Download or read book Topological Transformations for Efficient Structural Analysis written by Ali Kaveh and published by Springer Nature. This book was released on 2022-10-23 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author has published many papers and books on topological transformations for optimal analysis of structures, where many methods and algorithms are developed. However, the framework of this book generalizes many concepts and makes the previously developed methods conceptually more attractive. The aim of the present work is two folds. On the one hand, it shows to mathematicians how the apparently pure mathematical concepts can be applied to the efficient solution of problems in structural mechanics. On the other hand, it illustrates to engineers the important role of mathematical concepts for the solution of engineering problems. The present framework provides efficient means for looking at problems and developing ideas by transforming the models (structures, networks, systems) to other spaces (higher dimension, lower dimension, or identical dimension) to simplify the problems. This book is attractive for those who look at the deeper aspects of concepts and helps the reader to develop his/her own ideas. In general, it opens a new horizon for improving the existing methods in civil, mechanical, and electrical engineering.
Download or read book Cohomology Theory of Topological Transformation Groups written by W.Y. Hsiang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, applications of algebraic topology to the study of topological transformation groups were originated in the work of L. E. 1. Brouwer on periodic transformations and, a little later, in the beautiful fixed point theorem ofP. A. Smith for prime periodic maps on homology spheres. Upon comparing the fixed point theorem of Smith with its predecessors, the fixed point theorems of Brouwer and Lefschetz, one finds that it is possible, at least for the case of homology spheres, to upgrade the conclusion of mere existence (or non-existence) to the actual determination of the homology type of the fixed point set, if the map is assumed to be prime periodic. The pioneer result of P. A. Smith clearly suggests a fruitful general direction of studying topological transformation groups in the framework of algebraic topology. Naturally, the immediate problems following the Smith fixed point theorem are to generalize it both in the direction of replacing the homology spheres by spaces of more general topological types and in the direction of replacing the group tl by more general compact groups.
Download or read book Topological Theory of Graphs written by Yanpei Liu and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-03-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces polyhedra as a tool for graph theory and discusses their properties and applications in solving the Gauss crossing problem. The discussion is extended to embeddings on manifolds, particularly to surfaces of genus zero and non-zero via the joint tree model, along with solution algorithms. Given its rigorous approach, this book would be of interest to researchers in graph theory and discrete mathematics.
Download or read book A Combinatorial Introduction to Topology written by Michael Henle and published by Courier Corporation. This book was released on 1994-01-01 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.
Download or read book Topology of Manifolds written by Raymond Louis Wilder and published by American Mathematical Soc.. This book was released on 1965 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topology based Methods in Visualization written by Helwig Hauser and published by Springer Science & Business Media. This book was released on 2007-05-24 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents 13 peer-reviewed papers as written results from the 2005 workshop "Topology-Based Methods in Visualization" that was initiated to enable additional stimulation in this field. It contains a survey of the state-of-the-art, as well original work by leading experts that has not been published before, spanning both theory and applications. It captures key concepts and novel ideas and serves as an overview of current trends in its subject.
Download or read book Analysis And Topology written by Cabiria Andreian Cazacu and published by World Scientific. This book was released on 1998-11-06 with total page 737 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to investigate further the interdisciplinary interaction between Mathematical Analysis and Topology. It provides an attempt to study various approaches in the topological applications and influence to Function Theory, Calculus of Variations, Functional Analysis and Approximation Theory. The volume is dedicated to the memory of S Stoilow.
Download or read book Topological Dynamics written by Walter Helbig Gottschalk and published by American Mathematical Soc.. This book was released on 1955 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Topology written by Solomon Lefschetz and published by Princeton University Press. This book was released on 2015-12-08 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, which may be used as a self-contained text for a beginning course, Professor Lefschetz aims to give the reader a concrete working knowledge of the central concepts of modern combinatorial topology: complexes, homology groups, mappings in spheres, homotopy, transformations and their fixed points, manifolds and duality theorems. Each chapter ends with a group of problems. Originally published in 1949. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Topological Polymer Chemistry written by Yasuyuki Tezuka and published by Springer Nature. This book was released on 2022-02-25 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive description of topological polymers, an emerging research area in polymer science and polymer materials engineering. The precision polymer topology designing is critical to realizing the unique polymer properties and functions leading to their eventual applications. The prominent contributors are led by Principal Editor Yasuyuki Tezuka and Co-Editor Tetsuo Deguchi. Important ongoing achievements and anticipated breakthroughs in topological polymers are presented with an emphasis on the spectacular diversification of polymer constructions. The book serves readers collectively to acquire comprehensive insights over exciting innovations ongoing in topological polymer chemistry, encompassing topological geometry analysis, classification, physical characterization by simulation and the eventual chemical syntheses, with the supplementary focus on the polymer folding, invoked with the ongoing breakthrough of the precision AI prediction of protein folding. The current revolutionary developments in synthetic approaches specifically for single cyclic (ring) polymers and the topology-directed properties/functions uncovered thereby are outlined as a showcase example. This book is especially beneficial to academic personnel in universities and to researchers working in relevant institutions and companies. Although the level of the book is advanced, it can serve as a good reference book for graduate students and postdocs as a source of valuable knowledge of cutting-edge topics and progress in polymer chemistry.
