Series: The IMA Volumes in Mathematics and its Applications , Vol. 151
2009, X, 222 p., Hardcover
ISBN: 978-1-4419-0998-5
Due: August 2009
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.
Foreword.- Preface.- Spectral techniques to explore point clouds in Euclidean space, with applications to collective coordinates in structural biology.- Rational parametrizations, intersection theory, and Newton polytopes.- Some discrete properties of the space of line transversals to disjoint balls.- Algebraic geometry and kinematics.- Rational offset surfaces and their modeling applications.- A list of challenges for real algebraic plane curve visualization software.- A subdivision method for arrangement computation of semi-algebraic curves.- Invariant-based characterization of the relative position of two projective conics.- A note on planar hexagonal meshes.- List of workshop participants.
Series: Undergraduate Texts in Mathematics
2009, Approx. 520 p. 80 illus., Hardcover
ISBN: 978-0-387-98097-3
Due: September 2009
Includes applications that cover:
Approximation by polynomials
Discrete dynamical systems
Differential equations
Fourier series and physics
Fourier series and approximation
Wavelets
Convexity and optimization
Appropriate for math enthusiasts with a prior knowledge of both calculus and linear algebra
This new approach to real analysis stresses the use of the subject in applications, by showing how the principles and theory of real analysis can be applied in a variety of settings. The applications range from Fourier series and polynomial approximation to discrete dynamical systems and nonlinear optimization. Users will be prepared for more intensive work in each topic through these applications and their accompanying exercises. Chapter topics under the abstract analysis heading include: the real numbers, series, the topology of R^n, functions, normed vector spaces, differentiation and integration, and limits of functions. Applications cover approximation by polynomials, discrete dynamical systems, differential equations, Fourier series and physics, Fourier series and approximation, wavelets, and convexity and optimization. This book is appropriate for math enthusiasts with a prior knowledge of both calculus and linear algebra.
Preface.- Review.- The Real Numbers.- Series.- Topology of Rn.- Functions.- Differentiation and Integration.- Norms and Inner Products.- Limits of Functions.- Metric Spaces.- Approximation by Polynomials.- Discrete Dynamical Systems.- Differential Equations.- Fourier Series and Physics.- Fourier Series and Approximation.- Wavelets.- Convexity and Optimization.- References.- Index.
Series: Springer Monographs in Mathematics
2009, VI, 164 p., Hardcover
ISBN: 978-3-642-03027-7
Due: September 17, 2009
This book presents the basic methods of regular perturbation theory of Hamiltonian systems, including KAM-theory, splitting of asymptotic manifolds, the separatrix map, averaging, anti-integrable limit, etc. in a readable way. Although concise, it discusses all main aspects of the basic modern theory of perturbed Hamiltonian systems and most results are given with complete proofs.
It will be a valuable reference for Hamiltonian systems, and of special interest to researchers and graduate students of the KAM community.
Researchers and graduate students of the KAM community and scientists working in mechanics
Hamiltonian dynamics
KAM theory
perturbation theory
Series: Stochastic Modelling and Applied Probability , Vol. 62
2009, Approx. 300 p., Hardcover
ISBN: 978-3-642-02546-4
Due: September 21, 2009
Continuous-time Markov decision processes (MDPs), also known as controlled Markov chains, are used for modeling decision-making problems that arise in operations research (for instance, inventory, manufacturing, and queueing systems), computer science, communications engineering, control of populations (such as fisheries and epidemics), and management science, among many other fields. This volume provides a unified, systematic, self-contained presentation of recent developments on the theory and applications of continuous-time MDPs. The MDPs in this volume include most of the cases that arise in applications, because they allow unbounded transition and reward/cost rates. Much of the material appears for the first time in book form.
Researchers, mathematicians and graduate students interested in stochastic control, operations research, industrial engineering, management science, computer science, communications engineering, probability
Markov decision processes
controlled Markov chains
stochastic control
stochastic dynamic programming
Series: Fundamental Theories of Physics , Vol. 162
2009, Approx. 600 p., Hardcover
ISBN: 978-90-481-3014-6
Due: September 2009
Our current perspective on gravitation has arisen over millennia, through falling apples, lift thought experiments and stars spiraling into black holes. In this volume, the worldfs leading scientists offer a multifaceted approach to mass by giving a concise and introductory presentation into their particular research on gravity. The main theme is mass and its motion within general relativity and other theories of gravity, particularly for compact bodies. Within this framework, all articles are tied together coherently, covering post-Newtonian and related methods as well as the self-force approach to the analysis of motion in curved space-time, closing with an overview of the historical development and a snapshot on the actual state of the art.
All contributions reflect the fundamental role of mass in physics, from issues related to Newtonfs laws via the effect of self-force and radiation reactions within theories of gravitation to the role of the Higgs boson in modern physics. Precision measurements are described in detail, modified theories of gravity reproducing experimental data are investigated as alternatives to dark matter, and the fundamental problem of reconciling any theory of gravity with the physics of quantum fields is addressed. Auxiliary chapters set the framework for theoretical contributions within the wider context of experimental physics.
The book is based upon the lectures of the CNRS School on Mass held in Orleans, France, in June 2008.