericksen |
| Publisher | : World Scientific |
| Total Pages | : 656 |
| Release | : 2005 |
| Genre | : Science |
| ISBN | : 9812562834 |
This book is a unique and comprehensive collection of pioneering contributions to the mechanics of crystals by J L Ericksen, a prominent and leading contributor to the study of the mechanics and mathematics of crystalline solids over the past 35 years.It presents a splendid corpus of research papers that cover areas on crystal symmetry, constitutive equations, defects and phase transitions — all topics of current importance to a broad group of workers in the field.The volume thus provides in one place material that is frequently referenced by numerous researchers on crystals across a spectrum of activities in areas of continuum mechanics, applied mathematics, engineering and materials science.Each group of papers or chapters in the book is preceded by a summary introduction that describes how the papers on that topic fit together, and in which Ericksen sketches the context of each paper and shares with the reader his thinking and insightfulness in writing it. The volume, edited by internationally renowned scholars whose works in finite elasticity and continuum mechanics have appeared in a variety of books and prestigious journals published over the past four decades, also includes a very interesting brief autobiography by Ericksen. In it he describes his early life in Oregon, his wartime experiences, his student days and postgraduate study, his introduction to scientific work, and what motivated him in his research. An English translation and revision of the first paper in this volume, originally published in Russian, appears here for the first time.
| Author | : Erol Başar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 554 |
| Release | : 2012-12-06 |
| Genre | : Medical |
| ISBN | : 3642745571 |
This volume is based on contributions to the second Brain Dynamics Conference, held in Berlin on August 10-14, 1987, as a satellite conference of the Budapest Congress of the International Brain Research Organization. Like the volume resulting from the first conference, Dynamics of Sensory and Cognitive Processing by the Brain, the present work covers new approaches to brain function, with emphasis on electromagnetic fields, EEG, event-related potentials, connectivistic views, and neural networks. Close attention is also paid to research in the emerging field of deterministic chaos and strange attractors. The diversity of this collection of papers reflects a multipronged advance in a hitherto relatively neglected domain, i. e., the study of signs of dynamic processes in organized neural tissue in order both to explain them and to exploit them for clues to system function. The need is greater than ever for new windows. This volume reflects a historical moment, the moment when a relatively neglected field of basic research into available signs of dynamic processes ongoing in organized neural tissue is expanding almost explosively to complement other approaches. From the topics treated, this book should appeal, as did its predecessor, to neuroscientists, neurologists, scientists studying complex systems, artificial intelligence, and neural networks, psychobiologists, and all basic and clinical investigators concerned with new techniques of monitoring and analyzing the brain's electromagnetic activity.
| Author | : L. Kuipers |
| Publisher | : Courier Corporation |
| Total Pages | : 416 |
| Release | : 2012-05-24 |
| Genre | : Mathematics |
| ISBN | : 0486149994 |
The theory of uniform distribution began with Hermann Weyl's celebrated paper of 1916. In later decades, the theory moved beyond its roots in diophantine approximations to provide common ground for topics as diverse as number theory, probability theory, functional analysis, and topological algebra. This book summarizes the theory's development from its beginnings to the mid-1970s, with comprehensive coverage of both methods and their underlying principles. A practical introduction for students of number theory and analysis as well as a reference for researchers in the field, this book covers uniform distribution in compact spaces and in topological groups, in addition to examinations of sequences of integers and polynomials. Notes at the end of each section contain pertinent bibliographical references and a brief survey of additional results. Exercises range from simple applications of theorems to proofs of propositions that expand upon results stated in the text.
| Author | : Andrew F. Hayes |
| Publisher | : SAGE |
| Total Pages | : 401 |
| Release | : 2008 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 1412927900 |
A must-have volume for every communication researcher's library, The SAGE Sourcebook of Advanced Data Analysis Methods for Communication Research provides an introductory treatment of various advanced statistical methods applied to research in the field of communication. Written by authors who use these methods in their own research, each chapter gives a non-technical overview of what the method is and how it can be used to answer communication-related questions or aide the researcher dealing with difficult data problems. Students and faculty interested in diving into a new statistical topic—such as latent growth modeling, multilevel modeling, propensity scoring, or time series analysis—will find each chapter an excellent springboard for acquiring the background needed to jump into more advanced, technical readings.
| Author | : Mary Jane Smith, PhD, RN, FAAN |
| Publisher | : Springer Publishing Company |
| Total Pages | : 506 |
| Release | : 2018-03-10 |
| Genre | : Medical |
| ISBN | : 0826159923 |
Three-time recipient of the AJN Book of the Year Award! Praise for the third edition: “This is an outstanding edition of this book. It has great relevance for learning about, developing, and using middle range theories. It is very user friendly, yet scholarly." Score: 90, 4 Stars -Doody's Medical Reviews The fourth edition of this invaluable publication on middle range theory in nursing reflects the most current theoretical advances in the field. With two additional chapters, new content incorporates exemplars that bridge middle range theory to advanced nursing practice and research. Additional content for DNP and PhD programs includes two new theories: Bureaucratic Caring and Self-Care of Chronic Illness. This user-friendly text stresses how theory informs practice and research in the everyday world of nursing. Divided into four sections, content sets the stage for understanding middle range theory by elaborating on disciplinary perspectives, an organizing framework, and evaluation of the theory. Middle Range Theory for Nursing, Fourth Edition presents a broad spectrum of 13 middle range theories. Each theory is broken down into its purpose, development, and conceptual underpinnings, and includes a model demonstrating the relationships among the concepts, and the use of the theory in research and practice. In addition, concept building for research through the lens of middle range theory is presented as a rigorous 10-phase process that moves from a practice story to a conceptual foundation. Exemplars are presented clarifying both the concept building process and the use of conceptual structures in research design. This new edition remains an essential text for advanced practice, theory, and research courses. New to the Fourth Edition: Reflects new theoretical advances Two completely new chapters New content for DNP and PhD programs Two new theories: Bureaucratic Caring and Self-Care of Chronic Illness Two articles from Advances in Nursing Science documenting a historical meta-perspective on middle range theory development Key Features: Provides a strong contextual foundation for understanding middle range theory Introduces the Ladder of Abstraction to clarify the range of nursing’s theoretical foundation Presents 13 middle range theories with philosophical, conceptual, and empirical dimensions of each theory Includes Appendix summarizing middle range theories from 1988 to 2016
