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Early geometrical thinking in the environment of patterns, mosaics and isometries
This book discusses the learning and teaching of geometry, with a special focus on kindergarten and primary education. It examines important new trends and developments in research and practice, and emphasizes theoretical, empirical and developmental issues. Further, it discusses various topics, including curriculum studies and implementation, spatial abilities and geometric reasoning, as well as the psychological roots of geometrical thinking and teacher preparation in geometry education. It considers these issues from historical, epistemological, cognitive semiotic and educational points of view in the context of students' difficulties and the design of teaching and curricula.
Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems
This book is about the dynamics of coupled map lattices (CML) and of related spatially extended systems. It will be useful to post-graduate students and researchers seeking an overview of the state-of-the-art and of open problems in this area of nonlinear dynamics. The special feature of this book is that it describes the (mathematical) theory of CML and some related systems and their phenomenology, with some examples of CML modeling of concrete systems (from physics and biology). More precisely, the book deals with statistical properties of (weakly) coupled chaotic maps, geometric aspects of (chaotic) CML, monotonic spatially extended systems, and dynamical models of specific biological systems.
Dynamics beyond uniform hyperbolicity : A global geometric and probabilistic perspective
In broad terms, the goal of dynamics is to describe the long-term evolution of systems for which an ""infinitesimal"" evolution rule, such as a differential equation or the iteration of a map, is known.This book aims to put such recent developments in a unified perspective, and to point out open problems and likely directions for further progress. It is aimed willing to get a quick, yet broad, view of this part of dynamics. Main ideas, methods, and results are discussed, at variable degrees of depth, with references to the original works for details and complementary information.
Dynamical Vision ; ICCV 2005 and ECCV 2006 Workshops, WDV 2005 and WDV 2006, Beijing, China, October 21, 2005, Graz, Austria, May 13, 2006, Revised Papers
Classical multiple-view geometry studies the reconstruction of a static scene - served by a rigidly moving camera. However, in many real-world applications the scene may undergo much more complex dynamical changes. For instance, the scene may consist of multiple moving objects (e.g., a trafic scene) or arti- lated motions (e.g., a walking human) or even non-rigid dynamics (e.g., smoke, fire, or a waterfall). In addition, some applications may require interaction with the scene through a dynamical system (e.g., vision-guided robot navigation and coordination). To study the problem of reconstructing dynamical scenes, many new al- braic, geometric, statistical, and computational tools have recently emerged in computer vision, computer graphics, image processing, and vision-based c- trol.
Drawing Ideas
Focuses on the three key types of drawing, explanatory sketches, notational sketches and visual narratives that help designers think through and communicate their ideas. Through these three fundamentals, Drawing Ideas provides a thorough course in creating clear graphic layouts and diagrams, including expressive human forms, thumbnailing a process, adding effective colour and text and more. In addition, a drawing boot camp provides a refesher course in accurately drawing geometric forms. By getting back to the basics, readers will not only benefit from updated freehand drawing skills, but will also succeed in presenting and explaining their drawings and designs to others.
Domain Decomposition Methods in Science and Engineering
Domain decomposition is an active, interdisciplinary research area that is devoted to the development, analysis and implementation of coupling and decoupling strategies in mathematics, computational science, engineering and industry.This book special focus has been on numerical analysis, computational issues,complex heterogeneous problems, industrial problems, and software development.
Disordered Materials : An Introduction
This self-contained text introduces the physics of structurally disordered condensed systems at the level of advanced undergraduate and graduate students. Among the topics are the geometry and symmetries of the structural units used as building blocks of extended structures, the various kinds of disorder, the phenomenology and the main theories of the glass transition, the structure of amorphous systems and the techniques to investigate it, the evolution of system's structure with its size (clusters) and the presence of orientational order in the absence of translational order (quasicrystals). In the second edition, the treatment of the mode coupling theory of the glass transition has been enlarged and connects now to a new section on collective excitations in disordered systems. Special attention has been devoted to nanometer-sized disordered systems, with emphasis on cluster-assembled materials. Questions of what governs the occurrence and stability of quasicrystals, the features of the amorphous to quasicrystal transformation and its reverse transition are discussed. The conditions leading to nano-quasicrystalline phases of technological interest are examined. Throughout the text relevant recent experimental and theoretical results are discussed so as to give readers insight into the currently most vibrant research topics.
Discrete Geometry, Combinatorics and Graph Theory ; 7th China-Japan Conference, CJCDGCGT 2005, Tianjin, China, November 18-20, 2005, and Xi'an, China, November 22-24, 2005, Revised Selected Papers
Theis book includes discrete algorithmic geometry, combinatorics and graph theory
Discrete Geometry for Computer Imagery Vol. 4245 ; 13th International Conference, DGCI 2006, Szeged, Hungary, October 25-27, 2006, Proceedings
This book constitutes the refereed proceedings of the 13th International Conference on Discrete Geometry for Computer Imagery, DGCI 2006, held in Szeged, Hungary in October 2006. The 28 revised full papers and 27 revised poster papers presented together with two invited papers were carefully reviewed and selected from 99 submissions.
Discrete geometry for computer imagery ; Vol. 3429 ; 12th International Conference, DGCI 2005, Poitiers, France, April 11-13, 2005, Proceedings
This book constitutes the refereed proceedings of the 12th International Conference on Discrete Geometry for Computer Imagery, DGCI 2005, held in Poitiers, France in April 2005. The 36 revised full papers presented together with an invited paper were carefully reviewed and selected from 53 submissions. The papers are organized in topical sections on applications, discrete hierarchical geometry, discrete tomography, discrete topology, object properties, reconstruction and recognition, uncertain geometry, and visualization.
