Book Fractional Differential Equations

Download or read Fractional Differential Equations PDF, written by Juan J. Nieto and published by MDPI. This book was released on 2019-11-19 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus provides the possibility of introducing integrals and derivatives of an arbitrary order in the mathematical modelling of physical processes, and it has become a relevant subject with applications to various fields, such as anomalous diffusion, propagation in different media, and propogation in relation to materials with different properties. However, many aspects from theoretical and practical points of view have still to be developed in relation to models based on fractional operators. This Special Issue is related to new developments on different aspects of fractional differential equations, both from a theoretical point of view and in terms of applications in different fields such as physics, chemistry, or control theory, for instance. The topics of the Issue include fractional calculus, the mathematical analysis of the properties of the solutions to fractional equations, the extension of classical approaches, or applications of fractional equations to several fields.

Book Handbook of Continued Fractions for Special Functions

Download or read Handbook of Continued Fractions for Special Functions PDF, written by Annie A.M. Cuyt and published by Springer Science & Business Media. This book was released on 2008-04-12 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, the Handbook of mathematical functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over 700 000 copies! But so far no project has been devoted to the systematic study of continued fraction representations for these functions. This handbook is the result of such an endeavour. We emphasise that only 10% of the continued fractions contained in this book, can also be found in the Abramowitz and Stegun project or at the Wolfram website!

Book Geometry of Continued Fractions

    Book Details:
  • Author : Oleg N. Karpenkov
  • Publisher : Springer Nature
  • Release : 2022-05-28
  • ISBN : 3662652773
  • Pages : 462 pages

Download or read Geometry of Continued Fractions PDF, written by Oleg N. Karpenkov and published by Springer Nature. This book was released on 2022-05-28 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The second edition now includes a geometric approach to Gauss Reduction Theory, classification of integer regular polygons and some further new subjects. Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.

Book Continued Fractions

    Book Details:
  • Author :
  • Publisher :
  • Release :
  • ISBN : 9814479438
  • Pages : pages

Download or read Continued Fractions PDF, written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Analytic Theory of Continued Fractions III

Download or read Analytic Theory of Continued Fractions III PDF, written by Lisa Jacobsen and published by Springer. This book was released on 2006-11-14 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Geometry of Continued Fractions

    Book Details:
  • Author : Oleg Karpenkov
  • Publisher : Springer Science & Business Media
  • Release : 2013-08-15
  • ISBN : 3642393683
  • Pages : 405 pages

Download or read Geometry of Continued Fractions PDF, written by Oleg Karpenkov and published by Springer Science & Business Media. This book was released on 2013-08-15 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.

Book Continued Fractions and Signal Processing

Download or read Continued Fractions and Signal Processing PDF, written by Tomas Sauer and published by Springer Nature. This book was released on 2021-09-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Besides their well-known value in number theory, continued fractions are also a useful tool in modern numerical applications and computer science. The goal of the book is to revisit the almost forgotten classical theory and to contextualize it for contemporary numerical applications and signal processing, thus enabling students and scientist to apply classical mathematics on recent problems. The books tries to be mostly self-contained and to make the material accessible for all interested readers. This provides a new view from an applied perspective, combining the classical recursive techniques of continued fractions with orthogonal problems, moment problems, Prony’s problem of sparse recovery and the design of stable rational filters, which are all connected by continued fractions.

Book Stabilization and Control of Fractional Order Systems  A Sliding Mode Approach

Download or read Stabilization and Control of Fractional Order Systems A Sliding Mode Approach PDF, written by Bijnan Bandyopadhyay and published by Springer. This book was released on 2014-07-22 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last two decades fractional differential equations have been used more frequently in physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, electro chemistry and many others. It opens a new and more realistic way to capture memory dependent phenomena and irregularities inside the systems by using more sophisticated mathematical analysis. This monograph is based on the authors’ work on stabilization and control design for continuous and discrete fractional order systems. The initial two chapters and some parts of the third chapter are written in tutorial fashion, presenting all the basic concepts of fractional order system and a brief overview of sliding mode control of fractional order systems. The other parts contain deal with robust finite time stability of fractional order systems, integral sliding mode control of fractional order systems, co-operative control of multi-agent systems modeled as fractional differential equation, robust stabilization of discrete fractional order systems, high performance control using soft variable structure control and contraction analysis by integer and fractional order infinitesimal variations.

Book Analytic Theory of Continued Fractions II

Download or read Analytic Theory of Continued Fractions II PDF, written by Wolfgang J. Thron and published by Springer. This book was released on 2006-11-14 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Continued Fractions and Orthogonal Functions

Download or read Continued Fractions and Orthogonal Functions PDF, written by S. Clement Cooper and published by CRC Press. This book was released on 2020-12-17 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference - the proceedings of a research conference held in Loen, Norway - contains information on the analytic theory of continued fractions and their application to moment problems and orthogonal sequences of functions. Uniting the research efforts of many international experts, this volume: treats strong moment problems, orthogonal polynomials and Laurent polynomials; analyses sequences of linear fractional transformations; presents convergence results, including truncation error bounds; considers discrete distributions and limit functions arising from indeterminate moment problems; discusses Szego polynomials and their applications to frequency analysis; describes the quadrature formula arising from q-starlike functions; and covers continued fractional representations for functions related to the gamma function.;This resource is intended for mathematical and numerical analysts; applied mathematicians; physicists; chemists; engineers; and upper-level undergraduate and agraduate students in these disciplines.

