Geometric Methods and Applications

As an introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer, this book fills the gap between standard geometry books, which are primarily theoretical, and applied books ...

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Author: Jean Gallier

Publisher: Springer Science & Business Media

ISBN: 9781461301370

Category: Mathematics

Page: 566

View: 868

As an introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer, this book fills the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, or robotics that do not cover the underlying geometric concepts in detail. Gallier offers an introduction to affine, projective, computational, and Euclidean geometry, basics of differential geometry and Lie groups, and explores many of the practical applications of geometry. Some of these include computer vision, efficient communication, error correcting codes, cryptography, motion interpolation, and robot kinematics. This comprehensive text covers most of the geometric background needed for conducting research in computer graphics, geometric modeling, computer vision, and robotics and as such will be of interest to a wide audience including computer scientists, mathematicians, and engineers.

Modern Geometry Methods and Applications

This is the first volume of a three-volume introduction to modern geometry which emphasizes applications to other areas of mathematics and theoretical physics.

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Author: B.A. Dubrovin

Publisher: Springer Science & Business Media

ISBN: 0387976639

Category: Mathematics

Page: 470

View: 827

This is the first volume of a three-volume introduction to modern geometry which emphasizes applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory. This new edition offers substantial revisions, and the material is written in concrete language with terminology acceptable to physicists.

Applications of Analytic and Geometric Methods to Nonlinear Differential Equations

The majority of nonlinear evolution equations are nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations.

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Author: P.A. Clarkson

Publisher: Springer Science & Business Media

ISBN: 0792324579

Category: Science

Page: 477

View: 812

In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the `soliton' equations. (2) Twistor theory, using differential geometry, which has been used to solve the self-dual Yang--Mills (SDYM) equations, a four-dimensional system having important applications in mathematical physics. Both soliton and the SDYM equations have rich algebraic structures which have been extensively studied. Recently, it has been conjectured that, in some sense, all soliton equations arise as special cases of the SDYM equations; subsequently many have been discovered as either exact or asymptotic reductions of the SDYM equations. Consequently what seems to be emerging is that a natural, physically significant system such as the SDYM equations provides the basis for a unifying framework underlying this class of integrable systems, i.e. `soliton' systems. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. The majority of nonlinear evolution equations are nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations. Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations. (ABSTRACT) In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years; the inverse scattering transform (IST), for `soliton' equations and twistor theory, for the self-dual Yang--Mills (SDYM) equations. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. Additionally, it contains articles on perturbed soliton equations, Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations.

Geometrical Methods in Robotics

Subsequent chapters develop the structure of Lie groups and how these relate to planar kinematics, line geometry, representation theory, and other topics.

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Author: J. M. Selig

Publisher: Springer Verlag

ISBN: UOM:39015037841288

Category: Technology & Engineering

Page: 269

View: 961

Subsequent chapters develop the structure of Lie groups and how these relate to planar kinematics, line geometry, representation theory, and other topics. Having provided the conceptual framework, the author then demonstrates the power and elegance of these methods to robotics, notably to the statics and dynamics of robots, to the problems of gripping solid objects, to the numbers of postures of robots, and to screw systems.

Applications of Geometric Algebra in Computer Science and Engineering

The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications.

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Author: Leo Dorst

Publisher: Springer Science & Business Media

ISBN: 0817642676

Category: Mathematics

Page: 478

View: 110

Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.

Algebraic and Geometric Methods in Discrete Mathematics

This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Methods in Applied Discrete Mathematics, held on January 11, 2015, in San Antonio, Texas.

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Author: Heather A. Harrington

Publisher: American Mathematical Soc.

