On the regularity of the pressure field of relaxed solutions to Euler equations with variable density

In this paper we improve the regularity in time of the gradient of the pressure field in the solution of relaxed version of variational formulation proposed by V. I. Arnold and by Y. Brenier, for the incompressible Euler equations with variable density. We obtain that the pressure field is not only a measure, but a function in Lloc2((0,T);BVloc(D)) as an extension of the work of Ambrosio and Figalli (2008) in [1] to the variable density case. © 2013 Elsevier Ltd.

Partial regularity of weak solutions of the liquid crystal equilibrium system

For a parameter, we consider the modified relaxed energy of the liquid crystal system. Each minimizer of the modified relaxed energy is a weak solution to the liquid crystal equilibrium system. We prove the partial regularity of minimizers of the modified relaxed energy. We also prove the existence of infinitely many weak solutions for the special boundary value x.

The Crystal-t Algorithm: A New Approach To Calculate The Sle Of Lipidic Mixtures Presenting Solid Solutions.

Lipidic mixtures present a particular phase change profile highly affected by their unique crystalline structure. However, classical solid-liquid equilibrium (SLE) thermodynamic modeling approaches, which assume the solid phase to be a pure component, sometimes fail in the correct description of the phase behavior. In addition, their inability increases with the complexity of the system. To overcome some of these problems, this study describes a new procedure to depict the SLE of fatty binary mixtures presenting solid solutions, namely the Crystal-T algorithm. Considering the non-ideality of both liquid and solid phases, this algorithm is aimed at the determination of the temperature in which the first and last crystal of the mixture melts. The evaluation is focused on experimental data measured and reported in this work for systems composed of triacylglycerols and fatty alcohols. The liquidus and solidus lines of the SLE phase diagrams were described by using excess Gibbs energy based equations, and the group contribution UNIFAC model for the calculation of the activity coefficients of both liquid and solid phases. Very low deviations of theoretical and experimental data evidenced the strength of the algorithm, contributing to the enlargement of the scope of the SLE modeling.

Corrosion Kinetics And Topography Analysis Of Ti-6al-4v Alloy Subjected To Different Mouthwash Solutions.

This study evaluated the corrosion kinetics and surface topography of Ti-6Al-4V alloy exposed to mouthwash solutions (0.12% chlorhexidine digluconate, 0.053% cetylpyridinium chloride and 3% hydrogen peroxide) compared to artificial saliva (pH6.5) (control). Twenty Ti-6Al-4V alloy disks were used and divided into 4 groups (n=5). For the electrochemical assay, standard tests as open circuit potential and electrochemical impedance spectroscopy (EIS) were applied at baseline, 7 and 14days after immersion in the solutions. Scanning electron microscopy, atomic force microscopy and profilometry (average roughness - Ra) were used for surface characterization. Total weight loss of disks was calculated. Data were analyzed by ANOVA and Bonferroni's test (α=0.05). Hydrogen peroxide generated the lowest polarization resistance (Rp) values for all periods (P<0.05). For the capacitance (Cdl), similar results were observed among groups at baseline (P=0.098). For the 7 and 14-day periods, hydrogen peroxide promoted the highest Cdl values (P<0.0001). Hydrogen peroxide promoted expressive superficial changes and greater Ra values than the others (P<0.0001). It could be concluded that solutions containing cetylpyridinium chloride and chlorhexidine digluconate might be the mouthwashes of choice during the post-operatory period of dental implants. However, hydrogen peroxide is counter-indicated in these situations. Further studies evaluating the dynamics of these solutions (tribocorrosion) and immersing the disks in daily cycles (two or three times a day) to mimic a clinical situation closest to the application of mouthwashes in the oral cavity are warranted to prove our results.

