Clones with finitely many relative R-classes

For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A iff each one is a substitution instance of the other using operations from C. We study the clones for which there are only finitely many relative R-classes.Comment: 41 pages; proofs improved, examples adde

A Finite Set Intersection Theorem

Suppose 0, ⩽ r < m, and ℱ is a family of k-subsets of an n-set such that the intersection of any two different members of ℱ has cardinality congruent to r (mod m). If k ≢ r (mod m) then ❘ℱ❘ ⩽ n. The case of equality is also investigated

Wave steadiness in aluminas

Plate impact experiments have been carried out on two aluminas of differing grain size using the Cambridge 50 mm gas gun. Tiles were constructed in thicknesses of 4,8 and 12 mm and were impacted by 3 mm thick copper projectiles fired at 550 m s-1. The longitudinal stress in the tiles was recorded using manganin stress gauges and a 1 GS s-1 storage oscilloscope. Measurements were made of the elastic precursor of the deformation wave in each of these experiments. It was found that the elastic precursor varied significantly with thickness and that different behaviours were shown by the large and small grain size material