A canonical ordering of polybenzenes and polymantanes using a prime number factorization technique

The correlation described over twenty years ago by Matula between the prime factorization of integers and the class of alkanes is re-examined with a view to explaining the probable reason why there have, to date, been no major extensions of this idea. By considering the class of alkanes as a one-dimensional one-parameter system, a new perspective on the method is gained that is amenable to extension, but in a different direction than originally anticipated. With this new perspective, the classes of polybenzenes and polymantanes are seen to be the representatives of two- and three-dimensional one-parameter systems, respectively. A nomenclature, comparable to one that Matula used for alkanes, is created that gives a unique canonical name to all possible combinations of either polybenzene or polymantane modules. Such a nomenclature contains a built-in means of positioning the molecule in the field of interest in accordance with arbitrary pre-selected criteria, such as Patterson's rules, and also coding that indicates symmetries inherent in the structure of this molecule.     

Nuclear spin relaxation in stoichiometric and thallium-doped thallous halide melts

Relaxation times for ^203,205Tl, ^79,81Br and ^35,37Cl are reported for molten TlBr, TlCl and TlBr : Tl. For Br and Cl, relaxation is predominantly quadrupolar; for Tl the relaxation indicates contact hyperfine interaction with paramagnetic centres produced thermally and by adding Tl.     

Even circuits in planar graphs

We prove that a planar graph can be partitioned into edge-disjoint circuits of even length, if and only if every vertex has even valency and every block has an even number of edges.