Applications involving oxidation with KBrO3: III. Rapid potentiometric methods for vanadium alone or in mixtures

A rapid and reliable method is given for the determination of vanadium based on oxidation of the V(IV) with a known excess of bromate to V(V). The unreacted oxidant as well as V(V) are subsequently reduced with sulfurous acid to V(IV). The resulting Br^?1 was potentiometrically titrated with Hg(I) using silver amalgam as the indicator electrode. The method finds application to the analysis of some binary and ternary mixtures.     

Electronic structure of orotic acid III geometric feature and thermal properties of some transition metal orotic acid complexes

The complexes of orotic acid with Co(II), Ni(II), Fe(III), Cu(II), and Cd(II) were prepared and their stoichiometry were determined by elemental analysis. Co(II) and Ni(II) give complexes with orotic acid of 1:1 ratio whereas that of the remaining transition metals give complexes of 1:2 ratio. The stereochemistry of the studied metal complexes has been established by analyses of their electronic spectra and magnetic susceptibilities. The mode of bonding in the studied series of metal complexes was established via, analysis of their infrared spectra. The present analysis leads to the conclusion that all metal ions studied coordinate to orotic acid via N(1) and the adjacent carboxylate group. Thermal decomposition studies of orotic acid complexes have been carried out as to understand the status of water molecules present in these complexes as well as to know their general decomposition pattern. Theoretical investigation of the electronic structure of the studied metal complexes has been carried out. MO computations at the HF-level were performed. Charge density distribution, extent of distortion from regular geometry, dipole moment, and orientation were computed and discussed.     

Glycerol: A Promising Benign Solvent for Catalyst‐free One‐pot Multi‐component Synthesis of 1H‐Pyrozolo[1,2‐b]phthalazine‐5,10‐diones and 2H‐Indazolo[2,1‐b]phthalazine‐triones Under Controlled Microwaves Irradiation

A simple green and efficient one‐pot multi‐component synthesis of 1H‐pyrozolo[1,2‐b]phthalazine‐5,10‐diones and 2H‐indazolo[2,1‐b]phthalazine‐triones has been developed utilizing one‐pot multi‐component reaction of aromatic aldehydes, active methylene reagents, phthalic anhydride, and hydrazine hydrate or alternatively phthalhydrazide in glycerol without catalyst under controlled microwave heating. The current synthetic protocol offers several advantages such as excellent yields, high EcoScale and atom economy, simple working up reactants and products, and the absence of hazardous catalysts or solvents.     

On Romanovski–Jacobi polynomials and their related approximation results

The aim of this article is to present the essential properties of a finite class of orthogonal polynomials related to the probability density function of the F -distribution over the positive real line. We introduce some basic properties of the Romanovski–Jacobi polynomials, the Romanovski–Jacobi–Gauss type quadrature formulae and the associated interpolation, discrete transforms, spectral differentiation and integration techniques in the physical and frequency spaces, and basic approximation results for the weighted projection operator in the nonuniformly weighted Sobolev space. We discuss the relationship between such kinds of finite orthogonal polynomials and other classes of infinite orthogonal polynomials. Moreover, we derive spectral Galerkin schemes based on a Romanovski–Jacobi expansion in space and time to solve the Cauchy problem for a scalar linear hyperbolic equation in one and two space dimensions posed in the positive real line. Two numerical examples demonstrate the robustness and accuracy of the schemes.     

Applications involving oxidation with ethanolic iodine. Rapid potentiometric method for some reductants

Rapid potentiometric method was adopted for the determination of small amounts of hexacyanoferrate(II), thiosulfate, thiocyanate, and ascorbic acid, based on oxidation with ethanolic iodine at different pH values and subsequently titration of iodide with mercury(II) using silver amalgam as indicator electrode. The potential breaks at the vicinity of the endpoints were sharp enough for their accurate detection. The method provides for accurate determination of small amounts of some reductants of analytical importance.     

Colorimetric Estimation of Melatonin in Pharmaceutical Formulations

 Three simple and sensitive colorimetric methods (A–C) for the determination of melatonin in bulk samples and in pharmaceutical formulations are described. They are based on the formation of coloured species by reaction of ninhydrin with the drug (method A, λ_max 397 nm) by oxidation of the indol moiety in melatonin with potassium persulphate (method B, λ_max 450 nm) or by reduction of osmium (VIII) (method C, λ_max 516 nm). Regression analysis of Beer-Lambert plots showed good correlations in concentration ranges between 0.8–14.2, 70.0–140.0 and 2.0–40.0 μg/mL for methods A, B and C, respectively. The molar absorptivity, Sandell sensitivity and detection limit were calculated. For more accurate analysis, Ringbom optimum concentration ranges were calculated. The validity of the proposed methods was tested by analysing pharmaceutical formulations containing melatonin. The relative standard deviations were ≤ 0.95% with recoveries 99.0–101.33%. Received October 20, 1999. Revision February 10, 1999.     

A fractional‐order Jacobi Tau method for a class of time‐fractional PDEs with variable coefficients

This paper presents a shifted fractional‐order Jacobi orthogonal function (SFJF) based on the definition of the classical Jacobi polynomial. A new fractional integral operational matrix of the SFJF is presented and derived. We propose the spectral Tau method, in conjunction with the operational matrices of the Riemann–Liouville fractional integral for SFJF and derivative for Jacobi polynomial, to solve a class of time‐fractional partial differential equations with variable coefficients. In this algorithm, the approximate solution is expanded by means of both SFJFs for temporal discretization and Jacobi polynomials for spatial discretization. The proposed tau scheme, both in temporal and spatial discretizations, successfully reduced such problem into a system of algebraic equations, which is far easier to be solved. Numerical results are provided to demonstrate the high accuracy and superiority of the proposed algorithm over existing ones. Copyright © 2015 John Wiley & Sons, Ltd.     

On the rate of convergence of the Legendre spectral collocation method for multi-dimensional nonlinear Volterra-Fredholm integral equations

While the approximate solutions of one-dimensional nonlinear Volterra-Fredholm integral equations with smooth kermels are now well understood,no systematic studies of the numerical solutions of their multi-dimensional counterparts exist.In this paper,we provide an efficient numerical approach for the multi-dimensional nonlinear Volterra-Fredholm integral equations based on the multi-variate Legendre-collocation approach.Spectral collocation methods for multi-dimensional nonlinear integral equations are known to cause major difficulties from a convergence analysis point of view.Consequently,rigorous error estimates are provided in the weighted Sobolev space showing the exponential decay of the numerical errors.The existence and uniqueness of the numerical solution are established.Numerical experiments are provided to support the theoretical convergence analysis.The results indicate that our spectral collocation method is more flexible with better accuracy than the existing ones.