ABSTRACT
Objective To establish a mathematical model to describe the skeletal class Ⅲ malocclusion of patient dental and basal bone arch form, for providing a data reference and basis for further study. Methods Thirty-five patients with skeletal classⅢmalocclusion were selected in this study for computed tomography CBCT. The data of 3-D image were analyzed, and dental arch marker (Fa) and base bone arch marker (Ba) were determined. The reference plane was determined by least square method. Software Matlab 7.0 was used to calculate two-dimensional coordinate system. Based on this, a mathematical model was established to describe the dental and basal bone arch form and then to validate the mathematical model. Results (1) The mathematical model can be used to describe the dental arch form of skeletal classⅢmalocclusion, maxillary:Y=46.12 [1-(2X/70.99)2]1.052;mandibular:Y=39.16 [1-(2X/64.51)2]1.038. (2) The mathematical model can be used to describe the basal bone arch form of skeletal classⅢmalocclusion, maxillary:Y=43.14 [1-(2X/75.09)2]1.061;mandibular:Y=39.03 [1-(2X/60.63)2]1.021. (3) Fa was located at Ba labial side in the maxilla, the distance was positive. Fa was located at Ba lingual side in the mandibular, and the distance was negative. (4) The fitting correlation coefficient of beta-function curve and each tooth on the dental and basal bone arch of skeletal class Ⅲ malocclusion were greater than 0.7 (P<0.05). Conclusion In this study, the mathematical model can be used to describe the dental and basal bone arch form of the skeletal classⅢmalocclusion, which can guide further research.
ABSTRACT
The Beta, Gamma and Weibull distribution function were studied in ten hectares of a "terra-firme" rainforest (Madeireira Dois Mil Co.) in Itacoatiara, Amazonas, Brazil. Measurements were made on 2035 trees with DBH 20 cm. Functions were compared by the Kolmogorov-Smirnov (K-S) and Residual Graphic Analysis (RGA) methods. The Weibull function performed best, followed by the Beta and Gamma function, when compared by the 'D' value of the K-S test. The Weibull and Beta functions were significant at 5%, while the Gamma was not significant, according to the K-S test. No outliers were detected for the Weibull function using RGA, indicating that variances were uniform across diameter classes, suggesting good fit of this function to this site. The Beta function can be used, but presents some bias. The Gamma function is not recommended.
Foram estudadas as funções de distribuição Beta, Gama e Weibull em dez hectares de floresta tropical úmida de terra-firme da Madeireira Dois Mil, localizada no município de Itacoatiara, Amazonas, Brasil. Foram medidas todas as árvores com DAP 20 cm num total de 2.035 indivíduos. Para avaliar a função que melhor ajustou a distribuição de diâmetros nesta floresta foi utilizado o teste de Kolmogorov-Smirnov e a Análise gráfica dos resíduos. O menor valor de "D" do teste Kolmogorov-Smirnov foi encontrado para a função Weibull, seguido da função Beta e por último da função Gama. As funções Weibull e Beta foram significativas ao nível de 5% de probabilidade pelo teste de Kolmogorov-Smirnov, mas a Gama foi não significativa. Pela análise gráfica dos resíduos foi encontrado também melhor resultado para a função Weibull, pois não apresentou pontos discrepantes, ocorrendo para todas as classes uma variância uniforme dos pontos em torno da linha. Desta forma, a função Weibull foi a que apresentou melhor ajuste. A função Beta pode ser utilizada, porém para algumas classes podem ocorrer subestimativas. A função Gama não é recomendada.