On point sets fixing a convex body from within.
On Polyhedra with Transitivity Properties.
On Polytopes Cut by Flats.
On prior distributions which give rise to a dominated Bayesian experiment.
On projective toric varieties whose defining ideals have minimal generators of the highest degree
It is known that generators of ideals defining projective toric varieties of dimension embedded by global sections of normally generated line bundles have degree at most . We characterize projective toric varieties of dimension whose defining ideals must have elements of degree as generators.
On properties of geodesic -preinvex functions.
On quantum limits on flat tori.
On quasistars in -cubes
On rainbowness of semiregular polyhedra
We introduce the rainbowness of a polyhedron as the minimum number such that any colouring of vertices of the polyhedron using at least colours involves a face all vertices of which have different colours. We determine the rainbowness of Platonic solids, prisms, antiprisms and ten Archimedean solids. For the remaining three Archimedean solids this parameter is estimated.
On reduced pairs of bounded closed convex sets.
In this paper certain criteria for reduced pairs of bounded closed convex set are presented. Some examples of reduced and not reduced pairs are enclosed.
On Reuleaux triangles in Minkowski planes.
On rhombic dodecahedra.
On Schläfli's reduction formula.
On Separating Two Simple Polygons by a Single Translation.
On set covariance and three-point test sets
The information contained in the measure of all shifts of two or three given points contained in an observed compact subset of is studied. In particular, the connection of the first order directional derivatives of the described characteristic with the oriented and the unoriented normal measure of a set representable as a finite union of sets with positive reach is established. For smooth convex bodies with positive curvatures, the second and the third order directional derivatives of the characteristic...
On seven points in the boundary of a plane convex body in large relative distances.
On shadow boundaries of centrally symmetric convex bodies.
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.