This paper studies the construction of highly symmetric compactly supported wavelets for hexagonal data/image and triangle surface multiresolution processing. Recently hexagonal image processing has attracted attention. Compared with the conventional square lattice, the hexagonal lattice has several advantages, including that it has higher symmetry. It is desirable that the filter banks for hex...

This paper concerns the construction of highly symmetric compactly supported wavelets for hexagonal data/image and triangle surface multiresolution processing. Recently hexagonal image processing has attracted attention. Compared with the conventional square lattice, the hexagonal lattice has several advantages, including that it has higher symmetry. It is desirable that the filter banks for he...

Kepler’s Conjecture, recently proved by T. Hales, states that the densest packing of spheres in 3-space has spheres centered along the face-centered cubic (fcc) lattice. A lattice is a free Z-module formed by taking the span of a collection of linearly independent vectors in R over the integers. The two-dimensional analogue of Kepler’s Conjecture, proved by L. F. Toth in 1940, states that the d...

Simple pair potentials are constructed which give hexagonal-or square-lattice ground states in two dimensions, depending on the value of a single parameter controlling the width of the potential well. Molecular dynamics calculations for free clusters of a few hundred particles are used to examine a structural transition from the square lattice, at low temperatures, to the hexagonal lattice at h...

The applicability of standard lattice percolation models to a random two-dimensional grain structure is explored. A random network based on the triangle lattice is proposed as a more appropriate model, and results in a higher percolation threshold (0.711 compared with 0.653 for the standard hexagonal lattice). The triple junction constraint inherent in grain boundary structures is subsequently ...

We have synthesized novel crystalline ropes of "polygonized" single-wall carbon nanotubes (SWCNTs). The tubes exhibit rounded-hexagonal cross sections in contrast to the earlier observations of nearly circular tubes. To investigate the structural characteristics of the lattice of SWCNTs we have performed extensive molecular-dynamics simulations. We find several metastable structures of the latt...

Lanthanum (La) doped Ceria (CeO2) has attracted considerable interest as a candidate material for thermal barrier coating (TBC) because of its low thermal conductivity and potential capability to be operated above 1250°C. In this study, La2Ce2O7 powder was synthesized through the ball mill method. The crystal structure of La3+ su...

We find the generating function of self-avoiding walks (SAWs) and trails on a semi-regular lattice called the 3.122 lattice in terms of the generating functions of simple graphs, such as SAWs, self-avoiding polygons and tadpole graphs on the hexagonal lattice. Since the growth constant for these graphs is known on the hexagonal lattice we can find the growth constant for both walks and trails o...