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Author : Stephen Barr
Publisher : Courier Corporation
Page : 244 pages
File Size : 52,6 Mb
Release : 2012-12-04
Category : Mathematics
ISBN : 9780486152745
Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.
Author : Stephen Barr
Publisher : Courier Corporation
Page : 242 pages
File Size : 46,6 Mb
Release : 1989-01-01
Category : Mathematics
ISBN : 0486259331
"A mathematician named Klein Thought the Moebius band was divine. Said he: 'If you glue The edges of two, You'll get a weird bottle like mine.' " — Stephen Barr In this lively book, the classic in its field, a master of recreational topology invites readers to venture into such tantalizing topological realms as continuity and connectedness via the Klein bottle and the Moebius strip. Beginning with a definition of topology and a discussion of Euler's theorem, Mr. Barr brings wit and clarity to these topics: New Surfaces (Orientability, Dimension, The Klein Bottle, etc.) The Shortest Moebius Strip The Conical Moebius Strip The Klein Bottle The Projective Plane (Symmetry) Map Coloring Networks (Koenigsberg Bridges, Betti Numbers, Knots) The Trial of the Punctured Torus Continuity and Discreteness ("Next Number," Continuity, Neighborhoods, Limit Points) Sets (Valid or Merely True? Venn Diagrams, Open and Closed Sets, Transformations, Mapping, Homotopy) With this book and a square sheet of paper, the reader can make paper Klein bottles, step by step; then, by intersecting or cutting the bottle, make Moebius strips. Conical Moebius strips, projective planes, the principle of map coloring, the classic problem of the Koenigsberg bridges, and many more aspects of topology are carefully and concisely illuminated by the author's informal and entertaining approach. Now in this inexpensive paperback edition, Experiments in Topology belongs in the library of any math enthusiast with a taste for brainteasing adventures
Author : Miguel A. Labrador,Pedro M. Wightman
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 54,8 Mb
Release : 2009-02-27
Category : Technology & Engineering
ISBN : 9781402095856
The eld of wireless sensor networks continues to evolve and grow in both practical and research domains. More and more wireless sensor networks are being used to gather information in real life applications. It is common to see how this technology is being applied in irrigation systems, intelligent buildings, bridges, security mec- nisms,militaryoperations,transportation-relatedapplications,etc.Atthesametime, new developments in hardware, software, and communication technologies are - panding these possibilities. As in any other technology, research brings new dev- opments and re nements and continuous improvements of current approaches that push the technology even further. Looking toward the future, the technology seems even more promising in two directions. First, a few years from now more powerful wireless sensor devices will be available, and wireless sensor networks will have applicability in an endless number of scenarios, as they will be able to handle traf c loads not possible today, make more computations, store more data, and live longer because of better energy sources. Second,a few years from now, the opposite scenario might also be possible. The availability of very constrained, nanotechnology-made wireless sensor devices will bring a whole new world of applications, as they will be able to operate in - vironments and places unimaginable today. These two scenarios, at the same time, will both bring new research challenges that are always welcome to researchers.
Author : J. van Mill
Publisher : Elsevier
Page : 401 pages
File Size : 51,5 Mb
Release : 1988-12-01
Category : Mathematics
ISBN : 9780080933689
The first part of this book is a text for graduate courses in topology. In chapters 1 - 5, part of the basic material of plane topology, combinatorial topology, dimension theory and ANR theory is presented. For a student who will go on in geometric or algebraic topology this material is a prerequisite for later work. Chapter 6 is an introduction to infinite-dimensional topology; it uses for the most part geometric methods, and gets to spectacular results fairly quickly. The second part of this book, chapters 7 & 8, is part of geometric topology and is meant for the more advanced mathematician interested in manifolds. The text is self-contained for readers with a modest knowledge of general topology and linear algebra; the necessary background material is collected in chapter 1, or developed as needed. One can look upon this book as a complete and self-contained proof of Toruńczyk's Hilbert cube manifold characterization theorem: a compact ANR X is a manifold modeled on the Hilbert cube if and only if X satisfies the disjoint-cells property. In the process of proving this result several interesting and useful detours are made.
