Invariants of binary differential equations

In this paper, we study binary differential equations a(x, y)dy (2) + 2b(x, y) dx dy + c(x, y)dx (2) = 0, where a, b, and c are real analytic functions. Following the geometric approach of Bruce and Tari in their work on multiplicity of implicit differential equations, we introduce a definition of the index for this class of equations that coincides with the classical Hopf`s definition for positive binary differential equations. Our results also apply to implicit differential equations F(x, y, p) = 0, where F is an analytic function, p = dy/dx, F (p) = 0, and F (pp) not equal aEuro parts per thousand 0 at the singular point. For these equations, we relate the index of the equation at the singular point with the index of the gradient of F and index of the 1-form omega = dy -aEuro parts per thousand pdx defined on the singular surface F = 0.

Effect of power densities and irradiation times on the degree of conversion and temperature increase of a microhybrid dental composite resin

The different parameters used for the photoactivation process provide changes in the degree of conversion (DC%) and temperature rise (TR) of the composite resins. Thus, the purpose of this study was to evaluate the DC (%) and TR of the microhybrid composite resin photoactivated by a new generation LED. For the KBr pellet technique, the composite resin was placed into a metallic mould (1-mm thickness and 4-mm diameter) and photoactivated as follows: continuous LED LCU with different power density values (50-1000 mW/cm(2)). The measurements for the DC (%) were made in a FTIR Spectrometer Bomen (model MB-102, Quebec-Canada). The spectroscopy (FTIR) spectra for both uncured and cured samples were analyzed using an accessory for the diffuse reflectance. The measurements were recorded in the absorbance operating under the following conditions: 32 scans, 4-cm(-1) resolution, and a 300 to 4000-cm(-1) wavelength. The percentage of unreacted carbon-carbon double bonds (% C=C) was determined from the ratio of the absorbance intensities of aliphatic C=C (peak at 1638 cm(-1)) against an internal standard before and after the curing of the specimen: aromatic C-C (peak at 1608 cm-1). For the TR, the samples were made in a metallic mould (2-mm thickness and 4-mm diameter) and photoactivated during 5, 10, and 20 s. The thermocouple was attached to the multimeter to allow the temperature readings. The DC (%) and TR were calculated by the standard technique and submitted to ANOVA and Tukey`s test (p < 0.05). The degree of conversion values varied from 35.0 (+/- 1.3) to 45.0 (+/- 2.4) for 5 s, 45.0 (+/- 1.3) to 55.0 (+/- 2.4) for 10 s, and 47.0 (+/- 1.3) to 52.0 (+/- 2.4) for 20 s. For the TR, the values ranged from 0.3 (+/- 0.01) to 5.4 (+/- 0.11)degrees C for 5 s, from 0.5 (+/- 0.02) to 9.3 (+/- 0.28)degrees C for 10 s, and from 1.0 (+/- 0.06) to 15.0 (+/- 0.95)degrees C for 20 s. The power densities and irradiation times showed a significant effect on the degree of conversion and temperature rise.

A robust Bayesian approach to null intercept measurement error model with application to dental data

Measurement error models often arise in epidemiological and clinical research. Usually, in this set up it is assumed that the latent variable has a normal distribution. However, the normality assumption may not be always correct. Skew-normal/independent distribution is a class of asymmetric thick-tailed distributions which includes the Skew-normal distribution as a special case. In this paper, we explore the use of skew-normal/independent distribution as a robust alternative to null intercept measurement error model under a Bayesian paradigm. We assume that the random errors and the unobserved value of the covariate (latent variable) follows jointly a skew-normal/independent distribution, providing an appealing robust alternative to the routine use of symmetric normal distribution in this type of model. Specific distributions examined include univariate and multivariate versions of the skew-normal distribution, the skew-t distributions, the skew-slash distributions and the skew contaminated normal distributions. The methods developed is illustrated using a real data set from a dental clinical trial. (C) 2008 Elsevier B.V. All rights reserved.

Alkoxy Chain Effect on the Viscosity of a Quaternary Ammonium Ionic Liquid: Molecular Dynamics Simulations

The viscosity of ionic liquids based on quaternary ammonium cations is reduced when one of the alkyl chains is replaced by an alkoxy chain (Zhou et al. Chem. Eur. J. 2005, 11, 752.). A microscopic picture of the role played by the ether function in decreasing the viscosity of quaternary ammonium ionic liquids is provided here by molecular dynamics (MD) simulations. A model for the ionic liquid N-ethyl-N,N-dimethyl-N-(2-methoxyethyl)ammonium bis(trifluoromethanesulfonyl)imide, MOENM(2)E TFSI, is compared to the tetraalky-lammonium counterpart. The alkoxy derivative has lower viscosity, higher ionic diffusion coefficients, and higher conductivity than the tetraalkyl system at the same density and temperature. A clear signature of the ether function on the liquid structure is observed in cation-cation correlations, but not in anion-anion or anion-cation correlations. In both the alkyl and the alkoxy ionic liquids, there is aggregation of long chains of neighboring cations within micelle-like structures. The MD simulations indicate that the less effective assembly between the more flexible alkoxy chains, in comparison to alkyl chains, is the structural reason for higher ionic mobility in MOENM(2)E TFSI.