Differential-geometric methods are gaining increasing importance in the understanding of a wide range of fundamental natural phenomena. Very often, the starting point for such studies is a variational problem formulated for a convenient Lagrangian. From a formal point of view, a Lagrangian is a smooth real function defined on the total space of the tangent bundle to a manifold satisfying some regularity conditions. The main purpose of this book is to present: (a) an extensive discussion of the geometry of the total space of a vector bundle; (b) a detailed exposition of Lagrange geometry; and (c) a description of the most important applications. New methods are described for construction geometrical models for applications. The various chapters consider topics such as fibre and vector bundles, the Einstein equations, generalized Einstein--Yang--Mills equations, the geometry of the total space of a tangent bundle, Finsler and Lagrange spaces, relativistic geometrical optics, and the geometry of time-dependent Lagrangians. Prerequisites for using the book are a good foundation in general manifold theory and a general background in geometrical models in physics. For mathematical physicists and applied mathematicians interested in the theory and applications of differential-geometric methods.
The title of this book is no surprise for people working in the field of Analytical Mechanics. However, the geometric concepts of Lagrange space and Hamilton space are completely new. The geometry of Lagrange spaces, introduced and studied in [76],[96], was ext- sively examined in the last two decades by geometers and physicists from Canada, Germany, Hungary, Italy, Japan, Romania, Russia and U.S.A. Many international conferences were devoted to debate this subject, proceedings and monographs were published [10], [18], [112], [113],... A large area of applicability of this geometry is suggested by the connections to Biology, Mechanics, and Physics and also by its general setting as a generalization of Finsler and Riemannian geometries. The concept of Hamilton space, introduced in [105], [101] was intensively studied in [63], [66], [97],... and it has been successful, as a geometric theory of the Ham- tonian function the fundamental entity in Mechanics and Physics. The classical Legendre’s duality makes possible a natural connection between Lagrange and - miltonspaces. It reveals new concepts and geometrical objects of Hamilton spaces that are dual to those which are similar in Lagrange spaces. Following this duality Cartan spaces introduced and studied in [98], [99],..., are, roughly speaking, the Legendre duals of certain Finsler spaces [98], [66], [67]. The above arguments make this monograph a continuation of [106], [113], emphasizing the Hamilton geometry.
This book is the first to present an overview of higher-order Hamilton geometry with applications to higher-order Hamiltonian mechanics. It is a direct continuation of the book The Geometry of Hamilton and Lagrange Spaces, (Kluwer Academic Publishers, 2001). It contains the general theory of higher order Hamilton spaces H(k)n, k>=1, semisprays, the canonical nonlinear connection, the N-linear metrical connection and their structure equations, and the Riemannian almost contact metrical model of these spaces. In addition, the volume also describes new developments such as variational principles for higher order Hamiltonians; Hamilton-Jacobi equations; higher order energies and law of conservation; Noether symmetries; Hamilton subspaces of order k and their fundamental equations. The duality, via Legendre transformation, between Hamilton spaces of order k and Lagrange spaces of the same order is pointed out. Also, the geometry of Cartan spaces of order k =1 is investigated in detail. This theory is useful in the construction of geometrical models in theoretical physics, mechanics, dynamical systems, optimal control, biology, economy etc.
This monograph is devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations. It presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1. A geometrical study of the notion of the higher-order Lagrange space is conducted, and the old problem of prolongation of Riemannian spaces to k-osculator manifolds is solved. Also, the geometrical ground for variational calculus on the integral of actions involving higher-order Lagrangians is dealt with. Applications to higher-order analytical mechanics and theoretical physics are included as well. Audience: This volume will be of interest to scientists whose work involves differential geometry, mechanics of particles and systems, calculus of variation and optimal control, optimization, optics, electromagnetic theory, and biology.
This book provides a comprehensive, up-to-date, and expert synthesis of location theory. What are the impacts of a firm’s geographic location on the locations of customers, suppliers, and competitors in a market economy? How, when, and why does this result in the clustering of firms in space? When and how is society made better or worse off as a result? This book uses dozens of locational models to address aspects of these three questions. Classical location problems considered include Greenhut-Manne, Hitchcock-Koopmans, and Weber-Launhardt. The book reinterprets competitive location theory, focusing on the linkages between Walrasian price equilibrium and the localization of firms. It also demonstrates that competitive location theory offers diverse ideas about the nature of market equilibrium in geographic space and its implications for a broad range of public policies, including free trade, industrial policy, regional development, and investment in infrastructure. With an extensive bibliography and fresh, interdisciplinary approach, the book will be an invaluable reference for academics and researchers with an interest in regional science, economic geography, and urban planning, as well as policy advisors, urban planners, and consultants.
Between 1945 and 1981 the Canadian population doubled, while the number of dwellings more than tripled. John Miron shows how changes in demographic structure and housing affordability affected postwar household formation and housing demand. He argues that no single explanation adequately reflects the extent of the impact of the demographic trends and the economic changes.
This book focuses on the relationship between the state and economy in the development of cities. It reviews and reinterprets fundamental theoretical models that explain how the operation of markets in equilibrium shapes the scale and organization of the commercial city in a mixed market economy within a liberal state. These models link markets for the factors of production, markets for investment and fixed capital formation, markets for transportation, and markets for exports in equilibrium both within the urban economy and the rest of the world. In each case, the model explains the urban economy by revealing how assumptions about causes and structures lead to predictions about scale and organization outcomes. By simplifying and contrasting these models, this book proposes another interpretation: that governance and the urban economy are outcomes negotiated by political actors motivated by competing notions of commonwealth and the individual desire for wealth and power. The book grounds its analysis in economic history, explaining the rise of commercial cities and the emergence of the urban economy. It then turns to factors of production, export, and factor markets, introducing and parsing the Mills model, breaking it down into its component parts and creating a series of simpler models that can better explain the significance of each economic assumption. Simplified models are also presented for real estate and fixed capital investment markets, transportation, and land use planning. The book concludes with a discussion of linear programming and the Herbert- Stevens and the Ripper-Varaiya models. A fresh presentation of the theories behind urban economics, this book emphasizes the links between state and economy and challenges the reader to see its theories in a new light. As such, this book will be of interest to scholars, students, and practitioners of economics, public policy, public administration, urban policy, and city and urban planning. >
The contributors identify important considerations for evaluating the current and future housing situation, clarify housing research issues and priorities, and indicate emergent policy issues. The essays are divided into six sections: economic, demographic, and institutional factors underlying the postwar demand for housing; principal aspects of the supply side of housing, including housing finance, technology, and regulation; housing-stock growth and changes in housing quality; the balance of supply and demand in terms of adequacy, suitability, and affordability; the changing settlement environment; and lessons, challenges, and issues for the future. The book also contains valuable summaries of housing policy initiatives undertaken between 1945 and 1986. An essential reference document on urban housing and city development in the postwar period in Canada, House, Home, and Community will be valuable to academics, planners, professionals, and students with interests related to housing.
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