Let a, b and c be positive integers and consider a hexagon with side lengths a,b,c,a,b,c whose angles are 120 (see Figure 1). The subject of our interest is lozenge tilings of such a hexagon using lozenges with all sides of length 1 and angles of 60 and 120. Figure 2 shows an example of a lozenge tiling of a hexagon with a = 3, b = 5 and c = 4. We introduce the following oblique angled coordina...

We investigate stationary spatially localized hexagon patterns of the two-dimensional (2D) Swift– Hohenberg equation in the parameter region where the trivial state and regular hexagon patterns are both stable. Using numerical continuation techniques, we trace out the existence regions of fully localized hexagon patches and of planar pulses which consist of a strip filled with hexagons that is ...

We define the notion of d i -regularity and regularity in generalized polygons, thus generalizing the notion of ‘regular point’ in a generalized quadrangle or hexagon. We show that a thick generalized polygon cannot contain too many regular points unless it is a projective plane, quadrangle or hexagon. For certain polygons (thick ‘odd’gons and 8-gons), we show that even a certain number of d2-r...

STATEMENT OF PROBLEM Although the implant-abutment connection may prevent crestal bone loss around dental implants, its failure often leads to treatment failure. Microgap and micromovement of the implant-abutment connection could be causes of bone resorption around dental implant neck. PURPOSE The purpose of this study was to compare torque resistance and microgaps between a new cone and inde...

the present study has been conducted on shemiranat county landscape, using lattice hexagon approach, for the first time, in order to achieve homogeneous units in degradation model. to this aim, with respect to the extent of the studied area, a lattice hexagon composed of 36 units (cells) was created and each grid cell was considered as a sub landscape. next, ecological vulnerability, degradatio...

In this paper, we propose a new hybrid Cross Hexagon Diamond Search algorithm (CHDS) using crossshaped search pattern as the initial step and asymmetric hexagon-shaped patterns and small diamond pattern as the subsequent steps for fast block motion estimation. In block motion estimation, search pattern with different shape or size and the center biased motion vector distribution characteristics...

The role of opposition in rough set theory is laid bare. There are two sources which generate oppositions in rough sets: approximations and relations. In the former case, we outline a hexagon and a cube of oppositions. In the second case, we define a classical square of oppositions and also a tetrahedron when considering the standpoint of two agents.

A new scheme for spontaneous formation of hexagonal optical patterns in photorefractive crystals with dominant reflection gratings and a single pump wave is proposed and realized experimentally. It is shown theoretically that spontaneous hexagon formation results from random small-angle scattering of the pump wave inside the crystal. The threshold of spontaneous hexagon formation is found.