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Scale Isometric Polytopal Graphs In Hypercubes And Cubic Lattices
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Book Synopsis Scale-isometric Polytopal Graphs in Hypercubes and Cubic Lattices by : M. Deza
Download or read book Scale-isometric Polytopal Graphs in Hypercubes and Cubic Lattices written by M. Deza and published by Imperial College Press. This book was released on 2004 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph identifies polytopes that are combinatorially l1-embeddable, within interesting lists of polytopal graphs, i.e. such that corresponding polytopes are either prominent mathematically (regular partitions, root lattices, uniform polytopes and so on), or applicable in chemistry (fullerenes, polycycles, etc.). The embeddability, if any, provides applications to chemical graphs and, in the first case, it gives new combinatorial perspective to l2-prominent affine polytopal objects. The lists of polytopal graphs in the book come from broad areas of geometry, crystallography and graph theory. The book concentrates on such concise and, as much as possible, independent definitions. The scale-isometric embeddability the main unifying question, to which those lists are subjected is presented with the minimum of technicalities.
Book Synopsis Scale-isometric Polytopal Graphs in Hypercubes and Cubic Lattices by : M. Deza
Download or read book Scale-isometric Polytopal Graphs in Hypercubes and Cubic Lattices written by M. Deza and published by World Scientific. This book was released on 2004 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph identifies polytopes that are ?combinatorially ?1-embeddable?, within interesting lists of polytopal graphs, i.e. such that corresponding polytopes are either prominent mathematically (regular partitions, root lattices, uniform polytopes and so on), or applicable in chemistry (fullerenes, polycycles, etc.). The embeddability, if any, provides applications to chemical graphs and, in the first case, it gives new combinatorial perspective to ??2-prominent? affine polytopal objects.The lists of polytopal graphs in the book come from broad areas of geometry, crystallography and graph theory. The book concentrates on such concise and, as much as possible, independent definitions. The scale-isometric embeddability ? the main unifying question, to which those lists are subjected ? is presented with the minimum of technicalities.
Book Synopsis Mathematical Treatment of Nanomaterials and Neural Networks by : Jia-Bao Liu
Download or read book Mathematical Treatment of Nanomaterials and Neural Networks written by Jia-Bao Liu and published by Frontiers Media SA. This book was released on 2021-12-03 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pattern Recognition on Oriented Matroids by : Andrey O. Matveev
Download or read book Pattern Recognition on Oriented Matroids written by Andrey O. Matveev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-09-11 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pattern Recognition on Oriented Matroids covers a range of innovative problems in combinatorics, poset and graph theories, optimization, and number theory that constitute a far-reaching extension of the arsenal of committee methods in pattern recognition. The groundwork for the modern committee theory was laid in the mid-1960s, when it was shown that the familiar notion of solution to a feasible system of linear inequalities has ingenious analogues which can serve as collective solutions to infeasible systems. A hierarchy of dialects in the language of mathematics, for instance, open cones in the context of linear inequality systems, regions of hyperplane arrangements, and maximal covectors (or topes) of oriented matroids, provides an excellent opportunity to take a fresh look at the infeasible system of homogeneous strict linear inequalities – the standard working model for the contradictory two-class pattern recognition problem in its geometric setting. The universal language of oriented matroid theory considerably simplifies a structural and enumerative analysis of applied aspects of the infeasibility phenomenon. The present book is devoted to several selected topics in the emerging theory of pattern recognition on oriented matroids: the questions of existence and applicability of matroidal generalizations of committee decision rules and related graph-theoretic constructions to oriented matroids with very weak restrictions on their structural properties; a study (in which, in particular, interesting subsequences of the Farey sequence appear naturally) of the hierarchy of the corresponding tope committees; a description of the three-tope committees that are the most attractive approximation to the notion of solution to an infeasible system of linear constraints; an application of convexity in oriented matroids as well as blocker constructions in combinatorial optimization and in poset theory to enumerative problems on tope committees; an attempt to clarify how elementary changes (one-element reorientations) in an oriented matroid affect the family of its tope committees; a discrete Fourier analysis of the important family of critical tope committees through rank and distance relations in the tope poset and the tope graph; the characterization of a key combinatorial role played by the symmetric cycles in hypercube graphs. Contents Oriented Matroids, the Pattern Recognition Problem, and Tope Committees Boolean Intervals Dehn–Sommerville Type Relations Farey Subsequences Blocking Sets of Set Families, and Absolute Blocking Constructions in Posets Committees of Set Families, and Relative Blocking Constructions in Posets Layers of Tope Committees Three-Tope Committees Halfspaces, Convex Sets, and Tope Committees Tope Committees and Reorientations of Oriented Matroids Topes and Critical Committees Critical Committees and Distance Signals Symmetric Cycles in the Hypercube Graphs
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 1164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Activity Report by : Tōkei Sūri Kenkyūjo (Japan)
Download or read book Activity Report written by Tōkei Sūri Kenkyūjo (Japan) and published by . This book was released on 2003 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The British National Bibliography by : Arthur James Wells
Download or read book The British National Bibliography written by Arthur James Wells and published by . This book was released on 2004 with total page 1264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Book Review Index written by and published by . This book was released on 2006 with total page 1426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every 3rd issue is a quarterly cumulation.
