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Abstract:The Pareto probability distribution is widely applied in different fields such us finance, physics, hydrology, geology and astronomy. This note deals with an application of the Pareto distribution to astrophysics and more precisely to the statistical analysis of masses of stars and of diameters of asteroids. In particular a comparison between the usual Pareto distribution and its truncated version is presented. Finally, a possible physical mechanism that produces Pareto tails for the distribution of the masses of stars is presented. PACS

Planetary nebulae are imaged using three different physical processes. The first process is the expansion of the shell, which can be modelled by the canonical laws of motion in the spherical case and by momentum conservation when gradients of density are present in the interstellar medium. The second process is the diffusion of particles that radiate from the advancing layer. Three‐dimensional diffusion from a sphere and one‐dimensional diffusion with drift are analysed. The third process is the composition of an image through an integral operation along the line of sight. The framework developed is applied to A39, the Ring nebula and the etched hourglass nebula MyCn 18.