the technical efficiency involved in cocoa production in cross river state was estimated using the stochastic frontier production function analysis. the effects of some selected socio- economic characteristics of the farmers on the efficiency indices were also estimated. the study relied upon primary data generated from interviewing cocoa farmers using a set of structured questionnaire. a multi...

The ring of projective invariants of eight ordered points on the line is a quotient of the polynomial ring on V , where V is a fourteen-dimensional representation of S8, by an ideal I8, so the modular fivefold (P1)8// GL(2) is Proj(Sym•(V )/I8). We show that there is a unique cubic hypersurface S in PV whose equation s is skew-invariant, and that the singular locus of S is the modular fivefold....