Discrete Geometry for Computer Imagery ; 14th IAPR International Conference, DGCI 2008, Lyon, France, April 16-18, 2008. Proceedings
This book constitutes the refereed proceedings of the 14th IAPR TC-18 International Conference on Discrete Geometry for Computer Imagery, DGCI 2008, held in Lyon, France, in April 2008.
Discrete Element Analysis Methods of Generic Differential Quadratures
This book presents numerical differential quadrature (DQ) - based methods recently developed by the author. Their ability for solving generic scientific and engineering problems is demonstrated. These methods are the generic differential quadrature, the extended differential quadrature and the related discrete element analysis methods. These novel numerical techniques are both efficient and reliable. They are suitable for developing solution algorithms for various computational mechanics problems with arbitrarily complex geometry. This is shown for several comprehensive examples such as bars and beams, trusses, frames, general field problems, elasticity problems or bending of plates.
Discrete Differential Geometry
Discrete differential geometry is an active mathematical terrain where differential geometry and discrete geometry meet and interact. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. Current progress in this field is to a large extent stimulated by its relevance for computer graphics and mathematical physics. This collection of essays, which documents the main lectures of the 2004 Oberwolfach Seminar on the topic, as well as a number of additional contributions by key participants, gives a lively, multi-facetted introduction to this emerging field.
Discrete and computational geometry; Japanese Conference, JCDCG 2004, Tokyo, Japan, October 8-11, 2004
This book constitutes the thoroughly refereed post-proceedings of the Japanese Conference on Discrete Computational Geometry, JCDCG 2004, held in Tokyo, Japan in October 2004, to honor Janos Pach on his fiftieth year. The 20 revised full papers presented were carefully selected during two rounds of reviewing and improvement from over 60 talks at the conference. All current issues in discrete algorithmic geometry are addressed.
Discovering Mathematics with Magma : Reducing the Abstract to the Concrete
This volume celebrates the first decade of the Computer Algebra system Magma. With a design based on the ontology and semantics of algebra, Magma enables users to rapidly formulate and perform calculations in the more abstract parts of mathematics. The book range over much of Magma's coverage of algorithmic algebra: from number theory and algebraic geometry, via representation theory and group theory to some branches of discrete mathematics and graph theory. A basic introduction to the Magma language is given in an appendix. The book is simultaneously an invitation to learn a new programming language in the context of contemporary research problems, and an exposition of the types of problem that can be investigated using computational algebra.
Direct Transistor-level Layout for Digital Blocks
The essential flaw in prior efforts is an over-reliance on geometric assumptions from large-scale cell-based layout algorithms. Individual transistors may seem simple, but they do not pack as gates do. Algorithms that ignore these shape-level issues suffer the consequences when thousands of devices are poorly packed. The approach described in this book can pack devices much more densely than a typical cell-based layout
Dirac Operators in Representation Theory
This monograph presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology. Dirac operators are widely used in physics, differential geometry, and group-theoretic settings (particularly, the geometric construction of discrete series representations). The related concept of Dirac cohomology, which is defined using Dirac operators, is a far-reaching generalization that connects index theory in differential geometry to representation theory. Using Dirac operators as a unifying theme, the authors demonstrate how some of the most important results in representation theory fit together when viewed from this perspective.
Diophantine Approximation : Festschrift for Wolfgang Schmidt
This volume contains 22 research and survey papers on recent developments in the field of diophantine approximation. The first article by Hans Peter Schlickewei is devoted to the scientific work of Wolfgang Schmidt. Further contributions deal with the subspace theorem and its applications to diophantine equations and to the study of linear recurring sequences. The articles are either in the spirit of more classical diophantine analysis or of geometric or combinatorial flavor. In particular, estimates for the number of solutions of diophantine equations as well as results concerning congruences and polynomials are established. Furthermore, the volume contains transcendence results for special functions and contributions to metric diophantine approximation and to discrepancy theory.
Differential Geometry of Curves and Surfaces : A Concise Guide
The study of curves and surfaces forms an important part of classical differential geometry. Differential Geometry of Curves and Surfaces: A Concise Guide presents traditional material in this field along with important ideas of Riemannian geometry.Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels.
Differential Geometry and Analysis on CR Manifolds
The study of CR manifolds lies at the intersection of three main mathematical disciplines: partial differential equations, complex analysis in several complex variables, and differential geometry. While the PDE and complex analytic aspects have been intensely studied in the last fifty years, much effort has recently been made to understand the differential geometric side of the subject. This monograph provides a unified presentation of several differential geometric aspects in the theory of CR manifolds and tangential Cauchy–Riemann equations. It presents the major differential geometric acheivements in the theory of CR manifolds, such as the Tanaka–Webster connection, Fefferman's metric, pseudo-Einstein structures and the Lee conjecture, CR immersions, subelliptic harmonic maps as a local manifestation of pseudoharmonic maps from a CR manifold, Yang–Mills fields on CR manifolds, to name a few. It also aims at explaining how certain results from analysis are employed in CR geometry.Motivated by clear exposition, many examples, explicitly worked-out geometric results, and stimulating unproved statements and comments referring to the most recent aspects of the theory.
