Download or read book Topology with Applications written by Somashekhar A. Naimpally and published by World Scientific. This book was released on 2013 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising.It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and far, discovered by F Riesz over 100 years ago. In addition, it is the first time that this form of topology is presented in the context of a number of new applications.
Download or read book Topology With Applications Topological Spaces Via Near And Far written by Somashekhar A Naimpally and published by World Scientific. This book was released on 2013-02-21 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising.It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and far, discovered by F Riesz over 100 years ago. In addition, it is the first time that this form of topology is presented in the context of a number of new applications.
Download or read book Computational Proximity written by James F. Peters and published by Springer. This book was released on 2016-04-20 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces computational proximity (CP) as an algorithmic approach to finding nonempty sets of points that are either close to each other or far apart. Typically in computational proximity, the book starts with some form of proximity space (topological space equipped with a proximity relation) that has an inherent geometry. In CP, two types of near sets are considered, namely, spatially near sets and descriptivelynear sets. It is shown that connectedness, boundedness, mesh nerves, convexity, shapes and shape theory are principal topics in the study of nearness and separation of physical aswell as abstract sets. CP has a hefty visual content. Applications of CP in computer vision, multimedia, brain activity, biology, social networks, and cosmology are included. The book has been derived from the lectures of the author in a graduate course on the topology of digital images taught over the past several years. Many of the students have provided important insights and valuable suggestions. The topics in this monograph introduce many forms of proximities with a computational flavour (especially, what has become known as the strong contact relation), many nuances of topological spaces, and point-free geometry.
Download or read book Transactions on Rough Sets XXI written by James F. Peters and published by Springer. This book was released on 2019-02-01 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 XXI in the series is a continuation of a number of research streams that have grown out of the seminal work of Zdzislaw Pawlak during the first decade of the 21st century.
Download or read book Algebraic Topology of Finite Topological Spaces and Applications written by Jonathan A. Barmak and published by Springer Science & Business Media. This book was released on 2011-08-24 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen's conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.
Download or read book Encyclopedia of Image Processing written by Phillip A. Laplante and published by CRC Press. This book was released on 2018-11-08 with total page 856 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopedia of Image Processing presents a vast collection of well-written articles covering image processing fundamentals (e.g. color theory, fuzzy sets, cryptography) and applications (e.g. geographic information systems, traffic analysis, forgery detection). Image processing advances have enabled many applications in healthcare, avionics, robotics, natural resource discovery, and defense, which makes this text a key asset for both academic and industrial libraries and applied scientists and engineers working in any field that utilizes image processing. Written by experts from both academia and industry, it is structured using the ACM Computing Classification System (CCS) first published in 1988, but most recently updated in 2012.
Download or read book Computational Geometry Topology and Physics of Digital Images with Applications written by James F. Peters and published by Springer Nature. This book was released on 2019-10-03 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the computational geometry, topology and physics of digital images and video frame sequences. This trio of computational approaches encompasses the study of shape complexes, optical vortex nerves and proximities embedded in triangulated video frames and single images, while computational geometry focuses on the geometric structures that infuse triangulated visual scenes. The book first addresses the topology of cellular complexes to provide a basis for an introductory study of the computational topology of visual scenes, exploring the fabric, shapes and structures typically found in visual scenes. The book then examines the inherent geometry and topology of visual scenes, and the fine structure of light and light caustics of visual scenes, which bring into play catastrophe theory and the appearance of light caustic folds and cusps. Following on from this, the book introduces optical vortex nerves in triangulated digital images. In this context, computational physics is synonymous with the study of the fine structure of light choreographed in video frames. This choreography appears as a sequence of snapshots of light reflected and refracted from surface shapes, providing a solid foundation for detecting, analyzing and classifying visual scene shapes.
Download or read book Royal Road To Topology A Convergence Of Filters written by Szymon Dolecki and published by World Scientific. This book was released on 2024-01-03 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological spaces are a special case of convergence spaces. This textbook introduces topology within a broader context of convergence theory. The title alludes to advantages of the present approach, which is more gratifying than many traditional ones: you travel more comfortably through mathematical landscapes and you see more.The book is addressed both to those who wish to learn topology and to those who, being already knowledgeable about topology, are curious to review it from a different perspective, which goes well beyond the traditional knowledge.Usual topics of classic courses of set-theoretic topology are treated at an early stage of the book — from a viewpoint of convergence of filters, but in a rather elementary way. Later on, most of these facts reappear as simple consequences of more advanced aspects of convergence theory.The mentioned virtues of the approach stem from the fact that the class of convergences is closed under several natural, essential operations, under which the class of topologies is not! Accordingly, convergence theory complements topology like the field of complex numbers algebraically completes the field of real numbers.Convergence theory is intuitive and operational because of appropriate level of its abstraction, general enough to grasp the underlying laws, but not too much in order not to lose intuitive appeal.
Download or read book Advances in Feature Selection for Data and Pattern Recognition written by Urszula Stańczyk and published by Springer. This book was released on 2017-11-16 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent developments and research trends in the field of feature selection for data and pattern recognition, highlighting a number of latest advances. The field of feature selection is evolving constantly, providing numerous new algorithms, new solutions, and new applications. Some of the advances presented focus on theoretical approaches, introducing novel propositions highlighting and discussing properties of objects, and analysing the intricacies of processes and bounds on computational complexity, while others are dedicated to the specific requirements of application domains or the particularities of tasks waiting to be solved or improved. Divided into four parts – nature and representation of data; ranking and exploration of features; image, shape, motion, and audio detection and recognition; decision support systems, it is of great interest to a large section of researchers including students, professors and practitioners.
