Nonlinear Computational Geometry


Nonlinear Computational Geometry
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Nonlinear Computational Geometry


Nonlinear Computational Geometry
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Author : Ioannis Z. Emiris
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-28

Nonlinear Computational Geometry written by Ioannis Z. Emiris and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-28 with Mathematics categories.


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.



Nonlinear Computational Geometry


Nonlinear Computational Geometry
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Author : Ioannis Z. Emiris
language : en
Publisher:
Release Date : 2009-10-29

Nonlinear Computational Geometry written by Ioannis Z. Emiris and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-29 with categories.




Surveys On Discrete And Computational Geometry


Surveys On Discrete And Computational Geometry
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Author : Jacob E. Goodman
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Surveys On Discrete And Computational Geometry written by Jacob E. Goodman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.


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.



Moment Sos Hierarchy The Lectures In Probability Statistics Computational Geometry Control And Nonlinear Pdes


Moment Sos Hierarchy The Lectures In Probability Statistics Computational Geometry Control And Nonlinear Pdes
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Author : Didier Henrion
language : en
Publisher: World Scientific
Release Date : 2020-11-04

Moment Sos Hierarchy The Lectures In Probability Statistics Computational Geometry Control And Nonlinear Pdes written by Didier Henrion and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-04 with Mathematics categories.


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.



Nonlinear Continua


Nonlinear Continua
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Author : Eduardo N. Dvorkin
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-27

Nonlinear Continua written by Eduardo N. Dvorkin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-27 with Science categories.


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.



Computational Methods In Nonlinear Analysis


Computational Methods In Nonlinear Analysis
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Author : Ioannis K. Argyros
language : en
Publisher: World Scientific
Release Date : 2013

Computational Methods In Nonlinear Analysis written by Ioannis K. Argyros and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.


The field of computational sciences has seen a considerable development in mathematics, engineering sciences, and economic equilibrium theory. Researchers in this field are faced with the problem of solving a variety of equations or variational inequalities. We note that in computational sciences, the practice of numerical analysis for finding such solutions is essentially connected to variants of Newton's method. The efficient computational methods for finding the solutions of fixed point problems, nonlinear equations and variational inclusions are the first goal of the present book. The second goal is the applications of these methods in nonlinear problems and the connection with fixed point theory. This book is intended for researchers in computational sciences, and as a reference book for an advanced computational methods in nonlinear analysis. We collect the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces, and present several applications and connections with fixed point theory. The book contains abundant and updated bibliography, and provides comparison between various investigations made in recent years in the field of computational nonlinear analysis.



Advances In Computational Nonlinear Mechanics


Advances In Computational Nonlinear Mechanics
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Author : I.S. Doltsinis
language : en
Publisher: Springer
Release Date : 2014-05-04

Advances In Computational Nonlinear Mechanics written by I.S. Doltsinis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Mathematics categories.


Advanced computational methods in nonlinear mechanics of solids and fluids are dealt with in this volume. Contributions consider large deformations of structures and solids, problems in nonlinear dynamics, aspects of earthquake analysis, coupled problems, convection-dominated phenomena, and compressible and incompressible viscous flows. Selected applications indicate the relevance of the analysis to the demands of industry and science. The contributors are from research institutions well-known for their work in this field.



Geometric Structures In Nonlinear Physics


Geometric Structures In Nonlinear Physics
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Author : Robert Hermann
language : en
Publisher: Math Science Press
Release Date : 1991

Geometric Structures In Nonlinear Physics written by Robert Hermann and has been published by Math Science Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.


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.



Nonlinear Analysis In Geometry And Applied Mathematics


Nonlinear Analysis In Geometry And Applied Mathematics
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Author : Shing-Tung Yau
language : en
Publisher:
Release Date : 2018

Nonlinear Analysis In Geometry And Applied Mathematics written by Shing-Tung Yau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.




Computational Methods In Commutative Algebra And Algebraic Geometry


Computational Methods In Commutative Algebra And Algebraic Geometry
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Author : Wolmer Vasconcelos
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-05-18

Computational Methods In Commutative Algebra And Algebraic Geometry written by Wolmer Vasconcelos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-18 with Mathematics categories.


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.