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Emerging Topics On Differential Geometry And Graph Theory
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Book Synopsis Emerging Topics on Differential Geometry and Graph Theory by : Lucas Bernard
Download or read book Emerging Topics on Differential Geometry and Graph Theory written by Lucas Bernard and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential geometry is a mathematical discipline that uses the methods of differential and integral calculus to study problems in geometry. Graph theory is also a growing area in mathematical research. In mathematics and computer science, graph theory is the study of mathematical structures used to model pairwise relations between objects from a certain collection. This book presents various theories and applications in both of these mathematical fields. Included are the concepts of dominating sets, one of the most widely studied concepts in graph theory, some current developments of graph theory in the fields of planar linkage mechanisms and geared linkage mechanisms, lie algebras and the application of CR Hamiltonian flows to the deformation theory of CR structures.
Book Synopsis Emerging Topics on Differential Geometry and Graph Theory by : Lucas Bernard
Download or read book Emerging Topics on Differential Geometry and Graph Theory written by Lucas Bernard and published by Nova Science Publishers. This book was released on 2014-05-14 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Discrete Differential Geometry by : Alexander I. Bobenko
Download or read book Discrete Differential Geometry written by Alexander I. Bobenko and published by American Mathematical Society. This book was released on 2023-09-14 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: An emerging field of discrete differential geometry aims at the development of discrete equivalents of notions and methods of classical differential geometry. The latter appears as a limit of a refinement of the discretization. Current interest in discrete differential geometry derives not only from its importance in pure mathematics but also from its applications in computer graphics, theoretical physics, architecture, and numerics. Rather unexpectedly, the very basic structures of discrete differential geometry turn out to be related to the theory of integrable systems. One of the main goals of this book is to reveal this integrable structure of discrete differential geometry. For a given smooth geometry one can suggest many different discretizations. Which one is the best? This book answers this question by providing fundamental discretization principles and applying them to numerous concrete problems. It turns out that intelligent theoretical discretizations are distinguished also by their good performance in applications. The intended audience of this book is threefold. It is a textbook on discrete differential geometry and integrable systems suitable for a one semester graduate course. On the other hand, it is addressed to specialists in geometry and mathematical physics. It reflects the recent progress in discrete differential geometry and contains many original results. The third group of readers at which this book is targeted is formed by specialists in geometry processing, computer graphics, architectural design, numerical simulations, and animation. They may find here answers to the question “How do we discretize differential geometry?” arising in their specific field. Prerequisites for reading this book include standard undergraduate background (calculus and linear algebra). No knowledge of differential geometry is expected, although some familiarity with curves and surfaces can be helpful.
Book Synopsis Foundations of Relational Realism by : Michael Epperson
Download or read book Foundations of Relational Realism written by Michael Epperson and published by Lexington Books. This book was released on 2013-06-20 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: If there is a central conceptual framework that has reliably borne the weight of modern physics as it ascends into the twenty-first century, it is the framework of quantum mechanics. Because of its enduring stability in experimental application, physics has today reached heights that not only inspire wonder, but arguably exceed the limits of intuitive vision, if not intuitive comprehension. For many physicists and philosophers, however, the currently fashionable tendency toward exotic interpretation of the theoretical formalism is recognized not as a mark of ascent for the tower of physics, but rather an indicator of sway—one that must be dampened rather than encouraged if practical progress is to continue. In this unique two-part volume, designed to be comprehensible to both specialists and non-specialists, the authors chart out a pathway forward by identifying the central deficiency in most interpretations of quantum mechanics: That in its conventional, metrical depiction of extension, inherited from the Enlightenment, objects are characterized as fundamental to relations—i.e., such that relations presuppose objects but objects do not presuppose relations. The authors, by contrast, argue that quantum mechanics exemplifies the fact that physical extensiveness is fundamentally topological rather than metrical, with its proper logico-mathematical framework being category theoretic rather than set theoretic. By this thesis, extensiveness fundamentally entails not only relations of objects, but also relations of relations. Thus, the fundamental quanta of quantum physics are properly defined as units of logico-physical relation rather than merely units of physical relata as is the current convention. Objects are always understood as relata, and likewise relations are always understood objectively. In this way, objects and relations are coherently defined as mutually implicative. The conventional notion of a history as “a story about fundamental objects” is thereby reversed, such that the classical “objects” become the story by which we understand physical systems that are fundamentally histories of quantum events. These are just a few of the novel critical claims explored in this volume—claims whose exemplification in quantum mechanics will, the authors argue, serve more broadly as foundational principles for the philosophy of nature as it evolves through the twenty-first century and beyond.
Book Synopsis Topics in differential geometry by : János Szenthe
Download or read book Topics in differential geometry written by János Szenthe and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis New Horizons In Differential Geometry And Its Related Fields by : Toshiaki Adachi
Download or read book New Horizons In Differential Geometry And Its Related Fields written by Toshiaki Adachi and published by World Scientific. This book was released on 2022-04-07 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents recent developments in geometric structures on Riemannian manifolds and their discretizations. With chapters written by recognized experts, these discussions focus on contact structures, Kähler structures, fiber bundle structures and Einstein metrics. It also contains works on the geometric approach on coding theory.For researchers and students, this volume forms an invaluable source to learn about these subjects that are not only in the field of differential geometry but also in other wide related areas. It promotes and deepens the study of geometric structures.
