Block designs and graph imbeddings

Heffter first observed that certain imbeddings of complete graphs give rise to BIBD's with k = 3 and λ = 2 (and sometimes λ = 1); Alpert established a one-to-one correspondence between BIBD's with k = 3 and λ = 2 and triangulation systems for complete graphs. In this paper we extend this correspondence to PBIBD's on two association classes with k = 3, λ₁ = 0 and λ₂ = 2, and triangulation systems for strongly regular graphs. The group divisible designs of Hanani are used to construct triangulations for the graphs K_n(m), in each case permitted by the euler formula. Conversely, triangular imbeddings of K_n(m) are constructed which lead to new group divisible designs. A process is developed for “doubling” a given PBIBD of an appropriate form. Various extensions of these ideas are discussed, as is an application to the construction of quasigroups.     

An experimental technique for characterizing dispersion in compounds of particulates in thermoplastics using small-angle light scattering

An experimental technique based on small-angle light scattering for characterizing dispersion of particles and presence of agglomerates in compounds of minerals in thermoplastics is described. The technique is critically discussed in terms of the Mie and Rayleigh-Gans theories of scattering. An experimental study of dispersion in compounds of polypropylene and polystyrene with calcium carbonate by mixing variously on two roll mills, an internal mixer, and a modular intermeshing co-rotating twin screw extruder.