This Volume presents a unified approach to calculate the plane stress distribution of stress and strain in thin elastic/plastic discs subject to various loading conditions.
This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics.
This categorical perspective on homotopy theory helps consolidate and simplify one''s understanding of derived functors, homotopy limits and colimits, and model categories, among others.
The aim of the textbook is two-fold: first to serve as an introductory graduate course in Algebraic Topology and then to provide an application-oriented presentation of some fundamental concepts in Algebraic Topology to the fixed point theory.
Many advanced mathematical disciplines, such as dynamical systems, calculus of variations, differential geometry and the theory of Lie groups, have a common foundation in general topology and calculus in normed vector spaces.
The central idea of the lecture course which gave birth to this book was to define the homotopy groups of a space and then give all the machinery needed to prove in detail that the nth homotopy group of the sphere Sn, for n greater than or equal to 1 is isomorphic to the group of the integers, that the lower homotopy groups of Sn are trivial and that the third homotopy group of S2 is also isomorphic to the group of the integers.
This book provides a foundation for arithmetic topology, a new branch of mathematics that investigates the analogies between the topology of knots, 3-manifolds, and the arithmetic of number fields.
This book carefully presents a unified treatment of equivariant Poincare duality in a wide variety of contexts, illuminating an area of mathematics that is often glossed over elsewhere.
This book presents contributions on topics ranging from novel applications of topological analysis for particular problems, through studies of the effectiveness of modern topological methods, algorithmic improvements on existing methods, and parallel computation of topological structures, all the way to mathematical topologies not previously applied to data analysis.
The featured review of the AMS describes the author's earlier work in the field of approach spaces as, 'A landmark in the history of general topology'.
The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions.
The second edition of this highly praised textbook provides an expanded introduction to the theory of ordered sets and its connections to various subjects.
The book presents a collection of results pertaining to the partial regularity of solutions to various variational problems, all of which are connected to the Dirichlet energy of maps between Riemannian manifolds, and thus related to the harmonic map problem.
This categorical perspective on homotopy theory helps consolidate and simplify one''s understanding of derived functors, homotopy limits and colimits, and model categories, among others.
