Bitopological Spaces Theory Relations With Generalized Algebraic Structures And Applications
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Bitopological Spaces Theory Relations With Generalized Algebraic Structures And Applications
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Author : Badri Dvalishvili
language : en
Publisher: Elsevier
Release Date : 2005-01-20
Bitopological Spaces Theory Relations With Generalized Algebraic Structures And Applications written by Badri Dvalishvili and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-20 with Mathematics categories.
This monograph is the first and an initial introduction to the theory of bitopological spaces and its applications. In particular, different families of subsets of bitopological spaces are introduced and various relations between two topologies are analyzed on one and the same set; the theory of dimension of bitopological spaces and the theory of Baire bitopological spaces are constructed, and various classes of mappings of bitopological spaces are studied. The previously known results as well the results obtained in this monograph are applied in analysis, potential theory, general topology, and theory of ordered topological spaces. Moreover, a high level of modern knowledge of bitopological spaces theory has made it possible to introduce and study algebra of new type, the corresponding representation of which brings one to the special class of bitopological spaces. It is beyond any doubt that in the nearest future the areas of essential applications will be the theories of linear topological spaces and topological groups, algebraic and differential topologies, the homotopy theory, not to mention other fundamental areas of modern mathematics such as geometry, mathematical logic, the probability theory and many other areas, including those of applied nature. Key Features:- First monograph is "Generalized Lattices"* The first introduction to the theory of bitopological spaces and its applications.
Theory And Applications Of Fractional Differential Equations
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Author : A.A. Kilbas
language : en
Publisher: Elsevier
Release Date : 2006-02-16
Theory And Applications Of Fractional Differential Equations written by A.A. Kilbas and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-16 with Mathematics categories.
This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.
Functional Analysis In Asymmetric Normed Spaces
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Author : Stefan Cobzas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-30
Functional Analysis In Asymmetric Normed Spaces written by Stefan Cobzas 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 2012-10-30 with Mathematics categories.
An asymmetric norm is a positive definite sublinear functional p on a real vector space X. The topology generated by the asymmetric norm p is translation invariant so that the addition is continuous, but the asymmetry of the norm implies that the multiplication by scalars is continuous only when restricted to non-negative entries in the first argument. The asymmetric dual of X, meaning the set of all real-valued upper semi-continuous linear functionals on X, is merely a convex cone in the vector space of all linear functionals on X. In spite of these differences, many results from classical functional analysis have their counterparts in the asymmetric case, by taking care of the interplay between the asymmetric norm p and its conjugate. Among the positive results one can mention: Hahn–Banach type theorems and separation results for convex sets, Krein–Milman type theorems, analogs of the fundamental principles – open mapping, closed graph and uniform boundedness theorems – an analog of the Schauder’s theorem on the compactness of the conjugate mapping. Applications are given to best approximation problems and, as relevant examples, one considers normed lattices equipped with asymmetric norms and spaces of semi-Lipschitz functions on quasi-metric spaces. Since the basic topological tools come from quasi-metric spaces and quasi-uniform spaces, the first chapter of the book contains a detailed presentation of some basic results from the theory of these spaces. The focus is on results which are most used in functional analysis – completeness, compactness and Baire category – which drastically differ from those in metric or uniform spaces. The book is fairly self-contained, the prerequisites being the acquaintance with the basic results in topology and functional analysis, so it may be used for an introduction to the subject. Since new results, in the focus of current research, are also included, researchers in the area can use it as a reference text.
Proceedings Of A Razmadze Mathematical Institute
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Author :
language : en
Publisher:
Release Date : 2008
Proceedings Of A Razmadze Mathematical Institute written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Proceedings Of The Fifth International Conference On Emerging Trends In Mathematical Sciences Computing Iemsc 24
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Author : Biswadip Basu Mallik
language : en
Publisher: Springer Nature
Release Date : 2024-10-31
Proceedings Of The Fifth International Conference On Emerging Trends In Mathematical Sciences Computing Iemsc 24 written by Biswadip Basu Mallik and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-31 with Technology & Engineering categories.
