A series of esters of 2,3,6,7-tetrakis(hexyloxy)dibenzo[a,c]phenazine-11-carboxylic acid was prepared in order to probe the effects of the ester groups on the liquid crystalline behavior. These compounds exhibit columnar hexagonal phases over broad temperature ranges. Variations in chain length, branching, terminal groups, and the presence of cyclic groups were found to modify transition temper...

The generalized hierarchical product of graphs was introduced by L. Barriére et al in 2009. In this paper, reformulated first Zagreb index of generalized hierarchical product of two connected graphs and hence as a special case cluster product of graphs are obtained. Finally using the derived results the reformulated first Zagreb index of some chemically important graphs such as square comb latt...

We theoretically investigate an antiferromagnetic structure in a hexagonal zigzag-chain compound Ce3TiBi5, which shows linear magnetoelectric effect metals and characteristic temperature dependence of magnetic susceptibility. find partial order as coexistence nonmagnetic state on zigzag chain staggered chains. The latter accompany in-plane toroidal dipole moments are responsible for the observe...

Empirical potential structure refinement (EPSR) simulations are performed on total neutron scattering data from powder samples of polytetrafluoroethylene (PTFE) and polychlorotrifluoroethylene (PCTFE), both at 300 K. Starting from single strands of polymer consisting of between 30 and 60 monomers of tetrafluoroethylene and chlorotrifluoroethylene in each case, hexagonal simulation cells are con...

We report on an experimental study of the self-organization and phase behavior of hairy-rod pi -conjugated branched side-chain polyfluorene, poly[9,9-bis(2-ethylhexyl)-fluorene-2,7-diyl]-i.e., poly[2,7-(9,9-bis(2-ethylhexyl)fluorene] (PF2/6) -as a function of molecular weight (M(n)) . The results have been compared to those of phenomenological theory. Samples for which M(n) =3-147 kg/mol were u...

Chain-folded lamellar crystalline complexes of amylose with aliphatic diols were prepared and characterized by transmission electron microscopy as well X-ray diffraction. Four allomorphs identified, depending on the complexing diol crystallization conditions, that consisted orthorhombic lattices antiparallel 6- or 7-fold single helices. Straight-chain n-diols (ethane-1,2-diol, butane-1,4-diol, ...

the padmakar-ivan (pi) index is a wiener-szeged-like topological index which reflectscertain structural features of organic molecules. the pi index of a graph g is the sum of alledges uv of g of the number of edges which are not equidistant from the vertices u and v. inthis paper we obtain the second and third extremals of catacondensed hexagonal systems withrespect to the pi index.

The hexagonal bipyramid fractal is a fractal in three dimensional space, which has fractal dimension two and which has six square projections. We consider its 2nd level approximation model, which is composed of 81 hexagonal bipyramid pieces. When this object is looked at from each of the 12 directions with square appearances, the pieces form a 9× 9 grid of squares which is just the grid of the ...

Using hexagonal grids to represent digital images have been studied for more than 40 years. Increased processing capabilities of graphic devices and recent improvements in CCD technology have made hexagonal sampling attractive for practical applications and brought new interests on this topic. The hexagonal structure is considered to be preferable to the rectangular structure due to its higher ...