On the weak monotonicity of Gini means and other mixture functions

Weak monotonicity was recently proposed as a relaxation of the monotonicity condition for averaging aggregation, and weakly monotone functions were shown to have desirable properties when averaging data corrupted with outliers or noise. We extended the study of weakly monotone averages by analyzing their ϕ-transforms, and we established weak monotonicity of several classes of averaging functions, in particular Gini means and mixture operators. Mixture operators with Gaussian weighting functions were shown to be weakly monotone for a broad range of their parameters. This study assists in identifying averaging functions suitable for data analysis and image processing tasks in the presence of outliers.

Weak monotonicity of Lehmer and Gini means

We analyze directional monotonicity of several mixture functions in the direction (1,1...,1), called weak monotonicity. Our particular focus is on power weighting functions and the special cases of Lehmer and Gini means. We establish limits on the number of arguments of these means for which they are weakly monotone. These bounds significantly improve the earlier results and hence increase the range of applicability of Gini and Lehmer means. We also discuss the case of affine weighting functions and find the smallest constant which ensures weak monotonicity of such mixture functions.

Influence of N2O flow rate on reliability of SiOx films deposited by SiH4-N2O gas mixture plasma

SiO_x films have several advantages as an interlayer dielectric in electronic devices owing to the strong adhesion between SiO_x and the substrate. In this study, the coating performance as a function of the N₂O flow rate was evaluated by electrochemical impedance spectroscopy and potentiodynamic polarization tests in an undisturbed environment. In addition, the coatings were examined by atomic force microscopy and Fourier transform infrared reflection spectroscopy. The SiO_x films on a stainless-steel substrate showed the highest coating performance at a N₂O flow rate of 120 sccm. This was attributed to the films having the lowest porosity value among those examined as a result of the fragmentation of SiO and SiO₂ bonds and the improved surface roughness.