Download or read book Constructive Algebra and Systems Theory written by Michiel Hazewinkel and published by . This book was released on 2006 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Constructive Algebra and Systems Theory written by and published by . This book was released on 1951 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computability Theory and Its Applications written by Peter Cholak and published by American Mathematical Soc.. This book was released on 2000 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles presents a snapshot of the status of computability theory at the end of the millennium and a list of fruitful directions for future research. The papers represent the works of experts in the field who were invited speakers at the AMS-IMS-SIAM 1999 Summer Conference on Computability Theory and Applications, which focused on open problems in computability theory and on some related areas in which the ideas, methods, and/or results of computability theory play a role. Some presentations are narrowly focused; others cover a wider area. Topics included from "pure" computability theory are the computably enumerable degrees (M. Lerman), the computably enumerable sets (P. Cholak, R. Soare), definability issues in the c.e. and Turing degrees (A. Nies, R. Shore) and other degree structures (M. Arslanov, S. Badaev and S. Goncharov, P. Odifreddi, A. Sorbi). The topics involving relations between computability and other areas of logic and mathematics are reverse mathematics and proof theory (D. Cenzer and C. Jockusch, C. Chong and Y. Yang, H. Friedman and S. Simpson), set theory (R. Dougherty and A. Kechris, M. Groszek, T. Slaman) and computable mathematics and model theory (K. Ambos-Spies and A. Kucera, R. Downey and J. Remmel, S. Goncharov and B. Khoussainov, J. Knight, M. Peretyat'kin, A. Shlapentokh).
Download or read book Varieties of Constructive Mathematics written by Douglas Bridges and published by Cambridge University Press. This book was released on 1987-04-24 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of constructive approaches to pure mathematics emphasizing the viewpoint of Errett Bishop's school. Considers intuitionism, Russian constructivism, and recursive analysis, with comparisons among the various approaches included where appropriate.
Download or read book Foundations of Constructive Mathematics written by M.J. Beeson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about some recent work in a subject usually considered part of "logic" and the" foundations of mathematics", but also having close connec tions with philosophy and computer science. Namely, the creation and study of "formal systems for constructive mathematics". The general organization of the book is described in the" User's Manual" which follows this introduction, and the contents of the book are described in more detail in the introductions to Part One, Part Two, Part Three, and Part Four. This introduction has a different purpose; it is intended to provide the reader with a general view of the subject. This requires, to begin with, an elucidation of both the concepts mentioned in the phrase, "formal systems for constructive mathematics". "Con structive mathematics" refers to mathematics in which, when you prove that l a thing exists (having certain desired properties) you show how to find it. Proof by contradiction is the most common way of proving something exists without showing how to find it - one assumes that nothing exists with the desired properties, and derives a contradiction. It was only in the last two decades of the nineteenth century that mathematicians began to exploit this method of proof in ways that nobody had previously done; that was partly made possible by the creation and development of set theory by Georg Cantor and Richard Dedekind.
Download or read book Perspectives in Mathematical System Theory Control and Signal Processing written by Jan C. Willems and published by Springer Science & Business Media. This book was released on 2010-02-28 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift, published on the occasion of the sixtieth birthday of Yutaka - mamoto (‘YY’ as he is occasionally casually referred to), contains a collection of articles by friends, colleagues, and former Ph.D. students of YY. They are a tribute to his friendship and his scienti?c vision and oeuvre, which has been a source of inspiration to the authors. Yutaka Yamamoto was born in Kyoto, Japan, on March 29, 1950. He studied applied mathematics and general engineering science at the Department of Applied Mathematics and Physics of Kyoto University, obtaining the B.S. and M.Sc. degrees in 1972 and 1974. His M.Sc. work was done under the supervision of Professor Yoshikazu Sawaragi. In 1974, he went to the Center for Mathematical System T- ory of the University of Florida in Gainesville. He obtained the M.Sc. and Ph.D. degrees, both in Mathematics, in 1976 and 1978, under the direction of Professor Rudolf Kalman.
