Download or read book How Surfaces Intersect in Space written by J. Scott Carter and published by World Scientific. This book was released on 1995 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. It will be of value to anyone who wants to understand the subject by way of examples. Undergraduates, beginning graduate students, and non-professionals will profit from reading the book and from just looking at the pictures.
Download or read book Calculating Intersections of Surfaces in Screen Space written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-08-16 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: When surfaces intersect, one may desire to highlight the intersection curve in order to make the shape of the penetrating surfaces more visible. Highlighting the intersection is especially helpful when the surfaces become transparent, because transparency makes the intersections less evident. A technique for locating intersections in screen space using only the information locally available to a pixel is discussed. The technique is designed to exploit parallelism at the pixel level and was implemented on the Pixel-Planes 5 graphics supercomputer. Banks, David C. Unspecified Center NASA-CR-191498, NAS 1.26:191498, ICASE-93-41, AD-A269019 NAS1-19480; RTOP 505-90-52-01...
Download or read book Knotted Surfaces and Their Diagrams written by J. Scott Carter and published by American Mathematical Society. This book was released on 2023-12-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the authors develop the theory of knotted surfaces in analogy with the classical case of knotted curves in 3-dimensional space. In the first chapter knotted surface diagrams are defined and exemplified; these are generic surfaces in 3-space with crossing information given. The diagrams are further enhanced to give alternative descriptions. A knotted surface can be described as a movie, as a kind of labeled planar graph, or as a sequence of words in which successive words are related by grammatical changes. In the second chapter, the theory of Reidemeister moves is developed in the various contexts. The authors show how to unknot intricate examples using these moves. The third chapter reviews the braid theory of knotted surfaces. Examples of the Alexander isotopy are given, and the braid movie moves are presented. In the fourth chapter, properties of the projections of knotted surfaces are studied. Oriented surfaces in 4-space are shown to have planar projections without cusps and without branch points. Signs of triple points are studied. Applications of triple-point smoothing that include proofs of triple-point formulas and a proof of Whitney's congruence on normal Euler classes are presented. The fifth chapter indicates how to obtain presentations for the fundamental group and the Alexander modules. Key examples are worked in detail. The Seifert algorithm for knotted surfaces is presented and exemplified. The sixth chapter relates knotted surfaces and diagrammatic techniques to 2-categories. Solutions to the Zamolodchikov equations that are diagrammatically obtained are presented. The book contains over 200 illustrations that illuminate the text. Examples are worked out in detail, and readers have the opportunity to learn first-hand a series of remarkable geometric techniques.
Download or read book Surfaces in 4 Space written by Scott Carter and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surfaces in 4-Space, written by leading specialists in the field, discusses knotted surfaces in 4-dimensional space and surveys many of the known results in the area. Results on knotted surface diagrams, constructions of knotted surfaces, classically defined invariants, and new invariants defined via quandle homology theory are presented. The last chapter comprises many recent results, and techniques for computation are presented. New tables of quandles with a few elements and the homology groups thereof are included. This book contains many new illustrations of knotted surface diagrams. The reader of the book will become intimately aware of the subtleties in going from the classical case of knotted circles in 3-space to this higher dimensional case. As a survey, the book is a guide book to the extensive literature on knotted surfaces and will become a useful reference for graduate students and researchers in mathematics and physics.
Download or read book An Excursion in Diagrammatic Algebra written by J. Scott Carter and published by World Scientific. This book was released on 2012 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to give as detailed a description as is possible of one of the most beautiful and complicated examples in low-dimensional topology. This example is a gateway to a new idea of higher dimensional algebra in which diagrams replace algebraic expressions and relationships between diagrams represent algebraic relations. The reader may examine the changes in the illustrations in a leisurely fashion; or with scrutiny, the reader will become familiar and develop a facility for these diagrammatic computations. The text describes the essential topological ideas through metaphors that are experienced in everyday life: shadows, the human form, the intersections between walls, and the creases in a shirt or a pair of trousers. Mathematically informed reader will benefit from the informal introduction of ideas. This volume will also appeal to scientifically literate individuals who appreciate mathematical beauty.
Download or read book Algebraic Frames for the Perception Action Cycle written by Gerald Sommer and published by Springer Science & Business Media. This book was released on 1997-08-27 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book constitutes the refereed proceedings of the International Workshop on Algebraic Frames for the Perception-Action Cycle, AFPAC '97, held in Kiel, Germany, in September 1997. The volume presents 12 revised full papers carefully reviewed and selected for inclusion in the book. Also included are 10 full invited papers by leading researchers in the area providing a representative state-of-the-art assessment of this rapidly growing field. The papers are organized in topical sections on PAC systems, low level and early vision, recognition of visual structure, processing of 3D visual space, representation and shape perception, inference and action, and visual and motor neurocomputation.
Download or read book Aperiodic Crystals written by Ted Janssen and published by Oxford University Press. This book was released on 2018-05-24 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past several decades, a This book deals with the characterisation of the structure, the structure determination and the study of the physical properties, especially dynamical and electronic properties of aperiodic crystals. The treatment is based on a description in a space with more dimensions than three, the so-called superspace. This allows us to generalise the standard crystallography and to look differently at the dynamics. The three main classes of aperiodic crystals, modulated phases, incommensurate composites and quasicrystals are treated from a unified point of view, which stresses similarities of the various systems. The book assumes as a prerequisite a knowledge of the fundamental techniques of crystallography and the theory of condensed matter, and covers the literature at the forefront of the field. Since the first edition of this book in 2007, the field of aperiodic crystals has developed considerably, with the discovery of new materials and new structures. Progress has been made in structure determination, in the interpretation and understanding of the structural characteristics and in the calculation of electrons and phonons. This new edition reflects these new developments, and it includes discussions of natural quasicrystals, incommensurate magnetic and multiferroic structures, photonic and mesoscopic quasicrystals. The second edition also includes a number of new exercises that give the reader an opportunityt to check their understanding of the material.
