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Least Action Principle Of Crystal Formation Of Dense Packing Type And Kepler's Conjectureby W Y Hsiang
World Scientific 2001; US$ 88.40The dense packing of microscopic spheres (i.e. atoms) is the basic geometric arrangement in crystals of mono-atomic elements with weak covalent bonds, which achieves the optimal "known density" of p/√18. In 1611, Johannes Kepler had already "conjectured" that p/√18 should be the optimal "density" of sphere packings. Thus, the central problems in the study of sphere packings are the proof of Kepler's conjecture that p/√18 is the optimal density, and the establishing of the least action principle that the hexagonal dense packings in crystals are the geometric consequence of optimization of density. This important book provides a self-contained proof of both, using vector algebra and spherical geometry as the main techniques... more...
Spanning Trees and Optimization Problemsby Kun-Mao Chao; Bang Ye Wu
Chapman & Hall/CRC 2004; US$ 89.95Spanning trees play an important role in the design of efficient routing algorithms and help solve computationally hard problems like the Steiner tree and the traveling salesperson problem. This is one of the most important concepts used in graph theory, as it forms the foundation of many theoretical results in practical fields like scheduling, clustering, data mining, and many others. Spanning Trees and Optimization Problems is the first book published on the use and applications associated with the modern study of spanning trees. It covers properties of spanning trees first, followed by the three categories of spanning trees: minimum spanning trees, shortest-paths trees, and minimum routing cost spanning trees. more...
Elementary Number Theory, Group Theory and Ramanujan Graphsby Giuliana Davidoff; Peter Sarnak; Alain Valette; C. M. Series
Cambridge University Press 2003; US$ 29.00This text is a self contained treatment of expander graphs and in particular their explicit construction. Expander graphs are both highly connected but sparse, and besides their interest within combinatorics and graph theory, they also find various applications in computer science and engineering. more...
Scale-isometric Polytopal Graphs In Hypercubes And Cubic Latticesby Michel Deza; Viatcheslav Grishukhin; Mikhail Shtogrin
World Scientific 2004; US$ 59.80This 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... more...
Shortest Connectivityby Dietmar Cieslik
Springer 2005; US$ 139.00The aim in this graduate level text is to outline the key mathematical concepts that underpin these important questions in applied mathematics. These concepts involve discrete mathematics (particularly graph theory), optimization, computer science, and several ideas in biology. more...
Random Graphs for Statistical Pattern Recognitionby David J. Marchette
John Wiley & Sons, Inc. 2005; US$ 132.00A timely convergence of two widely used disciplines Random Graphs for Statistical Pattern Recognition is the first book to address the topic of random graphs as it applies to statistical pattern recognition. Both topics are of vital interest to researchers in various mathematical and statistical fields and have never before been treated together in one book. The use of data random graphs in pattern recognition in clustering and classification is discussed, and the applications for both disciplines are enhanced with new tools for the statistical pattern recognition community. New and interesting applications for random graph users are also introduced. This important addition to statistical literature features: Information that previously... more...
The Pursuit of Perfect Packingby Tomaso Aste
CRC Press 2000; US$ 42.95In 1998 Thomas Hales dramatically announced the solution to the problem which has long teased eminent mathematicians: what is the densest possible arrangement of identical spheres? This text recounts the story of this problem and many others which have to do with packing things together. more...
Tolerance Graphsby Martin Charles Golumbic; Ann N. Trenk; B. Bollobas; W. Fulton; A. Katok; F. Kirwan; P. Sarnak; B. Simon
Cambridge University Press 2004; US$ 90.00The first rigorous treatment of tolerance graphs in book form. This book will act as a springboard for researchers, especially graduate students, to pursue new directions of investigation. With many examples and exercises it is also suitable for use as the text for a graduate course in graph theory. more...
Chromatic Polynomials And Chromaticity Of Graphsby F M Dong; K M Koh; K L Teo
World Scientific 2005; US$ 101.40This is the first book to comprehensively cover chromatic polynomials of graphs. It includes most of the known results and unsolved problems in the area of chromatic polynomials. Dividing the book into three main parts, the authors take readers from the rudiments of chromatic polynomials to more complex topics: the chromatic equivalence classes of graphs and the zeros and inequalities of chromatic polynomials. more...
Combinatorics of Symmetric Designsby Yury J. Ionin; Mohan S. Shrikhande; Bela Bollobas; William Fulton; Anatole Katok; Frances Kirwan; Peter Sarnak; Barry Simon
Cambridge University Press 2006; US$ 161.00This is a unified exposition of the theory of symmetric designs with emphasis on recent developments. The authors cover the combinatorial aspects of the theory giving particular attention to the construction of symmetric designs and related objects. For all researchers in combinatorial designs, coding theory, and finite geometries. more...