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Rigidity Theory And Applications
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Book Synopsis Rigidity Theory and Applications by : M.F. Thorpe
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 432 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.
Book Synopsis Euclidean Distance Matrices and Their Applications in Rigidity Theory by : Abdo Y. Alfakih
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.
Book Synopsis Rigidity and Symmetry by : Robert Connelly
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.
Book Synopsis Applications of Polynomial Systems by : David A. Cox
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.
Book Synopsis Mechanical Behaviour of Metal–Organic Framework Materials by : Jin-Chong Tan
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.
Book Synopsis Computers, Rigidity, and Moduli by : Shmuel Weinberger
Download or read book Computers, Rigidity, and Moduli written by Shmuel Weinberger and published by Princeton University Press. This book was released on 2005 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first to present a new area of mathematical research that combines topology, geometry, and logic. Shmuel Weinberger seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity. He provides applications to the problem of closed geodesics, the theory of submanifolds, and the structure of the moduli space of isometry classes of Riemannian metrics with curvature bounds on a given manifold. Ultimately, geometric complexity of a moduli space forces functions defined on that space to have many critical points, and new results about the existence of extrema or equilibria follow. The main sort of algorithmic problem that arises is recognition: is the presented object equivalent to some standard one? If it is difficult to determine whether the problem is solvable, then the original object has doppelgängers--that is, other objects that are extremely difficult to distinguish from it. Many new questions emerge about the algorithmic nature of known geometric theorems, about "dichotomy problems," and about the metric entropy of moduli space. Weinberger studies them using tools from group theory, computability, differential geometry, and topology, all of which he explains before use. Since several examples are worked out, the overarching principles are set in a clear relief that goes beyond the details of any one problem.
Book Synopsis Handbook of Geometric Constraint Systems Principles by : Meera Sitharam
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.
Book Synopsis Ergodic Theory and Its Connection with Harmonic Analysis by : Karl Endel Petersen
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.
Book Synopsis Counting on Frameworks by : Jack E. Graver
Download or read book Counting on Frameworks written by Jack E. Graver and published by Cambridge University Press. This book was released on 2001-09-06 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Book developing a mathematical theory of rigidity, for undergraduates working in modelling or graph theory.
Book Synopsis Algorithms and Computation by : Leizhen Cai
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.
Book Synopsis Nano-scale Materials by : S. N. Sahu
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
Book Synopsis Group Actions in Ergodic Theory, Geometry, and Topology by : Robert J. Zimmer
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.
Book Synopsis Formation Control of Multi-Agent Systems by : Marcio de Queiroz
Download or read book Formation Control of Multi-Agent Systems written by Marcio de Queiroz and published by John Wiley & Sons. This book was released on 2019-04-08 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Formation Control of Multi-Agent Systems: A Graph Rigidity Approach Marcio de Queiroz, Louisiana State University, USA Xiaoyu Cai, FARO Technologies, USA Matthew Feemster, U.S. Naval Academy, USA A comprehensive guide to formation control of multi-agent systems using rigid graph theory This book is the first to provide a comprehensive and unified treatment of the subject of graph rigidity-based formation control of multi-agent systems. Such systems are relevant to a variety of emerging engineering applications, including unmanned robotic vehicles and mobile sensor networks. Graph theory, and rigid graphs in particular, provides a natural tool for describing the multi-agent formation shape as well as the inter-agent sensing, communication, and control topology. Beginning with an introduction to rigid graph theory, the contents of the book are organized by the agent dynamic model (single integrator, double integrator, and mechanical dynamics) and by the type of formation problem (formation acquisition, formation manoeuvring, and target interception). The book presents the material in ascending level of difficulty and in a self-contained manner; thus, facilitating reader understanding. Key features: Uses the concept of graph rigidity as the basis for describing the multi-agent formation geometry and solving formation control problems. Considers different agent models and formation control problems. Control designs throughout the book progressively build upon each other. Provides a primer on rigid graph theory. Combines theory, computer simulations, and experimental results. Formation Control of Multi-Agent Systems: A Graph Rigidity Approach is targeted at researchers and graduate students in the areas of control systems and robotics. Prerequisite knowledge includes linear algebra, matrix theory, control systems, and nonlinear systems.
Download or read book Formation Control written by Hyo-Sung Ahn and published by Springer. This book was released on 2019-03-29 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph introduces recent developments in formation control of distributed-agent systems. Eschewing the traditional concern with the dynamic characteristics of individual agents, the book proposes a treatment that studies the formation control problem in terms of interactions among agents including factors such as sensing topology, communication and actuation topologies, and computations. Keeping pace with recent technological advancements in control, communications, sensing and computation that have begun to bring the applications of distributed-systems theory out of the industrial sphere and into that of day-to-day life, this monograph provides distributed control algorithms for a group of agents that may behave together. Unlike traditional control laws that usually require measurements with respect to a global coordinate frame and communications between a centralized operation center and agents, this book provides control laws that require only relative measurements and communications between agents without interaction with a centralized operator. Since the control algorithms presented in this book do not require any global sensing and any information exchanges with a centralized operation center, they can be realized in a fully distributed way, which significantly reduces the operation and implementation costs of a group of agents. Formation Control will give both students and researchers interested in pursuing this field a good grounding on which to base their work.
Book Synopsis Teichmüller Theory and Applications to Geometry, Topology, and Dynamics by : John Hamal Hubbard
Download or read book Teichmüller Theory and Applications to Geometry, Topology, and Dynamics written by John Hamal Hubbard and published by . This book was released on 2022-02 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Rigid Designation and Theoretical Identities by : Joseph LaPorte
Download or read book Rigid Designation and Theoretical Identities written by Joseph LaPorte and published by Oxford University Press. This book was released on 2013 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Joseph LaPorte offers an original account of the connections between the reference of words for properties and kinds, and theoretical identity statements. He argues that terms for properties, as well as for concrete objects, are rigid designators, and defends the Kripkean tradition of theoretical identities.
Book Synopsis Frontiers of High Pressure Research II by : Hans D. Hochheimer
Download or read book Frontiers of High Pressure Research II written by Hans D. Hochheimer and published by Springer Science & Business Media. This book was released on 2001-12-31 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Research Workshop, Pingree Park, CO, USA, from 10-15 June 2001
