Recurrent Sequences
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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.
Recurrence Sequences
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Author : Graham Everest
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-09-03
Recurrence Sequences written by Graham Everest and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-03 with Mathematics categories.
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.
Library Of Congress Subject Headings
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Author : Library of Congress
language : en
Publisher:
Release Date : 2004
Library Of Congress Subject Headings written by Library of Congress and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Subject headings, Library of Congress categories.
Supervised Sequence Labelling With Recurrent Neural Networks
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Author : Alex Graves
language : en
Publisher: Springer
Release Date : 2012-02-06
Supervised Sequence Labelling With Recurrent Neural Networks written by Alex Graves and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-06 with Technology & Engineering categories.
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.
Spoken Corpora In Applied Linguistics
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Author : Mari Carmen Campoy
language : en
Publisher: Peter Lang
Release Date : 2007
Spoken Corpora In Applied Linguistics written by Mari Carmen Campoy and has been published by Peter Lang this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Education categories.
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.
Anglistics In Lithuania
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Author : Jonė Grigaliūnienė
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2013-11-01
Anglistics In Lithuania written by Jonė Grigaliūnienė and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-01 with Language Arts & Disciplines categories.
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.
Uniform Distribution Of Sequences Of Integers In Residue Classes
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Author : W. Narkiewicz
language : en
Publisher: Springer
Release Date : 2006-12-08
Uniform Distribution Of Sequences Of Integers In Residue Classes written by W. Narkiewicz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
Library Of Congress Subject Headings
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Author : Library of Congress. Cataloging Policy and Support Office
language : en
Publisher:
Release Date : 2004
Library Of Congress Subject Headings written by Library of Congress. Cataloging Policy and Support Office and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Subject headings, Library of Congress categories.
Substitutions In Dynamics Arithmetics And Combinatorics
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Author : N. Pytheas Fogg
language : en
Publisher: Springer
Release Date : 2003-10-24
Substitutions In Dynamics Arithmetics And Combinatorics written by N. Pytheas Fogg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-24 with Mathematics categories.
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.
Asymptotic Behaviour Of Linearly Transformed Sums Of Random Variables
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Author : V.V. Buldygin
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-06-30
Asymptotic Behaviour Of Linearly Transformed Sums Of Random Variables written by V.V. Buldygin 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 1997-06-30 with Mathematics categories.
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.