Recurrent Sequences

Author : Dorin Andrica,Ovidiu Bagdasar
Publisher : Springer Nature
Page : 410 pages
File Size : 40,6 Mb
Release : 2020-09-23
Category : Mathematics
ISBN : 9783030515027

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Recurrent Sequences by Dorin Andrica,Ovidiu Bagdasar Pdf

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.

Author : Graham Everest, Alf van der Poorten,Igor Shparlinski,Thomas Ward
Publisher : American Mathematical Soc.
Page : 318 pages
File Size : 45,6 Mb
Release : 2015-09-03
Category : Electronic
ISBN : 9781470423155

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Recurrence Sequences by Graham Everest, Alf van der Poorten,Igor Shparlinski,Thomas Ward Pdf

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.

Author : Colin Boyd
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 55,8 Mb
Release : 1995-12
Category : Business & Economics
ISBN : 3540606939

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Cryptography and Coding by Colin Boyd Pdf

This monograph provides a formal and systematic exposition of the main results on the existence and optimality of equilibria in economies with increasing returns to scale. For that, a general equilibrium model is carefully constructed first by means of a precise formalization of consumers and firms, and the proof of an abstract existence result. The analysis shifts then to the study of specific normative and positive models which are particularizations the general one, and to the study of the efficiency of equilibrium allocations. The book provides an unified approach of the topic, it maintains a relatively low mathematical complexity and offers a highly self-contained exposition.

Author : Alex Graves
Publisher : Springer
Page : 146 pages
File Size : 47,6 Mb
Release : 2012-02-06
Category : Technology & Engineering
ISBN : 9783642247972

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Supervised Sequence Labelling with Recurrent Neural Networks by Alex Graves Pdf

Supervised sequence labelling is a vital area of machine learning, encompassing tasks such as speech, handwriting and gesture recognition, protein secondary structure prediction and part-of-speech tagging. Recurrent neural networks are powerful sequence learning tools—robust to input noise and distortion, able to exploit long-range contextual information—that would seem ideally suited to such problems. However their role in large-scale sequence labelling systems has so far been auxiliary. The goal of this book is a complete framework for classifying and transcribing sequential data with recurrent neural networks only. Three main innovations are introduced in order to realise this goal. Firstly, the connectionist temporal classification output layer allows the framework to be trained with unsegmented target sequences, such as phoneme-level speech transcriptions; this is in contrast to previous connectionist approaches, which were dependent on error-prone prior segmentation. Secondly, multidimensional recurrent neural networks extend the framework in a natural way to data with more than one spatio-temporal dimension, such as images and videos. Thirdly, the use of hierarchical subsampling makes it feasible to apply the framework to very large or high resolution sequences, such as raw audio or video. Experimental validation is provided by state-of-the-art results in speech and handwriting recognition.

Author : Library of Congress,Library of Congress. Office for Subject Cataloging Policy
Publisher : Unknown
Page : 1432 pages
File Size : 50,7 Mb
Release : 2005
Category : Subject headings, Library of Congress
ISBN : STANFORD:36105118576763

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Library of Congress Subject Headings by Library of Congress,Library of Congress. Office for Subject Cataloging Policy Pdf

Author : Mari Carmen Campoy,María José Luzón
Publisher : Peter Lang
Page : 288 pages
File Size : 48,5 Mb
Release : 2007
Category : Education
ISBN : 3039112759

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Spoken Corpora in Applied Linguistics by Mari Carmen Campoy,María José Luzón Pdf

This volume explores the opportunities that spoken corpora offer and the challenges of research with such corpora. The use and applications of spoken corpora are discussed from the perspective of both language analysis and language pedagogy. Twelve chapters written by corpus linguists analyse an extensive number of spoken corpora based on the oral production of speakers as varied as language learners, users of English as Lingua Franca, native speakers, or speakers of English in academic contexts. This book also highlights the growing emphasis on the use of corpus-based research by examining the implications of corpus findings in educational settings.