Book Synopsis Bulletin of the Institute of Mathematics, Academia Sinica by : Zhong yang yan jiu yuan. Shu xue yan jiu suo
Download or read book Bulletin of the Institute of Mathematics, Academia Sinica written by Zhong yang yan jiu yuan. Shu xue yan jiu suo and published by . This book was released on 1997 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Structure in Nature Is a Strategy for Design by : Peter Pearce
Download or read book Structure in Nature Is a Strategy for Design written by Peter Pearce and published by MIT Press. This book was released on 1990 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The structural designs that occur in nature - in molecules, in crystals, in living cells - appear in this fully illustrated book as a source of inspiration and study of design of man-made structures" -- BOOK JACKET.
Book Synopsis Geometry, Perspective Drawing, and Mechanisms by : Don Row
Download or read book Geometry, Perspective Drawing, and Mechanisms written by Don Row and published by World Scientific. This book was released on 2012 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to examine the geometry of our world and, by blending theory with a variety of every-day examples, to stimulate the imagination of the readers and develop their geometric intuition. It tries to recapture the excitement that surrounded geometry during the Renaissance as the development of perspective drawing gathered pace, or more recently as engineers sought to show that all the world was a machine. The same excitement is here still, as enquiring minds today puzzle over a random-dot stereogram or the interpretation of an image painstakingly transmitted from Jupiter. The book will give a solid foundation for a variety of undergraduate courses, to provide a basis for a geometric component of graduate teacher training, and to provide background for those who work in computer graphics and scene analysis. It begins with a self-contained development of the geometry of extended Euclidean space. This framework is then used to systematically clarify and develop the art of perspective drawing and its converse discipline of scene analysis and to analyze the behavior of bar-and-joint mechanisms and hinged-panel mechanisms. Spherical polyhedra are introduced and scene analysis is applied to drawings of these and associated objects. The book concludes by showing how a natural relaxation of the axioms developed in the early chapters leads to the concept of a matroid and briefly examines some of the attractive properties of these natural structures.
Book Synopsis Convexity and Its Applications by : GRUBER
Download or read book Convexity and Its Applications written by GRUBER and published by Birkhäuser. This book was released on 2013-11-11 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of surveys consists in part of extensions of papers presented at the conferences on convexity at the Technische Universitat Wien (July 1981) and at the Universitat Siegen (July 1982) and in part of articles written at the invitation of the editors. This volume together with the earlier volume «Contributions to Geometry» edited by Tolke and Wills and published by Birkhauser in 1979 should give a fairly good account of many of the more important facets of convexity and its applications. Besides being an up to date reference work this volume can be used as an advanced treatise on convexity and related fields. We sincerely hope that it will inspire future research. Fenchel, in his paper, gives an historical account of convexity showing many important but not so well known facets. The articles of Papini and Phelps relate convexity to problems of functional analysis on nearest points, nonexpansive maps and the extremal structure of convex sets. A bridge to mathematical physics in the sense of Polya and Szego is provided by the survey of Bandle on isoperimetric inequalities, and Bachem's paper illustrates the importance of convexity for optimization. The contribution of Coxeter deals with a classical topic in geometry, the lines on the cubic surface whereas Leichtweiss shows the close connections between convexity and differential geometry. The exhaustive survey of Chalk on point lattices is related to algebraic number theory. A topic important for applications in biology, geology etc.
