Exceptional Properties of Second and Third Order Ordinary Differential Equations of Maximal Symmetry

AbstractThe Riccati transformation is used in the reduction of order of second and third order ordinary differential equations of maximal symmetry. The sl(2,R) subalgebra is preserved under this transformation. The Riccati transformation is itself associated with the symmetry that is annihilated in the reduction of order. The solution symmetries and the intrinsically contact symmetries become nonlocal symmetries under the Riccati transformation. We investigate the fate and origins of the contact symmetries arising from the Riccati transformation. The exceptional properties of the second and third order equations of maximal symmetry are indicated. In the context of generalised symmetries we express the solution symmetries, contact symmetries, and the sl(2,R) elements in terms of a Jacobian. We show that a basis for the solution set of equations of maximal symmetry is given in terms of the solution set of a second order ordinary differential equation

Exceptional Properties of Second and Third Order Ordinary Differential Equations of Maximal Symmetry

AbstractThe Riccati transformation is used in the reduction of order of second and third order ordinary differential equations of maximal symmetry. The sl(2,R) subalgebra is preserved under this transformation. The Riccati transformation is itself associated with the symmetry that is annihilated in the reduction of order. The solution symmetries and the intrinsically contact symmetries become nonlocal symmetries under the Riccati transformation. We investigate the fate and origins of the contact symmetries arising from the Riccati transformation. The exceptional properties of the second and third order equations of maximal symmetry are indicated. In the context of generalised symmetries we express the solution symmetries, contact symmetries, and the sl(2,R) elements in terms of a Jacobian. We show that a basis for the solution set of equations of maximal symmetry is given in terms of the solution set of a second order ordinary differential equation

Efficacy of materials used by resource limited farmers in ethno-veterinary control of fleas in free-range chickens in the Eastern Cape Province, South Africa

Fleas are commonly controlled using commercial insecticides which are however expensive and inaccessible to resource-limited farmers. This has resulted in farmers resorting to the use of alternative remedies that are cheap and socially acceptable. However, information on the efficacy of these materials on fleas is lacking. The objectives of this study were to determine potential dermal irritation and efficacy of selected materials used in the control fleas in free-range chickens. The materials tested included used engine oil, Jeyes fluid (carbolic acid 13%), and plant material from Clutia pulchella and Calpurnia aurea. Distilled water and Karbadust (carbaryl 5%) were used as negative and positive controls, respectively. A complete randomized design was used where sixty free-range chickens were allocated to twelve treatment groups with five chickens each. The chickens were artificially infested with fleas, which were counted and recorded daily every morning for seven days. The results show that used engine oil, Jeyes fluid at (76.8%) and C. pulchella (100%) caused flea reduction in the order of 100, 99.8 and 85.5% three days post application of test materials. These reduction was similar to those of Karbadust (carbaryl 5%), a commercial insecticide that had a flea reduction of 100%. C. aurea (100%) and C. pulchella (75%) showed an efficacy of 75.5 and 60%, respectively. The different materials tested exhibited variable efficacy on fleas, where in certain cases it compared well with Karbadust used by farmers. The test materials did not cause any visible signs of irritation on chickens. Despite the efficacy of used engine oil and Jeyes fluid, they are environmental contaminants.Keywords: External parasites, flea control, skin irritation, used engine oilAfrican Journal of Biotechnology Vol. 12(14), pp. 1716-172

Simulations of Woodland Grassland Transitions Caused by Elephant

In South Africa, reintroduction of wildlife on small to medium sized farms is common. A primary concern for the landowners who introduce elephant is the effects they will have on tree and grass densities. It is possible that elephant impact can exacerbate a shift from woodland to grassland. In this paper it is shown how simulations can possibly assist in understanding the possible dynamics involved