Download or read book Methods of Algebraic Geometry in Control Theory Part I written by Peter Falb and published by Springer. This book was released on 2018-08-25 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An introduction to the ideas of algebraic geometry in the motivated context of system theory." Thus the author describes his textbook that has been specifically written to serve the needs of students of systems and control. Without sacrificing mathematical care, the author makes the basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis is on constructive methods and clarity rather than abstraction. The student will find here a clear presentation with an applied flavor, of the core ideas in the algebra-geometric treatment of scalar linear system theory. The author introduces the four representations of a scalar linear system and establishes the major results of a similar theory for multivariable systems appearing in a succeeding volume (Part II: Multivariable Linear Systems and Projective Algebraic Geometry). Prerequisites are the basics of linear algebra, some simple notions from topology and the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises are an integral part of the treatment and are used where relevant in the main body of the text. The present, softcover reprint is designed to make this classic textbook available to a wider audience. "This book is a concise development of affine algebraic geometry together with very explicit links to the applications...[and] should address a wide community of readers, among pure and applied mathematicians." —Monatshefte für Mathematik
Download or read book Constructive Commutative Algebra written by Ihsen Yengui and published by Springer. This book was released on 2015-12-11 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this book is to find the constructive content hidden in abstract proofs of concrete theorems in Commutative Algebra, especially in well-known theorems concerning projective modules over polynomial rings (mainly the Quillen-Suslin theorem) and syzygies of multivariate polynomials with coefficients in a valuation ring. Simple and constructive proofs of some results in the theory of projective modules over polynomial rings are also given, and light is cast upon recent progress on the Hermite ring and Gröbner ring conjectures. New conjectures on unimodular completion arising from our constructive approach to the unimodular completion problem are presented. Constructive algebra can be understood as a first preprocessing step for computer algebra that leads to the discovery of general algorithms, even if they are sometimes not efficient. From a logical point of view, the dynamical evaluation gives a constructive substitute for two highly nonconstructive tools of abstract algebra: the Law of Excluded Middle and Zorn's Lemma. For instance, these tools are required in order to construct the complete prime factorization of an ideal in a Dedekind ring, whereas the dynamical method reveals the computational content of this construction. These lecture notes follow this dynamical philosophy.
Download or read book Handbook of Constructive Mathematics written by Douglas Bridges and published by Cambridge University Press. This book was released on 2023-03-31 with total page 863 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives a complete overview of modern constructive mathematics and its applications through surveys by leading experts.
Download or read book The Metamathematics of Algebraic Systems written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Metamathematics of Algebraic Systems
Download or read book Model Based Control written by Paul M.J. van den Hof and published by Springer Science & Business Media. This book was released on 2009-08-05 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model-Based Control will be a collection of state-of-the-art contributions in the field of modelling, identification, robust control and optimization of dynamical systems, with particular attention to the application domains of motion control systems (high-accuracy positioning systems) and large scale industrial process control systems.The book will be directed to academic and industrial people involved in research in systems and control, industrial process control and mechatronics.
Download or read book Max linear Systems Theory and Algorithms written by Peter Butkovič and published by Springer Science & Business Media. This book was released on 2010-08-05 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent years have seen a significant rise of interest in max-linear theory and techniques. Specialised international conferences and seminars or special sessions devoted to max-algebra have been organised. This book aims to provide a first detailed and self-contained account of linear-algebraic aspects of max-algebra for general (that is both irreducible and reducible) matrices. Among the main features of the book is the presentation of the fundamental max-algebraic theory (Chapters 1-4), often scattered in research articles, reports and theses, in one place in a comprehensive and unified form. This presentation is made with all proofs and in full generality (that is for both irreducible and reducible matrices). Another feature is the presence of advanced material (Chapters 5-10), most of which has not appeared in a book before and in many cases has not been published at all. Intended for a wide-ranging readership, this book will be useful for anyone with basic mathematical knowledge (including undergraduate students) who wish to learn fundamental max-algebraic ideas and techniques. It will also be useful for researchers working in tropical geometry or idempotent analysis.
Download or read book Solving Polynomial Equations written by Alicia Dickenstein and published by Springer Science & Business Media. This book was released on 2005-04-27 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision. Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants, residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications.
