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Download or read book Sequences written by H. Halberstam and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: THIS volume is concerned with a substantial branch of number theory of which no connected account appears to exist; we describe the general nature of the constituent topics in the introduction. Although some excellent surveys dealing with limited aspects of the subject under con sideration have been published, the literature as a whole is far from easy to study. This is due in part to the extent of the literature; it is necessary to thread one's way through a maze of results, a complicated structure of inter-relationships, and many conflicting notations. In addition, however, not all the original papers are free from obscurities, and consequently some of these papers are difficult (a few even exceed ingly difficult) to master. We try to give a readable and coherent account of the subject, con taining a cross-section of the more interesting results. We felt that it would have been neither practicable nor desirable to attempt a compre hensive account; we treat each aspect of the subject from some special point of view, and select results accordingly. Needless to say, this approach entails the omission of many interesting and important results (quite apart from defects in the selection due to errors of judgement on our part). Those results selected for inclusion are, however, proved in complete detail and without the assumption of any prior knowledge on the part of the reader.
Book Synopsis Automatic Sequences by : Jean-Paul Allouche
Download or read book Automatic Sequences written by Jean-Paul Allouche and published by Cambridge University Press. This book was released on 2003-07-21 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uniting dozens of seemingly disparate results from different fields, this book combines concepts from mathematics and computer science to present the first integrated treatment of sequences generated by 'finite automata'. The authors apply the theory to the study of automatic sequences and their generalizations, such as Sturmian words and k-regular sequences. And further, they provide applications to number theory (particularly to formal power series and transcendence in finite characteristic), physics, computer graphics, and music. Starting from first principles wherever feasible, basic results from combinatorics on words, numeration systems, and models of computation are discussed. Thus this book is suitable for graduate students or advanced undergraduates, as well as for mature researchers wishing to know more about this fascinating subject. Results are presented from first principles wherever feasible, and the book is supplemented by a collection of 460 exercises, 85 open problems, and over 1600 citations to the literature.
Book Synopsis Recurrence Sequences by : Graham Everest
Download or read book Recurrence Sequences written by Graham Everest and published by American Mathematical Soc.. This book was released on 2015-09-03 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.
Book Synopsis Uniform Distribution of Sequences by : L. Kuipers
Download or read book Uniform Distribution of Sequences written by L. Kuipers and published by Courier Corporation. This book was released on 2012-05-24 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theory of Infinite Sequences and Series by : Ludmila Bourchtein
Download or read book Theory of Infinite Sequences and Series written by Ludmila Bourchtein and published by Springer Nature. This book was released on 2021-11-13 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook covers the majority of traditional topics of infinite sequences and series, starting from the very beginning – the definition and elementary properties of sequences of numbers, and ending with advanced results of uniform convergence and power series. The text is aimed at university students specializing in mathematics and natural sciences, and at all the readers interested in infinite sequences and series. It is designed for the reader who has a good working knowledge of calculus. No additional prior knowledge is required. The text is divided into five chapters, which can be grouped into two parts: the first two chapters are concerned with the sequences and series of numbers, while the remaining three chapters are devoted to the sequences and series of functions, including the power series. Within each major topic, the exposition is inductive and starts with rather simple definitions and/or examples, becoming more compressed and sophisticated as the course progresses. Each key notion and result is illustrated with examples explained in detail. Some more complicated topics and results are marked as complements and can be omitted on a first reading. The text includes a large number of problems and exercises, making it suitable for both classroom use and self-study. Many standard exercises are included in each section to develop basic techniques and test the understanding of key concepts. Other problems are more theoretically oriented and illustrate more intricate points of the theory, or provide counterexamples to false propositions which seem to be natural at first glance. Solutions to additional problems proposed at the end of each chapter are provided as an electronic supplement to this book.
Download or read book Sequence written by Lori Andrews and published by Macmillan. This book was released on 2007-04-03 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geneticist Alexandra Blake uses her expertise to investigate a serial killer plaguing military bases across the country, but when an another murder hits close to home, Alex and her boyfriend, a Texas congressman, find their lives in danger.
Download or read book Sequencing written by Arlene Cardozo and published by . This book was released on 1996-05 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numbers, Sequences and Series by : Keith Hirst
Download or read book Numbers, Sequences and Series written by Keith Hirst and published by Butterworth-Heinemann. This book was released on 1994-12-08 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concerned with the logical foundations of number systems from integers to complex numbers.
