Star-Shaped Compounds with Oxadiazole Fragments. III. Informativity of Molecular Parameters Developed for Columnar Mesomorphism Prediction of Star-Shaped Compounds Towards Polycatenar Molecules

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...

Dynamics of fluorescence depolarisation in star-shaped oligofluorene-truxene molecules.

Star-shaped molecules are of growing interest as organic optoelectronic materials. Here a detailed study of their photophysics using fluorescence depolarisation is reported. Fluorescence depolarisation dynamics are studied in branched oligofluorene-truxene molecules with a truxene core and well-defined three-fold symmetry, and are compared with linear fluorene oligomers. An initial anisotropy v...