We study a properly convex real projective manifold with (possibly empty) compact, strictly convex boundary, and which consists of a compact part plus finitely many convex ends. We extend a theorem of Koszul which asserts that for a compact manifold without boundary the holonomies of properly convex structures form an open subset of the representation variety. We also give a relative version fo...

For a convex curve in an even-dimensional aane space we introduce a series of convex domains (called Young hulls) describe their structure and give a formulas for the volume of the biggest of these domains. A simple smooth curve in R m is called convex if the total multiplicity of its intersection with any aane hyperplane does not exceed m. Note that each convex curve is nondegen-erate, i.e. ha...

We present a data structure which represents a wellshaped convex tetrahedral mesh, M, in linear space such that path traversals visiting a sequence of K tetrahedra require O (K/ lgB) I/O operations in the external memory model. As applications of our structure we show how to efficiently perform axis parallel box queries and how to report the intersection of M with an arbitrarily oriented plane.

We show that a PL-realization of a closed connected manifold of dimension n − 1 in R (n ≥ 3) is the boundary of a convex polyhedron if and only if the interior of each (n− 3)-face has a point, which has a neighborhood lying on the boundary of a convex n-dimensional body. This result is derived from a generalization of Van Heijenoort’s theorem on locally convex manifolds to the spherical case. O...

Uncertainty is an inherent property of all living systems. Curiously enough, computational models inspired by biological systems do not take, in general, under consideration this essential aspect of living systems. In this paper, after introducing the notion of a multi-fuzzy set (i.e. an orthogonal approach to the fuzzification of multisets), we introduce two variants of P systems with fuzzy co...

Let S be closed, m-convex subset of R d S locally a full ddimensional, with Q the corresponding set of Inc points of S If q is an essential inc point of order k then for some neighborhood U of q Q u is expressible as a union of k or fewer (d2)-dimenslonal manifolds, each containing q For S compact, if to every q E Q there corresponds a k > 0 such that q is an essential inc point of order k then...