Download or read book New Trends in Applied Analysis and Computational Mathematics written by Susanta Kumar Paikray and published by Springer Nature. This book was released on 2021-06-28 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume contains original research papers as the Proceedings of the International Conference on Advances in Mathematics and Computing, held at Veer Surendra Sai University of Technology, Odisha, India, on 7-8 February, 2020. It focuses on new trends in applied analysis, computational mathematics and related areas. It also includes certain new models, image analysis technique, fluid flow problems, etc. as applications of mathematical analysis and computational mathematics. The volume should bring forward new and emerging topics of mathematics and computing having potential applications and uses in other areas of sciences. It can serve as a valuable resource for graduate students, researchers and educators interested in mathematical tools and techniques for solving various problems arising in science and engineering.
Download or read book Transactions on Rough Sets XVII written by James F. Peters and published by Springer. This book was released on 2014-03-03 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 XVII is a continuation of a number of research streams which have grown out of the seminal work by Zdzislaw Pawlak during the first decade of the 21st century. The research streams represented in the papers cover both theory and applications of rough, fuzzy and near sets as well as their combinations.
Download or read book Basic Topology 1 written by Avishek Adhikari and published by Springer Nature. This book was released on 2022-07-04 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It studies metric spaces and general topology. It starts with the concept of the metric which is an abstraction of distance in the Euclidean space. The special structure of a metric space induces a topology that leads to many applications of topology in modern analysis and modern algebra, as shown in this volume. This volume also studies topological properties such as compactness and connectedness. Considering the importance of compactness in mathematics, this study covers the Stone–Cech compactification and Alexandroff one-point compactification. This volume also includes the Urysohn lemma, Urysohn metrization theorem, Tietz extension theorem, and Gelfand–Kolmogoroff theorem. The content of this volume is spread into eight chapters of which the last chapter conveys the history of metric spaces and the history of the emergence of the concepts leading to the development of topology as a subject with their motivations with an emphasis on general topology. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power, and active learning of the subject, all the while covering a wide range of theories and applications in a balanced unified way.
Download or read book General Topology and Applications written by Susan J. Andima and published by CRC Press. This book was released on 2020-08-26 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the proceedings of the Fifth Northeast Conference on General Topology and Applications, held at The College of Staten Island – The City University of New York. It provides insight into the relationship between general topology and other areas of mathematics.
Download or read book On Single Valued Neutrosophic Proximity Spaces written by Samed Özkan and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the notion of single-valued neutrosophic proximity spaces which is a generalisation of fuzzy proximity spaces [Katsaras AK. Fuzzy proximity spaces. Anal and Appl. 1979;68(1):100–110.] and intuitionistic fuzzy proximity spaces [Lee SJ, Lee EP. Intuitionistic fuzzy proximity spaces. Int J Math Math Sci. 2004;49:2617–2628.] was introduced and some of their properties were investigated. Then, it was shown that a single-valued neutrosophic proximity on a set X induced a single-valued neutrosophic topology on X. Furthermore, the existence of initial single-valued neutrosophic proximity structure is proved. Finally, based on this fact, the product of single-valued neutrosophic proximity spaces was introduced.
Download or read book Rough Sets written by Lech Polkowski and published by Springer. This book was released on 2017-06-22 with total page 737 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume set LNAI 10313 and LNAI 10314 constitutes the proceedings of the International Joint Conference on Rough Sets, IJCRS 2017, held in Olsztyn, Poland, in July 2017. The 74 revised full papers presented together with 16 short papers and 16 invited talks, were carefully reviewed and selected from 130 submissions. The papers in this two set-volume of IJCRS 2017 follow the track already rutted by RSCTC and JRS conferences which aimed at unification of many facets of rough set theory from theoretical aspects of the rough set idea bordering on theory of concepts and going through algebraic structures, topological structures, logics for uncertain reasoning, decision algorithms, relations to other theories of vagueness and ambiguity, then to extensions of the rough set idea like granular structures, rough mereology, and to applications of the idea in diverse fields of applied science including hybrid methods like rough-fuzzy, neuro-rough, neuro-rough-fuzzy computing. IJCRS 2017 encompasses topics spread among four main tracks: Rough Sets and Data Science (in relation to RSCTC series organized since 1998); Rough Sets and Granular Computing (in relation to RSFDGrC series organized since 1999); Rough Sets and Knowledge Technology (in relation to RSKT series organized since 2006); and Rough Sets and Intelligent Systems (in relation to RSEISP series organized since 2007).
Download or read book Introduction to Topological Manifolds written by John M. Lee and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.
Download or read book Topology Essentials written by Emil G. Milewski and published by Research & Education Assoc.. This book was released on 2013-01-01 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: REA’s Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Topology includes an overview of elementary set theory, relations and functions, ordinals and cardinals, topological spaces, continuous functions, metric spaces and normed spaces, countable spaces, and separation axioms.
