The problem addressed is the distributed reconfiguration of a system of two-dimensional, hexagonal mobile robots (modules), from an initial straight chain into an arbitrary shaped, connected goal configuration that satisfies a simple admissibility condition. We present algorithms that improve the efficiency of the deterministic algorithms presented in [16] and [15]. In this paper, we first pres...

The efficient compression of depth maps is becoming more and more important. We present a novel codec specifically suited for this task. In the encoding step we segment the image and extract betweenpixel contours. Subsequently we optimise the grey values at carefully selected mask points, including both hexagonal grid locations as well as freely chosen points. We use a chain code to store the c...

A combination of grazing incidence X-ray reflection/diffraction (GIXR/GIXD) and atomic force microscopy have been used to study the 3D structure in cadmium arachidate (CdA) and single phase zinc arachidate (ZnA) LB multilayers. The CdA multilayers have an ideal close packed herringbone structure. The molecules have a non-centred in-plane arrangement with specific orientational relation between ...

An edge cover C of an undirected graph is a set of edges such that every vertex has an adjacent edge in C. We show that a Glauber dynamics Markov chain for edge covers mixes rapidly for graphs with degrees at most three. Glauber dynamics have been studied extensively in the statistical physics community, with special emphasis on lattice graphs. Our results apply, for example, to the hexagonal l...

Textures in the hexagonal metals have attracted significant interest over the years because of the use of some hexagonal metals and alloys, e.g. Zircaloy cladding for nuclear reactor fuels, Ti alloys for aerospace and aircraft industry, and Mg alloys for automobile and computer, communication and consumer electronic (3C) appliances. From a mechanistic point of view, hexagonal metals are differe...

The Design of hexagonal patch is presented withsingle coaxial feed namelysimple hexagonalpatch,hexagonal patch with one triangular slot in ground for circular polarization. The circular polarization of two antennas are obtained with 1.31% axial ratio(AR) for simple hexagonal patch, 4.43% axial ratio hexagonal patch with slotted ground hexagonal patch antenna. The impedance band widths of these ...

A new microporous lanthanide metal-organic framework, {[Yb(BTB)(H2O) (DEF)2}n (1, DEF=N,N-Diethylformamide), with 1D nano-sized channels has been constructed by bridging helical chain secondary building units with 1,3,5-benzenetrisbenzoic acid (H3BTB) ligand. Structural characterization suggests that this complex crystallizes in the hexagonal space group P6122 and possesses 1D triangular channe...

We have studied the self-assembly of amphiphilic dendrons extended with linear polyethylene oxide (PEO) chains and their ion complexes. Keeping the dendron core and linear PEO chain compatible allows for the combination of dendritic core-shell and conventional blockcopolymer characteristics for complex mesophase behavior. An unexpected sequence of crystalline lamellar, cubic micellar (Pm3n), he...

The problem addressed is the distributed reconfiguration of a metamorphic robotic system composed of an arbitrary number of two dimensional hexagonal robots (modules) from specific initial to specific goal configurations. The initial configuration considered is a straight chain of robotic modules, while the goal configurations considered satisfy a more general “admissibility” condition. A centr...

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...