Comparison of physical and mechanical properties of microwave-polymerized acrylic resin after disinfection in sodium hypochlorite solutions

This study evaluated the color stability, surface roughness and flexural strength of a microwave-polymerized acrylic resin after immersion in sodium hypochlorite (NaOCl), simulating 20 min of disinfection daily during 180 days. Forty disk-shaped (15 x 4 mm) and 40 rectangular (65 x 10 x 3 mm) specimens were prepared with a microwave-polymerized acrylic resin (Onda-Cryl). Specimens were immersed in either 0.5% NaOCl, 1% NaOCl, Clorox/Calgon and distilled water (control). Color measurements were determined by a portable colorimeter. Three parallel lines, separated by 1.0 mm, were registered on each specimen before and after immersion procedures to analyze the surface roughness. The flexural strength was measured using a 3-point bending test in a universal testing machine with a 50 kgf load cell and a crosshead speed of 1 mm/min. Data were analyzed statistically by ANOVA and Tukey's test (?=0.05). There was no statistically significant differences (p>0.05) among the solutions for color, surface roughness and flexural strength. It may be concluded that immersion in NaOCl solutions simulating short-term daily use during 180 days did not influence the color stability, surface roughness and flexural strength of a microwave-polymerized acrylic resin.

Effect of fluoride-containing solutions on the surface of cast commercially pure titanium

This study evaluated the effects of fluoride-containing solutions on the surface of commercially pure titanium (CP Ti) obtained by casting. CP Ti specimens were fabricated and randomly assigned to 5 groups (n=10): group 1: stored in distilled water at 37 ± 1ºC; group 2: stored in distilled water at 37 ± 1ºC and daily immersed in 0.05% NaF for 3 min; group 3: stored in distilled water at 37 ± 1ºC and daily immersed in 0.2% NaF for 3 min; group 4: stored in distilled water at 37 ± 1ºC; and immersed in 0.05% NaF every 15 days for 3 min; and group 5: stored in distilled water at 37 ± 1ºC and immersed in 0.2% NaF every 15 days for 3 min. Surface roughness was measured with a profilometer immediately after metallographic polishing of the specimens (T0) and at 15-day intervals until completing 60 days of experiment (T15, T30, T45, T60). Data were analyzed statistically by ANOVA and Tukey's test (α=0.05). There was no statistically significant difference (p>0.05) in surface roughness among the solutions. In conclusion, fluoride-containing solutions (pH 7.0) used as mouthwashes do not damage the surface of cast CP Ti and can be used by patients with titanium-based restorations.

Effect of staining solutions and repolishing on color stability of direct composites

OBJECTIVES: The purpose of this study was to assess the color change of three types of composite resins exposed to coffee and cola drink, and the effect of repolishing on the color stability of these composites after staining. MATERIALS AND METHODS: Fifteen specimens (15 mm diameter and 2 mm thick) were fabricated from microhybrid (Esthet-X; Dentsply and Filtek Z-250; 3M ESPE) and high-density hybrid (Surefil; Dentsply) composites, and were finished and polished with aluminum oxide discs (Sof-Lex; 3M ESPE). Color of the specimens was measured according to the CIE L*a*b* system in a refection spectrophotometer (PCB 6807; BYK Gardner). After baseline color measurements, 5 specimens of each resin were immersed in different staining solutions for 15 days: G1 - distilled water (control), G2 - coffee, G3 - cola soft drink. Afterwards, new color measurement was performed and the specimens were repolished and submitted to new color reading. Color stability was determined by the difference (ΔE) between the coordinates L*, a*, and b* obtained from the specimens before and after immersion into the solutions and after repolishing. RESULTS: There was no statistically signifcant difference (ANOVA, Tukey's test; p>0.05) among the ΔE values for the different types of composites after staining or repolishing. For all composite resins, coffee promoted more color change (ΔE>3.3) than distilled water and the cola soft drink. After repolishing, the ΔE values of the specimens immersed in coffee decreased to clinically acceptable values (ΔE<3.3), but remained signifcantly higher than those of the other groups. CONCLUSIONS: No signifcant difference was found among composite resins or between color values before and after repolishing of specimens immersed in distilled water and cola. Immersing specimens in coffee caused greater color change in all types of composite resins tested in this study and repolishing contributed to decrease staining to clinically acceptable ΔE values.

