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Optics and Spectroscopy - Scattering of light by disordered structures is normally detrimental to their applicability in many optoelectronic devices. However, some micro and nanostructures are... 相似文献
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In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself. 相似文献
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Francis Jordan 《Topology and its Applications》2006,153(14):2386-2412
An abstract scheme using particular types of relations on filters leads to general unifying results on stability under supremum and product of local topological properties. We present applications for Fréchetness, strong Fréchetness, countable tightness and countable fan-tightness, some of which recover or refine classical results, some of which are new. The reader may find other applications as well. 相似文献
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Francis K. Bell 《Journal of Graph Theory》2003,43(2):137-149
It is shown that, if t is an integer ≥3 and not equal to 7 or 8, then there is a unique maximal graph having the path Pt as a star complement for the eigenvalue ?2. The maximal graph is the line graph of Km,m if t = 2m?1, and of Km,m+1 if t = 2m. This result yields a characterization of L(G ) when G is a (t + 1)‐vertex bipartite graph with a Hamiltonian path. The graphs with star complement Pr ∪ Ps or Pr ∪ Cs for ?2 are also determined. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 137–149, 2003 相似文献
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Francis J. Vasko John A. McNamara Dennis D. Newhart Floyd E. Wolf 《The Journal of the Operational Research Society》1994,45(11):1285-1292
The optimum assignment of structural steel shapes to rail cars is an important logistical problem in the steel industry. In this paper, we discuss an application at Bethlehem Steel that not only involves weight and dimensional constraints, but also customer unloading constraints. The formulation is a generalized bin packing problem which is solved by modifying and extending the first fit decreasing algorithm. The solution algorithm, SOLID (for Structural Optimal Loading IDentification), has been used extensively for one of Bethlehem's high tonnage customers providing very good practical (implementable) results that achieve the desired goals. Bethlehem has enhanced this approach for use with other customers. 相似文献
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Network location problems occur when new facilities must be located on a network, and the network distances between new and existing facilities are important. In urban, regional, or geographic contexts, there may be hundreds of thousands (or more) of existing facilities, in which case it is common to aggregate existing facilities, e.g. represent all the existing facility locations in a zip code area by a centroid. This aggregation makes the size of the problem more manageable for data collection and data processing purposes, as well as for purposes of analysis; at the same time, it introduces errors, and results in an approximating location problem being solved. There seems to be relatively little theory for doing aggregation, or evaluating the results of aggregation; most approaches are based on experimentation or computational studies. We propose a theory that has the potential to improve the means available for doing aggregation.This research was supported in part by the National Science Foundation, Grant No. DDM-9023392. 相似文献