Rigidity Theory And Applications

Author : M.F. Thorpe
Publisher : Springer Science & Business Media
ISBN 13 : 0306470896
Total Pages : 435 pages
Book Rating : 4.99/5 ( download)

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Download or read book Rigidity Theory and Applications written by M.F. Thorpe and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although rigidity has been studied since the time of Lagrange (1788) and Maxwell (1864), it is only in the last twenty-five years that it has begun to find applications in the basic sciences. The modern era starts with Laman (1970), who made the subject rigorous in two dimensions, followed by the development of computer algorithms that can test over a million sites in seconds and find the rigid regions, and the associated pivots, leading to many applications. This workshop was organized to bring together leading researchers studying the underlying theory, and to explore the various areas of science where applications of these ideas are being implemented.

Author : Abdo Y. Alfakih
Publisher : Springer
ISBN 13 : 3319978462
Total Pages : 251 pages
Book Rating : 4.68/5 ( download)

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Download or read book Euclidean Distance Matrices and Their Applications in Rigidity Theory written by Abdo Y. Alfakih and published by Springer. This book was released on 2018-10-13 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive and accessible exposition of Euclidean Distance Matrices (EDMs) and rigidity theory of bar-and-joint frameworks. It is based on the one-to-one correspondence between EDMs and projected Gram matrices. Accordingly the machinery of semidefinite programming is a common thread that runs throughout the book. As a result, two parallel approaches to rigidity theory are presented. The first is traditional and more intuitive approach that is based on a vector representation of point configuration. The second is based on a Gram matrix representation of point configuration. Euclidean Distance Matrices and Their Applications in Rigidity Theory begins by establishing the necessary background needed for the rest of the book. The focus of Chapter 1 is on pertinent results from matrix theory, graph theory and convexity theory, while Chapter 2 is devoted to positive semidefinite (PSD) matrices due to the key role these matrices play in our approach. Chapters 3 to 7 provide detailed studies of EDMs, and in particular their various characterizations, classes, eigenvalues and geometry. Chapter 8 serves as a transitional chapter between EDMs and rigidity theory. Chapters 9 and 10 cover local and universal rigidities of bar-and-joint frameworks. This book is self-contained and should be accessible to a wide audience including students and researchers in statistics, operations research, computational biochemistry, engineering, computer science and mathematics.

Author : Robert Connelly
Publisher : Springer
ISBN 13 : 1493907816
Total Pages : 378 pages
Book Rating : 4.16/5 ( download)

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Download or read book Rigidity and Symmetry written by Robert Connelly and published by Springer. This book was released on 2014-06-11 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures and to explore the interaction of geometry, algebra and combinatorics. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory, classical geometry, hyperbolic geometry and topology. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. The volume will be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and graduate levels, as well as post docs, structural engineers and chemists.

Author : Jin-Chong Tan
Publisher : Royal Society of Chemistry
ISBN 13 : 1839164085
Total Pages : 363 pages
Book Rating : 4.88/5 ( download)

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Download or read book Mechanical Behaviour of Metal–Organic Framework Materials written by Jin-Chong Tan and published by Royal Society of Chemistry. This book was released on 2023-03-24 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mechanical Behaviour of Metal-Organic Framework Materials, provides a convenient introduction on how chemistry determines structure-mechanical property relationships and functional performance.

Author : Meera Sitharam
Publisher : CRC Press
ISBN 13 : 1351647431
Total Pages : 787 pages
Book Rating : 4.34/5 ( download)

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Download or read book Handbook of Geometric Constraint Systems Principles written by Meera Sitharam and published by CRC Press. This book was released on 2018-07-20 with total page 787 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Geometric Constraint Systems Principles is an entry point to the currently used principal mathematical and computational tools and techniques of the geometric constraint system (GCS). It functions as a single source containing the core principles and results, accessible to both beginners and experts. The handbook provides a guide for students learning basic concepts, as well as experts looking to pinpoint specific results or approaches in the broad landscape. As such, the editors created this handbook to serve as a useful tool for navigating the varied concepts, approaches and results found in GCS research. Key Features: A comprehensive reference handbook authored by top researchers Includes fundamentals and techniques from multiple perspectives that span several research communities Provides recent results and a graded program of open problems and conjectures Can be used for senior undergraduate or graduate topics course introduction to the area Detailed list of figures and tables About the Editors: Meera Sitharam is currently an Associate Professor at the University of Florida’s Department of Computer & Information Science and Engineering. She received her Ph.D. at the University of Wisconsin, Madison. Audrey St. John is an Associate Professor of Computer Science at Mount Holyoke College, who received her Ph. D. from UMass Amherst. Jessica Sidman is a Professor of Mathematics on the John S. Kennedy Foundation at Mount Holyoke College. She received her Ph.D. from the University of Michigan.

