A honeycomb array is an analogue of a Costas array in the hexagonal grid; they were first studied by Golomb and Taylor in 1984. A recent result of Blackburn, Etzion, Martin and Paterson has shown that (in contrast to the situation for Costas arrays) there are only finitely many examples of honeycomb arrays, though their bound on the maximal size of a honeycomb array is too large to permit an ex...

We develop a description of spin waves in $3D$ quantum $XY$ antiferromagnet (AFM) terms macroscopic variables, magnetization and N\'eel vector densities. consider layered AFM with spins located on the honeycomb lattice. In discussed system, spectrum consists four modes, all well captured by our description. The gapless mode waves, i.e., magnons, is described system equations, which has structur...

A series of compounds with the composition Na(3-x)Sn(2-x)Sb(x)NaO6 (x = 0.0, 0.2, 0.4, 0.6, 0.7, 0.8, 0.9, and 1.0) has been prepared by solid-state reaction and characterized by powder X-ray diffraction, neutron diffraction (for x = 0.0), and impedance spectroscopy. The compounds have a layered structure derived from that of α-NaFeO2, with alternating Na3 planes and NaSn2O6 slabs with honeycom...

The elemental two-dimensional (2D) materials such as graphene, silicene, germanene, and black phosphorus have attracted considerable attention due to their fascinating physical properties. Structurally they possess the honeycomb or distorted honeycomb lattices, which are composed of six-atom rings. Here we find a new structure of 2D allotropes of group V elements composed of eight-atom rings, w...