Boolean Valued Analysis
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Boolean Valued Analysis
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Author : A. G. Kusraev
language : en
Publisher:
Release Date : 2014-01-15
Boolean Valued Analysis written by A. G. Kusraev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Boolean Valued Analysis
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Author : A. G. Kusraev
language : en
Publisher: Springer Science & Business Media
Release Date : 1999
Boolean Valued Analysis written by A. G. Kusraev 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 1999 with Mathematics categories.
Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the so-called non-standard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe.
Analysis Of Boolean Functions
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Author : Ryan O'Donnell
language : en
Publisher: Cambridge University Press
Release Date : 2014-06-05
Analysis Of Boolean Functions written by Ryan O'Donnell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-05 with Computers categories.
This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics.
Operator Theory And Harmonic Analysis
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Author : Alexey N. Karapetyants
language : en
Publisher: Springer Nature
Release Date : 2021-09-27
Operator Theory And Harmonic Analysis written by Alexey N. Karapetyants and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-27 with Mathematics categories.
This volume is part of the collaboration agreement between Springer and the ISAAC society. This is the first in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University in Rostov-on-Don, Russia. This volume is focused on general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multiparameter objects required when considering operators and objects with variable parameters.
Nonstandard Methods Of Analysis
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Author : A.G. Kusraev
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonstandard Methods Of Analysis written by A.G. Kusraev 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 2012-12-06 with Mathematics categories.
Nonstandard Methods of Analysis is concerned with the main trends in this field; infinitesimal analysis and Boolean-valued analysis. The methods that have been developed in the last twenty-five years are explained in detail, and are collected in book form for the first time. Special attention is paid to general principles and fundamentals of formalisms for infinitesimals as well as to the technique of descents and ascents in a Boolean-valued universe. The book also includes various novel applications of nonstandard methods to ordered algebraic systems, vector lattices, subdifferentials, convex programming etc. that have been developed in recent years. For graduate students, postgraduates and all researchers interested in applying nonstandard methods in their work.
Boolean Valued Analysis Approach To The Trace Problem Of Aw Algebras
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Author : Masanao Ozawa
language : en
Publisher:
Release Date : 1985
Boolean Valued Analysis Approach To The Trace Problem Of Aw Algebras written by Masanao Ozawa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
What Is Boolean Valued Analysis
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Author : Semën Samsonovič Kutateladze
language : en
Publisher:
Release Date : 2006
What Is Boolean Valued Analysis written by Semën Samsonovič Kutateladze and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Probabilistic Analysis Of Belief Functions
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Author : Ivan Kramosil
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Probabilistic Analysis Of Belief Functions written by Ivan Kramosil 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 2012-12-06 with Mathematics categories.
Inspired by the eternal beauty and truth of the laws governing the run of stars on heavens over his head, and spurred by the idea to catch, perhaps for the smallest fraction of the shortest instant, the Eternity itself, man created such masterpieces of human intellect like the Platon's world of ideas manifesting eternal truths, like the Euclidean geometry, or like the Newtonian celestial me chanics. However, turning his look to the sub-lunar world of our everyday efforts, troubles, sorrows and, from time to time but very, very seldom, also our successes, he saw nothing else than a world full of uncertainty and tem porariness. One remedy or rather consolation was that of the deep and sage resignation offered by Socrates: I know, that I know nothing. But, happy or unhappy enough, the temptation to see and to touch at least a very small por tion of eternal truth also under these circumstances and behind phenomena charged by uncertainty was too strong. Probability theory in its most sim ple elementary setting entered the scene. It happened in the same, 17th and 18th centuries, when celestial mechanics with its classical Platonist paradigma achieved its greatest triumphs. The origins of probability theory were inspired by games of chance like roulettes, lotteries, dices, urn schemata, etc. and probability values were simply defined by the ratio of successful or winning results relative to the total number of possible outcomes.
Infinitesimal Analysis
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Author : E.I. Gordon
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Infinitesimal Analysis written by E.I. Gordon 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 2013-03-14 with Mathematics categories.
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
Nonstandard Analysis And Vector Lattices
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Author : Semën Samsonovich Kutateladze
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonstandard Analysis And Vector Lattices written by Semën Samsonovich Kutateladze 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 2012-12-06 with Mathematics categories.
Nonstandard methods of analysis consist generally in comparative study of two interpretations of a mathematical claim or construction given as a formal symbolic expression by means of two different set-theoretic models: one, a "standard" model and the other, a "nonstandard" model. The second half of the twentieth century is a period of significant progress in these methods and their rapid development in a few directions. The first of the latter appears often under the name coined by its inventor, A. Robinson. This memorable but slightly presumptuous and defiant term, non standard analysis, often swaps places with the term Robinsonian or classical non standard analysis. The characteristic feature of Robinsonian analysis is a frequent usage of many controversial concepts appealing to the actual infinitely small and infinitely large quantities that have resided happily in natural sciences from ancient times but were strictly forbidden in modern mathematics for many decades. The present-day achievements revive the forgotten term infinitesimal analysis which reminds us expressively of the heroic bygones of Calculus. Infinitesimal analysis expands rapidly, bringing about radical reconsideration of the general conceptual system of mathematics. The principal reasons for this progress are twofold. Firstly, infinitesimal analysis provides us with a novel under standing for the method of indivisibles rooted deeply in the mathematical classics.