Book Synopsis Topics in Differential Geometry: A New Approach Using D-Differentiation by : Donal J. Hurley
Download or read book Topics in Differential Geometry: A New Approach Using D-Differentiation written by Donal J. Hurley and published by Springer Science & Business Media. This book was released on 2002 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: D-differentiation is a unified operation that enables aspects of differential geometry to be developed and presented from a new perspective. This book is the first comprehensive and self-contained treatment of this new method. It demonstrates, concisely but without sacrificing rigour or intelligibility, how even elementary concepts in differential geometry can be reformulated to obtain new and valuable insights. In addition, D-differentiation has applications in several areas of physics, such as classical mechanics, solid-state physics and general relativity. This book will prove useful to all users of D-differentiation - from advanced graduate students onwards - and to those researching into new approaches to some branches of physics and mathematics.
Book Synopsis Thirty Essays on Geometric Graph Theory by : János Pach
Download or read book Thirty Essays on Geometric Graph Theory written by János Pach and published by Springer Science & Business Media. This book was released on 2012-12-15 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods of "abstract" graph theory are often incapable of providing satisfactory answers to questions arising in such applications. In the past couple of decades, many powerful new combinatorial and topological techniques have been developed to tackle these problems. Today geometric graph theory is a burgeoning field with many striking results and appealing open questions. This contributed volume contains thirty original survey and research papers on important recent developments in geometric graph theory. The contributions were thoroughly reviewed and written by excellent researchers in this field.
Book Synopsis Topics in Modern Differential Geometry by : Stefan Haesen
Download or read book Topics in Modern Differential Geometry written by Stefan Haesen and published by Springer. This book was released on 2016-12-21 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.
Book Synopsis Global Riemannian Geometry: Curvature and Topology by : Ana Hurtado
Download or read book Global Riemannian Geometry: Curvature and Topology written by Ana Hurtado and published by Springer Nature. This book was released on 2020-08-19 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature the application of the Lichnerowicz formula for Dirac operators to the study of Gromov's invariants to measure the K-theoretic size of a Riemannian manifold. It is intended for both graduate students and researchers.
Book Synopsis Current Developments in Differential Geometry and Its Related Fields - Proceedings of the 4th International Colloquium on Differential Geometry and Its Related Fields by : Toshiaki Adachi
Download or read book Current Developments in Differential Geometry and Its Related Fields - Proceedings of the 4th International Colloquium on Differential Geometry and Its Related Fields written by Toshiaki Adachi and published by World Scientific. This book was released on 2015-10-22 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This volume contains contributions by the main participants of the 4th International Colloquium on Differential Geometry and its Related Fields (ICDG2014). These articles cover recent developments and are devoted mainly to the study of some geometric structures on manifolds and graphs. Readers will find a broad overview of differential geometry and its relationship to other fields in mathematics and physics."--
Book Synopsis Introduction to Differential Geometry by : Joel W. Robbin
Download or read book Introduction to Differential Geometry written by Joel W. Robbin and published by Springer Nature. This book was released on 2022-01-12 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.
Book Synopsis Trends in Differential Geometry, Complex Analysis and Mathematical Physics by :
Download or read book Trends in Differential Geometry, Complex Analysis and Mathematical Physics written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis New Scientific Applications of Geometry and Topology by : De Witt L. Sumners
Download or read book New Scientific Applications of Geometry and Topology written by De Witt L. Sumners and published by American Mathematical Soc.. This book was released on 1992 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry and topology are subjects generally considered to be "pure" mathematics. Recently, however, some of the methods and results in these two areas have found new utility in both wet-lab science (biology and chemistry) and theoretical physics. Conversely, science is influencing mathematics, from posing questions that call for the construction of mathematical models to exporting theoretical methods of attack on long-standing problems of mathematical interest. Based on an AMS Short Course held in January 1992, this book contains six introductory articles on these intriguing new connections. There are articles by a chemist and a biologist about mathematics, and four articles by mathematicians writing about science and mathematics involved. Because this book communicates the excitement and utility of mathematics research at an elementary level, it is an excellent textbook in an advanced undergraduate mathematics course.
Book Synopsis An Excursion Through Discrete Differential Geometry by : American Mathematical Society. Short Course, Discrete Differential Geometry
Download or read book An Excursion Through Discrete Differential Geometry written by American Mathematical Society. Short Course, Discrete Differential Geometry and published by American Mathematical Soc.. This book was released on 2020-09-02 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete Differential Geometry (DDG) is an emerging discipline at the boundary between mathematics and computer science. It aims to translate concepts from classical differential geometry into a language that is purely finite and discrete, and can hence be used by algorithms to reason about geometric data. In contrast to standard numerical approximation, the central philosophy of DDG is to faithfully and exactly preserve key invariants of geometric objects at the discrete level. This process of translation from smooth to discrete helps to both illuminate the fundamental meaning behind geometric ideas and provide useful algorithmic guarantees. This volume is based on lectures delivered at the 2018 AMS Short Course ``Discrete Differential Geometry,'' held January 8-9, 2018, in San Diego, California. The papers in this volume illustrate the principles of DDG via several recent topics: discrete nets, discrete differential operators, discrete mappings, discrete conformal geometry, and discrete optimal transport.
Author :Alexander I. Bobenko TU Berlin Publisher :Springer Science & Business Media ISBN 13 :3764386215 Total Pages :341 pages Book Rating :4.7/5 (643 download)
Book Synopsis Discrete Differential Geometry by : Alexander I. Bobenko TU Berlin
Download or read book Discrete Differential Geometry written by Alexander I. Bobenko TU Berlin and published by Springer Science & Business Media. This book was released on 2008-03-27 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on a newly emerging field of discrete differential geometry providing an excellent way to access this exciting area. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. The carefully edited collection of essays gives a lively, multi-facetted introduction to this emerging field.
Download or read book Differential Geometry written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