Download or read book Real Analysis written by Mark Bridger and published by John Wiley & Sons. This book was released on 2011-10-14 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique approach to analysis that lets you apply mathematics across a range of subjects This innovative text sets forth a thoroughly rigorous modern account of the theoretical underpinnings of calculus: continuity, differentiability, and convergence. Using a constructive approach, every proof of every result is direct and ultimately computationally verifiable. In particular, existence is never established by showing that the assumption of non-existence leads to a contradiction. The ultimate consequence of this method is that it makes sense—not just to math majors but also to students from all branches of the sciences. The text begins with a construction of the real numbers beginning with the rationals, using interval arithmetic. This introduces readers to the reasoning and proof-writing skills necessary for doing and communicating mathematics, and it sets the foundation for the rest of the text, which includes: Early use of the Completeness Theorem to prove a helpful Inverse Function Theorem Sequences, limits and series, and the careful derivation of formulas and estimates for important functions Emphasis on uniform continuity and its consequences, such as boundedness and the extension of uniformly continuous functions from dense subsets Construction of the Riemann integral for functions uniformly continuous on an interval, and its extension to improper integrals Differentiation, emphasizing the derivative as a function rather than a pointwise limit Properties of sequences and series of continuous and differentiable functions Fourier series and an introduction to more advanced ideas in functional analysis Examples throughout the text demonstrate the application of new concepts. Readers can test their own skills with problems and projects ranging in difficulty from basic to challenging. This book is designed mainly for an undergraduate course, and the author understands that many readers will not go on to more advanced pure mathematics. He therefore emphasizes an approach to mathematical analysis that can be applied across a range of subjects in engineering and the sciences.
Download or read book New Trends in Systems Theory written by Giuseppe Conte and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 741 pages. Available in PDF, EPUB and Kindle. Book excerpt: The University of Genoa - Ohio State University Joint Conference on New Trends in Systems Theory was held at the Badia di S. Andrea in Genoa on July 9-11, 1990. This Proceedings volume contains articles based on two of the three Plenary talks and most of the shorter presentations. The papers are arranged by author, and no attempt has been made to organize them by topic. We would like to thank the members of the Scientific Committee and of the Program Committee, the speakers and authors, and everyone who attended the conference. Approximately 120 researchers and students from all over the world visited Genoa for the meeting, representing a wide spectrum of areas in pure and applied control and systems theory. The success of the conference depended on their high level of scientific and engineering expertise, not to mention their enthusiasm. The Conference on New Trends in Systems Theory would not have been possible without the help of a great many institutions and people. We would like to thank the University of Genoa, particularly Professor Enrico Beltrametti, and the Ohio State University's Columbian Quincentenary Committee led by Professor Christian Zacher, for encouragement and financial assistance. The University of Genoa Mathematics Department and Communication, Computer and System Sciences Department supplied assistance and technical help. The staff of the Consorzio Genova Ricerche, particularly Ms. Piera Ponta and Ms. Camilla Marconi, worked diligently over many months and especially during the conference itself to insure a smooth and enjoyable meeting.
Download or read book Approximate Commutative Algebra written by Lorenzo Robbiano and published by Springer Science & Business Media. This book was released on 2009-09-18 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximate Commutative Algebra is an emerging field of research which endeavours to bridge the gap between traditional exact Computational Commutative Algebra and approximate numerical computation. The last 50 years have seen enormous progress in the realm of exact Computational Commutative Algebra, and given the importance of polynomials in scientific modelling, it is very natural to want to extend these ideas to handle approximate, empirical data deriving from physical measurements of phenomena in the real world. In this volume nine contributions from established researchers describe various approaches to tackling a variety of problems arising in Approximate Commutative Algebra.
Download or read book Computer Aided Systems Theory EUROCAST 2009 written by Roberto Moreno Díaz and published by Springer. This book was released on 2009-09-30 with total page 967 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of CAST as Computer Aided Systems Theory was introduced by F. Pichler in the late 1980s to refer to computer theoretical and practical developments as tools for solving problems in system science. It was thought of as the third component (the other two being CAD and CAM) required to complete the path from computer and systems sciences to practical developments in science and engineering. Franz Pichler, of the University of Linz, organized the first CAST workshop in April 1988, which demonstrated the acceptance of the concepts by the scientific and technical community. Next, the University of Las Palmas de Gran Canaria joined the University of Linz to organize the first international meeting on CAST (Las Palmas, February 1989) under the name EUROCAST'89. This proved to be a very successful gathering of systems theorists, computer scientists and engineers from most European countries, North America and Japan. It was agreed that EUROCAST international conferences would be organized every two years, alternating between Las Palmas de Gran Canaria and a continental European location. From 2001 the conference has been held exclusively in Las Palmas. Thus, successive EUROCAST meetings took place in Krems (1991), Las Palmas (1993), In- bruck (1995), Las Palmas (1997), Vienna (1999), Las Palmas (2001), Las Palmas (2003) Las Palmas (2005) and Las Palmas (2007), in addition to an extra-European CAST c- ference in Ottawa in 1994.