Download or read book Nonlinear Dynamics and Chaos written by J. M. T. Thompson and published by John Wiley & Sons. This book was released on 2002-02-15 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ein angesehener Bestseller - jetzt in der 2.aktualisierten Auflage! In diesem Buch finden Sie die aktuellsten Forschungsergebnisse auf dem Gebiet nichtlinearer Dynamik und Chaos, einem der am schnellsten wachsenden Teilgebiete der Mathematik. Die seit der ersten Auflage hinzugekommenen Erkenntnisse sind in einem zusätzlichen Kapitel übersichtlich zusammengefasst.
Download or read book Thermodynamics in Geochemistry written by Gregor Munro Anderson and published by Oxford University Press, USA. This book was released on 1993 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation This textbook and reference outlines the principles and applications of thermodynamics in geochemistry.
Download or read book Introduction to Differential Geometry of Space Curves and Surfaces written by Taha Sochi and published by Lulu.com. This book was released on with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Structure and Dynamics of Non Rigid Molecular Systems written by Y.G. Smeyers and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of scientific papers related to the structure and dynamics of non-rigid molecules. This frontline topic was born a few decades ago, when Longuet-Higgins proposed his famous theory of Molecular Symmetry Groups (Mol. Phys. 6, (1962) 457). Unfortunately, since this early paper, very few publications have been devoted to the study of non-rigid molecules. Let us mention some books which dedicate some chapters to them: Induced Representations in Crystals and Molecules, by S. L. Altmann, Academic Publishers, 1977; Molecular Symmetry and Spectroscopy, by P. R. Bunker, Academic Publishers, 1979; and finally Large Amplitude Motion in Molecules, Vols. I and II, by several authors, Springer Verlag, 1979. More recently an International Symposium on Non-Rigid Molecules was held in Paris, France, from 1-7 July 1982, the proceedings of which were published in the volume entitled Symmetries and Properties of Non-Rigid Molecules. A Comprehensive Survey, edited by J. Maruani et al., Elsevier, 1983. Finally, we should mention the very specialized work The Permutational Approach to Dynamic Stereochemistry, by J. Brocas et al., McGraw-Hill, 1983. The purpose of this book is to fill in this information on the structure and dynamics of non-rigid systems. To this aim, we have gathered a collection of recent papers written by the most qualified specialists in the world, covering a large field from van der Waals molecules to inorganic complexes and organic polyrotor molecules, as well as considering statistical and dynamic aspects.
Download or read book Implicit Curves and Surfaces Mathematics Data Structures and Algorithms written by Abel Gomes and published by Springer Science & Business Media. This book was released on 2009-05-12 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Implicit objects have gained increasing importance in geometric modeling, visualisation, animation, and computer graphics, because their geometric properties provide a good alternative to traditional parametric objects. This book presents the mathematics, computational methods and data structures, as well as the algorithms needed to render implicit curves and surfaces, and shows how implicit objects can easily describe smooth, intricate, and articulatable shapes, and hence why they are being increasingly used in graphical applications. Divided into two parts, the first introduces the mathematics of implicit curves and surfaces, as well as the data structures suited to store their sampled or discrete approximations, and the second deals with different computational methods for sampling implicit curves and surfaces, with particular reference to how these are applied to functions in 2D and 3D spaces.
Download or read book Mostly Surfaces written by Richard Evan Schwartz and published by American Mathematical Soc.. This book was released on 2011 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.
Download or read book Proceedings of the Symposium on the Chemistry and Physics of Composite Media written by Micha Tomkiewicz and published by . This book was released on 1985 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Jahn Teller Effect written by Horst Köppel and published by Springer Science & Business Media. This book was released on 2009-12-08 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Jahn-Teller effect continues to be a paradigm for structural instabilities and molecular dynamical processes. This volume provides a survey of the current Jahn-Teller interactions at the interface of quantum chemistry and condensed matter physics.
Download or read book Conical Intersections written by Wolfgang Domcke and published by World Scientific. This book was released on 2004 with total page 868 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is widely recognized nowadays that conical intersections ofmolecular potential-energy surfaces play a key mechanistic role in thespectroscopy of polyatomic molecules, photochemistry and chemicalkinetics. This invaluable book presents a systematic exposition of thecurrent state of knowledge about conical intersections, which has beenelaborated in research papers scattered throughout the chemicalphysics literature.
Download or read book Numerical Methods in Geotechnical Engineering written by Thomas Benz and published by CRC Press. This book was released on 2010-05-25 with total page 976 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods in Geotechnical Engineering contains 153 scientific papers presented at the 7th European Conference on Numerical Methods in Geotechnical Engineering, NUMGE 2010, held at Norwegian University of Science and Technology (NTNU) in Trondheim, Norway, 2 4 June 2010.The contributions cover topics from emerging research to engineering pra
