graphs on surfaces and their applications encyclopaedia of mathematical sciences

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Graphs On Surfaces And Their Applications

Author : Sergei K. Lando
ISBN : 9783540383611
Genre : Mathematics
File Size : 61. 48 MB
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Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.

Graphs On Surfaces

Author : Joanna A. Ellis-Monaghan
ISBN : 9781461469711
Genre : Mathematics
File Size : 50. 74 MB
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Graphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications. The authors illustrate the interdependency between duality, medial graphs and knots; how this interdependency is reflected in algebraic invariants of graphs and knots; and how it can be exploited to solve problems in graph and knot theory. Taking a constructive approach, the authors emphasize how generalized duals and related ideas arise by localizing classical constructions, such as geometric duals and Tait graphs, and then removing artificial restrictions in these constructions to obtain full extensions of them to embedded graphs. The authors demonstrate the benefits of these generalizations to embedded graphs in chapters describing their applications to graph polynomials and knots. Graphs on Surfaces: Dualities, Polynomials, and Knots also provides a self-contained introduction to graphs on surfaces, generalized duals, topological graph polynomials, and knot polynomials that is accessible both to graph theorists and to knot theorists. Directed at those with some familiarity with basic graph theory and knot theory, this book is appropriate for graduate students and researchers in either area. Because the area is advancing so rapidly, the authors give a comprehensive overview of the topic and include a robust bibliography, aiming to provide the reader with the necessary foundations to stay abreast of the field. The reader will come away from the text convinced of advantages of considering these higher genus analogues of constructions of plane and abstract graphs, and with a good understanding of how they arise.

Medical Image Computing And Computer Assisted Intervention Miccai 2015

Author : Nassir Navab
ISBN : 9783319245744
Genre : Computers
File Size : 79. 70 MB
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The three-volume set LNCS 9349, 9350, and 9351 constitutes the refereed proceedings of the 18th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2015, held in Munich, Germany, in October 2015. Based on rigorous peer reviews, the program committee carefully selected 263 revised papers from 810 submissions for presentation in three volumes. The papers have been organized in the following topical sections: quantitative image analysis I: segmentation and measurement; computer-aided diagnosis: machine learning; computer-aided diagnosis: automation; quantitative image analysis II: classification, detection, features, and morphology; advanced MRI: diffusion, fMRI, DCE; quantitative image analysis III: motion, deformation, development and degeneration; quantitative image analysis IV: microscopy, fluorescence and histological imagery; registration: method and advanced applications; reconstruction, image formation, advanced acquisition - computational imaging; modelling and simulation for diagnosis and interventional planning; computer-assisted and image-guided interventions.

Riemann And Klein Surfaces Automorphisms Symmetries And Moduli Spaces

Author : Milagros Izquierdo
ISBN : 9781470410933
Genre : Mathematics
File Size : 25. 9 MB
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This volume contains the proceedings of the conference on Riemann and Klein Surfaces, Symmetries and Moduli Spaces, in honor of Emilio Bujalance, held from June 24-28, 2013, at Linköping University. The conference and this volume are devoted to the mathematics that Emilio Bujalance has worked with in the following areas, all with a computational flavor: Riemann and Klein surfaces, automorphisms of real and complex surfaces, group actions on surfaces and topological properties of moduli spaces of complex curves and Abelian varieties.

Newsletter

Author : New Zealand Mathematical Society
ISBN : UOM:39015060913897
Genre : Mathematics
File Size : 65. 17 MB
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Introduction To Modern Number Theory

Author : Yu. I. Manin
ISBN : 3540276920
Genre : Mathematics
File Size : 71. 69 MB
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This edition has been called ‘startlingly up-to-date’, and in this corrected second printing you can be sure that it’s even more contemporaneous. It surveys from a unified point of view both the modern state and the trends of continuing development in various branches of number theory. Illuminated by elementary problems, the central ideas of modern theories are laid bare. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories.

Algebraic Geometry I

Author : V.I. Danilov
ISBN : 3540637052
Genre : Mathematics
File Size : 43. 37 MB
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"... To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics." --Acta Scientiarum Mathematicarum

Introduction To Tensor Analysis And The Calculus Of Moving Surfaces

Author : Pavel Grinfeld
ISBN : 9781461478676
Genre : Mathematics
File Size : 36. 81 MB
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This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.

Mathematics

Author : A. D. Aleksandrov
ISBN : 9780486157870
Genre : Mathematics
File Size : 87. 86 MB
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Major survey offers comprehensive, coherent discussions of analytic geometry, algebra, differential equations, calculus of variations, functions of a complex variable, prime numbers, linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.

Encyclopedia Of Analytical Surfaces

Author : S.N. Krivoshapko
ISBN : 9783319117737
Genre : Science
File Size : 80. 6 MB
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This encyclopedia presents an all-embracing collection of analytical surface classes. It provides concise definitions and description for more than 500 surfaces and categorizes them in 38 classes of analytical surfaces. All classes are cross references to the original literature in an excellent bibliography. The encyclopedia is of particular interest to structural and civil engineers and serves as valuable reference for mathematicians.

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