Inverse limits provide a powerful tool for constructing complicated spaces from simple ones. They also turn the study of a dynamical system consisting of a space and a self-map into a study of a (like
Inverse limits with set-valued functions are quickly becoming a popular topic of research due to their potential applications in dynamical systems and economics. This brief provides a concise introduc
This book brings together the concept of resolution, which limits what we can determine about our physical world, with linear inverse problems, with an emphasis on showcasing real examples and practic
This book provides an up-to-date account of the precise experiments used to explore the nature of universal gravitation that can be performed in a terrestrial laboratory. The experiments required are at the limits of sensitivity of mechanical measurements. The problems of experiment design are discussed, and critical accounts given of the principal experiments testing the inverse square law and the principle of equivalence, and measuring the constant of gravitation. An analysis of the effects of noise and other disturbances is also provided, further highlighting the care that is needed in experimental design and performance. The motivation for undertaking such experiments is also discussed. The book will be of value to graduate students, researchers and teachers who are engaged in either theoretical or experimental studies of gravitation, and who wish to understand the nature and problems of laboratory experiments in this field.
In most mathematics departments at major universities one of the three or four basic first-year graduate courses is in the subject of algebraic topology. This introductory textbook in algebraic topology is suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises. The four main chapters present the basic material of the subject: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature of the book is the inclusion of many optional topics which are not usually part of a first course due to time constraints, and for which elementary expositions are sometimes hard to find. Among these are: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James r
This book, first published in 2000, develops aspects of category theory fundamental to the study of algebraic K-theory. Ring and module theory illustrates category theory which provides insight into more advanced topics in module theory. Starting with categories in general, the text then examines categories of K-theory. This leads to the study of tensor products and the Morita theory. The categorical approach to localizations and completions of modules is formulated in terms of direct and inverse limits, prompting a discussion of localization of categories in general. Finally, local-global techniques which supply information about modules from their localizations and completions and underlie some interesting applications of K-theory to number theory and geometry are considered. Many useful exercises, concrete illustrations of abstract concepts placed in their historical settings and an extensive list of references are included. This book will help all who wish to work in K-theory to ma
This book provides an up-to-date account of the precise experiments used to explore the nature of universal gravitation that can be performed in a terrestrial laboratory. The experiments required are at the limits of sensitivity of mechanical measurements. The problems of experiment design are discussed, and critical accounts given of the principal experiments testing the inverse square law and the principle of equivalence, and measuring the constant of gravitation. An analysis of the effects of noise and other disturbances is also provided, further highlighting the care that is needed in experimental design and performance. The motivation for undertaking such experiments is also discussed. The book will be of value to graduate students, researchers and teachers who are engaged in either theoretical or experimental studies of gravitation, and who wish to understand the nature and problems of laboratory experiments in this field.
