In this work, we construct the projectively distinct (k, n)-arcs in PG (3, 4) over Galois field GF (4), where k 5, and we found that the complete (k, n)-arcs, where 3 n 21, moreover we prove geometrically that the maximum complete (k, n)-arc in PG (3, 4) is (85, 21)-arc. A (k, n)-arcs is a set of k points no n+ 1 of which are collinear. A (k, n)-arcs is complete if it is not contained in a (k+ 1, n)-arcs

A small number of researches were done in the design and synthesis of enkephalin analogues that are able to resist degradation effect of proteolytic enzymes with good bioavailability and half-lives.Through studying structure activity relationships we tried to incorporate phthalyl group, tryptophan and lysine amino acids in different positions in the basic backbone structure of the naturally occurring opioid Leu⁵- and Met⁵- enkephalin, in the hope that such insertion of these amino acids could induce interesting addition in the biological activity of these analogues with enhancement of their bioavailability, in addition to decrease side effects as addiction liability.

These synthesized peptides are: