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An Introduction To Inverse Limits With Set Valued Functions
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Book Synopsis An Introduction to Inverse Limits with Set-valued Functions by : W.T. Ingram
Download or read book An Introduction to Inverse Limits with Set-valued Functions written by W.T. Ingram and published by Springer Science & Business Media. This book was released on 2012-08-11 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse limits with set-valued functions are quickly becoming a popular topic of research due to their potential applications in dynamical systems and economics. This brief provides a concise introduction dedicated specifically to such inverse limits. The theory is presented along with detailed examples which form the distinguishing feature of this work. The major differences between the theory of inverse limits with mappings and the theory with set-valued functions are featured prominently in this book in a positive light. The reader is assumed to have taken a senior level course in analysis and a basic course in topology. Advanced undergraduate and graduate students, and researchers working in this area will find this brief useful.
Book Synopsis An Introduction to Inverse Limits with Set-valued Functions by :
Download or read book An Introduction to Inverse Limits with Set-valued Functions written by and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse Limits written by W.T. Ingram and published by Springer Science & Business Media. This book was released on 2011-11-06 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse limits provide a powerful tool for constructing complicated spaces from simple ones. They also turn the study of a dynamical system consisting of a space and a self-map into a study of a (likely more complicated) space and a self-homeomorphism. In four chapters along with an appendix containing background material the authors develop the theory of inverse limits. The book begins with an introduction through inverse limits on [0,1] before moving to a general treatment of the subject. Special topics in continuum theory complete the book. Although it is not a book on dynamics, the influence of dynamics can be seen throughout; for instance, it includes studies of inverse limits with maps from families of maps that are of interest to dynamicists such as the logistic and the tent families. This book will serve as a useful reference to graduate students and researchers in continuum theory and dynamical systems. Researchers working in applied areas who are discovering inverse limits in their work will also benefit from this book.
Book Synopsis Topics on Continua by : Sergio Macías
Download or read book Topics on Continua written by Sergio Macías and published by Springer. This book was released on 2018-07-24 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a significant companion text to the existing literature on continuum theory. It opens with background information of continuum theory, so often missing from the preceding publications, and then explores the following topics: inverse limits, the Jones set function T, homogenous continua, and n-fold hyperspaces. In this new edition of the book, the author builds on the aforementioned topics, including the unprecedented presentation of n-fold hyperspace suspensions and induced maps on n-fold hyperspaces. The first edition of the book has had a remarkable impact on the continuum theory community. After twelve years, this updated version will also prove to be an excellent resource within the field of topology.
Book Synopsis Set-Valued, Convex, and Nonsmooth Analysis in Dynamics and Control by : Rafal K. Goebel
Download or read book Set-Valued, Convex, and Nonsmooth Analysis in Dynamics and Control written by Rafal K. Goebel and published by SIAM. This book was released on 2024-06-26 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set-valued analysis, convex analysis, and nonsmooth analysis are relatively modern branches of mathematical analysis that have become increasingly relevant in current control theory and control engineering literature. This book serves as a broad introduction to analytical tools in these fields and to their applications in dynamical and control systems and is the first to cover these topics with this scope and at this level. Both continuous-time and discrete-time mutlivalued dynamics, modeled by differential and difference inclusions, are considered. Set-Valued, Convex, and Nonsmooth Analysis in Dynamics and Control: An Introduction is aimed at graduate students in control engineering and applied mathematics and researchers in control engineering who have no prior exposure to set-valued, convex, and nonsmooth analysis. The book will also be of interest to advanced undergraduate mathematics students and mathematicians with no prior exposure to the topic. The expected mathematical background is a course on nonlinear differential equations / dynamical systems and a course on real analysis. Knowledge of some control theory is helpful, but not essential.
