G3 Shape Adjustable GHT-Bézier Developable Surfaces and Their Applications

In this article, we proposed a novel method for the construction of generalized hybrid trigonometric (GHT-Bézier) developable surfaces to tackle the issue of modeling and shape designing in engineering. The GHT-Bézier developable surface is obtained by using the duality principle between the points and planes with GHT-Bézier curve. With different shape control parameters in their domain, a class of GHT-Bézier developable surfaces can be established (such as enveloping developable GHT-Bézier surfaces, spine curve developable GHT-Bézier surfaces, geodesic interpolating surfaces for GHT-Bézier surface and developable GHT-Bézier canal surfaces), which possess many properties of GHT-Bézier surfaces. By changing the values of shape parameters the effect on the developable surface is obvious. In addition, some useful geometric properties of GHT-Bézier developable surface and the G1, G2 (Farin-Boehm and Beta) and G3 continuity conditions between any two GHT-Bézier developable surfaces are derived. Furthermore, various useful and representative numerical examples demonstrate the convenience and efficiency of the proposed method.

Comparison of Anti-Bacterial Efficacy between Passive Ultrasonic Irrigation and 980 nm-GaAlAs Laser Application in Two Root Types

Background and Objectives: The purpose of the present study was to investigate the anti-bacterial efficacy of passive ultrasonic irrigation (PUI) and a 980-nm-gallium-aluminum-arsenide (GaAlAs) laser using a real-time DNA-based quantitative polymerase chain reaction (qPCR) assay and scanning electron microscopy (SEM). Materials and Methods: Eighty-six extracted single- and double-rooted human teeth were used in the experiment. The following four experimental groups were evaluated, as well as a control group: group 1: single root + PUI (n = 20); group 2: single root + laser application (n = 20); group 3: double roots + PUI (n = 20); group 4: double roots + laser application (n =20); control group (n = 6): 3 single roots, 3 double roots. The qPCR assay was performed in three stages to evaluate the efficacy of the adjunctive method against Enterococcus faecalis. SEM analysis was also used to examine the microstructure of root canal surfaces. The data were statistically analyzed using the Friedman test and the Kruskal–Wallis test with Bonferroni adjustment. Results: The decrease in the DNA levels from S1 (before preparation) to S2 (just after preparation) was highly significant in all groups, and decreases in DNA levels from S2 to S3 (after incubation for 1 week) were found in all experimental groups except group 1. An inter-group analysis showed that PUI was significantly more effective in terms of antibacterial efficacy than GaAlAs laser irradiation in single root (p < 0.05). However, in double roots, experimental groups did not show significantly lower DNA levels than the control group (p > 0.05). SEM images showed that cleaning of the root canal surface and reduction of dentin debris were achieved only in single-rooted teeth when using PUI application. Conclusions: Two adjunctive methods were effective in reducing E. faecalis in single rooted tooth.

Efficacy of EDDY, passive ultrasonic irrigation and manual irrigation on the removal of orange-brown precipitate

Aim: The aim of this study was to compare the different irrigation activation techniques for removing the orange-precipitate formed after irrigation with sodium hypochlorite (NaOCl) and chlorhexidine (CHX). Methodology: In total, 45-single rooted extracted human teeth were prepared with the ProTaper NEXT rotary system. The roots were respectively irrigated with 5% NaOCl and 2% CHX solutions, and an orange-precipitate formed on the canal walls. The teeth were divided longitudinally, and the precipitate was evaluated with a dental operating microscope (DOM) at 16x magnification before the sections were joined. The halves of roots were then combined, and EDDY, passive ultrasonic activation (PUI) and manual irrigation (MI) techniques were applied for 1 min with 5 ml of distilled water to remove the precipitate. The halves were re-evaluated under the DOM and the residual of percentage of precipitate removed was calculated. The data were evaluated statistically by Kruskal-Wallis tests. Results: A residual orange-precipitate was found in all groups. Although the orange precipitate was effectively removed in the EDDY group, there was no statistically significant difference among EDDY, PUI and MI (p> 0.05). Conclusions: None of the techniques used completely removed the orange precipitate from the root canal surfaces. Among the irrigation activation techniques, there was no superior technique for removing the orange-precipitate from the root canals. How to cite this article: İnce Yusufoglu S, Keskin NB. Efficacy of EDDY, passive ultrasonic ırrigation and manual irrigation on the removal of orange-brown precipitate. Int Dent Res 2021;11(1):1-5. https://doi.org/10.5577/intdentres.2021.vol11.no1.1 Linguistic Revision: The English in this manuscript has been checked by at least two professional editors, both native speakers of English.

Surfaces of Revolution and Canal Surfaces with Generalized Cheng–Yau 1-Type Gauss Maps

In the present work, the notion of generalized Cheng–Yau 1-type Gauss map is proposed, which is similar to the idea of generalized 1-type Gauss maps. Based on this concept, the surfaces of revolution and the canal surfaces in the Euclidean three-space are classified. First of all, we show that the Gauss map of any surfaces of revolution with a unit speed profile curve is of generalized Cheng–Yau 1-type. At the same time, an oriented canal surface has a generalized Cheng–Yau 1-type Gauss map if, and only if, it is an open part of a surface of revolution or a torus.

IDENTIFYING CANAL SURFACES IN E4 : CHARACTERIZATION OF A SPECIAL CASE

This study, develops a way for representation of canal surfaces in 4-dimensional Euclidean space E4 . It examines the fundamental forms, Gaussian and mean curvature for a special type canal surface. Moreover, the conditions of both Weingarten and linear Weingarten canal surfaces are given for this new special type. Finally, the graphs of the projections of the canal surfaces using different radius functions in E4 are presented.

Classifications of Canal Surfaces with the Gauss Maps in Minkowski 3-Space

In this work, we study the canal surfaces foliated by pseudo spheres S12 along a Frenet curve in terms of their Gauss maps in Minkowski 3-space. Such kind of surfaces with pointwise 1-type Gauss maps are classified completely. For example, the canal surface with proper pointwise 1-type Gauss map of the first kind if and only if it is a part of a minimal surface of revolution.