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Graph Transformations ; 4th International Conference, ICGT 2008, Leicester, United Kingdom, September 7-13, 2008. Proceedings
This book constitutes the refereed proceedings of the 4th International Conference on Graph Transformations, ICGT 2008, held in Leicester, UK, in September 2008.The 27 revised full papers presented together with 5 tutorial and workshop papers and 3 invited lectures were carefully selected from 57 submissions. All current aspects in graph drawing are addressed including hypergraphs and termgraph rewriting, applications of graph transformation, execution of graph transformations, compositional systems, validation and verification, graph languages and special transformation concepts, as well as patterns and model transformations.
Graph theory and combinatorial optimization
Graph theory is very much tied to the geometric properties of optimization and combinatorial optimization. Moreover, graph theory's geometric properties are at the core of many research interests in operations research and applied mathematics. Its techniques have been used in solving many classical problems including maximum flow problems, independent set problems, and the traveling salesman problem. Graph Theory and Combinatorial Optimization explores the field's classical foundations and its developing theories, ideas and applications to new problems. The book examines the geometric properties of graph theory and its widening uses in combinatorial optimization theory and application.
Graph drawing ; 15th International symposium, GD 2007, Sydney, Australia, September 24-26, 2007. Revised Papers
The 16th International Symposium on Graph Drawing (GD 2008) was held in Hersonissos, near Heraklion, Crete, Greece, September 21-24, 2008, and was attended by 91 participants from 19 countries. In response to the call for papers the Program Committee received 83 s- missions,eachdescribing originalresearchand/or a systemdemonstration.Tamassia showed how graph drawing techniques can be used as an e?ective tool in computer security and pointed to future research directions in this area. Following what is now a tradition, the 15th Annual Graph Drawing Contest was held during the conference, also including a Graph Drawing Challenge to the conference attendees.
Graph drawing ; 14th International symposium, GD 2006, Karlsruhe, Germany, September 18-20, 2006, Revised Papers
The 33 revised full papers and 5 revised short papers presented together with 2 invited talks, 1 system demo, 2 poster papers address all current aspects in graph drawing, ranging from foundational and methodological issues to applications for various classes of graphs in a variety of fields.
Granite genesis : in-situ melting and crustal evolution
In this book we suggest an alternative model for the origin of granite in terms of in-situ meltingintracrustal convection that physically determines the process from partial melting of mid-upper crustal rocks to formation of a convecting magma layer. We illustrate the model using the geological, geochemical and geophysical studies from Australia, North and South America, Europe and China, and conclude that heat convection within a crustal partial melting layer is essential for formation of granite magma and that without convection, partial melting of rocks produces migmatites rather than granites. Granite is layer-like within the crust, and shape and size of granite bodies reflect the geometric relationship between an irregular upper surface of the crystallised magma layer and erosion surface. Repeated melting of the crust generates downward-younging granite sequences. Chemical and isotopic compositions of granites indicate differentiation within the magma rather than different deep sources.
Grammatical Picture Generation : A Tree-Based Approach
The book presents important types of picture generators, using a tree-based approach to stress their common algorithmic basis, the treatment influenced by the theory of computation, and the theory of formal languages in particular. It guides the reader through the basics of the tree-based approach on to dedicated chapters on line-drawing languages, collage grammars, iterated function systems, grid picture languages, languages of fractals, and languages of coloured collages, while presenting results about (un)decidable, NP-complete, or efficiently solvable problems, normal forms, hierarchies of language classes, and related phenomena.
Global Aspects of Complex Geometry
This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kähler geometry, and group actions to Hodge theory and characteristic p-geometry.
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 of Müntz Spaces and Related Questions
Starting point and motivation for this volume is the classical Muentz theorem which states that the space of all polynomials on the unit interval, whose exponents have too many gaps, is no longer dense in the space of all continuous functions. The resulting spaces of Muentz polynomials are largely unexplored as far as the Banach space geometry is concerned and deserve the attention that the authors arouse. They present the known theorems and prove new results concerning, for example, the isomorphic and isometric classification and the existence of bases in these spaces. Moreover they state many open problems. Although the viewpoint is that of the geometry of Banach spaces they only assume that the reader is familiar with basic functional analysis. In the first part of the book the Banach spaces notions are systematically introduced and are later on applied for Muentz spaces. They include the opening and inclination of subspaces, bases and bounded approximation properties and versions of universality.
Geometry for Computer Graphics : Formulae, Examples and Proofs
Geometry is the cornerstone of computer graphics and computer animation, and provides the framework and tools for solving problems in two and three dimensions. This may be in the form of describing simple shapes such as a circle, ellipse, or parabola, or complex problems such as rotating 3D objects about an arbitrary axis. Geometry for Computer Graphics draws together a wide variety of geometric information that will provide a sourcebook of facts, examples, and proofs for students, academics, researchers, and professional practitioners.
Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics
This book explores the foundations of hamiltonian dynamical systems and statistical mechanics, in particular phase transition, from the point of view of geometry and topology. A broad participation of topology in these fields has been lacking and this book will provide a welcome overview of the current research in the area, in which the author himself is a pioneer. Using geometrical thinking to solve fundamental problems in these areas, compared to the purely analytical methods usually used in physics could be highly productive. The author skillfully guides the reader, whether mathematician or physicists through the background needed to understand and use these techniques.
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 Properties for Incomplete Data
Computer vision and image analysis require interdisciplinary collaboration between mathematics and engineering. This book addresses the area of high-accuracy measurements of length, curvature, motion parameters and other geometrical quantities from acquired image data. It is a common problem that these measurements are incomplete or noisy, such that considerable efforts are necessary to regularise the data, to fill in missing information, and to judge the accuracy and reliability of these results. This monograph brings together contributions from researchers in computer vision, engineering and mathematics who are working in this area.
Geometric Problems on Maxima and Minima
Questions of maxima and minima have great practical significance, with applications to physics, engineering, and economics; they have also given rise to theoretical advances, notably in calculus and optimization. Indeed, while most texts view the study of extrema within the context of calculus, this carefully constructed problem book takes a uniquely intuitive approach to the subject: it presents hundreds of extreme-value problems, examples, and solutions primarily through Euclidean geometry.