ISBN: 9781470423216

Category: Commutative algebra -- Computational aspects and applications -- Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)

Page: 277

View: 755

This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Methods in Applied Discrete Mathematics, held on January 11, 2015, in San Antonio, Texas. The papers present connections between techniques from “pure” mathematics and various applications amenable to the analysis of discrete models, encompassing applications of combinatorics, topology, algebra, geometry, optimization, and representation theory. Papers not only present novel results, but also survey the current state of knowledge of important topics in applied discrete mathematics. Particular highlights include: a new computational framework, based on geometric combinatorics, for structure prediction from RNA sequences; a new method for approximating the optimal solution of a sum of squares problem; a survey of recent Helly-type geometric theorems; applications of representation theory to voting theory and game theory; a study of fixed points of tensors; and exponential random graph models from the perspective of algebraic statistics with applications to networks. This volume was written for those trained in areas such as algebra, topology, geometry, and combinatorics who are interested in tackling problems in fields such as biology, the social sciences, data analysis, and optimization. It may be useful not only for experts, but also for students who wish to gain an applied or interdisciplinary perspective.

Digital Geometry

The first book on digital geometry by the leaders in the field.

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Author: Reinhard Klette

Publisher: Morgan Kaufmann

ISBN: 1558608613

Category: Computers

Page: 656

View: 719

The first book on digital geometry by the leaders in the field.

Geometric Methods in PDE s

This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday of Ermanno Lanconelli.

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Author: Giovanna Citti

Publisher: Springer

ISBN: 9783319026664

Category: Mathematics

Page: 373

View: 541

The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday of Ermanno Lanconelli. They describe a number of new achievements and/or the state of the art in their discipline of research, providing readers an overview of recent progress and future research trends in PDEs. In particular, the volume collects significant results for sub-elliptic equations, potential theory and diffusion equations, with an emphasis on comparing different methodologies and on their implications for theory and applications.

Geometric Methods in Inverse Problems and PDE Control

This IMA Volume in Mathematics and its Applications GEOMETRIC METHODS IN INVERSE PROBLEMS AND PDE CONTROL contains a selection of articles presented at 2001 IMA Summer Program with the same title.

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Author: Chrisopher B. Croke

Publisher: Springer Science & Business Media

ISBN: 9781468493757

Category: Mathematics

Page: 330

View: 724

This IMA Volume in Mathematics and its Applications GEOMETRIC METHODS IN INVERSE PROBLEMS AND PDE CONTROL contains a selection of articles presented at 2001 IMA Summer Program with the same title. We would like to thank Christopher B. Croke (University of Penn sylva nia), Irena Lasiecka (University of Virginia), Gunther Uhlmann (University of Washington), and Michael S. Vogelius (Rutgers University) for their ex cellent work as organizers of the two-week summer workshop and for editing the volume. We also take this opportunity to thank the National Science Founda tion for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume contains a selected number of articles based on lectures delivered at the IMA 2001 Summer Program on "Geometric Methods in Inverse Problems and PDE Control. " The focus of this program was some common techniques used in the study of inverse coefficient problems and control problems for partial differential equations, with particular emphasis on their strong relation to fundamental problems of geometry. Inverse coef ficient problems for partial differential equations arise in many application areas, for instance in medical imaging, nondestructive testing, and geophys ical prospecting. Control problems involving partial differential equations may arise from the need to optimize a given performance criterion, e. g. , to dampen out undesirable vibrations of a structure , or more generally, to obtain a prescribed behaviour of the dynamics.

Computational Geometry Methods Algorithms and Applications

The volume presents discussions of every aspect of this dating technique, as well as chronicles of its development and views of future advancements and applications.

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Author: International Workshop on Computational Geometry

Publisher: Springer Science & Business Media

ISBN: 3540548912

Category: Computers

Page: 320

View: 908

Radiocarbon After Four Decades: An Interdisciplinary Perspective commemorates the 40th anniversary of radiocarbon dating. The volume presents discussions of every aspect of this dating technique, as well as chronicles of its development and views of future advancements and applications. All of the 64 authors played major roles in establishment, development or application of this revolutionary scientific tool. The 35 chapters provide a solid foundation in the essential topics of radiocarbon dating: Historical Perspectives; The Natural Carbon Cycle; Instrumentation and Sample Preparation; Hydrology; Old World Archaeology; New World Archaeology; Earth Sciences; and Biomedical Applications.

