Hyperplanes and hyperplane complements in the Segre product of partial linear spaces are investigated. The parallelism of such a complement is characterized in terms of the point-line incidence. Assumptions, under which the automorphisms of the complement are the restrictions of the automorphisms of the ambient space, are given. An affine covering for the Segre product of Veblenian gamma spaces...

A convexity structure satisfies the separation property 5'4 if any two disjoint convex sets extend to complementary half-spaces. This property is investigated for alignment spaces, n-ary convexities, and graphs. In particular, it is proven that a) an n-ary convexity is $4 iff every pair of disjoint polytopes with at most n vertices can be separated by complementary half spaces, and b) an interv...

Recently a novel approach to nonlinear function approximation using hinging hyperplanes, was reported by L. Breiman 3]. In this contribution we have combined smooth hinging hyperplanes and the eecient initializa-tion procedure existing for hinging hyperplanes in 3], with a Gauss-Newton procedure, see 4], to perform the nal adjustment of the smooth hinging hyperplanes. This combination uses the ...