Adhesion of Epiphany and AH Plus sealers to human root dentin treated with different solutions

This study evaluated comparatively the adhesion of Epiphany and AH Plus endodontic sealers to human root dentin treated with 1% NaOCl and 1% NaOCl+17% EDTA, using the push-out test. Sixty root cylinders obtained from maxillary canines had the canals prepared and were randomly assigned to 3 groups (n=20), according to root dentin treatment: GI - distilled water (control), GII - 1% NaOCl and GIII - 1% NaOCl+17% EDTA. Each group was divided into 2 subgroups (n=10) filled with either Epiphany or AH Plus. Bond strength push-out test data (kN) were obtained and analyzed statistically by ANOVA and Tukey's post-hoc test. There was statistically significant difference between sealers (AH Plus: 0.78 ± 0.13; Epiphany: 0.61 ± 0.19; p<0.01) and among root dentin treatments (distilled water: 0.58 ± 0.19; 1% NaOCl: 0.71 ± 0.12; 1% NaOCl+17% EDTA: 0.80 ± 0.17; p<0.05). In conclusion, AH Plus sealer presented greater adhesion to dentin than Epiphany, regardless of the treatment of root canal walls.

Ex vivo analysis of root canal cleaning using Endo-PTC associated to NaOCl and different irrigant solutions

The aim of this study was to assess qualitatively, by means of SEM images, the cleaning of the dentin walls of root canals after chemical-surgical preparation using Endo-PTC cream with 0.5% and 1% sodium hypochlorite and different final irrigating solutions. Seventy-two single-rooted human teeth were divided into eight groups and prepared using Endo-PTC cream with sodium hypochlorite (NaOCl) at different concentrations, and irrigated with NaOCl at different concentrations. Final irrigation was performed with either EDTA-T or EDTA-C. The best results were obtained with Group 1, followed by Groups 5, 2, 7, 8, 3, 6 and 4. We can conclude that the use of 0.5% NaOCl during instrumentation and final flush of the root canals was more efficient in cleaning than was 1% sodium hypochlorite. EDTA-T was more efficient in removing smear layer than EDTA-C, and the cervical third presented better cleaning of the root canal walls than did the middle third, which showed cleaner dentin walls than the apical third.

Accuracy of three electronic apex locators in the presence of different irrigating solutions

The present study compared the accuracy of three electronic apex locators (EALs) - Elements Diagnostic®, Root ZX® and Apex DSP® - in the presence of different irrigating solutions (0.9% saline solution and 1% sodium hypochlorite). The electronic measurements were carried out by three examiners, using twenty extracted human permanent maxillary central incisors. A size 10 K file was introduced into the root canals until reaching the 0.0 mark, and was subsequently retracted to the 1.0 mark. The gold standard (GS) measurement was obtained by combining visual and radiographic methods, and was set 1 mm short of the apical foramen. Electronic length values closer to the GS (± 0.5 mm) were considered as accurate measures. Intraclass correlation coefficients (ICCs) were used to verify inter-examiner agreement. The comparison among the EALs was performed using the McNemar and Kruskal-Wallis tests (p < 0.05). The ICCs were generally high, ranging from 0.8859 to 0.9657. Similar results were observed for the percentage of electronic measurements closer to the GS obtained with the Elements Diagnostic® and the Root ZX® EALs (p > 0.05), independent of the irrigating solutions used. The measurements taken with these two EALs were more accurate than those taken with Apex DSP®, regardless of the irrigating solution used (p < 0.05). It was concluded that Elements Diagnostic® and Root ZX® apex locators are able to locate the cementum-dentine junction more precisely than Apex DSP®. The presence of irrigating solutions does not interfere with the performance of the EALs.

Evaluation of capillaries with different inner coatings for DNA analysis using dilute polymer solutions by capillary electrophoresis

In this work three capillary columns, one with uncoated inner wall and two with covalently-bound internal coatings - poly(vinyl alcohol) (PVA) and poly(dimethylacrylamide) (PDMA) - both covalently covered - were used to separate DNA fragments and compared to DNA separation using replaceable polymer solutions. The separations were performed using hydroxyethylcellulose (HEC) (90-105 kDa) in concentrations ranging from 0.00 to 2.00% m/v. The results indicated that the separation efficiency was higher in the PVA capillary than in the PDMA in all evaluated concentrations of HEC. In addition, higher resolution was also observed in PVA-coated capillary since in PDMA the shape of the peaks was not reproducible when subsequent runs were performed. Contrary to what has previously been reported in the literature, no reasonable separation was possible in bare fused silica.

