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1.
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. 相似文献
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Navjeet Kaur Yamini Verma Pooja Grewal Neha Ahlawat Pranshu Bhardwaj Nirmala Kumari Jangid 《合成通讯》2020,50(9):1286-1334
AbstractFew conversions cannot take place with ground-state reactions even with the help of a catalyst, therefore they are made to occur under photochemical conditions. The transfer of electrons took place even with the photochemical excitement of one molecule where redox reaction cannot occur at the ground state. The ground-state reactions resulted in the formation of side products. The substrates did not require any sort of chemical activation for C–N bond construction in the course of photochemical reactions. The source of energy; light has always been the interest of researchers in order to induce chemical reactions ever since the starting of scientific chemistry. The present review encloses the chemistry of photochemical transformations with a focus on their synthetic uses. The organic photochemical reactions prevent the polluting or harmful reagents thus, provides a possibility for sustainable procedures as well as green chemistry. This review article displays the formation of numerous of five-membered fused nitrogen-heterocyclic compounds. 相似文献
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Collisions of I2 in the E electronic state with rare gas atoms result in electronic energy transfer to the D, beta, and D' ion-pair electronic states. Rate constants for each of these channels have been measured when I2 is initially prepared in the J = 55, nu = 1 and 2 levels in the E state. The rate constants and effective hard sphere collision cross sections confirm the trends observed when nu = 0 in the E state is initially prepared: He collisions favor population of the D state, while Ar collisions favor population of the beta state. Final state vibrational level distributions are determined by spectral simulation and are found to be qualitatively consistent with the trends in the Franck-Condon factors. The experimental distributions are also compared to the recent quantum scattering calculations of Tscherbul and Buchachenko. 相似文献
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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. 相似文献
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