Book Synopsis Handbook of MRI Pulse Sequences by : Matt A. Bernstein
Download or read book Handbook of MRI Pulse Sequences written by Matt A. Bernstein and published by Elsevier. This book was released on 2004-09-21 with total page 1041 pages. Available in PDF, EPUB and Kindle. Book excerpt: Magnetic Resonance Imaging (MRI) is among the most important medical imaging techniques available today. There is an installed base of approximately 15,000 MRI scanners worldwide. Each of these scanners is capable of running many different "pulse sequences", which are governed by physics and engineering principles, and implemented by software programs that control the MRI hardware. To utilize an MRI scanner to the fullest extent, a conceptual understanding of its pulse sequences is crucial. Handbook of MRI Pulse Sequences offers a complete guide that can help the scientists, engineers, clinicians, and technologists in the field of MRI understand and better employ their scanner. Explains pulse sequences, their components, and the associated image reconstruction methods commonly used in MRI Provides self-contained sections for individual techniques Can be used as a quick reference guide or as a resource for deeper study Includes both non-mathematical and mathematical descriptions Contains numerous figures, tables, references, and worked example problems
Book Synopsis Sequences, Groups, and Number Theory by : Valérie Berthé
Download or read book Sequences, Groups, and Number Theory written by Valérie Berthé and published by Birkhäuser. This book was released on 2018-04-09 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.
Book Synopsis A Handbook of Integer Sequences by : N.J.A. Sloane
Download or read book A Handbook of Integer Sequences written by N.J.A. Sloane and published by Academic Press. This book was released on 2014-05-10 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Handbook of Integer Sequences contains a main table of 2300 sequences of integers that are collected from all branches of mathematics and science. This handbook describes how to use the main table and provides methods for analyzing and describing unknown and important sequences. This compilation also serves as an index to the literature for locating references on a particular problem and quickly finds numbers such as 712, number of partitions of 30, 18th Catalan number, or expansion of ? to 60 decimal places. Other topics include the method of differences, self-generating sequences, polyominoes, permutations, and puzzle sequences. This publication is a good source for students and researchers who are confronted with strange and important sequences.
Book Synopsis Indian Geological Sequences by : Jai Krishna
Download or read book Indian Geological Sequences written by Jai Krishna and published by Elsevier. This book was released on 2024-06-28 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: Indian Geological Sequences: Salient Features and Major Events focuses on the first ever differentiation of the entire Indian record into a five tier hierarchical succession of geological sequences – five giga to 12 mega to 25 1st order to 68 2nd order to over 100 3rd order ones as its basic skeleton. Using the developed grid of sequence timelines, the diverse inter-disciplinary geological manifestations on the broad tectono-stratigraphically homogeneous supra-region of GTM (Gondwanian Tethyan Margin from Arabia to Australia) have been mutually integrated towards chronicling of events with precision never ever realized earlier. The giga-sequences GS-I to GS-IV comprising eight mega-sequences MS-I to MS-VIII deal with the Precambrian in brief. GS-V (¬ 635 ma onward) MS-IX (¬ 635-444 ma) and MS-XII (¬ 61.6 onward) include orogenies while MS-X (¬ 444-259 ma) and MS-XI (¬ 259-61.6 ma) are dominated by dismemberment tectonics. The prime focus is on the correlation of events across scores of sedimentary basins from outcrop to subsurface, onshore to offshore, marine to non-marine, shallow to deep water, plant to animal, micro to macro-fossils, and Proto-Paleo-Neotethys to Indian Ocean. Among the major Phanerozoic events time precised are the ¬ 500 ma Acantha Zone mega MFS accretion of the then alien TH to the Indian margin, and the ¬ 50 ma P8 Zone mega MFS impingement of India on Asia while the important dismemberment events include the ¬ 159 ma late Middle Oxfordian Orientalis Zone Schilli Subzone 1st order MFS initiation of the Indian Ocean which culminated in steps with oceanic separation of Sri Lanka from Antarctica at the ¬ 107 ma early Middle Albian Dentatus Zone mega MFS, ¬ 90 ma 1st order SB initiation of separation of Madagascar so also of Mascaranes basin, NER, Central Indian basin, Wharton basin, separation of Greater Seychelles from India at the ¬ 64.5 ma intra Danian 2nd order Quadratus Zone MFS and ¬ 24 ma Complanata Zone MFS thrusting due south of Greater Himalaya upon Lesser Himalaya. Indian Geological Sequences: Salient Features and Major Events is a valuable reference for researchers and scientists in the field of Earth Sciences. Relates multi-dimensional geological events of one region to another in a vast supra-region through precisely dated sequence timelines Links macro- and micro-evolutionary advent and extinction events to macro- and micro-geological events Includes multidisciplinary data sources, from sedimentological, geochemical, and geophysical records
Book Synopsis Algorithms on Strings, Trees, and Sequences by : Dan Gusfield
Download or read book Algorithms on Strings, Trees, and Sequences written by Dan Gusfield and published by Cambridge University Press. This book was released on 1997-05-28 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: String algorithms are a traditional area of study in computer science. In recent years their importance has grown dramatically with the huge increase of electronically stored text and of molecular sequence data (DNA or protein sequences) produced by various genome projects. This book is a general text on computer algorithms for string processing. In addition to pure computer science, the book contains extensive discussions on biological problems that are cast as string problems, and on methods developed to solve them. It emphasises the fundamental ideas and techniques central to today's applications. New approaches to this complex material simplify methods that up to now have been for the specialist alone. With over 400 exercises to reinforce the material and develop additional topics, the book is suitable as a text for graduate or advanced undergraduate students in computer science, computational biology, or bio-informatics. Its discussion of current algorithms and techniques also makes it a reference for professionals.
