The electrolytic separation from thorium nitrate of thorium c (212Bi) and thorium b (212Pb) in chloride solution

An electrodeposition process is described for separating thorium C and thorium B from radio-chemically “old” samples of thorium nitrate in hot 0.5N hydrochloric acid solution. The thorium C is first deposited on either platinum or nickel cathodes of special design using a controlled potential at the cathode, followed by the deposition of thorium B. Weights of the order of 10^-15 g ThC are involved.     

Ramanujan graphs

A large family of explicitk-regular Cayley graphsX is presented. These graphs satisfy a number of extremal combinatorial properties.

1. For eigenvaluesλ ofX eitherλ=±k or ¦λ¦≦2 √k?1. This property is optimal and leads to the best known explicit expander graphs.
2. The girth ofX is asymptotically ≧4/3 log _k?1 ¦X¦ which gives larger girth than was previously known by explicit or non-explicit constructions.