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 ≥
Authors:D. Beals, W. Britt, J. Bibler, and D. Brooks
The use of solid phase extraction (SPE) disks was studied for the quantification of selected radionuclides in aqueous solutions.
The extraction of four radionuclides using six types (two commerical, four test materials) of 3M EmporeTM RAD disks was studied. The radionuclides studied were: technetium-99 (two types of disks), cesium-137 (two types), strontium-90
(one type), plutonium-238 (one type). Extractions were tested from DI water, river water and seawater. Extraction efficiency,
kinetics (flow rate past the disk), capacity, and potential interferences were studied as well as quantification methods.
Consider a family of closed unit circular discs in the plane. Two discs are called neighbours if they have a point in common. Let N(d) denote the maximum possible number of neighbours of one disc in a family of unit circular discs, where the distance between any two circle centers is at least d. HereN(d) is determined for 1 between any two circle centers is at least d. HereN(d) is determined for 1
In the present paper lattice packings of open unit discs are considered in the Euclidean plane. Usually, efficiency of a packing
is measured by its density, which in case of lattice packings is the quotient of the area of the discs and the area of the
fundamental domain of the packing. In this paper another measure, the expandability radius is introduced and its relation
to the density is studied. The expandability radius is the radius of the largest disc which can be used to substitute a disc
of the packing without overlapping the rest of the packing. Lower and upper bounds are given for the density of a lattice
packing of given expandability radius for any feasible value. The bounds are sharp and the extremal configurations are also
presented. This packing problem is related to a covering problem studied by Bezdek and Kuperberg [BK97].
Two studies expanding the customary use of 3M EmporeTM Rad Disks have been conducted. In the first study,226Ra and228Ra were determined simultaneously by an improved method that used a single gamma-spectroscopy analysis. In the second study,
various tracer materials and procedures were used to correct for yield losses in the determination of90Sr and99Tc in synthetic samples that contained significant interferences.
be a line. Assume that for every point x ∈ L/K the two tangent segments from x to K have the same length, and the line joining the two contact points passes through a fixed
point in the plane. Then K is an Euclidean disc.