Minimal research exists for non-chromatographic separations of rare-earth metallofullerenes containing di-metallic (M2), di-metallic carbide (M2C2), and tri-metallic nitride (M3N) clusters trapped inside fullerene cages. Herein, we demonstrate a non-HPLC method (i.e., SAFA, Stir and Filter Approach) for purifying Er3N@Ih-C80, a rare-earth, metallic nitride clusterfullerene. We describe a strate...

An edge-coloring of a graph G with colors 1, . . . , t is an interval t-coloring if all colors are used, and the colors of edges incident to each vertex of G are distinct and form an interval of integers. A graph G is interval colorable if G has an interval t-coloring for some positive integer t. Let N be the set of all interval colorable graphs. For a graph G ∈ N, the least and the greatest va...

We study the integer sequence vn of numbers of lines in hypersurfaces of degree 2n−3 of Pn, n > 1. We prove a number of congruence properties of these numbers of several different types. Furthermore, the asymptotics of the vn are described (in an appendix by Don Zagier). An attempt is made at a similar analysis of two other enumerative sequences: the numbers of rational plane curves and the num...

A graph is called C4-free if it contains no cycle of length four as an induced subgraph. We prove that if a C4-free graph has n vertices and at least c1n 2 edges then it has a complete subgraph of c2n vertices, where c2 depends only on c1. We also give estimates on c2 and show that a similar result does not hold for H-free graphs—unless H is an induced subgraph of C4. The best value of c2 is de...

A comprehensive, calculated line list of frequencies and transition probabilities for the singly deuterated isotopologue of H3 , H2D +, is presented. The line list, called ST1, contains over 22 million rotational-vibrational transitions occurring between more than 33 thousand energy levels; it covers frequencies up to 18 500 cm−1. All energy levels with rotational quantum number, J, up to 20 ar...

Variationally exact rovibrational levels for the H3 + and H2D ÷ molecules are calculated using a recently published accurate potential. Vibrational fundamentals are va1=3191 cm-1 and vE=2494 (2521.6) cm-1 for H3 + and vl=3000cm-1, v~=2184cm-x and v3=2310cm-1 for H~D +. For H3 + calculated ground state rotational constants are B0 = 43.51 (43-57) cm-1, Co = 20.59 (20-71) cm-1, Dj ° = 0.04 (0.05) ...