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Introduction To Global Analysis

Author: Donald W. Kahn
Publisher: Courier Corporation
ISBN: 9780486152295
Size: 73.73 MB
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This text introduces the methods of mathematical analysis as applied to manifolds, including the roles of differentiation and integration, infinite dimensions, Morse theory, Lie groups, and dynamical systems. 1980 edition.

Handbook Of Global Analysis

Author: Demeter Krupka
Publisher: Elsevier
ISBN: 9780080556734
Size: 13.54 MB
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This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics. This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics - Written by world-experts in the field - Up-to-date contents

Global Analysis

Author: Ilka Agricola
Publisher: American Mathematical Soc.
ISBN: 0821829513
Size: 66.89 MB
Format: PDF
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This book introduces the reader to the world of differential forms and their uses in geometry, analysis, and mathematical physics. It begins with a few basic topics, partly as review, then moves on to vector analysis on manifolds and the study of curves and surfaces in $3$-space. Lie groups and homogeneous spaces are discussed, providing the appropriate framework for introducing symmetry in both mathematical and physical contexts. The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics. There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics.

The Convenient Setting Of Global Analysis

Author: Andreas Kriegl
Publisher: American Mathematical Soc.
ISBN: 0821807803
Size: 23.91 MB
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This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. The approach is simple: a mapping is called smooth if it maps smooth curves to smooth curves. Up to Frechet spaces, this notion of smoothness coincides with all known reasonable concepts. In the same spirit, calculus of holomorphic mappings (including Hartogs' theorem and holomorphic uniform boundedness theorems) and calculus of real analytic mappings are developed. Existence of smooth partitions of unity, the foundations of manifold theory in infinite dimensions, the relation between tangent vectors and derivations, and differential forms are discussed thoroughly. Special emphasis is given to the notion of regular infinite dimensional Lie groups. Many applications of this theory are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.

Housing Policy Matters

Author: Shlomo Angel
Publisher: Oxford University Press
ISBN: 9780195350326
Size: 31.35 MB
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This book unifies housing policy by integrating industrialized and developing-country interventions in the housing sector into a comprehensive global framework. One hundred indicators are used to compare housing policies and conditions in 53 countries. Statistical analysis confirms that--after accounting for economic development--enabling housing policies result in improved housing conditions.

Global Analysis On Foliated Spaces

Author: Calvin C. Moore
Publisher: Springer Science & Business Media
ISBN: 1461395925
Size: 24.68 MB
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Global analysis has as its primary focus the interplay between the local analysis and the global geometry and topology of a manifold. This is seen classicallv in the Gauss-Bonnet theorem and its generalizations. which culminate in the Ativah-Singer Index Theorem [ASI] which places constraints on the solutions of elliptic systems of partial differential equations in terms of the Fredholm index of the associated elliptic operator and characteristic differential forms which are related to global topologie al properties of the manifold. The Ativah-Singer Index Theorem has been generalized in several directions. notably by Atiyah-Singer to an index theorem for families [AS4]. The typical setting here is given by a family of elliptic operators (Pb) on the total space of a fibre bundle P = F_M_B. where is defined the Hilbert space on Pb 2 L 1p -llbl.dvollFll. In this case there is an abstract index class indlPI E ROIBI. Once the problem is properly formulated it turns out that no further deep analvtic information is needed in order to identify the class. These theorems and their equivariant counterparts have been enormously useful in topology. geometry. physics. and in representation theory.

Climate Change Impacts On Fisheries And Aquaculture

Author: Bruce F. Phillips
Publisher: John Wiley & Sons
ISBN: 1119154049
Size: 62.34 MB
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The first comprehensive review of the current and future effects of climate change on the world’s fisheries and aquaculture operations The first book of its kind, Climate Change Impacts on Fisheries and Aquaculture explores the impacts of climate change on global fisheries resources and on marine aquaculture. It also offers expert suggestions on possible adaptations to reduce those impacts. The world's climate is changing more rapidly than scientists had envisioned just a few years ago, and the potential impact of climate change on world food production is quite alarming. Nowhere is the sense of alarm more keenly felt than among those who study the warming of the world's oceans. Evidence of the dire effects of climate change on fisheries and fish farming has now mounted to such an extent that the need for a book such as this has become urgent. A landmark publication devoted exclusively to how climate change is affecting and is likely to affect commercially vital fisheries and aquaculture operations globally, Climate Change Impacts on Fisheries and Aquaculture provides scientists and fishery managers with a summary of and reference point for information on the subject which has been gathered thus far. Covers an array of critical topics and assesses reviews of climate change impacts on fisheries and aquaculture from many countries, including Japan, Mexico, South Africa, Australia, Chile, US, UK, New Zealand, Pacific Islands, India and others Features chapters on the effects of climate change on pelagic species, cod, lobsters, plankton, macroalgae, seagrasses and coral reefs Reviews the spread of diseases, economic and social impacts, marine aquaculture and adaptation in aquaculture under climate change Includes special reports on the Antarctic Ocean, the Caribbean Sea, the Arctic Ocean and the Mediterranean Sea Extensive references throughout the book make this volume both a comprehensive text for general study and a reference/guide to further research for fisheries scientists, fisheries managers, aquaculture personnel, climate change specialists, aquatic invertebrate and vertebrate biologists, physiologists, marine biologists, economists, environmentalist biologists and planners.

Global Analysis

Author: Shiing-Shen Chern
Publisher: American Mathematical Soc.
ISBN: 0821814141
Size: 25.64 MB
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Includes bibliographical references.

Global Analysis

Author: Donald Clayton Spencer
Publisher: Princeton University Press
ISBN: 1400871239
Size: 54.90 MB
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Global analysis describes diverse yet interrelated research areas in analysis and algebraic geometry, particularly those in which Kunihiko Kodaira made his most outstanding contributions to mathematics. The eminent contributors to this volume, from Japan, the United States, and Europe, have prepared original research papers that illustrate the progress and direction of current research in complex variables and algebraic and differential geometry. The authors investigate, among other topics, complex manifolds, vector bundles, curved 4-dimensional space, and holomorphic mappings. Bibliographies facilitate further reading in the development of the various studies. Originally published in 1970. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.