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Helfgott and Gessel gave the number of domino tilings of an Aztec Rectangle with defects of size one on the boundary of one side. In this paper we extend this to the case of domino tilings of an Aztec Rectangle with defects on all boundary sides.
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The Tangent Method of Colomo and Sportiello is applied to the study of the asymptotics of domino tilings of large Aztec rectangles, with some fixed distribution of defects along a boundary. The associated non-intersecting lattice path configurations are made of Schröder paths whose weights involve two parameters \(\gamma \) and q keeping track resp...
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Due to some deficiencies in the existing researches of cutting element wear of polycrystalline diamond compact (PDC) drill bit and to reduce the wear rate of cutting element of PDC bit, accurately illustrate the effect of tooth-distributing angle on cutting element, and improve the service life of PDC drill bit, we use the geometry knowledge of PDC...

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... Initial prototype devices were fabricated on 7 mm x 7 mm chips without photolithographic patterning of metal or polymer layers. The diamond was selectively grown by David Sabens of the Dept. of Chemical Engineering [249], on a 1 µm-thick thermal oxide film on a Si wafer to result in the pattern shown in The die-level first prototype diamond-on-polymer devices were fabricated using the process shown in Figure 3-4. First, diamond was selectively-grown on the chip using BEN and MPCVD processes (1). ...
... are absent, as indicated by the arrows: therefore it was concluded that Au was not exposed to the PBS, and that the sensing was performed by the diamond nucleation surface as the active surface. Thus, it was shown for the first time that the diamond nucleation surface could be used for electrochemical sensing, justifying the further development of microfabricated diamond electrode arrays on a flexible polymer substrate [246,249]. ...
... X-ray photoelectron spectroscopy (XPS) measurements showed that after release, there was a Si x O y C z interfacial region on the diamond nucleation surface, resulting from reactions between methane, hydrogen and SiO 2 at the SiO 2 -diamond interface that occurs during the early stage of CVD growth [249]. This interfacial region, which becomes the top surface of the diamond-on-polymer electrodes, impaired the ability of these electrodes, which had been seeded with a diamond slurry, to be used for electrochemical sensing. ...