Download or read book Optimization and Nonstandard Analysis written by J.E. Rubio and published by CRC Press. This book was released on 1994-08-10 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents an up-to-date overview of optimization and control theory, including existence theory, modelling, approximation and numerical methods. It also provides a self-contained treatment of the theory and practice of non-standard analysis and its applications, illustrated with problems and research material based on optimization theory. A complete set of detailed exercises and a thorough bibliography arranged by topic are included.;College or university bookstores may order five or more copies at a special student price, available upon request.
Download or read book Optimization and Nonstandard Analysis written by Julio Enrique Rubio and published by . This book was released on 1994 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Infinitesimal Analysis written by E.I. Gordon and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960's with the epithet 'nonstandard', infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics. The book sets forth the basics of the theory, as well as the most recent applications in, for example, functional analysis, optimization, and harmonic analysis. The concentric style of exposition enables this work to serve as an elementary introduction to one of the most promising mathematical technologies, while revealing up-to-date methods of monadology and hyperapproximation. This is a companion volume to the earlier works on nonstandard methods of analysis by A.G. Kusraev and S.S. Kutateladze (1999), ISBN 0-7923-5921-6 and Nonstandard Analysis and Vector Lattices edited by S.S. Kutateladze (2000), ISBN 0-7923-6619-0
Download or read book Optimization and Nonsmooth Analysis written by Frank H. Clarke and published by SIAM. This book was released on 1990-01-01 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Reviews said of this book that it was 'destined to become a classical reference.' This book has appeared in Russian translation and has been praised both for its lively exposition and its fundamental contributions. The author first develops a general theory of nonsmooth analysis and geometry which, together with a set of associated techniques, has had a profound effect on several branches of analysis and optimization. Clarke then applies these methods to obtain a powerful, unified approach to the analysis of problems in optimal control and mathematical programming. Examples are drawn from economics, engineering, mathematical physics, and various branches of analysis in this reprint volume.
Download or read book Nonstandard Analysis written by Leif O. Arkeryd and published by Springer Science & Business Media. This book was released on 1997-04-30 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of appli cability of NSA more widely known and available to research mathemati cians.
Download or read book Nonstandard Analysis written by R. Lutz and published by Lecture Notes in Mathematics. This book was released on 1981-10 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Developments in Nonstandard Mathematics written by Nigel J Cutland and published by CRC Press. This book was released on 2020-01-30 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains expository papers and articles reporting on recent research by leading world experts in nonstandard mathematics, arising from the International Colloquium on Nonstandard Mathematics held at the University of Aveiro, Portugal in July 1994. Nonstandard mathematics originated with Abraham Robinson, and the body of ideas that have developed from this theory of nonstandard analysis now vastly extends Robinson's work with infinitesimals. The range of applications includes measure and probability theory, stochastic analysis, differential equations, generalised functions, mathematical physics and differential geometry, moreover, the theory has implicaitons for the teaching of calculus and analysis. This volume contains papers touching on all of the abovbe topics, as well as a biographical note about Abraham Robinson based on the opening address given by W.A>J> Luxemburg - who knew Robinson - to the Aveiro conference which marked the 20th anniversary of Robinson's death. This book will be of particular interest to students and researchers in nonstandard analysis, measure theory, generalised functions and mathematical physics.
Download or read book Nonstandard Analysis in Practice written by Francine Diener and published by Springer Science & Business Media. This book was released on 1995-12-14 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the graduate mathematician and researcher to the effective use of nonstandard analysis (NSA). It provides a tutorial introduction to this modern theory of infinitesimals, followed by nine examples of applications, including complex analysis, stochastic differential equations, differential geometry, topology, probability, integration, and asymptotics. It ends with remarks on teaching with infinitesimals.
Download or read book Introduction to Nonstandard Analysis written by Vladislav Ėlievich Li︠a︡nt︠s︡e and published by . This book was released on 1997 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Nonstandard Analysis (briefly NSA) there was solved the old problem of substantiation of differential and integral calculus with application of infinitesimals. (This problem seemed to be unsolvable from the times of Leibniz and Euler.) NSA has changed the face of the whole of Mathematics: it is a new mathematical outlook. It is necessary to emphasise that NSA does not object, does not contradict to the Ordinary Mathematics (briefly OM). NSA extends, supplements OM. (This means that all objects, which exist in OM, exist in NSA, too, and all statements which are true in OM retain to be true in NSA.) NSA often simplifies OM and makes it more transparent. NSA states new mathematical theorems and problems. In fact, NSA is a work of the only scientist, namely A. Robinson (1961). His approach to NSA was constructive. In this book we have chosen an axiomatic approach, due to E. Nelson (1977), which is less difficult to learn and apply. (Our exposition, contrary to that of Nelson, is not always strictly logical. Our aim is only some popularization of NSA, and not its foundations.) The text includes some own results of authors. Good supplements to this book are (D-R], [Die], [Lut], [Dav], [Alb], [Cut].
Download or read book Hyperspaces written by Alejandro Illanes and published by CRC Press. This book was released on 1999-01-04 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents hyperspace fundamentals, offering a basic overview and a foundation for further study. Topics include the topology for hyperspaces, examples of geometric models for hyperspaces, 2x and C(X) for Peano continua X, arcs in hyperspaces, the shape and contractability of hyperspaces, hyperspaces and the fixed point property, and Whitney maps. The text contains examples and exercises throughout, and provides proofs for most results.
Download or read book Nonsmooth Optimization Analysis And Algorithms With Applications To Optimal Control written by Marko M Makela and published by World Scientific. This book was released on 1992-05-07 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained elementary study for nonsmooth analysis and optimization, and their use in solution of nonsmooth optimal control problems. The first part of the book is concerned with nonsmooth differential calculus containing necessary tools for nonsmooth optimization. The second part is devoted to the methods of nonsmooth optimization and their development. A proximal bundle method for nonsmooth nonconvex optimization subject to nonsmooth constraints is constructed. In the last part nonsmooth optimization is applied to problems arising from optimal control of systems covered by partial differential equations. Several practical problems, like process control and optimal shape design problems are considered.
Download or read book Pseudo Differential Equations And Stochastics Over Non Archimedean Fields written by Anatoly Kochubei and published by CRC Press. This book was released on 2001-08-03 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides comprehensive coverage of the most recent developments in the theory of non-Archimedean pseudo-differential equations and its application to stochastics and mathematical physics--offering current methods of construction for stochastic processes in the field of p-adic numbers and related structures. Develops a new theory for parabolic equat
Download or read book Library of Congress Subject Headings written by Library of Congress. Cataloging Policy and Support Office and published by . This book was released on 2009 with total page 1596 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 2005 with total page 1432 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differential Geometry with Applications to Mechanics and Physics written by Yves Talpaert and published by CRC Press. This book was released on 2000-09-12 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential forms; Lie derivative and Lie algebra; n-form integration on n-manifold; Riemann geometry; and more. It includes 133 solved exercises.
Download or read book Geometric Function Theory in One and Higher Dimensions written by Ian Graham and published by CRC Press. This book was released on 2003-03-18 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference details valuable results that lead to improvements in existence theorems for the Loewner differential equation in higher dimensions, discusses the compactness of the analog of the Caratheodory class in several variables, and studies various classes of univalent mappings according to their geometrical definitions. It introduces the in
Download or read book Applications Of Orlicz Spaces written by M.M. Rao and published by CRC Press. This book was released on 2002-02-08 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents previously unpublished material on the fundumental pronciples and properties of Orlicz sequence and function spaces. Examines the sample path behavior of stochastic processes. Provides practical applications in statistics and probability.