Author : Jonė Grigaliūnienė,Inesa Šeškauskienė
Publisher : Cambridge Scholars Publishing
Page : 284 pages
File Size : 46,8 Mb
Release : 2013-11-01
Category : Language Arts & Disciplines
ISBN : 9781443853859

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Anglistics in Lithuania by Jonė Grigaliūnienė,Inesa Šeškauskienė Pdf

This collection of papers offers diverse yet highly professional accounts of multiple cross-linguistic and cross-cultural aspects of English studies in Lithuania. It is valuable for the wide variety of empirical data presented, for the insights into both English and Lithuanian, which, when studied individually, sometimes cannot escape a narrower treatment. Most of the essays in this volume deal with semantics, pragmatics and grammar, while others focus on phonetics and language pedagogy. The collection is also notable for its use of various different methodologies, including triple CL – corpus linguistic, cognitive linguistic and contrastive linguistic – principles of investigation. A particular strength of the book is its focus on the contrastive aspect of study. Further, many of the contributions included here have profound implications for both translation and teaching.

Author : W. Narkiewicz
Publisher : Springer
Page : 133 pages
File Size : 48,6 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540390633

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Uniform Distribution of Sequences of Integers in Residue Classes by W. Narkiewicz Pdf

Author : N. Pytheas Fogg
Publisher : Springer
Page : 404 pages
File Size : 52,7 Mb
Release : 2003-10-24
Category : Mathematics
ISBN : 9783540457145

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Substitutions in Dynamics, Arithmetics and Combinatorics by N. Pytheas Fogg Pdf

A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure. The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems.

Author : V.V. Buldygin,Serguei Solntsev
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 55,5 Mb
Release : 1997-06-30
Category : Mathematics
ISBN : 0792346327

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Asymptotic Behaviour of Linearly Transformed Sums of Random Variables by V.V. Buldygin,Serguei Solntsev Pdf

Limit theorems for random sequences may conventionally be divided into two large parts, one of them dealing with convergence of distributions (weak limit theorems) and the other, with almost sure convergence, that is to say, with asymptotic prop erties of almost all sample paths of the sequences involved (strong limit theorems). Although either of these directions is closely related to another one, each of them has its own range of specific problems, as well as the own methodology for solving the underlying problems. This book is devoted to the second of the above mentioned lines, which means that we study asymptotic behaviour of almost all sample paths of linearly transformed sums of independent random variables, vectors, and elements taking values in topological vector spaces. In the classical works of P.Levy, A.Ya.Khintchine, A.N.Kolmogorov, P.Hartman, A.Wintner, W.Feller, Yu.V.Prokhorov, and M.Loeve, the theory of almost sure asymptotic behaviour of increasing scalar-normed sums of independent random vari ables was constructed. This theory not only provides conditions of the almost sure convergence of series of independent random variables, but also studies different ver sions of the strong law of large numbers and the law of the iterated logarithm. One should point out that, even in this traditional framework, there are still problems which remain open, while many definitive results have been obtained quite recently.

Author : Adrian-Horia Dediu,Carlos Martín-Vide,Bianca Truthe
Publisher : Springer
Page : 580 pages
File Size : 48,9 Mb
Release : 2013-03-15
Category : Computers
ISBN : 9783642370649

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Language and Automata Theory and Applications by Adrian-Horia Dediu,Carlos Martín-Vide,Bianca Truthe Pdf

This book constitutes the refereed proceedings of the 7th International Conference on Language and Automata Theory and Applications, LATA 2013, held in Bilbao, Spain in April 2013. The 45 revised full papers presented together with 5 invited talks were carefully reviewed and selected from 97 initial submissions. The volume features contributions from both classical theory fields and application areas (bioinformatics, systems biology, language technology, artificial intelligence, etc.). Among the topics covered are algebraic language theory; algorithms for semi-structured data mining; algorithms on automata and words; automata and logic; automata for system analysis and program verification; automata, concurrency and Petri nets; automatic structures; cellular automata; combinatorics on words; computability; computational complexity; computational linguistics; data and image compression; decidability questions on words and languages; descriptional complexity; DNA and other models of bio-inspired computing; document engineering; foundations of finite state technology; foundations of XML; fuzzy and rough languages; grammars (Chomsky hierarchy, contextual, multidimensional, unification, categorial, etc.); grammars and automata architectures; grammatical inference and algorithmic learning; graphs and graph transformation; language varieties and semigroups; language-based cryptography; language-theoretic foundations of artificial intelligence and artificial life; parallel and regulated rewriting; parsing; pattern recognition; patterns and codes; power series; quantum, chemical and optical computing; semantics; string and combinatorial issues in computational biology and bioinformatics; string processing algorithms; symbolic dynamics; symbolic neural networks; term rewriting; transducers; trees, tree languages and tree automata; weighted automata.

