Topological Cordial Labeling of Some Graphs

A topological cordial labeling of a graph G = (V(G), E(G)) with |V(G)| = n is an injective function f :V(G) →2X where X is any non – empty set such that |X| < n and {f(V(G))} forms a topology on X, that induces a function f*: E(G) →{0,1} defined by f*(uv) = 1 if f(u)∩f(v) is not an empty set and not a singleton set and 0 otherwise for all uv ϵ E(G) such that |ef (0) – ef (1)| ≤ 1, where ef (0) = number of edges labelled with 0 and ef (1) = number of edges labelled with 1. The graph which admits a topological cordial labeling is called a topological cordial graph. In this paper, topological cordial labeling of some special graphs are discussed

Study of Mach reflection in inviscid flows

In this paper, we study the Mach reflection phenomenon in inviscid flows using a higher order discontinuous Galerkin method and overset grids. We use the shock capturing procedure proposed in Siva Prasad Kochi et al. using overset grids to capture the discontinuities occurring in the supersonic flow over a wedge accurately. In this procedure, we obtain a coarse grid solution first and using the troubled cell data, we construct an overset grid which is approximately aligned to all the discontinuities. We rerun the solver with the coarse grid solution as the initial condition while using the troubled cell indicator and the limiter only on the overset grid. This allows us to capture the discontinuities accurately. Using this procedure, we have obtained the solution for Mach $3.0$ and $4.0$ flow over a wedge for various wedge angles and determined the detachment criterion and the Von Neumann condition accurately. We have also determined the Mach stem height for various wedge angles for these Mach numbers. We have also demonstrated the hysteresis that occurs in the transition from regular reflection to Mach reflection.Comment: 11 pages, 8 Figures, 2 Table

Evidence for reversion towards anthelmintic susceptibility in Teladorsagia circumcincta in response to resistance management programmes

AbstractMaintaining production and economic viability in the face of resistance to multiple anthelmintic actives is a challenge for farmers in many countries. In this situation, most farmers in New Zealand rely on the use of combination products, containing multiple actives with similar spectra of activity, in order to maintain control. However, there are concerns that use of combinations, once resistance has already developed to the individual actives, could rapidly lead to complete failure of all actives. This study followed seven farms, previously diagnosed with resistance to at least two classes of anthelmintic, which were implementing a tailored programme of ‘best practice parasite management’. The aim was to ascertain whether the programmes, which included the almost exclusive use of combination anthelmintics, were able to prevent resistance from developing further. Strategies implemented on each farm varied, but had consistent underlying principles i.e. to avoid over-use of anthelmintics; to minimise parasite challenge to susceptible stock; to maintain refugia of susceptibility and to ensure that only effective anthelmintics were used. Annual faecal egg count reduction tests (FECRT) were undertaken in lambs on all farms to monitor anthelmintic efficacy over 5 years. The efficacy of albendazole, ivermectin and levamisole was calculated and the changes in efficacy against Teladorsagia circumcincta assessed. Overall, there was a significant improvement in the effectiveness of both levamisole and ivermectin against T. circumcincta, and a positive but non-significant trend in efficacy of albendazole, i.e. there was evidence for reversion towards susceptibility. Hence, the almost exclusive use of combination anthelmintics, integrated with other resistance management strategies, did not result in further resistance development despite all farms exhibiting resistance to multiple actives at the outset. What-is-more, the measured increases in anthelmintic efficacy suggests that adoption of best practice management strategies may extend the useful life of anthelmintics even after resistance has been diagnosed