In this paper the degree of approximation function f, which is periodic with respect to hexagon lattice by matrix means T(A)n(f) its hexagonal Fourier series in generalized H?lder metric, where A a lower triangular infinite nonnegative real numbers nonincreasing row estimated.

It is shown that gravitational lensing by point masses arranged in an infinitely extended regular lattice can be studied analytically using the Weierstrass functions. In particular, we draw the critical curves and the caustic networks for the lenses arranged in regular-polygonal – square, equilateral triangle, regular hexagon – grids. From this, the mean number of positive parity images as a fu...

Multistrategy Learning of Self-Organizing Map (SOM) and Particle Swarm Optimization (PSO) is commonly implemented in clustering domain due to its capabilities in handling complex data characteristics. However, some of these multistrategy learning architectures have weaknesses such as slow convergence time always being trapped in the local minima. This paper proposes multistrategy learning of SO...

An efficient numerical method is developed for computing the transmission and reflection spectra of finite two-dimensional photonic crystals composed of circular cylinders in a triangular lattice. Our method manipulates a pair of operators defined on a set of curves and it remains effective when the radius of the cylinders is larger than √ 3/4 of the lattice constant — a condition where differe...

We propose a simple family of valence-bond crystals as potential ground states the $S=1/2$ and $S=1$ Heisenberg antiferromagnet on pyrochlore lattice. Exponentially numerous in linear size system, these can be visualized hard-hexagon coverings, with each hexagon representing resonating ring. This ensemble spontaneously breaks rotation, inversion, translation symmetries. A simple, yet accurate, ...

Jaeger’s directed cycle double cover conjecture can be formulated as a problem of existence of special perfect matchings in a class of graphs that we call hexagon graphs. In this work, we explore the structure of hexagon graphs. We show that hexagon graphs are braces that can be generated from the ladder on 8 vertices using two types of McCuaig’s augmentations.

Currently, wireless sensor network (WSN) is being applied in a lot of different applications. To a large extent the effectiveness of the WSNs depends on the exposure provided by the sensor deployment proposal. There are different deployment demands in different environment. Firstly, we cover the existing deployment method of sensor nodes (SNs) in WSN. We investigate random and deterministic sen...

Let a, b and c be positive integers and consider a hexagon with side lengths a,b,c,a,b,c whose angles are 120◦ (see Figure 1). The subject of our interest is rhombus tilings of such a hexagon using rhombi with all sides of length 1 and angles 60◦ and 120◦. Figure 2 shows an example of a rhombus tiling of a hexagon with a = 3, b = 5 and c = 4. A first natural question to be asked is how many rho...

There are many long-standing open problems on cubic bridgeless graphs, for instance, Jaeger’s directed cycle double cover conjecture. On the other hand, many structural properties of braces have been recently discovered. In this work, we bijectively map the cubic bridgeless graphs to braces which we call the hexagon graphs, and explore the structure of hexagon graphs. We show that hexagon graph...