Book Synopsis Implicit Functions and Solution Mappings by : Asen L. Dontchev
Download or read book Implicit Functions and Solution Mappings written by Asen L. Dontchev and published by Springer. This book was released on 2014-06-18 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis. This second edition of Implicit Functions and Solution Mappings presents an updated and more complete picture of the field by including solutions of problems that have been solved since the first edition was published, and places old and new results in a broader perspective. The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. Updates to this edition include new sections in almost all chapters, new exercises and examples, updated commentaries to chapters and an enlarged index and references section.
Book Synopsis Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables by : Shoumei Li
Download or read book Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables written by Shoumei Li and published by Springer Science & Business Media. This book was released on 2002-10-31 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a clear, systematic treatment of convergence theorems of set-valued random variables (random sets) and fuzzy set-valued random variables (random fuzzy sets). Topics such as strong laws of large numbers and central limit theorems, including new results in connection with the theory of empirical processes are covered. The author's own recent developments on martingale convergence theorems and their applications to data processing are also included. The mathematical foundations along with a clear explanation such as Hölmander's embedding theorem, notions of various convergence of sets and fuzzy sets, Aumann integrals, conditional expectations, selection theorems, measurability and integrability arguments for both set-valued and fuzzy set-valued random variables and newly obtained optimizations techniques based on invariant properties are also given.
Download or read book Topology written by K. Kuratowski and published by Elsevier. This book was released on 2014-05-12 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology, Volume I deals with topology and covers topics ranging from operations in logic and set theory to Cartesian products, mappings, and orderings. Cardinal and ordinal numbers are also discussed, along with topological, metric, and complete spaces. Great use is made of closure algebra. Comprised of three chapters, this volume begins with a discussion on general topological spaces as well as their specialized aspects, including regular, completely regular, and normal spaces. Fundamental notions such as base, subbase, cover, and continuous mapping, are considered, together with operations such as the exponential topology and quotient topology. The next chapter is devoted to the study of metric spaces, starting with more general spaces, having the limit as its primitive notion. The space is assumed to be metric separable, and this includes problems of cardinality and dimension. Dimension theory and the theory of Borei sets, Baire functions, and related topics are also discussed. The final chapter is about complete spaces and includes problems of general function theory which can be expressed in topological terms. The book includes two appendices, one on applications of topology to mathematical logics and another to functional analysis. This monograph will be helpful to students and practitioners of algebra and mathematics.
Book Synopsis Set-Valued Analysis by : Jean-Pierre Aubin
Download or read book Set-Valued Analysis written by Jean-Pierre Aubin and published by Springer Science & Business Media. This book was released on 2009-03-02 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An elegantly written, introductory overview of the field, with a near perfect choice of what to include and what not, enlivened in places by historical tidbits and made eminently readable throughout by crisp language. It has succeeded in doing the near-impossible—it has made a subject which is generally inhospitable to nonspecialists because of its ‘family jargon’ appear nonintimidating even to a beginning graduate student." —The Journal of the Indian Institute of Science "The book under review gives a comprehensive treatment of basically everything in mathematics that can be named multivalued/set-valued analysis. ...The book is highly recommended for mathematicians and graduate students who will find here a very comprehensive treatment of set-valued analysis." —Mathematical Reviews "This book provides a thorough introduction to multivalued or set-valued analysis... The style is lively and vigorous, the relevant historical comments and suggestive overviews increase the interest for this work...Graduate students and mathematicians of every persuasion will welcome this unparalleled guide to set-valued analysis." —Zentralblatt Math
Book Synopsis Set-Valued Force Laws by : Christoph Glocker
Download or read book Set-Valued Force Laws written by Christoph Glocker and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: As one of the oldest natural sciences, mechanics occupies a certain pioneering role in determining the development of exact sciences through its interaction with mathematics. As a matter of fact, there is hardly an area in mathematics that hasn't found an application of some form in mechanics. It is thus almost inevitable that theoretical methods in mechanics are highly developed and laid out on different levels of abstraction. With the spread of digital processors this goes as far as the implementation in commercial computer codes, where the user is merely con fronted on the surface with the processes that run in the background, i. e. mechan ics as such: in teaching and research, as well as in the context of industry, me chanics is much more, and must remain much more than the mere production of data with the help of a processor. Mechanics, as it is talked about here, tradition ally includes a wide spectrum, ranging from applied mechanics, analytical and technical mechanics to modeling. and experimental mechanics, as well as technical realization. It also includes the subdisciplines of rigid body mechanics, continuum mechanics, or fluid mechanics, to mention only a few. One of the fundamental and most important concepts used by nearly all natural sciences is the concept of linearization, which assumes the differentiability of mappings. As a matter of fact, all of classical mechanics is based on the avail ability of this quality.
