Assessment of the convergence angle of teeth prepared for full crown by preclinical dental students

The objective of this study was to measure the buccolingual and mesiodistal convergence angles of six typodont teeth (# 26, 36, 45, 15, 21, and 13), prepared by preclinical dental students at Ajman University, for porcelain fused to a metal full crown and to compare them with the recommended convergence angle (6.5°). Additionally, we sought to compare the angles recorded for the six sets of teeth and relate the results according to the tooth position and surface and to know which one shows the greater tendency of straying from the normal convergence angle. Materials and methods: The angle of convergence of one hundred ninety-eight typodont teeth preparations was measured both buccolingually and mesiodistally by using a Dino-lite pro digital microscope (AM-413ZT Taiwan) with a Dinocapture (2.0 version 1.5.27.A, AnMo Electronics Corporation). All the results were recorded, and the data were analyzed by means of a one-sample t-test and one-way ANOVA. Results: The mean total convergence angle for this study was 11.29°± 6.66° from both surfaces, which is greater than the recommended value of 6.5° and statistically significant (p<0.000). Only 7.07% of teeth met the ideal convergence angle from both surfaces, and the one-sample test showed a statistically significant difference (p<0.057) from the recommended convergence angle, except for the mesiodistal convergence angle of the lower-right second premolar, which revealed no significant difference. The mean convergence angle for the buccolingual surface was 12.42°± 6.16°, which was higher than that of the mesiodistal surface (10.16°± 7°). One-way ANOVA showed a significant difference between all selected teeth (p<0.000), and a paired samples t-test showed a significant difference within two teeth only, the lower-right second premolar and upper-right canine (p<0.000), in which the mesiodistal measurement showed a lower convergence angle than the buccolingual angle. Conclusions: Preclinical students prepared teeth with a convergence angle higher than the recommended convergence angle. However, all the recorded angles were within the range of previous studies. It was concluded that the recommended convergence angle was difficult to achieve in preclinical practice.

Mean Convergence of Entire Interpolations in Weighted Space

We investigate the convergence of entire Lagrange interpolations and of Hermite interpolations of exponential type $$\tau $$ τ , as $$\tau \rightarrow \infty $$ τ → ∞ , in weighted $$L^p$$ L p -spaces on the real line. The weights are reciprocals of entire functions that depend on $$\tau $$ τ and may be viewed as smoothed versions of a target weight w. The convergence statements are obtained from weighted Marcinkiewicz inequalities for entire functions. We apply our main results to deal with power weights.

On mean convergence of Fourier-Jacobi series

We establish the order of growth of modified Lebesgue constants of Fourier-Jacobi sums in $L_{p,w}$ spaces.

Convergence of Complex Uncertain Double Sequences

Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities. This paper introduces the convergence concepts of convergence almost surely (a.s.), convergence in measure, convergence in mean, convergence in distribution and convergence uniformly almost surely complex uncertain double sequences. In addition, relationships among the introduced classes of sequences have been introduced.