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Geometry of Quantum Theory ; 2nd ed.
This book a classic on the foundations of quantum theory. This view, which is essentially geometric and relies on the concept of symmetry. The mathematical treatment of symmetry in quantum theory is based on the theory of group representations, and this book includes a self-contained treatment of the parts of this theory that are most useful in quantum physics.
Geometry of Principal Sheaves
The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities. Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is devoted to the theory of connections on principal sheaves, incorporating connections on vector
Geometry and monadology : Leibniz’s Analysis Situs and philosophy of space
Reconstructs, from both historical and theoretical points of view, Leibniz’s geometrical studies, focusing in particular on the research Leibniz carried out in the last years of his life. It is indeed the first ever comprehensive historical reconstruction of Leibniz’s geometry that meets the interests of both mathematicians and philosophers. The main purpose of the work is to offer a better understanding of the Leibnizean philosophy of space and mature metaphysics, through a pressing confrontation with the problems of geometric foundations. Regarding the scope of these problems, the book also deals in depth with Leibniz’s theory of sensibility, thus favouring the comparison and contrast between Leibniz’s philosophy and Kant’s transcendentalist solution. The Appendix references to a number of previously unpublished manuscripts on geometry from the Leibniz Archiv in Hannover, which disclose new theories, points of view and technicalities of Leibniz’s thought.
Geometry and Dynamics of Groups and Spaces : In Memory of Alexander Reznikov
Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.
Geometrical Geodesy : Using Information and Computer Technology
This book reviews developments in geodesy and hydrography, using a wide variety of electronic and acoustic instruments. The aim is to take stock of the latest fundamental geodetic constants for the 2000s, to focus on dissimilar ellipsoidal areas, distances, and conversion of applications, referenced to an abundant bibliography. It presents a mixture of issues, dealing with reference and time systems, datums, and s-transformations, elucidate multi-dimensional aspects of the information, communication, and computation technology, including the use of parallel computers. Stressing the hands-on methodology, the handbook is of interest to geodetic engineers, consultants, hydrographers, and engineers with an interest in the field of earth sciences.
Geometrical dynamics of complex systems : A unified modelling approach to physics, control, biomechanics, neurodynamics and psycho-socio-economical dynamics
This volume presents a comprehensive introduction into rigorous geometrical dynamics of complex systems of various natures. By "complex systems", in this book are meant high-dimensional nonlinear systems, which can be (but not necessarily are) adaptive. This monograph proposes a unified geometrical approach to dynamics of complex systems of various kinds: engineering, physical, biophysical, psychophysical, sociophysical, econophysical, etc. The main objective of this book is to show that high-dimensional nonlinear systems in "real life" can be modeled and analyzed using rigorous mathematics, which enables their complete predictability and controllability, as if they were linear systems.
Geometric Topology : Localization, Periodicity and Galois Symmetry : the 1970 MIT notes
The seminal `MIT notes' of Dennis Sullivan were issued in June 1970 and were widely circulated at the time, but only privately. The notes had a major influence on the development of both algebraic and geometric topology, pioneering the localization and completion of spaces in homotopy theory, including P-local, profinite and rational homotopy theory, the Galois action on smooth manifold structures in profinite homotopy theory, and the K-theory orientation of PL manifolds and bundles. This is the first time that this major work has actually been published, and made available to anyone interested in topology.
Geometric Qp Functions
This book documents the rich structure of the holomorphic Q functions which are geometric in the sense that they transform naturally under conformal mappings. Particular emphasis is placed on recent developments based on the interaction between geometric function/measure theory and other branches of mathematical analysis, including potential theory, complex variables, harmonic analysis, functional analysis, and operator theory." "Largely self-contained, this book will be an instructional and reference work for advanced courses and research in conformal analysis, geometry, or function spaces.
Geometric numerical integration : Structure-preserving algorithms for ordinary differential equations
Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches.
Geometric Modelling, Numerical Simulation, and Optimization : Applied Mathematics at SINTEF
This book present scurrent activities of the Department of AppliedMathem- ics at SINTEF, the largest independent research organisation in Scandinavia. The book contains fteenpaperscontributedby employeesandfellowpartners from collaborating institutions. The research and development work within the department is focused on three main subject areas,andthestructureof the book refectsthisclustering: Part I Geometric Modelling Part II Numerical Simulation Part III Optimization Addressing Mathematics for Industry and Society, each contribution - scribesa problems ettingthatis of practical relevanceinone of thethreeareas and communicates the authors' own experiences in tackling these problems.
Geometric Modeling and Algebraic Geometry
The two ?elds of Geometric Modeling and Algebraic Geometry, though closely - lated, are traditionally represented by two almost disjoint scienti?c communities. Both ?elds deal with objects de?ned by algebraic equations, but the objects are studied in different ways. While algebraic geometry has developed impressive - sults for understanding the theoretical nature of these objects, geometric modeling focuses on practical applications of virtual shapes de?ned by algebraic equations. Recently, however, interaction between the two ?elds has stimulated new research. For instance, algorithms for solving intersection problems have bene?ted from c- tributions from the algebraic side.
