This paper introduces graph polynomials based on a concept from the game of Go. Suppose that, for each vertex of a graph, we either leave it uncoloured or choose a colour uniformly at random from aâ€¦ (More)

Under suitable recursive conditions, the conjugacy problem for HNN extensions of the form ( G, (,,;'â‚¬/: xk' = t~' xl> tj, k,â– â– , / > 1, /' 6 / ) is solvable if and only if the inverse subsemigroupâ€¦ (More)

The chromatic polynomial P (G, Î») gives the number of proper colourings of a graph G in at most Î» colours. If P (G, Î») = P (H1, Î»)P (H2, Î») /P (Kr, Î»), then G is said to have a chromaticâ€¦ (More)

Improper inhalation technique with beta-agonist metered-dose inhalers (MDIs) decreases efficacy of the bronchodilator. The success of demonstrating the correct technique and the pharmacist's role inâ€¦ (More)