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Quenched and annealed heat kernel estimates are established for Fontes–Isopi–Newman (FIN) processes on spaces equipped with a resistance form. These results are new even in the case of the one-dimensional FIN diffusion, and also apply to fractals such as the Sierpinski gasket and carpet. [ABSTRACT FROM AUTHOR]

Abstract: Objective: This study has been designed to evaluate the interaction of axial wall heights with inclination angles in full crown tooth preparations. The interaction of these parameters was related to the resulting preparation surface area. Materials and methods: A right regular pyramid was used to simulate a single mandibular molar preparation with known convergence angles and vertical heights. Various combinations of these two variables allowed the calculation of surface areas with a formula for the area of a pyramid and right triangles through trigonometric manipulations. The pyramidal model system had a 9-mm square base with vertical heights from 3- to 5-mm and single-side inclination angles from 2 to 25°. The occlusal surface was a flat, square or rectangular surface and was included in the total area. Results: A percentage of surface area lost or gained served as the dependent variables. The significance levels were set at 10.0% or greater magnitude of loss/gain in a surface area compared to the ideal 2°-level. Significant area loss was demonstrated in all α-level comparisons. The largest change was found in the 5-mm height grouping compared to the 3-mm height grouping, −36.6% difference between groups at the 2°-level. Conclusions: Axial single-side inclination angles greater than 10° in 3- and 4-mm height-molars are detrimental to maximum surface area in full crown restorations. The 5-mm axial wall height with ≤10° single wall has been shown to maximize the luting agent surface area between restoration and tooth structure. [Copyright &y& Elsevier]