An edge of a hexagonal system H is said to be forcing if it belongs to exactly one perfect matching of H. Using the concept of Z-transformation of hexagonal system, we give a characterization for the hexagonal systems with forcing edges and determine all forcing edges is such systems. We also give the generating function of all hexagonal systems with forcing edges. A hexaoonal system, also call...

We consider a Fröhlich-type Hamiltonian on a hexagonal lattice. Aiming to describe nanotubes, we choose this 2-dimensional lattice to be periodic and to have a large extension in one (x) direction and a small extension in the other (y) direction. We study the existence of solitons in this model using both analytical and numerical methods. We find exact solutions of our equations and discuss som...

We define the higher dimensional hexagonal graphs as the generalization of a triangular plane tessellation, and consider it as a multiprocessor interconnection network. Nodes in a k-dimensional (k-D) hexagonal network are placed at the vertices of a k-D triangular tessellation, so that each node has up to 2k þ 2 neighbors. In this paper, we propose a simple addressing scheme for the nodes, whic...

In the study of pattern formation in symmetric physical systems, a three-dimensional structure in thin domains is often modelled as a two-dimensional one. This paper is concerned with functions in {\bb R}^{3} that are invariant under the action of a crystallographic group and the symmetries of their projections into a function defined on a plane. A list is obtained of the crystallographic group...

A novel application and generalization of sigma–delta ( ) modulation has emerged in three-phase power-electronic converters. A conventional modulator with scalar signals and binary quantizer is generalized to a modulator with vector signals and a hexagonal quantizer. Indeed, power-electronic switching states may be thought of as determining the quantizer outputs. The output spectrum is a key pe...

A simple Ising-like model for the stacking thermodynamics of ice 1 is constructed for nuclei in supercooled water, and combined with classical nucleation theory. For relative stabilities of cubic and hexagonal ice I within the range of experimental estimates, this predicts critical nuclei are stacking disordered at strong sub-cooling, consistent with recent experiments. At higher temperatures n...