The Proceedings of the Fifth International Conference on Emerging Trends in Mathematical Sciences & Computing (IEMSC-24) contains papers that present the current scientific as well as technological innovations by leading academicians, eminent researchers, and experts throughout the globe in the twin domain of Mathematical Sciences as well as Computing. The papers focus on the recent advances in the field of Theoretical Computer Science as well as its blending with Mathematical techniques. The book aims to disseminate new technical ideas and features that can be incorporated in day-to-day life for the benefit of the society. The research papers exhibit scientific advancements in diversified spectrum that includes Differential as well as Integral Equations with applications, Computational Fluid Dynamics, Nanofluids, Network Theory & Optimization, Control Theory, Machine Learning & Artificial Intelligence, Big Data Analytics, IoT, Cryptography, Fuzzy Automata, Statistics, and many more. The proceedings primarily focus on the amalgamation of mathematical methods with computing. The potential readers will get access to diverse ideas and innovations in the field of computing together with its growing interactions in various fields of mathematics. This book serves as a valuable reference resource for researchers in academia and industry.
Topological Groups And Related Structures An Introduction To Topological Algebra
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Author : Alexander Arhangel’skii
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-01
Topological Groups And Related Structures An Introduction To Topological Algebra written by Alexander Arhangel’skii 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 2008-05-01 with Mathematics categories.
Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately.
Transactions On Rough Sets Xiii
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Author :
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-14
Transactions On Rough Sets Xiii written by 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 2011-01-14 with Computers categories.
The LNCS journal Transactions on Rough Sets is devoted to the entire spectrum of rough sets related issues, from logical and mathematical foundations, through all aspects of rough set theory and its applications, such as data mining, knowledge discovery, and intelligent information processing, to relations between rough sets and other approaches to uncertainty, vagueness, and incompleteness, such as fuzzy sets and theory of evidence. Volume XIII contains 14 papers which introduce a number of new advances in both the foundations and the applications of rough sets. These are mathematical structures of generalized rough sets in infinite universes, approximations of arbitrary binary relations, and attribute reduction in decision-theoretic rough sets. Methodological advances introduce rough set-based and hybrid methodologies for learning theory, attribution reduction, decision analysis, risk assessment, and data mining tasks such as classification and clustering. In addition, this volume contains regular articles on mining temporal software metrics data, C-GAME discretization method, perceptual tolerance intersection as an example of a near set operation and compression of spatial data with quadtree structures.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2006
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1995
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Aeronautics categories.
Topological Groups And Related Structures
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Author : A. V. Arkhangelʹskiĭ
language : en
Publisher: atlantis press
Release Date : 2008
Topological Groups And Related Structures written by A. V. Arkhangelʹskiĭ and has been published by atlantis press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This book presents a large amount of material, both classic and recent (on occasion, unpublished) about the relations of Algebra and Topology. It therefore belongs to the area called Topological Algebra. More specifically, the objects of the study are subtle and sometimes unexpected phenomena that occur when the continuity meets and properly feeds an algebraic operation. Such a combination gives rise to many classic structures, including topological groups and semigroups, paratopological groups, etc. Special emphasis is given to tracing the influence of compactness and its generalizations on the properties of an algebraic operation, causing on occasion the automatic continuity of the operation. The main scope of the book, however, is outside of the locally compact structures, thus distinguishing the monograph from a series of more traditional textbooks.The book is unique in that it presents very important material, dispersed in hundreds of research articles, not covered by any monograph in existence. The reader is gently introduced to an amazing world at the interface of Algebra, Topology, and Set Theory. He/she will find that the way to the frontier of the knowledge is quite short -- almost every section of the book contains several intriguing open problems whose solutions can contribute significantly to the area.