Convergence Analysis of Some Methods for Minimizing a Nonsmooth Convex Function

In this paper, we analyze a class of methods for minimizing a proper lower semicontinuous extended-valued convex function . Instead of the original objective function f , we employ a convex approximation f k + 1 at the k th iteration. Some global convergence rate estimates are obtained. We illustrate our approach by proposing (i) a new family of proximal point algorithms which possesses the global convergence rate estimate even it the iteration points are calculated approximately, where are the proximal parameters, and (ii) a variant proximal bundle method. Applications to stochastic programs are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45249/1/10957_2004_Article_417694.pd

Effects of polishing procedures on color stability of composite resins

The purpose of this study was to investigate the effect of different polishing methods on color stability of posterior, universal and nanohybrid composite resin restorative materials upon exposure to a staining agent. Twenty-five specimens were prepared for each of 5 different composite resins (Filtek Z250, Filtek P60, Quadrant LC, Grandio and Filtek Supreme). Specimens were divided into 5 groups and different polishing procedures, including polishing discs (Pd), polishing discs then diamond polishing paste (PdP), polishing discs then a liquid polishing system (Biscover) (PdB), and combinations of these (PdPB) were used. Unpolished specimens served as the control (C). The specimens were stored for 48 h in a coffee solution. The color of all specimens was measured before and after exposure with a colorimeter, and total color change (DE*) were calculated. The data were analyzed with a two-way ANOVA and the means were compared by Tukey HSD test (a=0.05). The lowest color difference was observed in the groups PdP and C, while the highest color difference was observed in PdPB, and PdB. When comparing the five different restorative materials, no significant difference was observed between FiltekP60 and FiltekZ250, and these materials demonstrated significantly less color change than Quadrant LC and the nanohybrid materials (Grandio, Filtek Supreme). The posterior (Filtek P60) and universal (Filtek Z250) composite resin restorative materials, which do not contain tetraethyleneglycol dimethacrylate (TEGDMA), were found to be less stainable than the nanohybrid (Grandio, Filtek Supreme) and universal (Quadrant LC) composite resins, which contain TEGDMA. The use of diamond polishing paste after polishing with polishing discs significantly decreased staining when compared to the groups that used polishing discs alone, for all restorative materials tested. The highest color change values were obtained for the specimens that were polished with the Biscover liquid polish system (PdB and PdPB groups)

Interaction between staining and degradation of a composite resin in contact with colored foods

Composite resins might be susceptible to degradation and staining when in contact with some foods and drinks. This study evaluated color alteration and changes in microhardness of a microhybrid composite after immersion in different colored foods and determined whether there was a correlation between these two variables. Eighty composite disks were randomly divided into 8 experimental groups (n = 10): kept dry; deionized water; orange juice; passion fruit juice; grape juice; ketchup; mustard and soy sauce. The disks were individually immersed in their respective test substance at 37 ºC, for a period of 28 days. Superficial analysis of the disk specimens was performed by taking microhardness measurements (Vickers, 50 g load for 45 seconds) and color alterations were determined with a spectrophotometer (CINTRA 10- using a CIEL*a*b* system, 400-700 nm wavelength, illuminant d65 and standard observer of 2º) at the following times: baseline (before immersion), 1, 7, 14, 21 and 28 days. Results were analyzed by ANOVA and Tukey's test (p < 0.05). Both variables were also submitted to Pearson's correlation test (p < 0.05). The passion fruit group underwent the greatest microhardness change, while the mustard group suffered the greatest color alteration. Significant positive correlation was found between the two variables for the groups deionized water, grape juice, soy sauce and ketchup. Not all color alteration could be associated with surface degradation

Micro-sized erosions in a nanofilled composite after repeated acidic beverage exposures: consequences of clusters dislodgments

Objective: To evaluate the hardness (KHN), color stability (DE), and superficial micromorphology of two categories of composites after immersion in either distilled water or grape juice for up to 45 days. MATERIAL AND METHODS: Cylindrical specimens (6 mm diameter x 2 mm thick) were obtained according to the factors: composite [Opallis (FGM) and Filtek Z350XT (3M ESPE)]; immersion solution (distilled water and grape juice); and evaluation time: 24 h and 7, 14, 21, 28, and 45 days. After photoactivation, the specimens were stored at 37ºC for 24 h. KHN (50 g/15 s) and ΔE were then repeatedly assessed according to the immersion solutions. Data were analyzed (three-way ANOVA/Tukey's test). Scanning electron microscopy (SEM) topographic analysis was also performed. RESULTS: In general, KHN of both composites reduced after 24 h, irrespective of the immersion solution and time. A significantly lower KHN was noted for Opallis compared with Filtek Z350XT in all parameters. An increase in ΔE over time was noted for both composites, irrespective of the immersion solution. Significantly higher ΔE was noted for Filtek Z350XT immersed in grape juice compared with Opallis, regardless of the evaluation time. The grape juice caused significantly higher DE compared with water in all periods. SEM analysis showed eroded areas for Filtek Z350XT but not for Opallis. CONCLUSIONS: The compositions and immersion solutions influence the composite hardness and the color stability. In spite of the higher hardness, the nanofilled composite is more susceptible to color change than the microhybrid when immersed in an acidic dyed solution