The effect of variability in the powder/liquid ratio on the strength of zinc phosphate cement

Aim: To investigate (a) variability in powder/liquid proportioning (b) effect of the extremes of any such variability on diametral tensile strength (DTS), in a commercial zinc phosphate cement. Statistical analyses (a = 0.05) were by Student's t-test in the case of powder/liquid ratio and one-way ANOVA and Tukey HSD for for pair-wise comparisons of mean DTS. The Null hypotheses were that (a) the powder-liquid mixing ratios observed would not differ from the manufacturer's recommended ratio (b) DTS of the set cement samples using the extreme powder/liquid ratios observed would not differ from those made using the manufacturer's recommended ratio. Methodology: Thirty-four undergraduate dental students dispensed the components according to the manufacturer's instructions. The maximum and minimum powder/liquid ratios (m/m), together with the manufacturer's recommended ratio (m/m), were used to prepare cylindrical samples (n = 3 x 34) for DTS testing. Results: Powder/liquid ratios ranged from 2.386 to 1.018.The mean ratio (1.644 (341) m/m) was not significantly different from the manufacturer's recommended value of 1.718 (p=0.189). DTS values for the maximum and minimum ratios (m/m), respectively, were both significantly different from each other (p<0.001) and from the mean value obtained from the manufacturer's recommended ratio (m/m) (p<0.001). Conclusions: Variability exists in powder/liquid ratio (m/m) for hand dispensed zinc phosphate cement. This variability can affect the DTS of the set material.

Uniformly convergent finite element and finite difference methods for singularly perturbed ordinary differential equations

This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.