We discuss theoretical aspects of the self-assembly of triangular tiles, in particular, right triangular tiles and equilateral triangular tiles, and the self-assembly of hexagonal tiles. We show that triangular tile assembly systems and square tile assembly systems cannot be simulated by each other in a non-trivial way. More precisely, there exists a deterministic square (hexagonal) tile assemb...

We have investigated the distributions of individually isolated and hydrophilically functionalized single-walled carbon nanotubes (p-SWNTs) in the Pluronic L121-water system at the reverse hexagonal phase using small-angle X-ray scattering (SAXS) and contrast-matched small-angle neutron scattering (SANS) measurements. As the p-SWNT-L121-water system is transitioned from the lamellar phase to th...

We predict the number of hexagonal systems consisting of and hexagons to be H and H with and signi cant digits respectively Further estimates for Hn up to n are also given Hexagonal Systems Informally speaking a hexagonal system can be viewed as a connected arrangement of hexagonal cells packed in the same way as the typical honeycomb arrangement in a bee hive More formally it is a nite connect...

The aim of this paper is to investigate resonance graphs 2- connected outerplane bipartite graphs, which include various families molecular graphs. Firstly, we present an algorithm for a binary coding perfect matchings these Further, with isomorphic are considered. In particular, it shown that if two evenly homeomorphic, then its isomorphic. Moreover, prove any 2-connected graph G there exists ...

This paper analyzes dynamic channel assignment in cellular systems where the base stations are placed at random. Using a simple dynamic channel assignment algorithm, random systems are compared to an ideal hexagonal systems. Under log-normal shadow fading the random system has capacity within 1dB of the hexagonal system. This paper looks at both the uplink and downlink and finds that performanc...

It is shown experimentally that GeSi nanocrystals in SiC created after high-dose Ge ion implantation and high-temperature annealing are hexagonal in a hexagonal 4H-SiC matrix and are of cubic structure in a cubic 3C-SiC matrix. This interesting fact could be explained by molecular dynamics as the force of the system nanocrystal-matrix to minimize its interface energy.

conclusions hexagonal water has no significant effect(s) on total cholesterol, hdl, and ldl; however, more experiments are needed to clarify all aspects of hexagonal water consumption on diabetes. background diabetes is one of the most prevalent abnormalities in all over the world. nowadays, there are lots of attempts to reduce its disturbances and defects by changing life style to access some ...

A simple way to calculate the number of k-matchings, k ~< 5, in hexagonal systems is presented. Some relations between the coefficients of the characteristic polynomial of the adjacency matrix of a hexagonal system and the number of matchings are obtained. (~) 1998 Elsevier Science B.V. All rights reserved

The Hofstadter problem is studied on the hexagonal lattice. We first establish a relation between the spectra for the hexagonal lattice and for its dual lattice, the triangular lattice. Following the idea of Faddeev and Kashaev, we then obtain the Bethe-Ansatz equations for this system.