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This note describes fast algorithms for computing the prime factors of connected, nonbipartite graphs with respect to the direct product, and of connected graphs with respect to the strong product. The complexities are O(mmin(n,∆)) for the direct product, and O(ma(G)∆) for the strong, where n is the order of the graph G to be factored, m its size, a(G) its arboricity, and ∆ its maximum degree. ...
Since its inception over 35 years ago, Rietveld refinement (Rietveld, 1969) has come a long way. In the beginning, the aim was to carry out crystal-structure refinement using neutron diffraction. As its primary purpose was refinement of the perfect crystal structures of polycrystalline samples, there was a need to introduce corrections to peak intensities and positions, as calculated for a perf...
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