Author : Fadi Al-Turjman
Publisher : Springer
Page : 238 pages
File Size : 43,7 Mb
Release : 2018-08-22
Category : Technology & Engineering
ISBN : 9783319935577
This book discusses the challenges in the convergence of technologies as the Internet of Things (IoT) evolves. These include sensing, computing, information processing, networking, and controlling intelligent technologies. The contributors first provide a survey of various assessment and evaluation approaches available for successful convergence. They then go on to cover several operational ideas to apply. The contributors then discuss the challenges involved bridging gaps in computation and the communication process, hidden networks, intelligent decision making, human-to-machine perception and large-scale IoT environments. The contributors aim to provide the reader an overview of trends in IoT in terms of performability and traffic modeling and efforts that can be spent in assessing the graceful degradation in IoT paradigms. Provides a survey of IoT assessment and evaluation approaches; Covers new and innovative operational ideas that apply to the IoT industry and the industries it affects; Includes chapters from researchers and industry leaders in IoT from around the world.
Author : De Witt L. Sumners,Nicholas R. Cozzarelli
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 40,8 Mb
Release : 1992
Category : Mathematics
ISBN : 0821855026
Geometry and topology are subjects generally considered to be "pure" mathematics. Recently, however, some of the methods and results in these two areas have found new utility in both wet-lab science (biology and chemistry) and theoretical physics. Conversely, science is influencing mathematics, from posing questions that call for the construction of mathematical models to exporting theoretical methods of attack on long-standing problems of mathematical interest. Based on an AMS Short Course held in January 1992, this book contains six introductory articles on these intriguing new connections. There are articles by a chemist and a biologist about mathematics, and four articles by mathematicians writing about science and mathematics involved. Because this book communicates the excitement and utility of mathematics research at an elementary level, it is an excellent textbook in an advanced undergraduate mathematics course.
Author : Roderich Moessner,Joel E. Moore
Publisher : Cambridge University Press
Page : 393 pages
File Size : 55,8 Mb
Release : 2021-04-29
Category : Mathematics
ISBN : 9781107105539
This important graduate level text unites the physical mechanisms behind the phenomena of topological matter within a theoretical framework.
Author : Afra J. Zomorodian
Publisher : Cambridge University Press
Page : 264 pages
File Size : 44,7 Mb
Release : 2005-01-10
Category : Computers
ISBN : 1139442635
The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.
Author : Morteza Rezanejad
Publisher : McGill University
Page : 207 pages
File Size : 43,7 Mb
Release : 2024-06-28
Category : Computers
ISBN : 8210379456XXX
Visual shape analysis plays a fundamental role in perception by man and by computer, allowing for inferences about properties of objects and scenes in the physical world. Mathematical approaches to describing visual form can benefit from the use of representations that simultaneously capture properties of an object's outline as well as its interior. Motivated by the success of medial models, this doctoral thesis revisits a quantity related to medial axis computations, the average outward flux of the gradient of the Euclidean distance function from a boundary, and then addresses three distinct problems using this measure. First, I consider the problem of view sphere partitioning for view-based object recognition from sparse views. View-based 3D object recognition requires a selection of model object views against which to match a query view. Ideally, for this to be computationally efficient, such a selection should be sparse. To address this problem, I introduce a novel hierarchical partitioning of the view sphere into regions within which the silhouette of a model object is qualitatively unchanged. To achieve this, I propose a part-based abstraction of a skeleton, as a graph, dubbed the Flux Graph, which allows for views to be grouped. Next, I consider the problem of mapping an initially-unknown 2D environment from possibly noisy sensed samples via an on-line procedure which robustly computes a retraction of its boundaries to obtain a topological representation. Here I motto an algorithm that allows for online map construction with loop closure. I demonstrate that the proposed method allows the robot to localize itself on a partially constructed map to calculate a path to unexplored parts of the environment (frontiers), to compute a robust terminating condition when the robot has fully explored the environment, and finally to achieve loop closure detection. I also show that the resulting map is stable under disturbances to the sensed boundary, and to variations in starting locations for exploration. Finally, I consider the problem of scene categorization from complex line drawings. In the context of human vision, we show that local ribbon symmetry between neighboring pairs of contours facilitates the categorization of complex real-world environments by human observers. In the context of computer vision, I demonstrate a high level of performance in the problem of convolutional neural network-based recognition of natural scenes from line drawings, even in the absence of color, texture and shading information.
Author : John G. Hocking,Gail S. Young
Publisher : Courier Corporation
Page : 384 pages
File Size : 54,7 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486141091
Superb one-year course in classical topology. Topological spaces and functions, point-set topology, much more. Examples and problems. Bibliography. Index.
