NMR studies of the chalcogen analogues of benzofuran. IV—Proton,carbon-13 and selenium-77 magnetic resonance in nitrobenzo[b]selenophenes

The ¹H, ¹³C and ⁷⁷Se chemical shifts have been measured for mononitrobenzo[ b ]selenophenes. For the homocyclic nuclei, the observed ¹H- and ¹³C-values calculated from the empirical increments of nitrobenzene. Anomalous effects are observed in the 2- and 3-substituted derivatives and the nature of the Se? NO₂ interactions in the former is discussed. ⁷⁷Se chemical shifts of the 4-, 5- and 7-nitro derivatives are approximately correlated with the CNDO calculated electron densities; they also compare well with those of selenoanisoles and other phenyl alkyl selenides. The chemical shifts are also compared with the corresponding values in other heterocycles containing a selenophene moiety.     

Stationary vacuum fields with a conformally flat three-space I. General theory

A generalized notion of conformastat space-times is introduced in relativity theory. In this sense, the conformastat space-time is stationary with the three-space of timelike Killing trajectories being conformally flat. A 3+1 decomposition of the field equations is given, and two classes of nonstatic conformastat vacuum fields are exhaustively investigated. The resulting three metrics form a NUT-type extension of the solution of the static conformastat vacuum problem. We conjecture that all conformastat vacuum space-times are axially symmetric.     

A class of Hamiltonian regular graphs

In this paper, we show that n ? 4 and if G is a 2-connected graph with 2n or 2n?1 vertices which is regular of degree n?2, then G is Hamiltonian if and only if G is not the Petersen graph.     

The i.r. spectrum of curium-244

The spectrum of curium-244 has been observed on the high resolution Fourier-transform spectrometer at Laboratoire Aimé Cotton. An electrodeless lamp containing 50 μg of CmI₃ was run for 12 hr and 800,000 points were taken. A total of 1743 lines have been ascribed to curium and 87% of the lines have been assigned to transitions between known energy levels.     

Indestructive deletions of edges from graphs

If G is a graph on p vertices with connectivity, or edge-connectivity, or minimum valency, at least k, we ask how many edges one can delete from G without reducing the appropriate quantity below k −1. When p and k are large, our answers are about , , and , respectively; we conjecture that the correct (best possible) answer is about in each case.