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The Lie Theory of Connected Pro-Lie Groups
Lie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonne quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them. If a complete topological group $G$ can be approximated by Lie groups in the sense that every identity neighborhood $U$ of $G$ contains a normal subgroup $N$ such that $G/N$ is a Lie group, then it is called a pro-Lie group. Every locally compact connected topological group and every compact group is a pro-Lie group. While the class of locally compact groups is not closed under the formation of arbitrary products, the class of pro-Lie groups is. For half a century, local...
Enumerative Combinatorics: Volume 1
An introduction, suitable for graduate students, showing connections to other areas of mathematics.
Highest Weight Representations Of Infinite Dimensional Lie Algebra
This book is a collection of a series of lectures given by Prof. V Kac at Tata Institute, India in Dec '85 and Jan '86. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations.The first is the canonical commutation relations of the infinite-dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gl∞ of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac-Moody) algebras. These algebras appear in...
Environmental Dilemmas and Policy Design
According to the logic of collective action, mere awareness of the causes of environmental degradation will not motivate rational agents to reduce pollution. Yet some government policies aim to enlist citizens in schemes of voluntary cooperation, drawing on an ethos of collective responsibility. Are such policies doomed to failure? This book provides a novel application of rational choice theory to a large-scale survey of environmental attitudes in The Netherlands. Its main findings are that rational citizens are motivated to cooperate towards a less polluted environment to a large extent, but that their willingness to assume responsibility depends on the social context of the collective action problem they face. This empirical study is an important volume in the development of a more consistent foundation for rational choice theory in policy analysis, which seeks to clarify major theoretical issues concerning the role of moral commitment, self-interest and reciprocity in environmental behaviour.
Control Theory in Engineering
The subject matter of this book ranges from new control design methods to control theory applications in electrical and mechanical engineering and computers. The book covers certain aspects of control theory, including new methodologies, techniques, and applications. It promotes control theory in practical applications of these engineering domains and shows the way to disseminate researchers’ contributions in the field. This project presents applications that improve the properties and performance of control systems in analysis and design using a higher technical level of scientific attainment. The authors have included worked examples and case studies resulting from their research in the field. Readers will benefit from new solutions and answers to questions related to the emerging realm of control theory in engineering applications and its implementation.
Control of Uncertain Systems
Invoking the machinery of Control Theory to control a real-world plant means, on the basis of available a priori knowledge of the plant, design ing/selecting a feasible controller accomplishing the control objective. A priori knowledge about the plant is normally represented as a mathemat ical model, given by physical laws or measurement data. Such a model is inevitably uncertain, due to measurement errors, simplified models of natural laws, neglected dynamics, and the desire to get a model tractable for further computations. Control of Uncertain Systems is therefore an im portant issue, both practically and philosophically. Basically, two different approaches exist: Adaptive Control and Rob...
Nonlinear Resonance Analysis
Nonlinear resonance analysis is a unique mathematical tool that can be used to study resonances in relation to, but independently of, any single area of application. This is the first book to present the theory of nonlinear resonances as a new scientific field, with its own theory, computational methods, applications and open questions. The book includes several worked examples, mostly taken from fluid dynamics, to explain the concepts discussed. Each chapter demonstrates how nonlinear resonance analysis can be applied to real systems, including large-scale phenomena in the Earth's atmosphere and novel wave turbulent regimes, and explains a range of laboratory experiments. The book also contains a detailed description of the latest computer software in the field. It is suitable for graduate students and researchers in nonlinear science and wave turbulence, along with fluid mechanics and number theory. Colour versions of a selection of the figures are available at www.cambridge.org/9780521763608.
Waste Management
Solid and liquid wastes generated as a result of various agricultural, municipal, industrial and several other processes have become a global concern. This book provides detailed information on eco-friendly approaches and low-cost strategies for solid and liquid waste management. It emphasizes how these wastes can be utilized as alternatives to expensive raw materials thus encouraging sustainable development. This book will be useful to all those who have a keen interest in waste management processes.