Book Synopsis Digital Nets and Sequences by : Josef Dick
Download or read book Digital Nets and Sequences written by Josef Dick and published by Cambridge University Press. This book was released on 2010-09-09 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: Indispensable for students, invaluable for researchers, this comprehensive treatment of contemporary quasi–Monte Carlo methods, digital nets and sequences, and discrepancy theory starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of the Monte Carlo method, quasi–Monte Carlo rules have increased in popularity, with many fruitful applications in mathematical practice. These rules require nodes with good uniform distribution properties, and digital nets and sequences in the sense of Niederreiter are known to be excellent candidates. Besides the classical theory, the book contains chapters on reproducing kernel Hilbert spaces and weighted integration, duality theory for digital nets, polynomial lattice rules, the newest constructions by Niederreiter and Xing and many more. The authors present an accessible introduction to the subject based mainly on material taught in undergraduate courses with numerous examples, exercises and illustrations.
Book Synopsis Computer Analysis of Sequence Data by : Annette M. Griffin
Download or read book Computer Analysis of Sequence Data written by Annette M. Griffin and published by Springer Science & Business Media. This book was released on 1994-02-08 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: DNA sequencing has become increasingly efficient over the years, resulting in an enormous increase in the amount of data gener ated. In recent years, the focus of sequencing has shifted, from being the endpoint of a project, to being a starting point. This is especially true for such major initiatives as the human genome project, where vast tracts of DNA of unknown function are sequenced. This sheer volume of available data makes advanced computer methods essen tial to analysis, and a familiarity with computers and sequence analy sis software a vital requirement for the researcher involved with DNA sequencing. Even for nonsequencers, a familiarity with sequence analysis software can be important. For instance, gene sequences already present in the databases can be extremely useful in the design of cloning and genetic manipulation experiments. This two-part work on Computer Analysis of Sequence Data is designed to be a practical aid to the researcher who uses computers for the acquisition, storage, or analysis of nucleic acid (and/or pro tein) sequences. Each chapter is written such that a competent scien tist with basic computer literacy can carry out the procedure successfully at the first attempt by simply following the detailed prac tical instructions that have been described by the author. A Notes section, which is included at the end of each chapter, provides advice on overcoming the common problems and pitfalls sometimes encoun tered by users of the sequence analysis software.
Book Synopsis Social Sequence Analysis by : Benjamin Cornwell
Download or read book Social Sequence Analysis written by Benjamin Cornwell and published by Cambridge University Press. This book was released on 2015-08-06 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Social sequence analysis includes a diverse and rapidly growing body of methods that social scientists have developed to help study complex ordered social processes, including chains of transitions, trajectories and other ordered phenomena. Social sequence analysis is not limited by content or time scale and can be used in many different fields, including sociology, communication, information science and psychology. Social Sequence Analysis aims to bring together both foundational and recent theoretical and methodological work on social sequences from the last thirty years. A unique reference book for a new generation of social scientists, this book will aid demographers who study life-course trajectories and family histories, sociologists who study career paths or work/family schedules, communication scholars and micro-sociologists who study conversation, interaction structures and small-group dynamics, as well as social epidemiologists.
Download or read book What Comes First? written by Nick Rebman and published by . This book was released on 2016-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers an introduction to sequencing in which the reader is asked to identify which action came first in a chain of events.
