We generalize a theorem of W. Jockusch and J. Propp on quartered Aztec diamonds by enumerating the tilings of quartered Aztec rectangles. We use subgraph replacement method to transform the dual graph of a quartered Aztec rectangle to the dual graph of a quartered lozenge hexagon, and then use Lindström-GesselViennot methodology to find the number of tilings of a quartered lozenge hexagon.

Like natural diamonds, synthetic diamonds can be produced in a variety of grades, depending on growth conditions. High growth rates can be realized with chemical vapor deposition, but the diamond produced is often not clear because of nitrogen deposits that render the crystals absorptive over the infrared-toultraviolet spectrum, resulting in crystals that appear gray or brown. To reduce absorpt...

The objective of the present study is to analyze and compare the cutting performance of segmented diamond blades when dry-cutting concrete. A cutting criteria is proposed to characterize the wear of the blades by measuring the variation of the external diameter and the weight loss of the blade. The results exhibit the cutting blade SB-A, which has twice the density of diamonds and large contact...