We prove a discrete Sobolev-Poincaré inequality for functions with arbitrary boundary values on Voronoi finite volume meshes. We use Sobolev’s integral representation and estimate weakly singular integrals in the context of finite volumes. We establish the result for star shaped polyhedral domains and generalize it to the finite union of overlapping star shaped domains. In the appendix we prove...

Degradable polymers are considered to present a promising solution combat plastic pollution.

The intersection body of a ball is again a ball. So, the unit ball Bd ⊂Rd is a fixed point of the intersection body operator acting on the space of all star-shaped origin symmetric bodies endowed with the Banach– Mazur distance. E. Lutwak asked if there is any other star-shaped body that satisfies this property. We show that this fixed point is a local attractor, i.e., that the iterations of th...

Solution-processable star-shaped and linear π-conjugated oligomers consisting of an electron-donating tetrathienoanthracene (TTA) core and electron-accepting diketopyrrolopyrrole (DPP) arms, namely, TTA-DPP4 and TTA-DPP2, were designed and synthesized. Based on density functional theory calculations, the star-shaped TTA-DPP4 has a larger oscillator strength than the linear TTA-DPP2, and consequ...

The paper concerns the star mappings understood as topological embedding of R into itself preserving the class of bodies which are star shaped at point 0. The main result is full characterization of star mappings (Theorem 2.8). At the end we give a solution of some related problem. MSC 2000: 52A30, 54C99, 54C05

A new class of star-shaped coil–rod diblock copolymer polystyrene-block-poly(3-hexylthiophene) (PS-bP3HT) with well-defined structures and the ratio of coil to rod blocks were synthesized by a combination of atom transfer radical polymerization, the Grignard metathesis method, and click reaction. The star-shaped PS-b-P3HT diblock copolymers covalently connected to a b-cyclodextrin (b-CD) core w...

Let P be an orthogonal polygon with n vertices. A sliding camera travels back and forth along an orthogonal line segment s ⊆ P corresponding to its trajectory. The camera sees a point p ∈ P if there is a point q ∈ s such that pq is a line segment normal to s that is completely contained in P . In the MinimumCardinality Sliding Cameras (MCSC) problem, the objective is to find a set S of sliding ...