It is shown that the Clar number can be arbitrarily larger than the cardinality of a maximal alternating set. In particular, a maximal alternating set of a hexagonal system need not contain a maximum cardinality resonant set, thus disproving a previously stated conjecture. It is known that maximum cardinality resonant sets and maximal alternating sets are canonical, but the proofs of these two ...

The thermodynamics and kinetics of the self-assembly of cylinder-forming diblock copolymers directed by the lateral confinement of hexagons have been studied by the combination of self-consistent field theory (SCFT) calculation and time-dependent Ginzburg-Landau (TDGL) theory simulation. The SCFT calculations are used to determine the stability of candidate 2D and 3D equilibrium phases formed i...

In this chapter, a novel receiver for Hexagonal Multicarrier Transmission (HMT) system based on the maximizing Signal-to-Interference-plus-Noise Ratio (Max-SINR) criterion is proposed. Theoretical analyses show that there is a timing offset between the prototype pulses of the proposed Max-SINR receiver and the traditional projection receiver. Meanwhile, the timing offset should be matched to th...

In this paper hexagonal patch shape with hexagonal slot, ultra wideband antenna is proposed. The total dimensions of antenna are 55×43.5mm. Sides of hexagonal patch are taken 13mm each and hexagonal slot sides are taken as 3mm each. The antenna resonates at two frequencies in ultra wideband range (UWB). There is enhancement in BW in upper range ultra wideband frequency from 6.2 GHz to 8.2GHz du...

This paper presents a UV (ultraviolet) lithography apparatus that utilizes an array composed of UV-LED (light emitting diode) collimation modules as a micro-patterning light source for PCB (printed circuit board) fabrication. To provide a uniform (non-uniformity > 90%) and collimated (FWHM < ±2°) exposure area, hexagonal light source modules are disposed in a hexagonal array. Each module is con...

We study the quantum capacitance in a topological insulator thin film system magnetized in the in-plane direction in the presence of an out-of-plane magnetic field and hexagonal warping. To first order, the modification in quantum capacitance due to hexagonal warping compared to the clean case, where both the in-plane magnetization and hexagonal warping are absent, is always negative, and incre...

Orderly arrayed granular crystals exhibit extraordinary capability to tune stress wave propagation. Granular system of higher dimension renders many more stress wave patterns, showing its great potential for physical and engineering applications. At nanoscale, one-dimensionally arranged buckyball (C60) system has shown the ability to support solitary wave. In this paper, stress wave behaviors o...

Spiral Architecture is a relative new and powerful approach to machine vision system. The geometrical arrangement of pixels on Spiral architecture can be described in terms of a hexagonal grid. However, all the existing hardware for capturing image and for displaying image are produced based on rectangular architecture. It has become a serious problem affecting the advanced research on Spiral A...