Design of Virtual Topology for Small Optical WDM Networks:

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Infants and small children grapple with topology in kicking off blankets; putting arms into sleeves, legs into pantlegs; in buttoning; in tying laces; in opening and closing drawers and doors; in crossing room-boundaries; etc. (Elsewhere I have topology for adults.) A simple trick illustrates topology: taking off a vest without taking off a coat, since (topological) the vest is outside the coat -- in the sense that a paper lying on the bottom of a wastebasket is really outside the basket, not in it, since being in would require removal of a boundary.

Pages: 84

Publisher: LAP LAMBERT Academic Publishing (April 30, 2012)

ISBN: 3848488949

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In other words, every stably complex manifold is cobordant to a manifold with a nicely behaving torus action. An informative setting for applications of toric topology to complex cobordism is provided by the combinatorial and convex-geometrical study of analogous polytopes. By way of application, we give an explicit construction of a quasitoric representative for every complex cobordism class as the quotient of a free torus action on a real quadratic complete intersection Topology of Algebraic Curves: and Factorization of Polynomials. Another topological property of a surface is its Euler-Poincaré characteristic, a number which can be calculated from any polyhedral decomposition of the surface. If V is the number of points (vertices) in the decomposition, E is the number of line segments (edges), and F is the number of regions (faces), then the characteristic is given by Χ=V-E+F and is the same for all possible polyhedral decomposition of the given surface Fractal and Chaos in the Classroom: Introductory Ideas. See Correcting topology errors for more information. A key goal of geodatabase topologies is to optimize the time spent on processing and validating the feature data that participates in a topology before it can be used. Generally speaking: Feature classes that participate in a topology are always available for use regardless of the state of the topology The Local Structure of Algebraic K-Theory (Algebra and Applications).

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