Nonlinear Computational Geometry

Author : Ioannis Z. Emiris,Frank Sottile,Thorsten Theobald
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 45,9 Mb
Release : 2009-10-28
Category : Mathematics
ISBN : 9781441909992

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Nonlinear Computational Geometry by Ioannis Z. Emiris,Frank Sottile,Thorsten Theobald Pdf

An original motivation for algebraic geometry was to understand curves and surfaces in three dimensions. Recent theoretical and technological advances in areas such as robotics, computer vision, computer-aided geometric design and molecular biology, together with the increased availability of computational resources, have brought these original questions once more into the forefront of research. One particular challenge is to combine applicable methods from algebraic geometry with proven techniques from piecewise-linear computational geometry (such as Voronoi diagrams and hyperplane arrangements) to develop tools for treating curved objects. These research efforts may be summarized under the term nonlinear computational geometry. This volume grew out of an IMA workshop on Nonlinear Computational Geometry in May/June 2007 (organized by I.Z. Emiris, R. Goldman, F. Sottile, T. Theobald) which gathered leading experts in this emerging field. The research and expository articles in the volume are intended to provide an overview of nonlinear computational geometry. Since the topic involves computational geometry, algebraic geometry, and geometric modeling, the volume has contributions from all of these areas. By addressing a broad range of issues from purely theoretical and algorithmic problems, to implementation and practical applications this volume conveys the spirit of the IMA workshop.

Author : Ioannis Z. Emiris,Frank Sottile,Thorsten Theobald
Publisher : Unknown
Page : 252 pages
File Size : 54,7 Mb
Release : 2009-10-29
Category : Electronic
ISBN : 144191000X

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Nonlinear Computational Geometry by Ioannis Z. Emiris,Frank Sottile,Thorsten Theobald Pdf

Author : Philipp Grohs,Martin Holler,Andreas Weinmann
Publisher : Springer Nature
Page : 701 pages
File Size : 42,9 Mb
Release : 2020-04-03
Category : Mathematics
ISBN : 9783030313517

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Handbook of Variational Methods for Nonlinear Geometric Data by Philipp Grohs,Martin Holler,Andreas Weinmann Pdf

This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.

Author : Jacob E. Goodman
Publisher : American Mathematical Soc.
Page : 568 pages
File Size : 47,5 Mb
Release : 2008
Category : Combinatorial geometry
ISBN : 9780821842393

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Surveys on Discrete and Computational Geometry by Jacob E. Goodman Pdf

This volume contains nineteen survey papers describing the state of current research in discrete and computational geometry as well as a set of open problems presented at the 2006 AMS-IMS-SIAM Summer Research Conference Discrete and Computational Geometry--Twenty Years Later, held in Snowbird, Utah, in June 2006. Topics surveyed include metric graph theory, lattice polytopes, the combinatorial complexity of unions of geometric objects, line and pseudoline arrangements, algorithmic semialgebraic geometry, persistent homology, unfolding polyhedra, pseudo-triangulations, nonlinear computational geometry, $k$-sets, and the computational complexity of convex bodies.

Author : Didier Henrion,Milan Korda,Jean Bernard Lasserre
Publisher : World Scientific
Page : 248 pages
File Size : 44,5 Mb
Release : 2020-11-04
Category : Mathematics
ISBN : 9781786348555

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Moment-sos Hierarchy, The: Lectures In Probability, Statistics, Computational Geometry, Control And Nonlinear Pdes by Didier Henrion,Milan Korda,Jean Bernard Lasserre Pdf

The Moment-SOS hierarchy is a powerful methodology that is used to solve the Generalized Moment Problem (GMP) where the list of applications in various areas of Science and Engineering is almost endless. Initially designed for solving polynomial optimization problems (the simplest example of the GMP), it applies to solving any instance of the GMP whose description only involves semi-algebraic functions and sets. It consists of solving a sequence (a hierarchy) of convex relaxations of the initial problem, and each convex relaxation is a semidefinite program whose size increases in the hierarchy.The goal of this book is to describe in a unified and detailed manner how this methodology applies to solving various problems in different areas ranging from Optimization, Probability, Statistics, Signal Processing, Computational Geometry, Control, Optimal Control and Analysis of a certain class of nonlinear PDEs. For each application, this unconventional methodology differs from traditional approaches and provides an unusual viewpoint. Each chapter is devoted to a particular application, where the methodology is thoroughly described and illustrated on some appropriate examples.The exposition is kept at an appropriate level of detail to aid the different levels of readers not necessarily familiar with these tools, to better know and understand this methodology.

Author : Jamshid Ghaboussi,David A. Pecknold,Xiping Steven Wu
Publisher : CRC Press
Page : 472 pages
File Size : 43,9 Mb
Release : 2017-07-06
Category : Mathematics
ISBN : 9781351682633

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Nonlinear Computational Solid Mechanics by Jamshid Ghaboussi,David A. Pecknold,Xiping Steven Wu Pdf

This book presents the fundamentals of nonlinear mechanics within a modern computational approach based mainly on finite element methods. Both material and geometric nonlinearities are treated. The topics build up from the mechanics of finite deformation of solid bodies through to nonlinear structural behaviour including buckling, bifurcation and snap-through. The principles are illustrated with a series of solved problems. This book serves as a text book for a second year graduate course and as a reference for practitioners using nonlinear analysis in engineering and design.

