in this paper we present explicit formulas for the eccentric connectivity index of three classesof chain hexagonal cacti. further, it is shown that the extremal chain hexagonal cacti withrespect to the eccentric connectivity index belong to one of the considered types. some openproblems and possible directions of further research are mentioned in the concluding section.

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. Recently there has been a renewed interest in the use of hexagonal images: biologically inspired approaches, representation of architectures for such images and general hexagonal image processing. We present multiscale hexagonal gradient...

The development of new polymerizable lyotropic liquid crystals (LLCs) utilizing charged amphiphilic molecules such as those based on long chain imidazolium compounds, is a relatively new design direction for producing robust membranes with controllable nano-structures. Here we have developed a novel polymerizable ionic liquid based LLC, 1-hexadecyl-3-methylimidazolium acrylate (C16mimAcr), wher...

We describe a bijection between hexagonal lattice animals and a special type of square lattice animals. Using this bijection we adopt Maple packages that automatically generates generating functions (and series expansions) for fixed square lattice lattice animals to that of fixed hexagonal animals on the two-dimensional hexagonal lattice confined to a strip 0 ≤ y ≤ k, for arbitrary k. In [Z1], ...

We propose a graphics processor unit (GPU)-accelerated method for real-time computing and rendering cellular automata (CA) that is applied to hexagonal grids. Based on our previous work [9] –which introduced first and second dimensional cases– this paper presents a model for hexagonal grid algorithms. Proposed method is novel and it encodes and transmits large CA key-codes to the graphics card ...

Using a real space implementation of the self-consistent field theory for the polymeric system, we explore microphases of ABC linear triblock copolymers. For the sake of numerical tractability, the calculation is carried out in a two-dimensional (2D) space. Seven microphases are found to be stable for the ABC triblock copolymer in 2D, which include lamellae, hexagonal lattice, core-shell hexago...

We report on the residual stresses in amorphous shape memory polymers reinforced with SiC particles. After 50% compression of the composite material at 25 °C, the SiC particles exhibit a compressive stress, which is almost completely released during heated recovery at 120 °C. The residual stresses in SiC hexagonal (6H) phase were estimated through the average change of the unit-cell volume. Lat...

The thin plate is a key structure in various musical instruments, including many percussion instruments and the soundboard of the piano, and also is the mechanism underlying electromechanical plate reverberation. As such, it is a suitable candidate for physical modelling approaches to audio effects and sound synthesis, such as finite difference methods—though great attention must be paid to the...