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.     

THE VISUAL PIGMENT CYANIDE EFFECT

The visual pigment of the Tokay gecko (Gekko gekko) with its in situ absorption maximum at 521 nm has its spectral position at 500 to 505 nm when chloride-deficient digitonin is used for the extraction. In this case the addition of chloride or bromide to the extract restores the maximum to 521 nm. This property, characteristic of gecko pigments in general, does not occur with any of the rhodopsins that have been tested. Simple salts of cyanide, a pseudohalogenoid with an ionic radius close to those of chloride and bromide and/or its hydrolysis product attacks both this gecko pigment and rhodopsins in the dark. This is seen as a slow thermal loss of photopigment if (sodium) cyanide is present at concentrations above 40 mM for the gecko pigment and 150 mM for the rhodopsins of the midshipman (Porichthys notatus) and of the frog (Rana pipiens). In all cases the loss of the photopigment is accompanied by the appearance of a spectral product with maximum absorption at about 340 nm. Cyanide addition has no effect on the photosensitivity of the native pigments and neither does it alter, as do chloride, bromide and other anions, the spectral absorbance curve. The spectral product at 340 nm also appears when the visual pigments are photolyzed in the presence of cyanide salts below the threshold concentrations given above. Incubation of digitonin-solubilized all-trans-retinal with (sodium) cyanide leads to a reaction product with absorption spectrum similar to that obtained with visual pigments under comparable conditions.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.