The need of polygonal elements to represent the domain is gaining interest among structural engineers. The objective is to perform static analysis and topology optimization of a given continuum domain using the rational fraction type shape functions of six node hexagonal elements. In this paper, the main focus is to perform the topology optimization of two-dimensional plate structures using Evo...

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...

Mobile ad hoc networks usually use various forms of flooding to discover the location and route of a node or to diffuse a given message. Flooding is useful because it finds a good path to a destination or quickly diffuses the message all over the network. With the flooding, however, also comes the problem of propagating many unnecessary messages throughout the network. In this paper, first, we ...

By applying a hexagon-diamond search (HDS) method to an ultrasound image, the path of an object is able to be monitored by extracting images into macro-blocks, thereby achieving image redundancy is reduced from one frame to another, and also ascertaining the motion vector within the parameters searched. The HDS algorithm uses six search points to form the six sides of the hexagon pattern, a cen...

We compare the two-loop corrections to the finite part of the light-like hexagon Wilson loop with the recent numerical results for the finite part of the MHV six-gluon amplitude in N = 4 SYM theory [hep-th]) and demonstrate that they coincide within the error bars and, at the same time, they differ from the BDS ansatz by a non-trivial function of (dual) conformal kinematical invariants. This pr...

Erdős asked whether every sufficiently large set of points in general position in the plane contains six points that form a convex hexagon without any points from the set in its interior. Such a configuration is called an empty convex hexagon. In this paper, we answer the question in the affirmative. We show that every set that contains the vertex set of a convex 9-gon also contains an empty co...

WSNs are energy constrained, and recent works are being carried out by many engineers and scientists to make the WSNs more energy efficient. Primarily, WSNs can be categorized into two types: random and deterministic. We have concentrated our research interest to design an energy efficient deterministic WSN. In this paper, a Seven Node Hexagonal Deployment (SNHD) scheme is proposed i.e. hexagon...

Cellular networks are generally modeled as node-weighted graphs, where the nodes represent cells and the edges represent the possibility of radio interference. An algorithm for the channel assignment problem must assign as many channels as the weight indicates to every node, such that any two channels assigned to the same node satisfy the co-site constraint, and any two channels assigned to adj...

Paul Erdős’s Empty Hexagon Problem asks if there exists a number H(6) such that for all sets of n ≥ H points in general position on the plane six of the points form the vertices of an empty convex hexagon. This problem is open.