The lattice Boltzmann method (LBM) has recently become an alternative and promising computational fluid dynamics approach for simulating complex fluid flows. Despite its enormous success in many practical applications, the standard LBM is restricted to the lattice uniformity in the physical space. This is the main drawback of the standard LBM for flow problems with complex geometry. Several app...

The purpose of the paper is to develop a new method for obtaining explicit formulas for the error of approximation of bivariate functions by sums of univariate functions. It should be remarked that formulas of this type have been known only for functions defined on a rectangle with sides parallel to coordinate axes. Our method, based on a maximization process over closed bolts, allows the consi...

In this paper, we study deployment patterns to achieve full coverage and -connectivity under different ratios of the sensor communication range (denoted by ) to the sensing range (denoted by ) for homogeneous wireless sensor networks (WSNs). In particular, we propose new patterns for 3and 5-connectivity. We also discover that there exists a hexagon-based universally elemental pattern that can g...

Grid and block-based motion vector estimation techniques are proposed for motion tracking in video sequences. The grid technique is referred to the hexagon-diamond pattern. While, block-based technique is referred to 16 × 16 pixels of blocks in a single frame in video sequences. The hexagon and diamond pattern is applied onto the 16 × 16 pixels blocks in a single frame for motion tracking purpo...

A hexagon quadrangle system of order n and index [HQS (n)] is a pair (X,H), where X is a finite set of n vertices and H is a collection of edge disjoint hexagon quadrangles (called blocks) which partitions the edge set of Kn, with vertex set X. A hexagon quadrangle system is said to be a 4-nesting [N(4) − HQS] if the collection of all the 4-cycles contained in the hexagon quadrangles is a /2-fo...

In this article, we study the question of tilings on a hexagon mesh with balanced 3-tiles. This problem has been studied by Conway and Lagarias in [CL90], by studying the tiling groups, in fact a group containing the tiling-groups, and their Cayley graphs. We will use two different approaches. The first one is based on matchings in bipartite graphs, which in this case are in correspondance with...

We have developed a method for quantifying the number, spacing, and distribution of stereocilia on the apical surface of hair cells using spatial autocorrelation analysis and statistics for directional data. Here, we illustrate the method using idealized hair bundles, and we apply it to scanning micrographs of turtle hair cells from the utricle and posterior canal, and to freeze-fracture prepar...

This paper presents a review related to Cloud Computing focusing on Cloud business requirements. From the review we recommend a number of methods managing Cloud services and evaluating its service performance, including the use of a pair of the Hexagon Models. Three organizational challenges of Cloud adoption are identified: (i) Organizational Sustainability; (ii) Portability and (iii) Linkage....

A long-standing conjecture in combinatorics, made by Erdős and Simonovits, is that the maximum number of edges in an n-vertex graph without a hexagon is asymptotically 1 2n 4/3 as n→∞. This conjecture corresponds to the asymptotic optimality of constructions of generalized quadrangles as a source of dense hexagon-free graphs. In this paper, we construct a counterexample to this conjecture. For ...