The classification of flag-transitive Steiner 3-designs

We solve the long-standing open problem of classifying all 3-(v,k,1) designs with a flag-transitive group of automorphisms (cf. A. Delandtsheer, Geom. Dedicata 41 (1992), p. 147; and in: "Handbook of Incidence Geometry", ed. by F. Buekenhout, Elsevier Science, Amsterdam, 1995, p. 273; but presumably dating back to 1965). Our result relies on the classification of the finite 2-transitive permutation groups.Comment: 27 pages; to appear in the journal "Advances in Geometry

Bottom Wall Construction of “Jodang” Trap Applied Selectively to Babylon Tiger (Babylonia Spirata) Snail Size

The objective of this research was to obtain net mesh bottom wall construction of “jodang” trap that selective to babylon tiger snails size, i.e. only shell length of l < 4.27 cm approximately could pass through. There were 3 designs shapes of bottom wall construction tested, i.e. rectangular shape of 2.4 ´ 2.8 (cm) and 2 diamond shapes with net mesh size of 5,6 cm and primary hanging ratio of E1 = 0.7 and 0.5. The results showed that rectangular shape bottom wall trap construction was better than those two other constructions. Only 6.78% of snails with l ³ 4.27 cm could escape the rectangular shape bottom wall trap construction. Whereas 41.90% and 17.46% of snail shells with l ³ 4.27 cm could escape from both the diamond mesh bottom wall trap construction. According to selectivity curve, the rectangular shape bottom wall trap construction could retained snails with shells length of l ³ 4.33 cm. The two others retained shells length of l ³ 4.14 cm and l ³ 4.60 cm

Construction of spherical cubature formulas using lattices

We construct cubature formulas on spheres supported by homothetic images of shells in some Euclidian lattices. Our analysis of these cubature formulas uses results from the theory of modular forms. Examples are worked out on the sphere of dimension n-1 for n=4, 8, 12, 14, 16, 20, 23, and 24, and the sizes of the cubature formulas we obtain are compared with the lower bounds given by Linear Programming

Constructing 3-designs from spreads and lines

Using the elements of a partial spread of PG(d, q) as points, a class of 3-designs is constructed