Julia sets of permutable Holomorphic maps

Let f and g be two permutable transcendental holomorphic maps in the plane. We shall discuss the dynamical properties of f, g and f o g and prove, among other things, that if either f has no wandering domains or f is of bounded type, then the Julia sets of f and f(g) coincide. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

Tracing of interference fringes using average gray value and simultaneous row and column scan

An algorithm for computer tracing of interference fringes is reported. The method uses the average gray-level value for thresholding, row and column scans for determining the type of the scan and simultaneous row and column scan for tracing. The proposed method yield good result even for low-contrast and high-noise images. The program for the interferogram tracing was written using MATLAB6.     

A comparative study of ruthenium(III) catalysed oxidation of L-leucine and L-isoleucine by alkaline permanganate. A kinetic and mechanistic approach

The kinetics of the Ru^III-catalysed oxidation of L-leucine and L-isoleucine by alkaline permanganate were studied and compared, spectrophotometrically using a rapid kinetic accessory. The reaction is first order with respect to [oxidant] and [catalyst] with an apparently less than unit order in [substrate] and [alkali] respectively. The results suggest the formation of a complex between the amino acid and the hydroxylated species of ruthenium(III). The complex reacts further with the alkaline permanganate species in a rate-determining step, resulting in the formation of a free radical, which again reacts with the alkaline permanganate species in a subsequent fast step to yield the products. The reaction constants involved in the mechanism were calculated. There is a good agreement between observed and calculated rate constants under different experimental conditions. The activation parameters with respect to the slow step of the mechanism for both the amino acids were calculated and discussed. Of the two amino acids, leucine is oxidised at a faster rate than isoleucine.     

Bismuth compounds in organic synthesis. A one-pot synthesis of homoallyl ethers and homoallyl acetates from aldehydes catalyzed by bismuth triflate

[reaction: see text] Three one-pot methods for the conversion of aldehydes to homoallyl ethers catalyzed by Bi(OTf)(3).xH(2)O (1 < x < 4) have been developed. The one-pot synthesis of homoallyl ethers can be achieved either by in situ generation of the acetal followed by its reaction with allyltrialkylsilane or by a three-component synthesis in which the aldehyde, trimethylorthoformate or an alkoxytrimethylsilane and allyltrimethylsilane are mixed together in the presence of bismuth triflate (0.1-1.0 mol %). In addition, a three-component synthesis of homoallyl acetates, which is achieved by reacting the aldehyde, acetic anhydride, and allyltrimethylsilane in the presence of bismuth triflate (3.0-5.0 mol %), has been developed. The use of a relatively nontoxic, easy to handle, and inexpensive catalyst adds to the versatility of these methods.     

Optimization of the process variables for the synthesis of cardanol-based novolac-type phenolic resin using response surface methodology

Models capable of predicting the maximum extent of conversion (p) of cardanol-based novolac-type phenolic resin, have been developed using response surface methodology to determine the optimum reaction conditions. Three-dimensional response surface and their contour plot were drawn. The maximum extent of conversion (98.93%) was predicted when the cardanol was condensed with formaldehyde (molar ratio 1:0.652) at 119.84 °C for a time period of 3 h with the catalyst (e.g., citric acid) concentration of 1.988% of total volume of cardanol and formaldehyde. The pH of the reaction mixture was maintained at 3.0. These predicted values for optimum process conditions were in good agreement with experimental data.