In a round-dance neighbour design, an odd number v of objects is arranged successively in (v − 1)=2 rings (circular blocks) such that any two of the objects are adjacent to one another in exactly one ring. A round-dance neighbour design is also a Hamiltonian decomposition of the complete graph on v vertices. We show how such designs can be constructed from terraces, which are building blocks fo...

Building an index tree is a common approach to speed up the k nearest neighbour search in large databases of many-dimensional records. Many applications require varying distance metrics by putting a weight on diierent dimensions. The main problem with k nearest neighbour searches using weighted euclidean metrics in a high dimensional space is whether the searches can be done eeciently We presen...

We have carried out a computational study for the nitrogen vacancy in charge states +3, +2 and +1 in AlN in the metastable zinc-blende phase. The vacancy and its four nearest-neighbour Al ions are treated as a molecular cluster, embedded in an infinite classical shell-model crystal. The following ground state properties, all of which are determinable from experiment, have been calculated: total...

In Meshless natura1 neighbour Petrov-Galerkin method, The natural neighbour interpolation is used as trial function and a weak form over the local polygonal sub-domains constructed by Delaunay triangular is used to obtain the discretized system of equilibrium equations, and it’s a new truly meshless method. This method simplified the formation of the equilibrium equations, facilitates the impos...