Preparation of rhodium–phyllosilicate catalysts without leaching in liquid-phase 1-hexene hydrogenation

Rhodium catalysts have been prepared on palygorskite and montmorillonite (clay) supports by reduction with hydrogen (1 atmosphere) at room temperature of a cationic organometallic rhodium compound anchored to the support. The activity of these catalysts for the hydrogenation of liquid-phase 1-hexene remains constant with increase of prehydrogenation time and with re-use for several runs. No rhodium leaching is observed.     

The auction algorithm for the transportation problem

The auction algorithm is a parallel relaxation method for solving the classical assignment problem. It resembles a competitive bidding process whereby unassigned persons bid simultaneously for objects, thereby raising their prices. Once all bids are in, objects are awarded to the highest bidder. This paper generalizes the auction algorithm to solve linear transportation problems. The idea is to convert the transportation problem into an assignment problem, and then to modify the auction algorithm to exploit the special structure of this problem. Computational results show that this modified version of the auction algorithm is very efficient for certain types of transportation problems.     

New Weyl groups forA 1 (1) and characters of singular highest weight modules

We consider singular Verma modules overA ₁ ⁽¹⁾ , i.e., Verma modules for which the central charge is equal to minus the dual Coxeter number. We calculate the characters of certain factor modules of these Verma modules. In one class of cases we are able to prove that these factor modules are actually the irreducible highest modules for those highest weights. We introduce new Weyl groups which are infinitely generated abelian groups and are proper subgroups or isomorphic between themselves. Using these Weyl groups we can rewrite the character formulae obtained in the paper in the form of the classical Weyl character formula for the finite-dimensional irreducible representations of semisimple Lie algebras (respectively Weyl-Kac character formula for the integrable highest weight modules over affine Kac-Moody algebras) so that the new Weyl groups play the role of the usual Weyl group (respectively affine Weyl group).     

Observation of nucleon clusters in the spontaneous decay of234U

The emission of Ne and Mg nuclei was detected in the spontaneous decay of²³⁴U with probabilities of, respectively, (3.9 ±1.0) × 10^?13 and (2.3 ±0.7) × 10^?13 relative toα-decay. The upper limits of this kind of decay for²³⁵U and²³⁶U have been established. Systematics of half-lives for cluster emission are found to be similar to the Geiger-Nuttall dependence forα-decay. Some evidence for the presence of hindrance to cluster emission from the odd-mass nuclei²³³U and²³⁵U is obtained.     

New FIR laser lines and frequency measurements for optically pumped CD3OH

Twenty new cw FIR laser lines in CD₃OH, optically pumped by a CO₂ laser, are reported. The frequencies of 39 of the stronger laser lines were measured relative to stabilized CO₂ lasers with a fractional uncertainty, as determined by the reproducibility of the FIR frequency itself, of 2 parts in 10⁷.Contribution of the U.S. Government, not subject to copyright.