Indiana University-Purdue University Indianapolis (IUPUI) / Background. Beam profile non-uniformity of light-curing units (LCUs) may result in suboptimal properties of resin-matrix composite (RMC) restorations. Objectives: The objective of this study was to evaluate the effect of curing-light beam profile of multiple light curing units (LCUs) on the degree of conversion (DC) and micro-flexural strength (μ-flexural strength) of RMC. Methods: Forty-five nano-filled hybrid RMC (Tetric EvoCeram, Ivoclar Vivadent, Amherst, NY) specimens were fabricated. Quartz tungsten halogen (QTH) (Optilux 401) (O), multiple emission peak (VALO Cordless) (V) and single emission peak (Demi Ultra) (DU) light-emitting-diode (LED) LCUs were investigated at different light-curing locations (LCLs): 1) the center of the LCU tip; 2) 1.5 mm to the left of the center of the LCU tip; and 3) 1.5 mm to the right of the center of the LCU tip. Specimens were stored wet in deionized water at 37C for 24 hours. The DC was measured on top and bottom surfaces using Attenuated Total Reflectance-Fourier Transform Infrared (ATR-FTIR) spectroscopy. Micro-flexural strength testing was performed using a universal mechanical testing machine at crosshead speed of 1 mm/min. Multi-factorial ANOVAs were used to analyze the data (α = 0.05). Results: All LCUs exhibited significant differences in DC between top and bottom surfaces at the different LCLs. Micro-flexural strength varied with LCL for DU. Conclusions: The non-uniform curing-light beam profile could have a significant effect on μ-flexural strength and DC on top and bottom surfaces of RMC specimens cured at different LCLs.

This thesis concerns an active research area within fractal geometry. In the first part, in Chapters 2 and 3, for directed graph iterated function systems (IFSs) defined on ℝ, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of standard (1-vertex directed graph) IFSs, with or without separation conditions. We also calculate their exact Hausdorff measure. Thus we are able to identify a new class of attractors for which the exact Hausdorff measure is known. We give a constructive algorithm for calculating the set of gap lengths of any attractor as a finite union of cosets of finitely generated semigroups of positive real numbers. The generators of these semigroups are contracting similarity ratios of simple cycles in the directed graph. The algorithm works for any IFS defined on ℝ with no limit on the number of vertices in the directed graph, provided a separation condition holds. The second part, in Chapter 4, applies to directed graph IFSs defined on ℝⁿ . We obtain an explicit calculable value for the power law behaviour as r → 0⁺ , of the qth packing moment of μ[subscript(u)], the self-similar measure at a vertex u, for the non-lattice case, with a corresponding limit for the lattice case. We do this (i) for any q ∈ ℝ if the strong separation condition holds, (ii) for q ≥ 0 if the weaker open set condition holds and a specified non-negative matrix associated with the system is irreducible. In the non-lattice case this enables the rate of convergence of the packing L[superscript(q)]-spectrum of μ[subscript(u)] to be determined. We also show, for (ii) but allowing q ∈ ℝ, that the upper multifractal q box-dimension with respect to μ[subscript(u)], of the set consisting of all the intersections of the components of F[subscript(u)], is strictly less than the multifractal q Hausdorff dimension with respect to μ[subscript(u)] of F[subscript(u)].