Author : Bernd Scholz-Reiter,Hans-Dietrich Stahlmann,Arnim Nethe
Publisher : Springer Science & Business Media
Page : 570 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642601200

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Process Modelling by Bernd Scholz-Reiter,Hans-Dietrich Stahlmann,Arnim Nethe Pdf

A process model is very often used for system analysis, design and management in various application areas. Using a process model has the advantage that it has only to be as precise as necessary within the parameters of the individual field of application, whereas the precision externally is less important. This makes process modeling easier and open for structuring. The contributions deal with different approaches to process modelling, especially in the areas of business process modelling, logistics and production processes and water systems.

Author : Valeri P. Ipatov
Publisher : John Wiley & Sons
Page : 400 pages
File Size : 54,9 Mb
Release : 2005-05-06
Category : Science
ISBN : 0470091789

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Spread Spectrum and CDMA by Valeri P. Ipatov Pdf

Spread spectrum and CDMA are cutting-edge technologies widely used in operational radar, navigation and telecommunication systems and play a pivotal role in the development of the forthcoming generations of systems and networks. This comprehensive resource presents the spread spectrum concept as a product of the advancements in wireless IT, shows how and when the classical problems of signal transmission/processing stimulate the application of spread spectrum, and clarifies the advantages of spread spectrum philosophy. Detailed coverage is provided of the tools and instruments for designing spread spectrum and CDMA signals answering why a designer will prefer one solution over another. The approach adopted is wide-ranging, covering issues that apply to both data transmission and data collection systems such as telecommunications, radar, and navigation. Presents a theory-based analysis complemented by practical examples and real world case studies resulting in a self-sufficient treatment of the subject Contains detailed discussions of new trends in spread spectrum technology such as multi-user reception, multicarrier modulation, OFDM, MIMO and space-time coding Provides advice on designing discrete spread spectrum signals and signal sets for time-frequency measuring, synchronization and multi-user communications Features numerous Matlab-based problems and other exercises to encourage the reader to initiate independent investigations and simulations This valuable text provides timely guidance on the current status and future potential of spread spectrum and CDMA and is an invaluable resource for senior undergraduates and postgraduate students, lecturers and practising engineers and researchers involved in the deployment and development of spread spectrum and CDMA technology. Supported by a Companion website on which instructors and lecturers can find a solutions manual for the problems and Matlab programming, electronic versions of some of the figures and other useful resources such as a list of abbreviations.

Author : Nicolai N. Vorobiev
Publisher : Birkhäuser
Page : 180 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034881074

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Fibonacci Numbers by Nicolai N. Vorobiev Pdf

Since their discovery hundreds of years ago, people have been fascinated by the wondrous properties of Fibonacci numbers. Being of mathematical significance in their own right, Fibonacci numbers have had an impact on areas like art and architecture, and their traces can be found in nature and even the behavior of the stock market. Starting with the basic properties of Fibonacci numbers, the present book explores their relevance in number theory, the theory of continued fractions, geometry and approximation theory. Rather than giving a complete account of the subject, a few chosen examples are treated exhaustively. They not only reveal the bearing of Fibonacci numbers on mathematics, but also provide very readable marvels of mathematical reasoning. This book is the translation of the 6th Russian edition (the first edition appeared in the early fifties and became a standard source of information on the subject).

Author : G.E. Bergum,Andreas N. Philippou,Alwyn F. Horadam
Publisher : Springer Science & Business Media
Page : 557 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400902237

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Applications of Fibonacci Numbers by G.E. Bergum,Andreas N. Philippou,Alwyn F. Horadam Pdf

This book contains 43 papers form among the 55 papers presented at the Sixth International Conference on Fibonacci Numbers and Their Applications which was held at Washington State University, Pullman, Washington, from July 18-22, 1994. These papers have been selected after a careful review by well known referees in the field, and they range from elementary number theory to probability and statistics. The Fibonacci numbers and recurrence relations are their unifying bond. It is anticipated that this book, like its five predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. October 30, 1995 The Editors Gerald E. Bergum South Dakota State University Brookings, South Dakota, U.S.A. Alwyn F. Horadam University of New England Armidale, N.S.W., Australia Andreas N. Philippou 26 Atlantis Street Aglangia, Nicosia Cyprus xxi THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Long, Calvin T., Co-Chair Horadam, A.F. (Australia), Co-Chair Webb, William A., Co-Chair Philippou, A.N. (Cyprus), Co-Chair Burke, John Ando, S. (Japan) DeTemple, Duane W.