Ideal-specific elimination orders form a star-shaped region

Star-Shaped and L-Shaped Orthogonal Drawings

An orthogonal drawing of a plane graph G is a planar drawing of G, denoted by D(G), such that each vertex of G is drawn as a point on the plane, and each edge of G is drawn as a sequence of horizontal and vertical line segments with no crossings. An orthogonal polygon P is called orthogonally convex if the intersection of any horizontal or vertical line L and P is either a single line segment o...

Convexifying star-shaped polygons

Star-Shaped Conjugated Systems

The present review deals with the preparation and the properties of star-shaped conjugated compounds. Three, four or six conjugated arms are attached to crossconjugated cores, which consist of single atoms (B, C, N), benzene or azine rings or polycyclic ring systems, as for example triphenylene or tristriazolotriazine. Many of these shape-persistent [n]star compounds tend to -stacking and self...

K-star-shaped Polygons

We introduce k-star-shaped polygons, polygons for which there exists at least one point x such that for any point y of the polygon, segment xy crosses the polygon’s boundary at most k times. The set of all such points x is called the k-kernel of the polygon. We show that the maximum complexity (number of vertices) of the k-kernel of an n-vertex polygon is Θ(n) if k = 2 and Θ(n) if k ≥ 4. We giv...

Wetting of a multiarm star-shaped molecule.

The equilibrium contact angles and line tensions of macroscopic droplets, composed of star-shaped polystyrene (PS) macromolecules, on silicon oxide substrates, are shown to be smaller than their linear analogs, by up to approximately 1 and 2 orders of magnitude, respectively, depending on the size and functionality of the star-shaped molecule. A precursor layer, of lateral dimensions and of thi...