On composition of some general fractional integral operators

In the present paper we derive three interesting expressions for the composition of two most general fractional integral oprators whose kernels involve the product of a general class of polynomials and a multivariableH-function. By suitably specializing the coefficients and the parameters in these functions we can get a large number of (new and known) interesting expressions for the composition of fractional integral operators involving classical orthogonal polynomials and simpler special functions (involving one or more variables) which occur rather frequently in problems of mathematical physics. We have mentioned here two special cases of the first composition formula. The first involves product of a general class of polynomials and the Fox’sH-functions and is of interest in itself. The findings of Buschman [1] and Erdélyi [4] follow as simple special cases of this composition formula. The second special case involves product of the Jacobi polynomials, the Hermite polynomials and the product of two multivariableH-functions. The present study unifies and extends a large number of results lying scattered in the lierature. Its findings are general and deep.     

A facile deprotection of oximes using glyoxylic acid in an aqueous medium

Oximes of ketones and aldehydes are efficiently deprotected with glyoxylic acid in an aqueous medium at room temperature. Oximes can be cleaved selectively in the presence of a TBDMS group. This method is high yielding, fast, clean, safe, cost effective, and therefore very suitable for practical organic synthesis.     

Iodometric microdetermination of carboxyl function by indirect and direct procedures

Two iodometric procedures have been described for the microdetermination of certain organic acids which can be adopted for evaluating 0.03–0.1 meq of these acids. These methods consist of treating the acid sample with an excess of neutral potassium iodide and iodate. In the indirect method the iodate used up is measured whereas the direct procedure is based on the titration of the liberated iodine. The latter procedure has been applied to determine acids in a water-alcohol medium also. The effect of various factors influencing the stoichiometry of the reactions involved has also been studied.     

Electron and positron impact excitation of hydrogen from the initially excited 22S state to 32S and 32P states

The total and differential cross sections for the electron and positron impact excitation of hydrogen from its initially excited metastable 2²S state to 3²S and 3²P states are reported. A distorted-wave approximation theory is used for the calculation. The angular correlation parameters, Ly and alignment angle are also reported for 2²S-3²P excitation. For comparison, similar first Born results are also obtained. Interesting features are noted on comparing our distorted wave results with the first Born results as well as with the other available results forn ²S andn ²P (n=2,3) excitations from the ground 1²S state of hydrogen.