Families of Line-Graphs and Their Quantization

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L ⁿ (G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.     

Charge location and fragmentation under electron impact. IV—the behaviour under electron impact of some N-methyl,N′-R-1,2,4-phosphadiazetidine-3-ones and related compounds

The ionization potentials of a series of N-methyl,N′-R-1,2,4-phosphadiazetidine-3-ones and related compounds have been determined. The nature of the highest occupied orbital of the molecules and the use of empirical rules to rationalize the variations in the ionization potentials are discussed. The changes in the fragmentation patterns are related to the different low ionization potential site(s) in each molecule. The occurrence of various rearrangement ions are discussed on a similar basis.     

Detecting proximities between quadrupolar nuclei by double-quantum NMR

A robust, easy to optimize, and efficient homonuclear correlation NMR experiment for half-integer quadrupolar nuclei in solids is described and has been experimentally tested on anhydrous Na2HPO4-(23Na, S= 3/2 nucleus) and as-synthesized AlPO4-14 (27Al, S= 5/2 nucleus), an aluminophosphate molecular sieve.     

Crystallographic parameters of 1-organylgermatranes

The crystallographic parameters and the translation groups of the elementary cells of the crystals of 1-methyl-, 1-ethyl-, 1-phenyl-, and 1--naphthylgermatranes have been determined by X-radiography. The volumes of the elementary cells (V), the number of molecules in them (N), the X-ray density of the crystals (x) and the packing coefficients for the molecules in the crystals (k) have been calculated from the linear and angular parameters.     

Properties of 8-Cyano-5-phenyl-7-trifluoromethyl-2,3-dihydroimidazo[1,2-a]pyridines

The alkylation, acylation, halogenation, nitration, oxidation, and hydrolysis reactions of 8-cyano-5-phenyl-7-trifluoromethyl-2,3-dihydroimidazo[1,2-a]pyridine have been studied. It was found that the 6-halo derivatives add alcohol to give covalent solvates. X-ray analysis has been carried out on one of the solvates (6-chloro-8-cyano-7-ethoxy-5-phenyl-7-trifluoromethyl-1,2,3,7-tetrahydroimidazo[1,2-a]pyridine) as well as on 8-cyano-5-phenyl-7-trifluoromethyl-2,3-dihydroimidazo[1,2-a]pyridine trifluoroacetate.     

Vierring-synthesen durch [3 + 1]-cycloaddition . Synthese von 3-imino-azetidinen aus azomethin-yliden und isonitrilen

Azomethine ylide 3 , generated by thermolysis of 3,4-diphenyl-Δ¹-1,2,3-triazoline-5,5-dimethyldicarboxylate 1 , can be trapped by isonitriles to give 3-imino-1,4-diphenylazetidine-2,2-dimethyldicarboxylates 5 . The IR, ¹H-NMR, ¹³C-NMR and mass spectral data of the new compounds are discussed.