Computational Geometry Methods Algorithms and Applications

This volume presents the proceedings of the Seventh International Workshop on Computational Geometry, CG'91, held at the University of Berne, Switzerland, March 21/22, 1991. Computational geometry is not a precisely defined field.

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Author: International Workshop on Computational Geometry

Publisher: Springer Science & Business Media

ISBN: 3540548912

Category: Computers

Page: 320

View: 915

Radiocarbon After Four Decades: An Interdisciplinary Perspective commemorates the 40th anniversary of radiocarbon dating. The volume presents discussions of every aspect of this dating technique, as well as chronicles of its development and views of future advancements and applications. All of the 64 authors played major roles in establishment, development or application of this revolutionary scientific tool. The 35 chapters provide a solid foundation in the essential topics of radiocarbon dating: Historical Perspectives; The Natural Carbon Cycle; Instrumentation and Sample Preparation; Hydrology; Old World Archaeology; New World Archaeology; Earth Sciences; and Biomedical Applications.

Geometric Methods in Signal and Image Analysis

A comprehensive guide to modern geometric methods for signal and image analysis, from basic principles to state-of-the-art concepts and applications.

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Author: Hamid Krim

Publisher: Cambridge University Press

ISBN: 9781107033900

Category: Computers

Page: 295

View: 258

A comprehensive guide to modern geometric methods for signal and image analysis, from basic principles to state-of-the-art concepts and applications.

Computational Geometry

For students this motivation will be especially welcome.

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Author: de Berg (M.T.)

Publisher: Springer Science & Business Media

ISBN: 3540656200

Category: Computers

Page: 367

View: 178

For students this motivation will be especially welcome.

Lectures on Geometric Methods in Mathematical Physics

A monograph on some of the ways geometry and analysis can be used in mathematical problems of physical interest. The roles of symmetry, bifurcation and Hamiltonian systems in diverse applications are explored.

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Author: Jerrold E. Marsden

Publisher: SIAM

ISBN: 1611970326

Category: Geometry, Differential

Page: 97

View: 789

A monograph on some of the ways geometry and analysis can be used in mathematical problems of physical interest. The roles of symmetry, bifurcation and Hamiltonian systems in diverse applications are explored.

Geometric Methods in the Algebraic Theory of Quadratic Forms

Several aspects of these new methods are addressed in this volume, which includes an introduction to motives of quadrics by A. Vishik, with various applications, notably to the splitting patterns of quadratic forms, papers by O. Izhboldin ...

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Author: Oleg T. Izhboldin

Publisher: Springer

ISBN: 9783540409908

Category: Mathematics

Page: 198

View: 564

The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadrics have been central to the proofs of fundamental results since the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems. Several aspects of these new methods are addressed in this volume, which includes an introduction to motives of quadrics by A. Vishik, with various applications, notably to the splitting patterns of quadratic forms, papers by O. Izhboldin and N. Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields with u-invariant 9, and a contribution in French by B. Kahn which lays out a general framework for the computation of the unramified cohomology groups of quadrics and other cellular varieties.

Handbook of Geometric Computing

This handbook is highly recommended for postgraduate students and researchers working on applications such as automated learning; geometric and fuzzy reasoning; human-like artificial vision; tele-operation; space maneuvering; haptics; ...

