Periodic Character And Patterns Of Recursive Sequences

Michael A. Radin Periodic Character and Patterns of Recursive Sequences Periodic Character and Patterns of Recursive Sequences Michael A. Radin Periodic Character and Patterns of Recursive Sequences 123 Michael A. Radin School of Mathematical Sciences Rochester Institute of Technology Rochester, NY, USA ISBN 978-3-030-01779-8 ISBN 978-3-030-01780-4 (eBook) https://doi.org/10.1007/978-3-030-01780-4 Library of Congress Control Number: 2018960765 Mathematics Subject Classification: 11J71, 00A06, 03B70, 03C13, 03D20, 03F52, 03F50, 03F55, 03F60, 11B37, 11Y55, 34Kxx, 34K11, 34K13, 35F05, 35F20, 35F35, 35F50, 39–XX, 39Axx © Springer Nature Switzerland AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Preface Understanding structures and details of patterns and repetitions is an essential part of the learning process that enhances our intuitions, analytical skills, and our deducting reasoning. For instance, it is essential to decipher the patterns and their repetitions when studying the weather systems, when learning to play a musical instrument, when studying a foreign language, when learning computer programming, when studying transportation routes and schedules, when analyzing engineering structures, and when studying behaviors and other similar applications. Investigation of patterns is often claimed in medical sciences to detect particular viruses and spread of diseases, studying the heartbeats and frequencies of occurrences. Moreover, patterns are very frequently applied in signal processing and other analogous phenomena with waves and periodic traits. The aim of this interdisciplinary book is to un