A Cyclopropabenzenylidenethenone (propadienone) via a new route to alkylidenecycloproparenes

Reaction of 1,1-dichloro-2,5-diphenylcyclopropabenzene 6 with Meldrum's acid 8 in the presence of pyridine leads to coupling of the cycloproparenyl cation 7 with the stabilized diketo anion 9. Subsequent, spontaneous, base-induced dehydrochlorination gives the alkylidenecyclopropabenzene 11 in a one-pot reaction. Flash vacuum thermolysis of 11 at 650 degrees C ejects acetone and carbon dioxide, giving cyclopropabenzenylidenethenone 12 that is isolated in an Ar matrix at 20 K and characterized by a strong ketene band at 2107 cm(-1) in the IR spectrum. [reaction: see text]     

On cubic Hermite coalescence hidden variable fractal interpolation functions

Hermite interpolation is a very important tool in approximation theory and numerical analysis, and provides a popular method for modeling in the area of computer aided geometric design. However, the classical Hermite interpolant is unique for a prescribed data set,and hence lacks freedom for the choice of an interpolating curve, which is a crucial requirement in design environment. Even though there is a rather well developed fractal theory for Hermite interpolation that offers a large flexibility in the choice of interpolants, it also has the shortcoming that the functions that can be well approximated are highly restricted to the class of self-affine functions. The primary objective of this paper is to suggest a C1-cubic Hermite interpolation scheme using a fractal methodology, namely, the coalescence hidden variable fractal interpolation, which works equally well for the approximation of a self-affine and non-self-affine data generating functions. The uniform error bound for the proposed fractal interpolant is established to demonstrate that the convergence properties are similar to that of the classical Hermite interpolant. For the Hermite interpolation problem, if the derivative values are not actually prescribed at the knots, then we assign these values so that the interpolant gains global C2-continuity. Consequently, the procedure culminates with the construction of cubic spline coalescence hidden variable fractal interpolants. Thus, the present article also provides an alternative to the construction of cubic spline coalescence hidden variable fractal interpolation functions through moments proposed by Chand and Kapoor [Fractals, 15(1)(2007), pp. 41-53].     

Indirect Complexometric Determination of Mercury(II) Using Potassium Bromide as Selective Masking Agent

 A complexometric method for the determination of mercury in presence of other metal ions based on the selective masking ability of potassium bromide towards mercury is described. Mercury(II) present in a given sample solution is first complexed with a known excess of EDTA and the surplus EDTA is titrated against zinc sulfate solution at pH 5–6 using xylenol orange as the indicator. A known excess of 10% solution of potassium bromide is then added and the EDTA released from Hg-EDTA complex is titrated against standard zinc sulfate solution. Reproducible and accurate results are obtained for 8 mg to 250 mg of mercury(II) with a relative error ± 0.28% and standard deviations ≤0.5 mg. The interference of various ions is studied. This method was applied to the determination of mercury(II) in its alloys. Received April 18, 2001 Revision October 10, 2001