Neutron activation analyses of ground samples of safe-packing insulation have shown that dust from different sources may be
differentiated by trace element content. Between 10 and 20 elements were identified in each of 54 samples, and comparison
of the activation “fingerprints” offers a good prospect for positively or negatively matching two or more samples.
A set of closed unit disks in the Euclidean plane is said to be double-saturated packing if no two disks have inner points
in common and any closed unit disk intersects at least two disks of the set. We prove that the density of a double saturated
packing of unit disks is ≥