Sets of probability distributions, independence, and convexity

This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli's discussion of "convex Bayesianism" (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of "strong independence" (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli's results and recent developments on the axiomatization of non-binary preferences, and its impact on "complete" independence, are described.

Degree of conversion of nanofilled and microhybrid composite resins photo-activated by different generations of LEDs

Objective: This study aimed at evaluating the degree of conversion (DC) of four composite resins, being one nanofilled and 3 microhybrid resins, photo-activated with second- and third-generation light-emitting diodes (LEDs). Material and methods: Filtek (TM) Z350 nanofilled composite resins and Amelogen (R) Plus, Vit-l-escence (TM) and Opallis microhybrid resins were photo-activated with two second-generation LEDs (Radii-cal and Elipar Free Light (TM) 2) and one third-generation LED (Ultra-Lume LED 5) by continuous light mode, and a quartz halogen-tungsten bulb (QHT, control). After 24 h of storage, the samples were pulverized into fine powder and 5 mg of each material were mixed with 100 mg of potassium bromide (KBr). After homogenization, they were pressed, which resulted in a pellet that was evaluated using an infrared spectromer (Nexus 470, Thermo Nicolet) equipped with TGS detector using diffuse reflectance (32 scans, resolution of 4 cm(-1)) coupled to a computer. The percentage of unreacted carbon-carbon double bonds (% C=C) was determined from the ratio of absorbance intensities of aliphatic C=C (peak at 1637 cm-1) against internal standard before and after curing of the specimen: aromatic C-C (peak at 1610 cm-1). Results: The ANOVA showed a significant effect on the interaction between the light-curing units (LCUs) and the composite resins (p<0.001). The Tukey's test showed that the nanofilled resin (Filtek (TM) Z350) and Opallis when photo-activated by the halogen lamp (QTH) had the lowest DC compared with the other microhybrid composite resins. The DC of the nanofilled resin (Filtek (TM) Z350) was also lower using LEDs. The highest degrees of conversion were obtained using the third-generation LED and one of second-generation LEDs (Elipar Free Light (TM) 2). Conclusions: The nanofilled resin showed the lowest DC, and the Vit-l-escence (TM) microhybrid composite resin showed the highest DC. Among the LCUs, it was not possible to establish an order, even though the second-generation LED Radii-cal provided the lowest DC.