By using the Transfer Matrix Method, explicit formulas for the embedding distribution of doubly hexagonal chain graphs are computed. Dedicated to Ante Graovac 1 Fasciagraphs and rotagraphs An interesting topic that I have learned from Ante Graovac in the 1980’s [1, 2] is that about fasciagraphs and rotagraphs. Such graphs are frequently studied in crystallography and in mathematical chemistry. ...

X-ray-diffraction patterns of hyaluronate fibres from a variety of sources were obtained. Sodium hyaluronate gives well-defined patterns which index on a hexagonal unit cell with dimensions a=1.17+/-nm and a fibre repeat-distance of 2.85+/-0.03nm. A further form of sodium hyaluronate is produced by annealing at 60 degrees C in 75% relative humidity. This stable state indexes on a hexagonal unit...

Iridates are of current great interest for their entangled spin-orbital state and possibly exotic properties. In this work, using density functional calculations, we have demonstrated that the hexagonal spin-chain materials Sr3MIrO6 (M = Ni, Co) are an iridate system in which the spin-orbit coupling (SOC) tunes the magnetic and electronic properties. The significant SOC alters the orbital state...

The deuterium nuclear magnetic resonance (2H NMR) spectrum of perdeuterated tetradecanol in a mixture of 1-palmitoyl-2-oleoyl-phosphatidylethanolamine (POPE) and water was used to compare the variation of the acyl chain orientational order parameter, S(n), with carbon position, n, in the liquid crystalline lamellar (La) and hexagonal (HI,) phases. The characteristic independence of S(n) with n ...

The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. A connected graph G is a cactus if any two of its cycles have at most one common vertex. Let G (n, r) be the set of cacti of order n and with r cycles, ξ(2n, r) the set of cacti of order 2n with a perfect matching and r cycles. In this paper, we give the sharp upper bounds of t...

Determining the maximum outerplanar subgraph of a given graph is known to be an NP-complete problem. In the literature there are no earlier experiment on approximating the maximum outerplanar subgraph problem. In this paper we compare solution quality and running times of different heuristics for finding maximum outerplanar subgraphs. We compare a greedy heuristic against a triangular cactus he...

A signaling pathway active on the ventral side of the Drosophila embryo defines dorsoventral polarity. A cell surface signal relayed by Toll, Tube and Pelle releases the Rel-related protein Dorsal from its cytoplasmic inhibitor Cactus; free Dorsal translocates into nuclei and directs expression of ventral fates. Using the yeast two-hybrid system and immunoprecipitation experiments, we define sc...