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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
3.
Sonya V. Roberson Albert J. Fahey Amit Sehgal Alamgir Karim 《Applied Surface Science》2002,200(1-4):150-164
We present a simple method for chemical modification of chlorosilane self-assembled monolayers (SAMs) on Si surfaces by exposure to a gradient of UV-ozone radiation to create stable substrates with a range of contact angles (θH2O≈5–95°) and surface energies on a single substrate. These gradient energy substrates are developed to potentially generate libraries for combinatorial studies of thin film phenomenology, where a systematic variation of interfacial surface energy represents one of the significant parameters along one axis. The graded oxidation process presents a systematic variation of surface chemical composition. We have utilized contact angle measurements and time-of-flight secondary ion mass spectrometry (ToF-SIMS) to investigate this variation for a series of ions, among which are SiCH3+, SiOH+ and COOH−. We show that the macroscopic measurements of surface free energy/contact angle correlate with the detailed analysis of surface chemistry (as assessed by ToF-SIMS) on these test substrates. 相似文献
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The Schiff base [1,2-bis(salicylidene amino)phenylene]cobalt(II) complex, chemically bonded to a carbamate-modified silica gel catalyst, has been prepared by a four step procedure. The oxidation of cyclohexane was studied in the presence of this catalyst under relatively mild conditions (150–200 °C, 15–20 atm) using molecular oxygen. The catalyst was found to be very selective for the production of cyclohexanol, with cyclohexanone formed in only a small amount (45:1). This is in contrast to the commercially available processes in which cyclohexanol and cyclohexanone are both formed in appreciable amounts. The t.g.a. analysis shows the catalyst to be stable up to 211 °C and atomic absorption spectroscopy indicated negligible metal loss during 50 h use of the catalyst up to 180 °C. 相似文献
6.
An efficient route for the regio- and stereoselective ring opening of N-tosylaziridines with zinc dihalides (ZnX2, X = Cl, Br, I) is described. Depending on the solvent and Zn(II) halide, β-halo amines or imidazolines are obtained selectively in good to excellent yields. 相似文献
7.
Akhilesh K. Verma Rupesh Kumar Amit Saxena Subho Mozumdar 《Tetrahedron letters》2005,46(31):5229-5232
A novel method for effecting the aza-Michael reactions of N-alkyl- and N-arylpiperazines with acrylonitrile using Cu-nanoparticles is described. The method features the use of 10 mol % Cu (14-17 nm) nanoparticles under mild reaction conditions to afford the addition products in good to excellent yields. The Cu-nanoparticles selectively catalysed the aza-Michael reaction of N-alkyl- and N-arylpiperazines in the presence of aromatic amino or aliphatic hydroxy groups. 相似文献
8.
A new tetradentate dihydrogen perchlorate macrocyclic ligand (2,4,9,11-tetraphenyl-1,5,8,12-tetraazacyclotetradeca-1,4,8,11-tetraene dihydrogen perchlorate) was prepared and characterised. The macrocycle behaves as a selective chelating ion-exchanger for some metal ions. The polystyrene-based membrane electrode is found to exhibit quite promising selectivity for Cr3+ ions. It can be used to estimate chromium concentrations in the range 3.16x 10(-6)-1.00x10(-1) M with a near-Nernstian slope of 17.5 mV per decade of concentration between pH 3.0 to 6.5. The electrode is found to possess a fast response time of 15 s and was used over a period of three months with good reproducibility (s = +/- 0.3 mV). The selectivity coefficient values for mono-, di- and trivalent cations indicate excellent selectivity for Cr3+ ions over a large number of other cations. Anions such as Cl- and SO4(2-) do not interfere and the electrode also works satisfactorily in a mixed organic-water solution. The sensor has been used as an indicator electrode for the potentiometric titration of Cr3+ with EDTA. The practical utility of the membrane sensor has also been demonstrated in solutions contaminated with detergents (CTAB and SDS). Above all, the membrane sensor has been very successfully used to determine Cr3+ in some foods. 相似文献
9.
Chen Wang Amit Fischer Avner Ehrlich Yaakov Nahmias Itamar Willner 《Chemical science》2020,11(17):4516
The enzymes glucose oxidase (GOx), acetylcholine esterase (AchE) and urease that drive biocatalytic transformations to alter pH, are integrated into pH-responsive DNA-based hydrogels. A two-enzyme-loaded hydrogel composed of GOx/urease or AchE/urease and a three-enzyme-loaded hydrogel composed of GOx/AchE/urease are presented. The biocatalytic transformations within the hydrogels lead to the dictated reconfiguration of nucleic acid bridges and the switchable control over the stiffness of the respective hydrogels. The switchable stiffness features are used to develop biocatalytically guided shape-memory and self-healing matrices. In addition, loading of GOx/insulin in a pH-responsive DNA-based hydrogel yields a glucose-triggered matrix for the controlled release of insulin, acting as an artificial pancreas. The release of insulin is controlled by the concentrations of glucose, hence, the biocatalytic insulin-loaded hydrogel provides an interesting sense-and-treat carrier for controlling diabetes.Biocatalytic control over the stiffness of pH-responsive hydrogels is applied to develop shape-memory, self-healing and controlled release matrices. 相似文献
10.
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