Existence of Solutions for Abstract Non-Autonomous Neutral Differential Equations

In this paper we discuss the existence of mild and classical solutions for a class of abstract non-autonomous neutral functional differential equations. An application to partial neutral differential equations is considered.

EXISTENCE OF SOLUTIONS FOR A FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATION WITH UNBOUNDED DELAY

In this article, we study the existence of mild solutions for fractional neutral integro-differential equations with infinite delay.

The erosion and abrasion-inhibiting effect of TiF4 and NaF varnishes and solutions on enamel in vitro

Objective. Previous in vitro study has shown that TiF(4) varnish might reduce enamel erosion. No data regarding the effect of this experimental varnish on enamel erosion plus abrasion, however, are available so far. Thus, this in vitro study aimed to analyse the effect of TiF4 compared with NaF varnishes and solutions, to protect against enamel erosion with or without abrasion. Methods. Enamel specimens were pre-treated with experimental-TiF4 (2.45% F), experimentalNaF (2.45% F), NaF-Duraphat (2.26% F), and placebo varnishes; NaF (2.26% F) and TiF4 (2.45% F) solutions. Controls remained untreated. The erosive challenge was performed using a soft drink (pH 2.6) 4 u 90 s / day (ERO) and the toothbrushing abrasion (ERO+ ABR) 2 u 10 s / day, for 5 days. Between the challenges, the specimens were exposed to artificial saliva. Enamel loss was measured profilometrically (lm). Results. Kruskal-Wallis / Dunn tests showed that all fluoridated varnishes (TiF4-ERO: 0.53 +/- 0.20, ERO+ ABR: 0.65 +/- 0.19/ NaF-ERO: 0.94 +/- 0.18, ERO+ ABR: 1.74 +/- 0.37 / Duraphat-ERO: 1.00 +/- 0.37, ERO+ ABR: 1.72 +/- 0.58) were able to significantly reduce enamel loss when compared with placebo varnish (ERO: 3.45 +/- 0.41 / ERO+ ABR: 3.20 +/- 0.66) (P < 0.0001). Placebo varnish, control (ERO: 2.68 +/- 0.53 / ERO+ ABR: 3.01 +/- 0.34), and fluoridated (NaF-ERO: 2.84 +/- 0.09 / ERO+ ABR: 2.40 +/- 0.21 / TiF4-ERO: 3.55 +/- 0.59 / ERO+ ABR: 4.10 +/- 0.38) solutions did not significantly differ from each other. Conclusion. Based on the results, it can be concluded that the TiF4 varnish seems to be a promising treatment to reduce enamel loss under mild erosive and abrasive conditions in vitro.