Book Synopsis The Golden Ratio And Fibonacci Numbers by : Richard A Dunlap
Download or read book The Golden Ratio And Fibonacci Numbers written by Richard A Dunlap and published by World Scientific. This book was released on 1997-12-16 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this invaluable book, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. In addition, the generation of the Fibonacci series and generalized Fibonacci series and their relationship to the golden ratio are presented. These concepts are applied to algorithms for searching and function minimization. The Fibonacci sequence is viewed as a one-dimensional aperiodic, lattice and these ideas are extended to two- and three-dimensional Penrose tilings and the concept of incommensurate projections. The structural properties of aperiodic crystals and the growth of certain biological organisms are described in terms of Fibonacci sequences.
Book Synopsis The Fifty-Nine Icosahedra by : H. S. M. Coxeter
Download or read book The Fifty-Nine Icosahedra written by H. S. M. Coxeter and published by Springer. This book was released on 2013-03-26 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fifty-Nine Icosahedra was originally published in 1938 as No. 6 of "University of Toronto Studies (Mathematical Series)". Of the four authors, only Coxeter and myself are still alive, and we two are the authors of the whole text of the book, in which any signs of immaturity may perhaps be regarded leniently on noting that both of us were still in our twenties when it was written. N either of the others was a professional mathematician. Flather died about 1950, and Petrie, tragically, in a road accident in 1972. Petrie's part in the book consisted in the extremely difficult drawings which consti tute the left half of each of the plates (the much simpler ones on the right being mine). A brief biographical note on Petrie will be found on p. 32 of Coxeter's Regular Polytopes (3rd. ed. , Dover, New York, 1973); and it may be added that he was still a schoolboy when he discovered the regular skew polygons that are named after him, and are the occasion for the note on him in Coxeter's book. (Coxeter also was a schoolboy when some of the results for which he will be most remembered were obtained; he and Petrie were schoolboy friends and used to work together on polyhedron and polytope theory. ) Flather's part in the book consisted in making a very beautiful set of miniature models of all the fifty-nine figures. These are still in existence, and in excellent preservation.
Download or read book Product Graphs written by Wilfried Imrich and published by Wiley-Interscience. This book was released on 2000-04-11 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to the four standard products of graphs and related topics Addressing the growing usefulness of current methods for recognizing product graphs, this new work presents a much-needed, systematic treatment of the Cartesian, strong, direct, and lexicographic products of graphs as well as graphs isometrically embedded into them. Written by two leading experts in this rapidly evolving area of combinatorics, Product Graphs: Structure and Recognition compiles and consolidates a wealth of information previously scattered throughout the literature, providing researchers in the field with ready access to numerous recent results as well as several new recognition algorithms and proofs. The authors explain all topics from the ground up and make the requisite theory and data structures easily accessible for mathematicians and computer scientists alike. Coverage includes * The basic algebraic and combinatorial properties ofproduct graph * Hypercubes, median graphs, Hamming graphs, triangle-free graphs, and vertex-transitive graphs * Colorings, automorphisms, homorphisms, domination, and the capacity of products of graphs Sample applications, including novel applications to chemical graph theory Clear connections to other areas of graph theory Figures, exercises, and hundreds of references
Book Synopsis Black Holes in Higher Dimensions by : Gary T. Horowitz
Download or read book Black Holes in Higher Dimensions written by Gary T. Horowitz and published by Cambridge University Press. This book was released on 2012-04-19 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book devoted to black holes in more than four dimensions, for graduate students and researchers.
Book Synopsis Shaping Space by : Marjorie Senechal
Download or read book Shaping Space written by Marjorie Senechal and published by Birkhäuser. This book was released on 1988 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
