14 research outputs found
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X-ray monochromator geometry for focusing synchrotron radiation above 10 keV
The relative merits of crystals versus mirrors for focusing synchrotron radiation at energies above 10 keV are explored. As mirrors have critical angles of reflection typically 1/20 of the Bragg scattering angles for crystals, large mirror surface areas are required. Sagittal focusing is weak for mirrors and limits the amount of radiation intercepted. Crystals bent to a simple cylindrical curvature are shown to accept large divergences of radiation for sagittal focusing. At a magnification near 1/3, the cylindrically curved crystals are shown to make the proper Bragg angle for energies above 5 keV and for divergences larger than 10 mrad and to produce x-ray beams which are approximately focused
Equitable colorings of bounded treewidth graphs
A proper coloring of a graph G is equitable if the sizes of any two color classes are di#er by at most one. The related notion is #-bounded coloring where each of the color classes is of cardinality #. We consider the problems to determine for a given graph G (and a given integer #) whether G has an equitable (#-bounded) coloring