Author : M. Husek,J. van Mill
Publisher : Elsevier
Page : 652 pages
File Size : 50,8 Mb
Release : 2002-11-13
Category : Mathematics
ISBN : 9780444509802
The book presents surveys describing recent developments in most of the primary subfields of General Topology and its applications to Algebra and Analysis during the last decade. It follows freely the previous edition (North Holland, 1992), Open Problems in Topology (North Holland, 1990) and Handbook of Set-Theoretic Topology (North Holland, 1984). The book was prepared in connection with the Prague Topological Symposium, held in 2001. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs slightly from those chosen in 1992. The following areas experienced significant developments: Topological Groups, Function Spaces, Dimension Theory, Hyperspaces, Selections, Geometric Topology (including Infinite-Dimensional Topology and the Geometry of Banach Spaces). Of course, not every important topic could be included in this book. Except surveys, the book contains several historical essays written by such eminent topologists as: R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardeŝić, J. Nagata, M.E. Rudin, J.M. Smirnov (several reminiscences of L. Vietoris are added). In addition to extensive author and subject indexes, a list of all problems and questions posed in this book are added. List of all authors of surveys: A. Arhangel'skii, J. Baker and K. Kunen, H. Bennett and D. Lutzer, J. Dijkstra and J. van Mill, A. Dow, E. Glasner, G. Godefroy, G. Gruenhage, N. Hindman and D. Strauss, L. Hola and J. Pelant, K. Kawamura, H.-P. Kuenzi, W. Marciszewski, K. Martin and M. Mislove and M. Reed, R. Pol and H. Torunczyk, D. Repovs and P. Semenov, D. Shakhmatov, S. Solecki, M. Tkachenko.
Author : Tamal Krishna Dey,Yusu Wang
Publisher : Cambridge University Press
Page : 455 pages
File Size : 47,9 Mb
Release : 2022-03-10
Category : Computers
ISBN : 9781009098168
This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.
Author : Robert Gilmore,Marc Lefranc
Publisher : John Wiley & Sons
Page : 618 pages
File Size : 48,6 Mb
Release : 2012-09-19
Category : Mathematics
ISBN : 9783527639427
A highly valued resource for those who wish to move from the introductory and preliminary understandings and the measurement of chaotic behavior to a more sophisticated and precise understanding of chaotic systems. The authors provide a deep understanding of the structure of strange attractors, how they are classified, and how the information required to identify and classify a strange attractor can be extracted from experimental data. In its first edition, the Topology of Chaos has been a valuable resource for physicist and mathematicians interested in the topological analysis of dynamical systems. Since its publication in 2002, important theoretical and experimental advances have put the topological analysis program on a firmer basis. This second edition includes relevant results and connects the material to other recent developments. Following significant improvements will be included: * A gentler introduction to the topological analysis of chaotic systems for the non expert which introduces the problems and questions that one commonly encounters when observing a chaotic dynamics and which are well addressed by a topological approach: existence of unstable periodic orbits, bifurcation sequences, multistability etc. * A new chapter is devoted to bounding tori which are essential for achieving generality as well as for understanding the influence of boundary conditions. * The new edition also reflects the progress which had been made towards extending topological analysis to higher-dimensional systems by proposing a new formalism where evolving triangulations replace braids. * There has also been much progress in the understanding of what is a good representation of a chaotic system, and therefore a new chapter is devoted to embeddings. * The chapter on topological analysis program will be expanded to cover traditional measures of chaos. This will help to connect those readers who are familiar with those measures and tests to the more sophisticated methodologies discussed in detail in this book. * The addition of the Appendix with both frequently asked and open questions with answers gathers the most essential points readers should keep in mind and guides to corresponding sections in the book. This will be of great help to those who want to selectively dive into the book and its treatments rather than reading it cover to cover. What makes this book special is its attempt to classify real physical systems (e.g. lasers) using topological techniques applied to real date (e.g. time series). Hence it has become the experimenter?s guidebook to reliable and sophisticated studies of experimental data for comparison with candidate relevant theoretical models, inevitable to physicists, mathematicians, and engineers studying low-dimensional chaotic systems.
Author : Stein, Denis
Publisher : KIT Scientific Publishing
Page : 168 pages
File Size : 40,7 Mb
Release : 2018-06-26
Category : Electronic
ISBN : 9783731507437
Author : Jiguo Yu,Cheng Xiuzhen,Jiang Honglu,Dongxiao Yu
Publisher : CRC Press
Page : 433 pages
File Size : 52,7 Mb
Release : 2018-02-05
Category : Computers
ISBN : 9781482298703
First Published in 2018. Routledge is an imprint of Taylor & Francis, an Informa company.
