Pulsed jet discharge matrix isolation and computational study of bromine atom complexes: Br···BrXCH(2) (X = H, Cl, Br)

Halogen atoms are important reactive radicals in the atmosphere. In this work, pulsed jet discharge matrix isolation spectroscopy and computational methods were used to characterize prereactive complexes of halogen atoms with simple halons. Our experiments combined matrix isolation techniques with a pulsed DC discharge nozzle, where a dilute CH(2)XBr (X = H, Cl, Br)/rare gas sample was gently discharged and the products were deposited onto a cold KBr window. The Br···BrCH(2)X (X = H, Cl, Br) complexes were characterized by infrared and electronic spectroscopy, supported by ab initio and density functional theory (DFT) calculations, which shed light on the structure of, bonding in, and binding energy of the complexes. The correlation of charge-transfer energy with donor ionization potential (Mulliken correlation) was examined, and the charge-transfer photochemistry of the complexes was explored.     

Permutation groups generated by cycles of fixed length

Combinatorial conditions on a set of cycles of fixed degree inS _n are studied, so that they generateA _n orS _n . It is shown thatA _n orS _n is so generated if and only if a graph associated with the set of cycles is connected, provided two of the cycles satisfy certain, not too restrictive, criteria. As a corollary, the minimum number of cycles of degreem ≧ 2 that generateA _n or S_n is determined.     

Every vertex a king

A king in a tournament is a vertex which can reach every other vertex via a 1-path or 2-path. A new inductive proof is given for the existence of an n-tournament with exactly k kings for all integers n ? k ? 1 with the following exceptions: k = 2 with n arbitrary, and n = k = 4 (in which cases no such n-tournament exists). Also, given an n-tournament T, the smallest order m is determined so that there exists an m-tournament W which contains T as a subtournament and so that every vertex of W is a king. Bounds are obtained in a similar problem in which the kings of W are exactly the vertices of T.     

The E1 and E2 strength in the electrofission of some heavy elements

Measurements of the electrofission cross section for ²³²Th, ²³⁸U and ²³⁷Np have been made for an electron energy range from 20 to 120 MeV. A comparison is made between the electrofission and photofission cross sections using the concept of virtual photons. It is deduced that the electrofission reaction for these elements proceeds through a significant E2 contribution as well as an E1 transition mode.     

Minimum path decompositions of oriented cubic graphs

Pullman [3] conjectured that if k is an odd positive integer, then every orientation of a regular graph of degree k has a minimum decomposition which contains no vertex which is both the initial vertex of some path in the decomposition and the terminal vertex of some other path in the decomposition. In this paper, the conjecture is established for cubic graphs, and its connection with Kelly's conjecture for tournaments is described.