An extension for residue difference sets

Low open fraction coded masks for x-ray backscatter imaging

“…Concerning imaging in the near-field (at closer ranges) with complex scenes, research using a ρ ϕ ¼ 0.5 MURA presented superior results over LOF arrays such as the no-two-holes-touching (NTHT) version of a MURA 10 and "new system" array. 11,12 Similar findings were also found when comparing the ρ ϕ ¼ 0.5 MURA with the other LOF arrays used for x-ray backscatter imaging. 13 The ρ ϕ ¼ 0.5 URA exhibits perfect PSF properties and has advantages over most, if not all LOF arrays published to date.…”

“…8, which were calculated using Eq. (11). The quadrant of blocks was comprised of aluminum and wax in the upper left and right quarters, and a cylindrical PVC block and copper in the lower left and right quarter.…”

Twelfth Power Qualified Residue Difference Sets

“…We call a definer if the qualifier m of a QRDS or MQRDS is in residue class n [6,7]. The author has shown that if n is a definer, then is also a definer [2,Theorem 3.3].…”

“…QRDS and MQRDS exist for the cases n D 2; 4; 6 [6,7,2], while both classes of set are nonexistent for n D 8 [2] and n D 10 [3]. The purpose of this report is to extend this analysis to n D 12 and prove the following theorem: Theorem 3.…”

“…Qualified residue difference sets are a class of combinatorial configuration, first introduced by Jennings and Byard [6]. These sets are defined as follows.…”