Topological Transformations
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Author | : Ali Kaveh |
Publisher | : Springer Nature |
Total Pages | : 198 |
Release | : 2022-10-23 |
Genre | : Technology & Engineering |
ISBN | : 303112300X |
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.
Author | : W.Y. Hsiang |
Publisher | : Springer Science & Business Media |
Total Pages | : 175 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642660525 |
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.
Author | : Deane Montgomery |
Publisher | : Courier Dover Publications |
Total Pages | : 305 |
Release | : 2018-06-13 |
Genre | : Mathematics |
ISBN | : 0486831582 |
An advanced monograph on the subject of topological transformation groups, this volume summarizes important research conducted during a period of lively activity in this area of mathematics. The book is of particular note because it represents the culmination of research by authors Deane Montgomery and Leo Zippin, undertaken in collaboration with Andrew Gleason of Harvard University, that led to their solution of a well-known mathematical conjecture, Hilbert's Fifth Problem. The treatment begins with an examination of topological spaces and groups and proceeds to locally compact groups and groups with no small subgroups. Subsequent chapters address approximation by Lie groups and transformation groups, concluding with an exploration of compact transformation groups.
Author | : Michael Henle |
Publisher | : Courier Corporation |
Total Pages | : 340 |
Release | : 1994-01-01 |
Genre | : Mathematics |
ISBN | : 9780486679662 |
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.
Author | : Kraft |
Publisher | : Springer Science & Business Media |
Total Pages | : 216 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461237025 |
In recent years, there has been increasing interest and activity in the area of group actions on affine and projective algebraic varieties. Tech niques from various branches of mathematics have been important for this study, especially those coming from the well-developed theory of smooth compact transformation groups. It was timely to have an interdisciplinary meeting on these topics. We organized the conference "Topological Methods in Alg~braic Transformation Groups," which was held at Rutgers University, 4-8 April, 1988. Our aim was to facilitate an exchange of ideas and techniques among mathematicians studying compact smooth transformation groups, alge braic transformation groups and related issues in algebraic and analytic geometry. The meeting was well attended, and these Proceedings offer a larger audience the opportunity to benefit from the excellent survey and specialized talks presented. The main topics concerned various as pects of group actions, algebraic quotients, homogeneous spaces and their compactifications. The meeting was made possible by support from Rutgers University and the National Science Foundation. We express our deep appreciation for this support. We also thank Annette Neuen for her assistance with the technical preparation of these Proceedings.
Author | : Gregory L. Naber |
Publisher | : Courier Corporation |
Total Pages | : 276 |
Release | : 2012-08-29 |
Genre | : Mathematics |
ISBN | : 0486153444 |
Extensive development of such topics as elementary combinatorial techniques, Sperner's Lemma, the Brouwer Fixed Point Theorem, and the Stone-Weierstrass Theorem. New section of solutions to selected problems.
Author | : Yanpei Liu |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 369 |
Release | : 2017-03-06 |
Genre | : Mathematics |
ISBN | : 3110479494 |
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.
Author | : Jerry King |
Publisher | : |
Total Pages | : 80 |
Release | : 1970 |
Genre | : Topology |
ISBN | : |
Author | : Graham Flegg |
Publisher | : Courier Corporation |
Total Pages | : 210 |
Release | : 2001-01-01 |
Genre | : Mathematics |
ISBN | : 9780486419619 |
Introductory text for first-year math students uses intuitive approach, bridges the gap from familiar concepts of geometry to topology. Exercises and Problems. Includes 101 black-and-white illustrations. 1974 edition.
Author | : David Gans |
Publisher | : |
Total Pages | : 424 |
Release | : 1969 |
Genre | : Mathematics |
ISBN | : |