Geometric Methods in Algebra and Number Theory
The transparency and power of geometric constructions has been a source of inspiration to generations of mathematicians. The beauty and persuasion of pictures, communicated in words or drawings, continues to provide the intuition and arguments for working with complicated concepts and structures of modern mathematics. This volume contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory.
Geometric Function Theory : Explorations in Complex Analysis
Complex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research, including invariant geometry, the Bergman metric, the automorphism groups of domains, harmonic measure, boundary regularity of conformal maps, the Poisson kernel, the Hilbert transform, the boundary behavior of harmonic and holomorphic functions, the inhomogeneous Cauchy–Riemann equations, and the corona problem.
Geometric and Topological Methods for Quantum Field Theory
This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of Raimar Wulkenhaar on Euclidean quantum field theory from a statistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on string compactification with unbroken supersymmetry. The authors show that this requirement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommutative geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start with introductory material before presenting more advanced results. Each chapter is self-contained and can be read independently.
Geometric Algebra for Computer Graphics
The first five chapters review the algebras of real numbers, complex numbers, vectors, and quaternions and their associated axioms, together with the geometric conventions employed in analytical geometry. As well as putting geometric algebra into its historical context, John Vince provides chapters on Grassmann’s outer product and Clifford’s geometric product, followed by the application of geometric algebra to reflections, rotations, lines, planes and their intersection. The conformal model is also covered, where a 5D Minkowski space provides an unusual platform for unifying the transforms associated with 3D Euclidean space.
Geomatics Solutions for Disaster Management
Natural and anthropogenic disasters have caused a large number of victims and significant social and economic losses in the last few years. There is no doubt that the risk prevention and disaster management sector needs drastic measures and improvements in order to decrease damage and save lives of inhabitants. Effective utilization of satellite positioning, remote sensing, and GIS in disaster monitoring and management requires research and development in numerous areas: data collection, access and delivery, information extraction and analysis, management and their integration with other data sources (airborne and terrestrial imagery, GIS data, etc.), data standardization, organizational and legal aspects of sharing of remote sensing information. This book provides researchers and practitioners with a good overview of what is being developed in this topical area.
Geomagnetics for aeronautical safety : A case study in and around the Balkans
Flying safely in aircraft implies the use of navigation instruments. Among them, the magnetic compass is still a first choice for orientation and it is compulsory in all aircraft. In our increasingly sophisticated but fragile world of global navigation systems and gyroscopic sensors, the compass is especially useful as a back-up: it is highly reliable and likely to survive in harsh electromagnetic aggressions or when all power supplies fail. This book examines in detail how the science of geomagnetism is able to promote correct use of the magnetic compass for navigation. A selected group of specialists met in Ohrid, Macedonia to expose their approaches to the question. Using techniques from Geology, Instrument science, Magnetism, Chaos theory and Potential Fields applied to the Balkan region and surroundings, they put together a roadmap to fully tackle the issue of measurement, analysis, mapping and forecasting the magnetic declination in support of aeronautical safety.
Geology and Ecosystems
This book includes an analysis of the relationship between the different geological, hydrochemical, hydrogeological and engineering-geological processes and the processes within surface ecosystems. The analysis of specific interactions between the lithosphere and biosphere provides an integrated concept of the role of the geological environment in the evolution of the biosphere. The practical significance of the book is reflected by the analysis of modern engineering activity associated with the mining of minerals, excessive groundwater withdrawal, disposal of industrial and domestic wastes (including radioactive wastes) and their impacts on all components of the environment. Geology and Ecosystems includes a scientific approach to the complex monitoring of the environment under different natural and anthropogenic conditions, including the monitoring of permafrost regions. An important part of the book is the analysis of the "water factor" impact on ecosystems and sustainable development. Influences of intensive groundwater extraction on river flow, vegetation and land subsidence are also considered.
Geological atlas of Africa : With notes on stratigraphy, tectonics, economic geology, geohazards, geosites and geoscientific education of each country
Here is the new edition of the first attempt to summarize the geology of Africa by presenting it in an atlas and to synthesize the stratigraphy, tectonics, economic geology, geohazards and geosites of each country and territory of the continent. Furthermore, the digitized geological maps are correlated and harmonized according to the current stratigraphic timetable. The atlas aims to contribute to capacity building in African Earth Sciences and to aid the initiation of research and enable the achievement of economic opportunities by providing a database of basic geological background information.
Geo-information for Disaster Management
Geo-information technology offers an opportunity to support disaster management: industrial accidents, road collisions, complex emergencies, earthquakes, fires, floods and similar catastrophes (for example the recent huge disaster with the Tsunami in South-East Asia on 26 December 2004). Access to needed information, facilitation of the interoperability of emergency services, and provision of high-quality care to the public are a number of the key requirements. The book provides a broad overview of the (geo-information) technology, software, systems needed, used and to be developed for disaster management. The book provokes a wide discussion on systems and requirements for use of geo-information under time and stress constraints and unfamiliar situations, environments and circumstances.
