Decay chain differential equations: Solution through matrix algebra

A matricial method to solve the decay chain differential equations system is presented. The quantity of each nuclide in the chain at a time t may be evaluated by analytical expressions obtained in a simple way using recurrence relations. This method may be applied to problems of radioactive buildup and decay and can be easily implemented computationally. (C) 2009 Elsevier B.V. All rights reserved.

Evaluation of the presence or absence of papilla between tooth and implant

Objective: The purpose of this study was to evaluate the papilla level adjacent to single-tooth implants in the maxillary anterior region in individuals with cleft lip, alveolus, and palate to verify whether there is correlation among the vertical distance, horizontal distance, dental/prosthetic crown shape, and periodontal/peri-implant biotype with the presence of interproximal papilla. Design: Cross-sectional. Setting: Hospital for Rehabilitation of Craniofacial Anomalies, University of Sao Paulo (HRAC/USP). Patients: 77 papillae in 40 patients. Interventions: The periodontal/peri-implant biotype was clinically evaluated and characterized as thin or thick. Intraoral photographs were used to evaluate the presence or absence of papilla. Main Outcome Measures: Classification in scores (0 to 3) and determination of length (CL) and width (CW) of crowns adjacent to papillae. The CW/CL ratio was calculated for each crown in order to characterize it as square-shaped or triangular-shaped. The vertical and horizontal distances were obtained by radiographic evaluation. Results: The correlations between vertical distance and papilla score and horizontal distance and papilla score were statistically significant (p= .02 and p = .01). There was no significant difference between crown shape and periodontal/peri-implant biotype in distinct correlations with the papilla score (p = .41 and p = .07). Conclusion: The results suggest that the vertical and horizontal distances may have independent or combined relationship with the existence of interproximal papilla; the periodontal/peri-implant biotype (phenotype) was not correlated with the presence or absence of papilla, as well as the shape of the dental/prosthetic crown.