Download or read book Topological in Hegel written by Borislav G. Dimitrov and published by Borislav Dimitrov. This book was released on 2018-01-23 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to critically examine whether it is methodologically possible to combine mathematical rigor – topology with a systematic dialectical methodology in Hegel, and if so, to provide as result of my interpretation the outline of Hegel’s Analysis Situs, also with the proposed models (build on the topological manifold, cobordism, topological data analysis, persistent homology, simplicial complexes and graph theory, to provide an indication of how the merger of Hegel’s dialectical logic and topology may be instrumental to a systematic logician and of how a systematic dialectical logic perspective may help mathematical model builders.
Download or read book Transformations and Geometries written by David Gans and published by . This book was released on 1969 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Towards a Theory of Thinking written by Britt Glatzeder and published by Springer Science & Business Media. This book was released on 2010-03-20 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is Thinking? – Trying to Define an Equally Fascinating and Elusive Phenomenon Human thinking is probably the most complex phenomenon that evolution has come up with until now. There exists a broad spectrum of definitions, from subs- ing almost all processes of cognition to limiting it to language-based, sometimes even only to formalizable reasoning processes. We work with a “medium sized” definition according to which thinking encompasses all operations by which cog- tive agents link mental content in order to gain new insights or perspectives. Mental content is, thus, a prerequisite for and the substrate on which thinking operations are executed. The largely unconscious acts of perceptual object stabilization, ca- gorization, emotional evaluation – and retrieving all the above from memory inscriptions – are the processes by which mental content is generated, and are, therefore, seen as prerequisites for thinking operations. In terms of a differentia specifica, the notion of “thinking” is seen as narrower than the notion of “cognition” and as wider than the notion of “reasoning”. Thinking is, thus, seen as a subset of cognition processes; and reasoning processes are seen as a subset of thinking. Besides reasoning, the notion of thinking includes also nonexplicit, intuitive, and associative processes of linking mental content. According to this definition, thinking is not dependant on language, i. e. also many animals and certainly all mammals show early forms of thinking.
Download or read book From Geometry to Topology written by H. Graham Flegg and published by Courier Corporation. This book was released on 2012-03-08 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4–12 give a largely intuitive presentation of selected topics. In the remaining five chapters, the author moves to a more conventional presentation of continuity, sets, functions, metric spaces, and topological spaces. Exercises and Problems. 101 black-and-white illustrations. 1974 edition.
Download or read book Topology written by Paul L. Shick and published by John Wiley & Sons. This book was released on 2011-10-14 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essentials of point-set topology, complete with motivation and numerous examples Topology: Point-Set and Geometric presents an introduction to topology that begins with the axiomatic definition of a topology on a set, rather than starting with metric spaces or the topology of subsets of Rn. This approach includes many more examples, allowing students to develop more sophisticated intuition and enabling them to learn how to write precise proofs in a brand-new context, which is an invaluable experience for math majors. Along with the standard point-set topology topics—connected and path-connected spaces, compact spaces, separation axioms, and metric spaces—Topology covers the construction of spaces from other spaces, including products and quotient spaces. This innovative text culminates with topics from geometric and algebraic topology (the Classification Theorem for Surfaces and the fundamental group), which provide instructors with the opportunity to choose which "capstone" best suits his or her students. Topology: Point-Set and Geometric features: A short introduction in each chapter designed to motivate the ideas and place them into an appropriate context Sections with exercise sets ranging in difficulty from easy to fairly challenging Exercises that are very creative in their approaches and work well in a classroom setting A supplemental Web site that contains complete and colorful illustrations of certain objects, several learning modules illustrating complicated topics, and animations of particularly complex proofs
Download or read book Proceedings of the 16th International Meshing Roundtable written by Michael L. Brewer and published by Springer Science & Business Media. This book was released on 2007-09-26 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the articles presented at the 16th International Meshing Roundtable (IMR) organized, in part, by Sandia National Laboratories and held in Seattle, Washington, U.S.A. in October, 2007. The volume presents recent results of mesh generation and adaptation which has applications to finite element simulation. It introduces theoretical and novel ideas with practical potential.
Download or read book Encyclopedia of the Human Brain written by and published by Elsevier. This book was released on 2002-07-04 with total page 3607 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past decade, enormous strides have been made in understanding the human brain. The advent of sophisticated new imaging techniques (e.g. PET, MRI, MEG, etc.) and new behavioral testing procedures have revolutionized our understanding of the brain, and we now know more about the anatomy, functions, and development of this organ than ever before. However, much of this knowledge is scattered across scientific journals and books in a diverse group of specialties: psychology, neuroscience, medicine, etc. The Encyclopedia of the Human Brain places all information in a single source and contains clearly written summaries on what is known of the human brain. Covering anatomy, physiology, neuropsychology, clinical neurology, neuropharmacology, evolutionary biology, genetics, and behavioral science, this four-volume encyclopedia contains over 200 peer reviewed signed articles from experts around the world. The Encyclopedia articles range in size from 5-30 printed pages each, and contain a definition paragraph, glossary, outline, and suggested readings, in addition to the body of the article. Lavishly illustrated, the Encyclopedia includes over 1000 figures, many in full color. Managing both breadth and depth, the Encyclopedia is a must-have reference work for life science libraries and researchers investigating the human brain.