Characterization of aqueous silver nitrate solutions for leakage tests

OBJECTIVE: To determine the pH over a period of 168 h and the ionic silver content in various concentrations and post-preparation times of aqueous silver nitrate solutions. Also, the possible effects of these factors on microleakage test in adhesive/resin restorations in primary and permanent teeth were evaluated. MATERIAL AND METHODS: A digital pHmeter was used for measuring the pH of the solutions prepared with three types of water (purified, deionized or distilled) and three brands of silver nitrate salt (Merck, Synth or Cennabras) at 0, 1, 2, 24, 48, 72, 96 and 168 h after preparation, and storage in transparent or dark bottles. Ionic silver was assayed according to the post-preparation times (2, 24, 48, 72, 96, 168 h) and concentrations (1, 5, 25, 50%) of solutions by atomic emission spectrometry. For each sample of each condition, three readings were obtained for calculating the mean value. Class V cavities were prepared with enamel margins on primary and permanent teeth and restored with the adhesive systems OptiBond FL or OptiBond SOLO Plus SE and the composite resin Filtek Z-250. After nail polish coverage, the permanent teeth were immersed in 25% or 50% AgNO3 solution and the primary teeth in 5% or 50% AgNO3 solutions for microleakage evaluation. ANOVA and the Tukey's test were used for data analyses (α=5%). RESULTS: The mean pH of the solutions ranged from neutral to alkaline (7.9±2.2 to 11.8±0.9). Mean ionic silver content differed depending on the concentration of the solution (4.75±0.5 to 293±15.3 ppm). In the microleakage test, significant difference was only observed for the adhesive system factor (p=0.000). CONCLUSIONS: Under the tested experimental conditions and based on the obtained results, it may be concluded that the aqueous AgNO3 solutions: have neutral/alkaline pH and service life of up to 168 h; the level of ionic silver is proportional to the concentration of the solution; even at 5% concentration, the solutions were capable of indicating loss of marginal seal in the composite restorations; the 3-step conventional adhesive system had better performance regarding microleakage in enamel on primary and permanent teeth.

Exact time-dependent solutions for a self-regulating gene

The exact time-dependent solution for the stochastic equations governing the behavior of a binary self-regulating gene is presented. Using the generating function technique to rephrase the master equations in terms of partial differential equations, we show that the model is totally integrable and the analytical solutions are the celebrated confluent Heun functions. Self-regulation plays a major role in the control of gene expression, and it is remarkable that such a microscopic model is completely integrable in terms of well-known complex functions.

Efficacy of sweet solutions for analgesia in infants between 1 and 12 months of age: a systematic review

Objective To compare the efficacy of oral sweet solutions to water or no treatment in infants aged 1-12 months during immunisation. Methods Randomised controlled trials (RCTs) were retrieved through internet searches or manual searches of reference lists. Search terms included newborn, infant, pain, sucrose and alternative names for sweet solutions. Summary estimates with 95% CIs were calculated and included relative risk (RR), risk difference (RD) and number needed to treat to benefit (NNTB) for dichotomous outcomes, and weighted mean differences (WMD) for continuous outcomes. Where pooling of results was not possible, a narrative summary of study results is presented. Results Of the 695 studies identified, 14 RCTs with 1674 injections met the inclusion criteria. Sucrose or glucose, compared to water or no treatment decreased crying during or following immunisation in 13 of the 14 studies. Infants receiving 30% glucose (three trials, 243 infants) had a decreased RR in crying incidence following immunisation (typical RR 0.80, 95% CI 0.69 to 0.93; RD -0.17, 95% CI -0.29 to -0.05; NNTB 6, 95% CI 3 to 20). With sucrose or glucose, there was a 10% WMD reduction in proportion of crying time (95% CI - 18 to - 2) and a 12 s reduction in crying duration (95% CI - 23 to -0.7 s). An optimal dose of sucrose or glucose could not be ascertained due to the varied volumes and concentrations used. Conclusion Infants aged 1-12 months administered sucrose or glucose before immunisation had moderately reduced incidence and duration of crying. Healthcare professionals should consider using sucrose or glucose before and during immunisation.

GLOBAL SOLUTIONS FOR ABSTRACT FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper we study the existence of global solutions for a class of abstract functional differential equation with nonlocal conditions. An application is considered.