Cubic graphs on twelve vertices and the line graph of a finite affine plane

It is shown by Rao and Rao that certain geometric properties characterize the line graph of a BIB design with parameters b, v, r, k, 1, provided r - 2k + 1 < 0. If r = k + 1, and $\text{k \#\&62; 2}$, a characterization of the line graph of a finite affine plane is obtained. If r - 2k + 1 = 0, the only possible value for k is 2 and consequently r = k + 1 resulting in the case of the line graph of a finite affine plane. It is shown here that if r = k + 1 and k = 2, there are exactly seven other non-isomorphic graphs with those properties which are not the line graph of a finite affine plane and these are the only cubic graphs on twelve vertices with no quadrilaterals.     

A new and rapid titration of antimony(III) with potassium dichromate, with iron(II) as inductor

The optimum conditions for the titration of antimony(III) with dichromate, and diphenyl-aminesulphonic acid as indicator, have been established. No iodine catalyst is used; the analytical reaction is based on an induced reaction with iron(II) as inductor. The titration can be done as easily as an iron(II) titration and the end-point is equally sharp. Titrations are possible with 0.01N solutions.     

Measurement of vibration with Young's fringe modulated speckle patterns in a photorefractive correlator

A technique has been proposed to analyze small in-plane component of vibrations by measuring the fringe shift, and analysing the correlation output of captured vibrating Young's fringes with a photorefractive correlator. Fringes are formed due to interference between the reconstructed speckled beam recorded for stationary object beam, and vibrated speckled beam transmitting through a BaTiO₃ crystal after introducing a small shift in the diffuser position. The correlation peak intensity is affected due to mismatch of vibrations between two piezo-mirrors in the object beam. High correlation output gives an indication of the frequency matching of known reference and unknown vibrations, thus giving information on the frequency of vibration. Vibration amplitudes of the order of a wavelength of light have been measured by counting the number of fringes passing past a line in the observation plane.     

Cobalt-catalyzed aziridination with diphenylphosphoryl azide (DPPA): direct synthesis of N-phosphorus-substituted aziridines from alkenes

A new catalytic aziridination system that consists of cobalt(II) tetraphenylporphyrin [Co(TPP)] as the catalyst and diphenylphosphoryl azide (DPPA) as the nitrene source has been developed. The cobalt-based catalytic system allows direct synthesis of N-phosphorus-substituted aziridines from alkenes with dinitrogen as the byproduct. Cobalt ion seems essential to the catalytic aziridination with DPPA as no or only trace amounts of the desired products were observed with other metal complexes of tetraphenylporphyrin.     

Studies on the interaction of Eu(III) with lawsone (2-hydroxy-1,4-naphthoquinone), lapachol (2-hydroxy-3-(3-methyl-2-butenyl)-1,4-naphthoquinone), juglone (5-hydroxy-1,4-naphthoquinone) and plumbagin (2-methyl-5-hydroxy-1,4-naphthoquinone)

pH-metric studies show that one mole of Eu(III) interacts with three molecules of each of juglone, plumbagin, lawsone and lapachol in solution. The stability and thermodynamics of these systems (50% aqueous acetone, 0.1 M KNO₃ ionic strength) are discussed and explained.     

Nucleophilic substitution of alkyl halides by zinc salts-32 preparation of tertiary alkyl esters and ethers under non-solvolytic conditions

Zinc salts of carboxylic acids, phenols and alcohols are found to react with tertiary alkyl halides in nonpolar solvents and in presence of a base yielding the corresponding esters and ethers in moderate to good yields.