Spectral Statistics and Luminosity Function of a Hard X-ray Complete Sample of Brightest AGNs

We investigated the statistics of the X-ray spectral properties of a complete flux-limited sample of bright AGNs from HEAO-1 all-sky catalogs to provide the bright end constraint of the evolution of AGN hard X-ray luminosity function (HXLF) and the AGN population synthesis model of the X-ray background. Spectral studies have been made using ASCA and XMM-Newton observation data for almost all AGNs in this sample.Comment: PTPTex v0.88, 2 pages with 4 figures, Proceedings of the "Stellar-Mass, Intermediate -Masss, and Supermassive Black Holes" in Kyoto, Japa

Leonardo's rule, self-similarity and wind-induced stresses in trees

Examining botanical trees, Leonardo da Vinci noted that the total cross-section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar structure and the branch diameters being adjusted to resist wind-induced loads