Some results on holomorphic generalized functions

In this note, we present three independent results within generalized complex analysis (in the Colombeau sense). The first of them deals with non-removable singularities; we construct a generalized function u on an open subset Omega of C(n), which is not a holomorphic generalized function on Omega but it is a holomorphic generalized function on Omega\S, where S is a hypersurface contained in Omega. The second result shows the existence of a holomorphic generalized function with prescribed values in the zero-set of a classical holomorphic function. The last result states the existence of a compactly supported solution to the (partial derivative) over bar operator.

Treatment of infrabony defects with or without enamel matrix proteins: A 24-month follow-up randomized pilot study

Objective: To evaluate a comparison of open-flap debridement (OFD) with or without the use of enamel matrix proteins (EMP) for the treatment of infrabony defects. Method and Materials: Ten volunteers (38 infrabony defects) were randomized to receive OFD + EMP (test site) and OFD (control site). Clinical outcomes included mean changes in Plaque Index, Gingival Index, probing pocket depth (PPD), relative attachment level (RAL), gingival recession, width of keratinized tissue, and dental mobility at baseline and at 24 months. Results: A significant reduction of 4.21 +/- 0.97 mm was observed in PPD for the OFD + EMP group (from 6.30 +/- 0.99 mm to 2.09 +/- 0.97 mm) and of 3.28 +/- 1.23 mm for the OFD group (from 6.13 +/- 0.88 mm to 2.85 +/- 1.42 mm) (P < .001). The reduction in PPD was statistically significantly greater for OFD + EMP compared to OFD (P = .03). The mean RAL decreased from 13.26 +/- 1.88 mm to 7.57 +/- 2.05 mm for the OFD + EMP group (a gain of 5.69 +/- 1.96 mm) and from 13.37 +/- 1.71 mm to 8.13 +/- 1.34 min (P < .001) for the OFD group (a gain of 5.24 +/- 1.55 mm). Gingival recession was higher it) the OFD + EMP group than in the OFD group. The mean keratinized tissue significantly decreased from 4.41 +/- 1.39 mm to 3.63 +/- 1.54 mm for OFD flap group (P < .01). Conclusion: Both treatment modalities were efficient in improving RAL and PPD. Within groups, there was a significant reduction in keratinized tissue for OFD and a significant postoperative recession for the OFD + EMP group. Infrabony defects treated with OFD + EMP showed significantly more PPD reduction when compared to OFD. (Quintessence Int 2010;41:125-134)

Polymerization stress, shrinkage and elastic modulus of current low-shrinkage restorative composites

Objective. To compare currently available low-shrinkage composites with others regarding polymerization stress, volumetric shrinkage (total and post-gel), shrinkage rate and elastic modulus. Methods. Seven BisGMA-based composites (Durafill/DU, Filtek Z250/FZ, Heliomolar/HM, Aelite LS Posterior/AP, Point 4/P4, Filtek Supreme/SU, ELS/EL), a silorane-based (Filtek LS, LS), a urethane-based (Venus Diamond, VD) and one based on a dimethacrylate-derivative of dimer acid (N`Durance, ND) were tested. Polymerization stress was determined in 1-mm high specimens inserted between two PMMA rods attached to a universal testing machine. Total volumetric shrinkage was measured using a mercury dilatometer. Maximum shrinkage rate was used as a parameter of the reaction speed. Post-gel shrinkage was measured using strain-gages. Elastic modulus was obtained by three-point bending. Data were submitted to one-way ANOVA/Tukey test (p = 0.05), except for elastic modulus (Kruskal-Wallis). Results. Composites ranked differently for total and post-gel shrinkage. Among the materials considered as ""low-shrinkage"" by the respective manufacturers, LS, EL and VD presented low post-gel shrinkage, while AP and ND presented relatively high values. Polymerization stress showed a strong correlation with post-gel shrinkage except for LS, which presented high stress. Elastic modulus and shrinkage rate showed weak relationships with polymerization stress. Significance. Not all low-shrinkage composites demonstrated reduced polymerization shrinkage. Also, in order to effectively reduce polymerization stress, a low post-gel shrinkage must be associated to a relatively low elastic modulus. (C) 2010 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.