Sequences

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Automatic Sequences

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Author : Jean-Paul Allouche
language : en
Publisher: Cambridge University Press
Release Date : 2003-07-21

Automatic Sequences written by Jean-Paul Allouche and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-21 with Computers categories.

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.

Computer Analysis Of Sequence Data

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Author : Annette M. Griffin
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-02-08

Computer Analysis Of Sequence Data written by Annette M. Griffin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-08 with Medical categories.

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.

Uniform Distribution Of Sequences

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Author : L. Kuipers
language : en
Publisher: Courier Corporation
Release Date : 2012-05-24

Uniform Distribution Of Sequences written by L. Kuipers and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-24 with Mathematics categories.

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.

Sequences

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Author : Jianlun Xu
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2017-06-30

Sequences written by Jianlun Xu and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-30 with categories.

The book is about arithmetic sequences, geometric sequences, recursive sequences, and arithmetic sequences of high order. The core of the book are important to high school students and college students. As a self-study guide, the book provides plenty of examples and explanations to help readers to grasp math concepts.

Recurrent Sequences

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Author : Dorin Andrica
language : en
Publisher: Springer Nature
Release Date : 2020-09-23

Recurrent Sequences written by Dorin Andrica and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-23 with Mathematics categories.

This self-contained text presents state-of-the-art results on recurrent sequences and their applications in algebra, number theory, geometry of the complex plane and discrete mathematics. It is designed to appeal to a wide readership, ranging from scholars and academics, to undergraduate students, or advanced high school and college students training for competitions. The content of the book is very recent, and focuses on areas where significant research is currently taking place. Among the new approaches promoted in this book, the authors highlight the visualization of some recurrences in the complex plane, the concurrent use of algebraic, arithmetic, and trigonometric perspectives on classical number sequences, and links to many applications. It contains techniques which are fundamental in other areas of math and encourages further research on the topic. The introductory chapters only require good understanding of college algebra, complex numbers, analysis and basic combinatorics. For Chapters 3, 4 and 6 the prerequisites include number theory, linear algebra and complex analysis. The first part of the book presents key theoretical elements required for a good understanding of the topic. The exposition moves on to to fundamental results and key examples of recurrences and their properties. The geometry of linear recurrences in the complex plane is presented in detail through numerous diagrams, which lead to often unexpected connections to combinatorics, number theory, integer sequences, and random number generation. The second part of the book presents a collection of 123 problems with full solutions, illustrating the wide range of topics where recurrent sequences can be found. This material is ideal for consolidating the theoretical knowledge and for preparing students for Olympiads.

Problems And Solutions In Biological Sequence Analysis

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Author : Mark Borodovsky
language : en
Publisher: Cambridge University Press
Release Date : 2006-09-04

Problems And Solutions In Biological Sequence Analysis written by Mark Borodovsky and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-04 with Science categories.

This book is the first of its kind to provide a large collection of bioinformatics problems with accompanying solutions. Notably, the problem set includes all of the problems offered in Biological Sequence Analysis, by Durbin et al. (Cambridge, 1998), widely adopted as a required text for bioinformatics courses at leading universities worldwide. Although many of the problems included in Biological Sequence Analysis as exercises for its readers have been repeatedly used for homework and tests, no detailed solutions for the problems were available. Bioinformatics instructors had therefore frequently expressed a need for fully worked solutions and a larger set of problems for use on courses. This book provides just that: following the same structure as Biological Sequence Analysis and significantly extending the set of workable problems, it will facilitate a better understanding of the contents of the chapters in BSA and will help its readers develop problem-solving skills that are vitally important for conducting successful research in the growing field of bioinformatics. All of the material has been class-tested by the authors at Georgia Tech, where the first ever MSc degree program in Bioinformatics was held.

Handbook Of Mri Pulse Sequences

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Author : Matt A. Bernstein
language : en
Publisher: Elsevier
Release Date : 2004-09-21

Handbook Of Mri Pulse Sequences written by Matt A. Bernstein and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-21 with Mathematics categories.

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

Indian Geological Sequences

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Author : Jai Krishna
language : en
Publisher: Elsevier
Release Date : 2024-06-18

Indian Geological Sequences written by Jai Krishna and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-18 with Science categories.

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

Sequence Stratigraphy Of The Jurassic Lowermost Cretaceous Hettangian Berriasian Of The North Sea Region

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Author : P. Copestake
language : en
Publisher: Geological Society of London
Release Date : 2023-07-26

Sequence Stratigraphy Of The Jurassic Lowermost Cretaceous Hettangian Berriasian Of The North Sea Region written by P. Copestake and has been published by Geological Society of London this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-26 with Science categories.

Sequence stratigraphy has become a powerful tool in the basin analysis of the North Sea Basin, and will continue to play an important role in the maximization of the remaining hydrocarbon potential of the region, whilst also supporting the energy transition in carbon capture and storage projects with Jurassic storage units. This Memoir provides a long-awaited, comprehensive documentation of Jurassic to lowermost Cretaceous sequence stratigraphy of the region (UK, Norway, Denmark and adjacent areas). The volume is amply illustrated by numerous well log displays, core images, seismic lines, chronostratigraphic diagrams and outcrop photographs. Individual chapters discuss the historical usage of sequence stratigraphy in the North Sea Jurassic, sequence stratigraphic concepts and models, application in hydrocarbon field development, definition of stratigraphic traps, well sequence interpretation methodology and controls on sequence development. To complete the volume there are further chapters on North Sea Jurassic lithostratigraphy and its relation to sequence stratigraphy, and descriptions of the biozones used to characterize and correlate the sequences.

A Handbook Of Integer Sequences

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Author : N.J.A. Sloane
language : en
Publisher: Academic Press
Release Date : 2014-05-10

A Handbook Of Integer Sequences written by N.J.A. Sloane and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

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.