Book Notes on Life Insurance

    Book Details:
  • Author : Gustavus Woodson Smith
  • Publisher :
  • Release : 1875
  • ISBN :
  • Pages : 210 pages

Download or read Notes on Life Insurance PDF, written by Gustavus Woodson Smith and published by . This book was released on 1875 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Integers  Fractions  and Arithmetic

Download or read Integers Fractions and Arithmetic PDF, written by Judith D. Sally and published by American Mathematical Soc.. This book was released on 2012 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, which consists of twelve interactive seminars, is a comprehensive and careful study of the fundamental topics of K-8 arithmetic. The guide aims to help teachers understand the mathematical foundations of number theory in order to strengthen and enrich their mathematics classes. Five seminars are dedicated to fractions and decimals because of their importance in the classroom curriculum. The standard topics are covered in detail, but are arranged in an order that is slightly different from the usual one. Multiplication is treated first, and with that in hand, common denominators and equivalent fractions are more readily understood and are available for use when discussing addition. The book is intended for the professional development of teachers. It is appropriate for teacher education programs as well as for enrichment programs such as Mathematical Circles for Teachers. There are numerous activities in each seminar that teachers can bring into their classrooms. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Book Foundations of Astronomy

    Book Details:
  • Author : Michael A. Seeds
  • Publisher : Cengage Learning
  • Release : 2012-01-01
  • ISBN : 1133711103
  • Pages : 672 pages

Download or read Foundations of Astronomy PDF, written by Michael A. Seeds and published by Cengage Learning. This book was released on 2012-01-01 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fascinating, engaging, and extremely visual, Foundations of Astronomy Twelth Edition emphasizes the scientific method throughout as it guides students to answer two fundamental questions: What are we? And how do we know? Updated with the newest developments and latest discoveries in the exciting study of astronomy, authors Michael Seeds and Dana Backman discuss the interplay between evidence and hypothesis, while providing not only fact but also a conceptual framework for understanding the logic of science. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Book Analytic Theory of Continued Fractions

Download or read Analytic Theory of Continued Fractions PDF, written by W. B. Jones and published by Springer. This book was released on 2006-11-17 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Noncommutative Localization in Algebra and Topology

Download or read Noncommutative Localization in Algebra and Topology PDF, written by Andrew Ranicki and published by Cambridge University Press. This book was released on 2006-02-09 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative localization is a powerful algebraic technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. Originally conceived by algebraists (notably P. M. Cohn), it is now an important tool not only in pure algebra but also in the topology of non-simply-connected spaces, algebraic geometry and noncommutative geometry. This volume consists of 9 articles on noncommutative localization in algebra and topology by J. A. Beachy, P. M. Cohn, W. G. Dwyer, P. A. Linnell, A. Neeman, A. A. Ranicki, H. Reich, D. Sheiham and Z. Skoda. The articles include basic definitions, surveys, historical background and applications, as well as presenting new results. The book is an introduction to the subject, an account of the state of the art, and also provides many references for further material. It is suitable for graduate students and more advanced researchers in both algebra and topology.

Book History of Continued Fractions and Pad   Approximants

Download or read History of Continued Fractions and Pad Approximants PDF, written by Claude Brezinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history of continued fractions is certainly one of the longest among those of mathematical concepts, since it begins with Euclid's algorithm for the great est common divisor at least three centuries B.C. As it is often the case and like Monsieur Jourdain in Moliere's "Ie bourgeois gentilhomme" (who was speak ing in prose though he did not know he was doing so), continued fractions were used for many centuries before their real discovery. The history of continued fractions and Pade approximants is also quite im portant, since they played a leading role in the development of some branches of mathematics. For example, they were the basis for the proof of the tran scendence of 11' in 1882, an open problem for more than two thousand years, and also for our modern spectral theory of operators. Actually they still are of great interest in many fields of pure and applied mathematics and in numerical analysis, where they provide computer approximations to special functions and are connected to some convergence acceleration methods. Con tinued fractions are also used in number theory, computer science, automata, electronics, etc ...

Book Metrical Theory of Continued Fractions

Download or read Metrical Theory of Continued Fractions PDF, written by M. Iosifescu and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is intended to be a complete treatment of the metrical the ory of the (regular) continued fraction expansion and related representations of real numbers. We have attempted to give the best possible results known so far, with proofs which are the simplest and most direct. The book has had a long gestation period because we first decided to write it in March 1994. This gave us the possibility of essentially improving the initial versions of many parts of it. Even if the two authors are different in style and approach, every effort has been made to hide the differences. Let 0 denote the set of irrationals in I = [0,1]. Define the (reg ular) continued fraction transformation T by T (w) = fractional part of n 1/w, w E O. Write T for the nth iterate of T, n E N = {O, 1, ... }, n 1 with TO = identity map. The positive integers an(w) = al(T - (W)), n E N+ = {1,2··· }, where al(w) = integer part of 1/w, w E 0, are called the (regular continued fraction) digits of w. Writing . for arbitrary indeterminates Xi, 1 :::; i :::; n, we have w = lim [al(w),··· , an(w)], w E 0, n--->oo thus explaining the name of T. The above equation will be also written as w = lim [al(w), a2(w),···], w E O.