О геологическом феномене - выпадении "каменной тучи" у Великого Устюга

In Velikij Ustug region stones with some specific features are known. According to ancient legends and chronicles these stones presumably are of meteoritic origin. The detailed mineralogo-petrographical, petrophysical and mineragraphycal analyses of one of such stones showed, that most probably it has Earth origin.Приведены данные по особенностям геоморфологии района выпадения «каменной тучи» предположительно метеоритного происхождения (1290 г.). На основе минералого-петрографического, петрофизического, минераграфического анализов камня, взятого с места выпадения «каменной тучи», определена его земная природа

Topologies and Laplacian spectra of a deterministic uniform recursive tree

The uniform recursive tree (URT) is one of the most important models and has been successfully applied to many fields. Here we study exactly the topological characteristics and spectral properties of the Laplacian matrix of a deterministic uniform recursive tree, which is a deterministic version of URT. Firstly, from the perspective of complex networks, we determine the main structural characteristics of the deterministic tree. The obtained vigorous results show that the network has an exponential degree distribution, small average path length, power-law distribution of node betweenness, and positive degree-degree correlations. Then we determine the complete Laplacian spectra (eigenvalues) and their corresponding eigenvectors of the considered graph. Interestingly, all the Laplacian eigenvalues are distinct.Comment: 7 pages, 1 figures, definitive version accepted for publication in EPJ