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A previous paper [4] shows how the connection parameters for tangent simple p-vectors of a manifold can be split into p vectors and certain definite elements γ. In this paper the ensuing differential geometry is extended to the properties of both contra- and covariant simple p- and (n-p)-vectors of this manifold. The five new invariant derivatives are proved to be similarly composed of a set of vectors and their derivatives. These allow for a simplified expression for the Gauss and Weingarten equations and consequently for the first variations of the respective areas and for the necessary minimal conditions. [ABSTRACT FROM AUTHOR]

Purpose: To evaluate the survival and clinical quality of individually layered indirect composite restorations (ICRs) in the mixed and permanent dentition at two study centers., Materials and Methods: A total of 155 adhesively cemented ICRs in 34 participants (aged 6 to 50 years and treated between 2008 and 2018) were evaluated for survival and clinical quality. All were individually layered restorations fabricated from laboratory sculptable composites by a specialized dental technician. Two calibrated independent investigators examined and graded each restoration as success, survival with repair, or failure based on the FDI criteria. The marginal quality and gap width of the restorations were analyzed by scanning electron microscopy. The periodontal health of treated teeth (TT) was evaluated in comparison with that of unrestored control teeth (CT) by measuring the pocket depth (PD), clinical attachment level (CAL), sulcus bleeding index (SBI), and the modified Turesky Plaque Index (TPI). A serial t-test (p 0.05) was used for statistical analysis of periodontal parameters. Success and functional survival rates were calculated using the Kaplan-Meier method., Results: Molar incisor hypomineralization (MIH) was the most common indication for treatment (41%). The median age at treatment was 14.9 years (68%-CI: 7.7-29.5). The median service time of the restorations was 5.7 ± 3.4 years. 132 restorations were classified as a success, 21 as survival with repair, and 1 as a failure. The success rates at 1, 5, and 10 years were 95.4%, 87.4%, and 78.8%, respectively, and the corresponding functional survival rates were 100.0%, 98.9%, and 98.9%. The clinical quality, encompassing esthetic, functional, and biological criteria, was rated as excellent or good in over 90%. Periodontal response, however, was the only criterion showing worse results since restored teeth (TPI = 1.9) had significantly more plaque than CT (TPI = 1.7; p = 0.0001). No significant differences were observed in PD, CAL, or SBI. The mean marginal gap width was 135.7 µm and 63.8% of the restorations had perfect margins., Conclusion: ICRs are suitable for minimally invasive restoration of large tooth structure defects in the developing dentition of children and adolescents and for long-term temporary restoration of the adult dentition.

Competing Interests: Die Autorinnen/Autoren geben an, dass kein Interessenkonflikt besteht.