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This book describes the mathematical theory of regularizing element transformations as foundation for mesh smoothing. It gives a thorough introduction to GETMe based mesh smoothing and its algorithms providing a framework to focus on efficiently improving minimal element quality,... overal mesh quality, and mesh validity. It addresses the improvement of various types of meshes like planar, surface, volumetric, mixed, isotropic or anisotropic meshes and addresses aspects of combining mesh smoothign with topological mesh modifications.
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The crossing number is a popular object of study with surprising connections. A rich body of material illustrates a wide variety of ideas and techniques in topological graph theory, discrete geometry, and computer science. The first part deals with the traditional crossing number..., crossing number values, crossing lemma, related parameters, computational complexity, and algorithms. The second part includes the rich history of alternative crossing numbers, the rectilinear crossing number, the pair crossing number, the independent odd crossing number, with interesting and non-trivial results. Finally, applications of the crossing number outside topological graph theory are included.
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This enumerative combinatorics text focuses on set partitions. It presents a complete survey of the field, open problems, and results in set partitions and pattern matching. The advantages and drawbacks of various solution techniques and approaches are also examined.
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While much information can be found on discrete and computational geometry, it is scattered among many sources. The Handbook of Discrete and Computational Geometry, Third Edition brings together all of the major results in both these fields into one volume. Thousands of results, ...theorems, algorithms, and tables definitively cover the field, while numerous applications from many different fields demonstrate practical usage. The material is readily accessible to the novice, but offers enough depth to appeal to the specialist. Every technical term is defined in an easy-to-use glossary. Over 200 figures illustrate the concepts presented and provide supporting examples.
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A 2006 CHOICE Outstanding Academic Title, this text provides comprehensive coverage of permutations. The second edition features a new chapter on modeling genomes by using permutations. Along with new applications such as genome sorting, this edition includes a set of warm-up exe...rcises to ease readers into a problem solving mode as well as new sections addressing the growth rate of permutation classes, permutation tableaux, superpatterns, and alternating subsequences. The text also discusses pattern avoidance, inversions, and linear orders.
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A symbol of the Divine, a good luck charm, a cosmogram of the world order, a template for fengshui - through the ages, the luoshu, or magic square of order three, has fascinated people of many different cultures. This book uncovers the history of the luoshu, from its Chinese orig...ins, shrouded in legend.
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This work focuses on the number theory of quadratic irrationalities in various forms, including continued fractions, orders in quadratic number fields, and binary quadratic forms. It presents classical results obtained by the famous number theorists Gauss, Legendre, Lagrange, and... Dirichlet. Collecting information previously scattered in the literature, the book covers the classical theory of continued fractions, quadratic orders, binary quadratic forms, and class groups based on the concept of a quadratic irrational.
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This book presents results established over the past 30 years on the Laplacian matrix of graphs developed using combinatorial matrix theory. The author focuses on the spectrum of Laplacian matrices, the algebraic connectivity of graphs, associated eigenvectors of the Laplacian ma...trix, and submatrices of the Laplacian matrix. All of these topics illustrate how the properties of a matrix can give information about the associated graph and vice versa. The text also covers relevant parts of graph theory, Laplacian matrices, and combinatorial matrix theory and includes sources for each theorem.
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This is the first book to provide an overview of combinatorial scientific computing (CSC). Bringing together a diverse group of researchers, it addresses many of the challenges faced in high-performance computing (HPC) by setting the stage for accelerated development and deployme...nt of fundamental enabling technologies in HPC. The text focuses on load balancing and parallelization on high-performance computers, large-scale optimization, automatic differentiation of numerical simulation code, and sparse matrix software tools. It also discusses key topics in CSC, important software tools, and special topics and applications.
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Presents theoretical, algorithmic, and application aspects of domination in graphs - discussing fundamental results and major research accomplishments. This book includes chapters on domination algorithms and NP-completeness as well as frameworks for domination.
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