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Author: Eduardo Bayro Corrochano

Publisher: Springer Science & Business Media

ISBN: 9783540282471

Category: Computers

Page: 779

View: 259

Many computer scientists, engineers, applied mathematicians, and physicists use geometry theory and geometric computing methods in the design of perception-action systems, intelligent autonomous systems, and man-machine interfaces. This handbook brings together the most recent advances in the application of geometric computing for building such systems, with contributions from leading experts in the important fields of neuroscience, neural networks, image processing, pattern recognition, computer vision, uncertainty in geometric computations, conformal computational geometry, computer graphics and visualization, medical imagery, geometry and robotics, and reaching and motion planning. For the first time, the various methods are presented in a comprehensive, unified manner. This handbook is highly recommended for postgraduate students and researchers working on applications such as automated learning; geometric and fuzzy reasoning; human-like artificial vision; tele-operation; space maneuvering; haptics; rescue robots; man-machine interfaces; tele-immersion; computer- and robotics-aided neurosurgery or orthopedics; the assembly and design of humanoids; and systems for metalevel reasoning.

Geometric Methods in Physics

R . V . Moody , and J . Patera , SIAM J . on Algebraic and Discrete Methods 5 ,
359 - 383 ( 1984 ) . 2 . J . Patera , SIGMA ( Symmetry , Integrability and Geometry
: Methods and Applications ) 1 ( 2005 ) , paper 025 , 6 pages , math - ph /
0512029 ...

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Author: Piotr Kielanowski

Publisher: American Institute of Physics

ISBN: UCSD:31822036967941

Category: Computers

Page: 282

View: 469

Bialowieza, Poland, 29 June-5 July 2008

Geometric Methods in Physics XXXV

This book features a selection of articles based on the XXXV Białowieża Workshop on Geometric Methods in Physics, 2016.

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Author: Piotr Kielanowski

Publisher: Birkhäuser

ISBN: 9783319635941

Category: Mathematics

Page: 282

View: 769

This book features a selection of articles based on the XXXV Białowieża Workshop on Geometric Methods in Physics, 2016. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, and with applications to classical and quantum physics. In 2016 the special session "Integrability and Geometry" in particular attracted pioneers and leading specialists in the field. Traditionally, the Białowieża Workshop is followed by a School on Geometry and Physics, for advanced graduate students and early-career researchers, and the book also includes extended abstracts of the lecture series.

Geometric Methods in Physics XXXVI

This book collects papers based on the XXXVI Białowieża Workshop on Geometric Methods in Physics, 2017.

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Author: Piotr Kielanowski

Publisher: Springer

ISBN: 9783030011567

Category: Mathematics

Page: 425

View: 789

This book collects papers based on the XXXVI Białowieża Workshop on Geometric Methods in Physics, 2017. The Workshop, which attracts a community of experts active at the crossroads of mathematics and physics, represents a major annual event in the field. Based on presentations given at the Workshop, the papers gathered here are previously unpublished, at the cutting edge of current research, and primarily grounded in geometry and analysis, with applications to classical and quantum physics. In addition, a Special Session was dedicated to S. Twareque Ali, a distinguished mathematical physicist at Concordia University, Montreal, who passed away in January 2016. For the past six years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising a series of advanced lectures for graduate students and early-career researchers. The extended abstracts of this year’s lecture series are also included here. The unique character of the Workshop-and-School series is due in part to the venue: a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in eastern Poland. Lectures are given in the Nature and Forest Museum, and local traditions are interwoven with the scientific activities.

Geometric Concepts for Geometric Design

Anyone attracted to or wishing a deeper understanding of the beauty of geometric mysteries will find this book an engaging and invaluable guide.

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Author: Wolfgang Boehm

Publisher: A K Peters, Ltd.

ISBN: 1568810040

Category: Computers

Page: 393

View: 355

Often a solution to a problem lies simply in finding its correct description. It is this underlying concept that consolidates the text of this unique and lively survey of geometric ideas. In Geometric Concepts for Geometric Design, its authors provide a way in which to visualize a variety of geometric problems and present the tools for their accurate representation. Disassociating fundamental ideas and methods from special applications, they clarify these concepts for the reader and allow him to apply the material to other problems of a geometric nature. Relying on the idea that a picture is worth a thousand words, the text is beautifully illustrated with a variety of elucidating figures and diagrams. Anyone attracted to or wishing a deeper understanding of the beauty of geometric mysteries will find this book an engaging and invaluable guide.