Its low weight, high melting point, and large degree of hardness make elemental boron a technologically interesting material. The large number of allotropes, mostly containing over a hundred atoms in the unit cell, and their difficult characterization challenge both experimentalists and theoreticians. Even the ground state of this element is still under discussion. For over 30 years, scientists...

The local structure of ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$, an archetypal strongly correlated electron system that displays a metal-insulator transition around 160 K, has been investigated via pair distribution function (PDF) analysis neutron and x-ray total scattering data. rhombohedral-to-monoclinic structural phase manifests as abrupt change on all length scales in the observed PDF. No monocl...

Image processing has traditionally involved the use of square operators on regular rectangular image lattices. For many years the concept of using hexagonal pixels for image capture has been investigated, and several advantages of such an approach have been highlighted. We present a design procedure for hexagonal gradient operators, developed within the finite element framework, for use on hexa...

In this note we give a simple proof of the classical fact that the hexagonal lattice gives the highest density circle packing among all lattices in R2. With the benefit of hindsight, we show that the problem can be restricted to the important class of well-rounded lattices, on which the density function takes a particularly simple form. Our proof emphasizes the role of well-rounded lattices for...

Resampling is a common operation in digital image processing systems. The standard procedure involves the (conceptual) reconstruction of a continuous image succeeded by sampling on the new lattice sites. When the reconstruction is done by classical interpolation functions, results might be sub-optimal because the information loss is not minimized. In the particular case of subsampling (i.e., re...

In this paper, the connection between triangular number , square number for construction and counting the lattice number in lattice vector quantization is presented. We also observe that unique hexagonal lattice can be formed from two triangular numbers and a square number combination. Furthermore, the number of multistage lattice is derived from lattice number . Analysis of the number of latti...

We report on the growth of 2D layered indium selenide films (0001)-oriented sapphire substrates by coevaporation. The θ − 2 x-ray diffractograms reveal that (00 l) planes are preferentially oriented parallel to substrate with a tendency deviate from stacking as function time. ϕ-scans performed for (107) and (10 10) orientations hexagonal (h) rhombohedral (r) phases, respectively, both polytypes...

The localization properties of the wave functions of vibrations in two-dimensional (2D) crystals are studied numerically for square and hexagonal lattices within the framework of an algebraic model. The wave functions of 2D lattices have remarkable localization properties, especially at the van Hove singularities (vHs). Finite-size sheets with a hexagonal lattice (graphene-like materials), in a...

Hexagonal image structure represents an image as a collection of hexagonal pixels rather than square pixels in the traditional image structure. However, all the existing hardware for capturing image and for displaying image are produced based on square pixel image structure. Therefore, it becomes important to find a proper software approach to mimic the hexagonal structure so that images repres...