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Scale-isometric Polytopal Graphs in Hypercubes and Cubic Lattices
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.
Diamond and Related Nanostructures
Over the past twenty years, the field of carbon structures has been invigorated by the discovery of fullerenes and carbon nanotubes. These nano-structured carbons have attracted a tremendous interest in the fundamental properties of discrete carbon molecules, leading to the discovery of novel complex crystalline and quasi-crystalline materials. As a consequence, a variety of applications have been developed, including technical and bio-medical materials and miniaturized tools. Diamond and Related Nanostructures focuses on the advances in the area of diamond-like carbon nanostructures (hyper-structures built from fullerenes and/or carbon nanotube junctions) and other related carbon nanostructures. Each chapter contributes to the topic from different fields, ranging from theory to synthesis and properties investigation of these new materials. This volume brings together the major findings in the field and provides a source of inspiration and understanding to advanced undergraduates, graduates, and researchers in the fields of Physics, Graph Theory, Crystallography, Computational and Synthetic Chemistry.
Advances in Algebra
This is the proceedings of the ICM2002 Satellite Conference on Algebras. Over 175 participants attended the meeting. The opening ceremony included an address by R Gonchidorazh, former vice-president of the Mongolian Republic in Ulaanbaatar. The topics covered at the conference included general algebras, semigroups, groups, rings, hopf algebras, modules, codes, languages, automation theory, graphs, fuzzy algebras and applications.
Analysis of Complex Networks
Mathematical problems such as graph theory problems are of increasing importance for the analysis of modelling data in biomedical research such as in systems biology, neuronal network modelling etc. This book follows a new approach of including graph theory from a mathematical perspective with specific applications of graph theory in biomedical and computational sciences. The book is written by renowned experts in the field and offers valuable background information for a wide audience.
Arrangements
Contains 15 contributions written by mathematicians from North America, Europe, and Asia, written in honor of the 60th birthday of Peter Orlik, one of the fathers of the topological study of general complex hyperplane arrangements. Topics include the cohomology of discriminantal arrangements and Orlik-Solomon algebras; plumbing graphs for normal surface-curve pairs; cohomology rings and nilpotent quotients of real and complex arrangements; remarks on critical points of phase functions and norms of Bethe vectors; and logarithmic forms and anti-invariant forms of reflection groups. Lacks a subject index. Annotation copyrighted by Book News, Inc., Portland, OR
Mathematical Reviews
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Torus Actions and Their Applications in Topology and Combinatorics
Here, the study of torus actions on topological spaces is presented as a bridge connecting combinatorial and convex geometry with commutative and homological algebra, algebraic geometry, and topology. This established link helps in understanding the geometry and topology of a space with torus action by studying the combinatorics of the space of orbits. Conversely, subtle properties of a combinatorial object can be realized by interpreting it as the orbit structure for a propermanifold or as a complex acted on by a torus. The latter can be a symplectic manifold with Hamiltonian torus action, a toric variety or manifold, a subspace arrangement complement, etc., while the combinatorial objects ...