Author : Robert Hermann
Publisher : Math Science Press
Page : 363 pages
File Size : 41,5 Mb
Release : 1991
Category : Mathematics
ISBN : 0915692422

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Geometric Structures in Nonlinear Physics by Robert Hermann Pdf

VOLUME 26 of INTERDISCIPLINARY MATHEMATICS, series expounding mathematical methodology in Physics & Engineering. TOPICS: Differential & Riemannian Geometry; Theories of Vorticity Dynamics, Einstein-Hilbert Gravitation, Colobeau-Rosinger Generalized Function Algebra, Deformations & Quantum Mechanics of Particles & Fields. Ultimate goal is to develop mathematical framework for reconciling Quantum Mechanics & concept of Point Particle. New ideas for researchers & students. Order: Math Sci Press, 53 Jordan Road, Brookline, MA 02146. (617) 738-0307.

Author : Michael Joswig,Thorsten Theobald
Publisher : Springer Science & Business Media
Page : 251 pages
File Size : 42,9 Mb
Release : 2013-01-04
Category : Mathematics
ISBN : 9781447148173

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Polyhedral and Algebraic Methods in Computational Geometry by Michael Joswig,Thorsten Theobald Pdf

Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry. The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations. The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics. Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.

Author : Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Publisher : CRC Press
Page : 1928 pages
File Size : 41,6 Mb
Release : 2017-11-22
Category : Computers
ISBN : 9781498711425

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Handbook of Discrete and Computational Geometry by Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman Pdf

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Author : Jacob E. Goodman,János Pach,Richard Pollack
Publisher : Springer Science & Business Media
Page : 652 pages
File Size : 43,9 Mb
Release : 2009-03-02
Category : Mathematics
ISBN : 9780387873633

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Twentieth Anniversary Volume: Discrete & Computational Geometry by Jacob E. Goodman,János Pach,Richard Pollack Pdf

This commemorative book contains the 28 major articles that appeared in the 2008 Twentieth Anniversary Issue of the journal Discrete & Computational Geometry, and presents a comprehensive picture of the current state of the field. The articles in this volume, a number of which solve long-outstanding problems in the field, were chosen by the editors of DCG for the importance of their results, for the breadth of their scope, and to show the intimate connections that have arisen between discrete and computational geometry and other areas of both computer science and mathematics. Apart from the articles, the editors present an expanded preface, along with a set of photographs of groups and individuals who have played a major role in the history of the field during the past twenty years.

Author : Jon Lee,Sven Leyffer
Publisher : Springer Science & Business Media
Page : 692 pages
File Size : 42,7 Mb
Release : 2011-12-02
Category : Mathematics
ISBN : 9781461419273

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Mixed Integer Nonlinear Programming by Jon Lee,Sven Leyffer Pdf

Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners — including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers — are interested in solving large-scale MINLP instances.

Author : Eduardo N. Dvorkin,Marcela B. Goldschmit
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 48,6 Mb
Release : 2006-01-27
Category : Science
ISBN : 9783540292647

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Nonlinear Continua by Eduardo N. Dvorkin,Marcela B. Goldschmit Pdf

This book develops a modern presentation of Continuum Mechanics, oriented towards numerical applications in the fields of nonlinear analysis of solids, structures and fluid mechanics. The kinematics of the continuum deformation, including pull-back / push-forward transformations between different configurations, stress and strain measures, balance principles, constitutive relations and variational principles are developed using general curvilinear coordinates. Even though the mathematical presentation of the different topics is quite rigorous, an effort is made to link formal developments with engineering physical intuition.

Author : Shing-Tung Yau
Publisher : Unknown
Page : 128 pages
File Size : 54,7 Mb
Release : 2018
Category : Electronic
ISBN : 1571463593

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Nonlinear Analysis in Geometry and Applied Mathematics by Shing-Tung Yau Pdf

Author : Alberto Bressan,Gui-Qiang G. Chen,Marta Lewicka,Dehua Wang
Publisher : Springer Science & Business Media
Page : 490 pages
File Size : 44,6 Mb
Release : 2011-04-19
Category : Mathematics
ISBN : 9781441995544

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Nonlinear Conservation Laws and Applications by Alberto Bressan,Gui-Qiang G. Chen,Marta Lewicka,Dehua Wang Pdf

This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 13--31, 2009. Hyperbolic conservation laws is a classical subject, which has experienced vigorous growth in recent years. The present collection provides a timely survey of the state of the art in this exciting field, and a comprehensive outlook on open problems. Contributions of more theoretical nature cover the following topics: global existence and uniqueness theory of one-dimensional systems, multidimensional conservation laws in several space variables and approximations of their solutions, mathematical analysis of fluid motion, stability and dynamics of viscous shock waves, singular limits for viscous systems, basic principles in the modeling of turbulent mixing, transonic flows past an obstacle and a fluid dynamic approach for isometric embedding in geometry, models of nonlinear elasticity, the Monge problem, and transport equations with rough coefficients. In addition, there are a number of papers devoted to applications. These include: models of blood flow, self-gravitating compressible fluids, granular flow, charge transport in fluids, and the modeling and control of traffic flow on networks.

Author : Wolmer Vasconcelos
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 53,5 Mb
Release : 2004-05-18
Category : Mathematics
ISBN : 3540213112

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Computational Methods in Commutative Algebra and Algebraic Geometry by Wolmer Vasconcelos Pdf

This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.