Author : Karl Endel Petersen
Publisher : Cambridge University Press
ISBN 13 : 0521459990
Total Pages : 452 pages
Book Rating : 4.90/5 ( download)

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Download or read book Ergodic Theory and Its Connection with Harmonic Analysis written by Karl Endel Petersen and published by Cambridge University Press. This book was released on 1995 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tutorial survey papers on important areas of ergodic theory, with related research papers.

Author : Leizhen Cai
Publisher : Springer
ISBN 13 : 364245030X
Total Pages : 761 pages
Book Rating : 4.03/5 ( download)

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Download or read book Algorithms and Computation written by Leizhen Cai and published by Springer. This book was released on 2013-12-12 with total page 761 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 24th International Symposium on Algorithms and Computation, ISAAC 2013, held in Hong Kong, China in December 2013. The 67 revised full papers presented together with 2 invited talks were carefully reviewed and selected from 177 submissions for inclusion in the book. The focus of the volume in on the following topics: computation geometry, pattern matching, computational complexity, internet and social network algorithms, graph theory and algorithms, scheduling algorithms, fixed-parameter tractable algorithms, algorithms and data structures, algorithmic game theory, approximation algorithms and network algorithms.

Author : David A. Cox
Publisher : American Mathematical Soc.
ISBN 13 : 1470451379
Total Pages : 250 pages
Book Rating : 4.70/5 ( download)

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Download or read book Applications of Polynomial Systems written by David A. Cox and published by American Mathematical Soc.. This book was released on 2020-03-02 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems of polynomial equations can be used to model an astonishing variety of phenomena. This book explores the geometry and algebra of such systems and includes numerous applications. The book begins with elimination theory from Newton to the twenty-first century and then discusses the interaction between algebraic geometry and numerical computations, a subject now called numerical algebraic geometry. The final three chapters discuss applications to geometric modeling, rigidity theory, and chemical reaction networks in detail. Each chapter ends with a section written by a leading expert. Examples in the book include oil wells, HIV infection, phylogenetic models, four-bar mechanisms, border rank, font design, Stewart-Gough platforms, rigidity of edge graphs, Gaussian graphical models, geometric constraint systems, and enzymatic cascades. The reader will encounter geometric objects such as Bézier patches, Cayley-Menger varieties, and toric varieties; and algebraic objects such as resultants, Rees algebras, approximation complexes, matroids, and toric ideals. Two important subthemes that appear in multiple chapters are toric varieties and algebraic statistics. The book also discusses the history of elimination theory, including its near elimination in the middle of the twentieth century. The main goal is to inspire the reader to learn about the topics covered in the book. With this in mind, the book has an extensive bibliography containing over 350 books and papers.

Author : S. N. Sahu
Publisher : Nova Publishers
ISBN 13 : 9781594549106
Total Pages : 496 pages
Book Rating : 4.09/5 ( download)

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Download or read book Nano-scale Materials written by S. N. Sahu and published by Nova Publishers. This book was released on 2006 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nano-Scale Materials - From Science to Technology

Author : Robert J. Zimmer
Publisher : University of Chicago Press
ISBN 13 : 022656813X
Total Pages : 724 pages
Book Rating : 4.33/5 ( download)

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Download or read book Group Actions in Ergodic Theory, Geometry, and Topology written by Robert J. Zimmer and published by University of Chicago Press. This book was released on 2019-12-23 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer, which lay out his program and contextualize his work over the course of his career. Zimmer’s body of work is remarkable in that it involves methods from a variety of mathematical disciplines, such as Lie theory, differential geometry, ergodic theory and dynamical systems, arithmetic groups, and topology, and at the same time offers a unifying perspective. After arriving at the University of Chicago in 1977, Zimmer extended his earlier research on ergodic group actions to prove his cocycle superrigidity theorem which proved to be a pivotal point in articulating and developing his program. Zimmer’s ideas opened the door to many others, and they continue to be actively employed in many domains related to group actions in ergodic theory, geometry, and topology. In addition to the selected papers themselves, this volume opens with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis, as well as a substantial introductory essay by Zimmer recounting the course of his career in mathematics. The volume closes with an afterword by Fisher on the most recent developments around the Zimmer program.