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Yellott (1978) has shown that there are Thurstone models with probability distributions of different types that are equivalent for complete experiments with three alternatives. This note generalizes and extends his tidings by showing that for any number of altematives n, there exists a pair of Thurstone models with probability distributions of different types that are equivalent for complete experiments with n alternatives, but which are not equivalent for complete experiments with n + 1 alternatives.

Tenacious adhesion of dust to surfaces in the vacuum environment of space is a significant obstacle to exploration and scientific discovery on the Moon, Mars and asteroids. Mitigating particle adhesion is also costly and difficult during semiconductor or optics processing on earth. Over the last eight years at Ball Aerospace & Technologies Corp (BATC), we have demonstrated the effectiveness of an ion beam process that dramatically reduces the adhesion of lunar simulant dust to quartz, glass, Kapton, Teflon and silicon surfaces in dry, ambient, and vacuum environments. Treated silvercoated Teflon coupons performed well in a space-simulated environment at NASA Glenn Research Center. Surface roughening on an Ångstrom-level scale was found to correlate well with reduced adhesion, as did contact angle hysteresis. The large difference in advancing and receding contact angles reflects topological and/or chemical heterogeneity. Differences in contact charging are not believed to be major players in dust adhesion reduction. The physical basis of the dust mitigating properties of these modified surfaces is believed to be substantially due to nanometer scale differences between treated and virgin surfaces. Lastly, because this process does not add material, unlike a lotus-like coating or the work function matching coating, nor does it require power like the electrodynamic screen, it is particularly attractive for optical or thermal control materials that cannot tolerate coatings or where power is not available.