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Particulate matter in the atmosphere is known to affect Earth's climate and to be harmful to human health. Accurately measuring particles from emission sources is important, as the results are used to inform policies and climate models. This study compares the results of two ELPI + devices, two PM10 cascade impactors and an eFilter, in combustion emission measurements. The comparison of the instruments in a realistic setting shows what types of challenges arise from measuring an emission aerosol with unknown particle morphologies and densities, different particle concentrations and high temperature. Our results show that the PM10 cascade impactors have very good intercorrelation when the collected mass is greater than 150 µg, but below that, the uncertainty of the results increases with decreasing mass. The raw signals of two ELPI + devices were nearly identical in most samples, as well as the particle number concentrations and size distributions calculated from raw signals; however, transforming the current distributions into mass distributions showed variation in the mass concentration of particles larger than 1 µm. The real-time time signal measured by eFilter was similar to the total current measured by ELPI+. The eFilter and PM10 cascade impactors showed similar particle mass concentrations, whereas ELPI + showed clearly higher ones in most cases. We concluded that the difference is at least partially due to volatile components being measured by ELPI+, but not by the mass collection measurements. Copyright © 2019 American Association for Aerosol Research [ABSTRACT FROM AUTHOR]

In this article, we focus on the result of V.F.R. Jones which says that the partition algebra is the algebra of all transformations commuting with the action of the symmetric group on tensor products of its permutation representation. In particular, we restrict the action of the symmetric group to the action of the alternating group. In this context, we compute a basis for the centralizer algebra and show when the centralizer is isomorphic to the partition algebra. [ABSTRACT FROM AUTHOR]