On simple polytopes.
On smooth points of boundaries of open sets
The notions of smooth points of the boundary of an open set and α(·) intrinsically paraconvex sets are introduced. It is shown that for an α(·) intrinsically paraconvex open set the set of smooth points is a dense -set of the boundary.
On solution sets of information inequalities
We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce structural properties of Bayesian networks, which is important within causal inference.
On some classes of curves in a projective space
On some packings of the hyperbolic plane by incongruent hypercyclic domains.
On some properties of hyperconvex spaces.
On some random convex sets
On some special surfaces connected with convex surfaces of the Lobachevskij space.
On some vector balancing problems
Let V be an origin-symmetric convex body in , n≥ 2, of Gaussian measure . It is proved that for every choice of vectors in the Euclidean unit ball , there exist signs with . The method used can be modified to give simple proofs of several related results of J. Spencer and E. D. Gluskin.
On splitting infinite-fold covers
Let X be a set, κ be a cardinal number and let ℋ be a family of subsets of X which covers each x ∈ X at least κ-fold. What assumptions can ensure that ℋ can be decomposed into κ many disjoint subcovers? We examine this problem under various assumptions on the set X and on the cover ℋ: among other situations, we consider covers of topological spaces by closed sets, interval covers of linearly ordered sets and covers of ℝⁿ by polyhedra and by arbitrary convex sets. We focus on...
On stabbing triangles by lines in 3-space
We give an example of a set of points in such that, for any partition of into triples, there exists a line stabbing of the triangles determined by the triples.
On star duality of mixed intersection bodies.
On starshapedness of the union of closed sets in
On support functions of Compact Convex Sets.
On Surface-Minimizing Polyhedral Decompositions.
On the abstract Hahn-Banach theorem due to Rodé.
On the affine convexity of convex curves and hypersurfaces.
On the Aleksandrov-Fenchel Inequality and the Stability of the Sphere.
On the algebraic form of Keller's conjecture
On the algebraic properties of convex bodies and some applications.