In the present investigations we study a general form of a convolution integral involving the Fox'sH-function. A convolutional structure associating theH-transforms specified for certain spaces of functions is also studied. Applications giving Leibnitz type expansions (and integral
analogues) are treated in the concluding part of the paper.
Authors:Shashi B. Kalia, Priyanka Sankhyan, R. Puri and J. Christopher
Non-isothermal techniques, i.e. thermogravimetry (TG) and differential scanning calorimetry (DSC), have been applied to investigate the thermal behaviour of carbaryl (1-naphthyl-N-methylcarbamate = 1-Naph-N-Mecbm) and its complexes, M(1-Naph-N-Mecbm)4X2, where M = Cu, X = Cl, NO3 and CH3COO and M = Zn, X = Cl. Carbaryl and Zn(1-Naph-N-Mecbm)4Cl2 complex exhibit two-stage thermal decomposition while the copper(II) complexes exhibit three and four-stage decomposition in their TG curves. The nature of the metal ion has been found to play highly influential role on the nature of thermal decomposition products as well as energy of activation ‘E∗’. The presence of different anions does not seem to alter the thermal decomposition patterns. The complexes display weak to medium intensity exothermic and endothermic DSC curves, while the free ligand exhibits two endothermic peaks. The kinetic and thermodynamic parameters namely, the energy of activation ‘E∗’, the frequency factor ‘A’ and the entropy of activation ‘S∗’ etc. have been rationalized in relation to the bonding aspect of the carbaryl ligand. The nature and chemical composition of the residues of the decomposition steps have been studied by elemental analysis and FTIR data.
A simple, selective, precise, and reproducible high-performance thin-layer chromatography (HPTLC) method for the analysis of vicine in herbal extracts and formulations containing Momordica charantia was developed. The study was performed on aluminum-based pre-coated TLC plates (silica gel 60F254). The chromatograms of samples were developed in twin trough glass chamber pre-saturated with mobile phase comprised of ethyl acetate-methanol-water-formic acid (7.5:3:1:0.1, v/v/v/v) at room temperature (25 ± 2°C). The densitometric analysis was carried out in absorbance mode at 278 nm. The optimized mobile phase showed a compact spot of vicine (RF = 0.31 ± 0.02) from the other constituents present in the samples. The linear regression analysis data for the calibration plots showed good linearity (r2 = 0.9990) with respect to peak area in the range of 200–1400 ng spot−1. The method was validated as per International Conference on Harmonization (ICH) guidelines. The limits of detection and quantification (50 and 150 ng spot−1, respectively) were also established. The proposed method has shown the excellent recovery (98.01–99.33%), which supports the suitability of the method for the analysis. Statistical analysis of the obtained data showed the selectivity of the proposed method for vicine estimation in the herbal samples.