Author :R. Tyrrell Rockafellar Publisher :Springer Science & Business Media ISBN 13 :3642024319 Total Pages :747 pages Book Rating :4.6/5 (42 download)
Book Synopsis Variational Analysis by : R. Tyrrell Rockafellar
Download or read book Variational Analysis written by R. Tyrrell Rockafellar and published by Springer Science & Business Media. This book was released on 2009-06-26 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
Book Synopsis Advanced Calculus by : Lynn Harold Loomis
Download or read book Advanced Calculus written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Book Synopsis Basic Category Theory by : Tom Leinster
Download or read book Basic Category Theory written by Tom Leinster and published by Cambridge University Press. This book was released on 2014-07-24 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: A short introduction ideal for students learning category theory for the first time.
Book Synopsis Introduction to Functions of a Complex Variable by : J. H. Curtiss
Download or read book Introduction to Functions of a Complex Variable written by J. H. Curtiss and published by CRC Press. This book was released on 2021-07-28 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes information on elementary general topology, the Cauchy Integral Theorem and concepts of homology and homotopy in their application to the Cauchy theory. It is intended for an introductory course in complex analysis at the first-year graduate and advanced undergraduate level.
Book Synopsis Introduction to Complex Analysis by : Hilary A. Priestley
Download or read book Introduction to Complex Analysis written by Hilary A. Priestley and published by Oxford University Press, USA. This book was released on 2003 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition of Priestley's well-known text is aimed at students taking an introductory core course in Complex Analysis, a classical and central area of mathematics.
Book Synopsis Applied Functional Analysis by : Jean-Pierre Aubin
Download or read book Applied Functional Analysis written by Jean-Pierre Aubin and published by John Wiley & Sons. This book was released on 2011-09-30 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: A novel, practical introduction to functional analysis In the twenty years since the first edition of Applied Functional Analysis was published, there has been an explosion in the number of books on functional analysis. Yet none of these offers the unique perspective of this new edition. Jean-Pierre Aubin updates his popular reference on functional analysis with new insights and recent discoveries-adding three new chapters on set-valued analysis and convex analysis, viability kernels and capture basins, and first-order partial differential equations. He presents, for the first time at an introductory level, the extension of differential calculus in the framework of both the theory of distributions and set-valued analysis, and discusses their application for studying boundary-value problems for elliptic and parabolic partial differential equations and for systems of first-order partial differential equations. To keep the presentation concise and accessible, Jean-Pierre Aubin introduces functional analysis through the simple Hilbertian structure. He seamlessly blends pure mathematics with applied areas that illustrate the theory, incorporating a broad range of examples from numerical analysis, systems theory, calculus of variations, control and optimization theory, convex and nonsmooth analysis, and more. Finally, a summary of the essential theorems as well as exercises reinforcing key concepts are provided. Applied Functional Analysis, Second Edition is an excellent and timely resource for both pure and applied mathematicians.
Book Synopsis Introduction to Real Analysis by : William F. Trench
Download or read book Introduction to Real Analysis written by William F. Trench and published by Prentice Hall. This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. The real number system. Differential calculus of functions of one variable. Riemann integral functions of one variable. Integral calculus of real-valued functions. Metric Spaces. For those who want to gain an understanding of mathematical analysis and challenging mathematical concepts.
