Mathematical algorithms applied to the multi-linear regression functions for the multicomponent determination of pharmaceutical dosage form containing three-component mixtures

In the presence of closely overlapping spectra, the quantitative multiresolution of ternary mixtures of three active compounds paracetamol (PAR), caffeine (CAF) and acetylsalycilic acid (ASP) in tablets, without using pretreatment such as separation step and graphical procedure of spectra was accomplished by the multivariate spectral calibration models, tri-linear regression calibration (TLRC), multi-linear regression calibration (MLRC) and Cramer's rule solution (CRS) of three linear equation functions in the matrix form. In the first two models, TLRC and MLRC are based on the use of the linear regression functions at selected wavelength sets in the spectral region of 210-300 nm. In the case of CRS model, A1(1) (1%, 1 cm) were used to obtain three linear equation functions and this linear equation system was resolved by the Cramer's rule for the prediction of PAR, CAF and ASP in samples. In the TLRC and CRS models, the selection of the appropriate wavelength set was performed by the Kaiser's technique. The algorithms of these mathematical calibration models were briefly described. The validation of TLRC, MLRC and CRS models was carried out by analyzing various synthetic ternary mixtures and by using the standard addition technique. These three calibration approaches were applied to the analysis of the real pharmaceutical tablets containing PAR, CAF and ASP. The obtained results were statistically compared with each other by using experimental and statistical tests. In the comparison of TLRC and MLRC models to the classical approach, CRS technique, the successful assay results were observed for the quantitative multiresolution of ternary mixture of the subject active compounds.     

X-ray-induced production of gold nanoparticles on a SiO(2)/Si system and in a poly(methyl methacrylate) matrix

Prolonged exposure to X-rays of HAuCl(4) deposited from an aqueous solution onto a SiO(2)/Si substrate or into a poly(methyl methacrylate) (PMMA) matrix induces reduction of the Au(3+) ions to Au(0) and subsequent nucleation to gold nanoclusters as recorded by X-ray photoelectron spectroscopy. The corresponding major oxidation product is determined as chlorine {HAuCl(4)(ads) + X-rays --> Au(ads) + (3/2)Cl(2)(ads) + HCl(ads)}, which is initially adsorbed onto the surface but eventually diffuses out of the system into the vacuum. The reduced gold atoms aggregate (three-dimensionally) into gold nanoclusters as evidenced by the variation in the binding energy during X-ray exposure, which starts as 1.3 eV but approaches a value that is 0.5 eV higher than that of the bulk gold. The disappearance of the oxidation product (Cl2p signal) and the growth of the nanoclusters (related to the measured binding energy difference between the Si2p of the oxide and Au4f of the reduced gold) exhibit first-order kinetics which is approximately 3 times slower than the reduction of Au(3+), indicating that both of the former processes are diffusion controlled. Similarly, gold ions incorporated into PMMA can also be reduced and aggregated to gold nanoclusters using 254 nm deep UV irradiation in air evidenced by UV-vis-NIR absorption spectrocopy.     

Determination of trace cadmium in waters by flame atomic absorption spectrophotometry after preconcentration with 1-nitroso-2-naphthol-3,6-disulfonic acid on Ambersorb 572

A procedure for the determination of trace amount of cadmium after adsorption of its 1-nitroso-2-naphthol-3,6-disulfonic acid chelate on Ambersorb 572 has been proposed. This chelate is adsorbed on the adsorbent in the pH range 3-8 from large volumes of aqueous solution of water samples with a preconcentration factor of 200. After being sorbed, cadmium was eluted by 5 mL of 2.0 mol L(-1) nitric acid solution and determined directly by flame atomic absorption spectrophotometery (FAAS). The detection limit (3sigma) of cadmium was 0.32 microg L(-1). The precision of the proposed procedure, calculated as the relative standard deviation of recovery in sample solution (100 mL) containing 5 microg of cadmium was satisfactory (1.9%). The adsorption of cadmium onto adsorbent can formally be described by a Langmuir equation with a maximum adsorption capacity of 19.6 mg g(-1) and a binding constant of 6.5 x 10(-3) L mg(-1). Various parameters, such as the effect of pH and the interference of a number of metal ions on the determination of cadmium, have been studied in detail to optimize the conditions for the preconcentration and determination of cadmium in water samples. This procedure was applied to the determination of cadmium in tap and river water samples.     

Spectrophotometric multicomponent determination of sunset yellow, tartrazine and allura red in soft drink powder by double divisor-ratio spectra derivative, inverse least-squares and principal component regression methods

Double divisor-ratio spectra derivative (graphical method), classical least-squares and principal component regression (two numerical methods) methods were developed for the spectrophotometric multicomponent analysis of soft drink powders and synthetic mixtures containing three colorants without any chemical separation. The graphical method is based on the use of derivative signals of the ratio spectra using double divisor. In this method, the linear determination ranges were 2-8 mug ml(-1) sunset yellow, 4-18 mug ml(-1) tartrazine and 2-8 mug ml(-1) allura red in 0.1 M HCl. In the numerical methods, a training set was randomly prepared by using 18 samples containing between 0 and 8 mug ml(-1) of sunset yellow, 0-18 mug ml(-1) of tartrazine and 0-8 mug ml(-1) of allura red. The chemometric calibrations were calculated by using the prepared training set and its absorbances at seven points (from 375.0 to 550.0 nm) in the spectral region 325-584 nm. The proposed methods were validated by using synthetic ternary mixtures and applied to the simultaneous determination of three colorants in soft drink powders. The obtained results were statistically compared with each other.     

Atomic absorption spectrophotometric determination of trace copper in waters, aluminium foil and tea samples after preconcentration with 1-nitroso-2-naphthol-3,6-disulfonic acid on Ambersorb 572

An atomic absorption spectrophotometric method for the determination of trace copper after adsorption of its 1-nitroso-2-naphthol-3,6-disulfonic acid chelate on Ambersorb 572 has been developed. This chelate is adsorbed on the adsorbent in the pH range 1–8. The copper chelate is eluted with 5 ml of 0.1 mol l⁻¹ potassium cyanide and determined by flame atomic absorption spectrometry (FAAS). The selectivity of the proposed procedure was also evaluated. Results show that iron(III), zinc(II), manganese(II) and cobalt(II) at the 50 μg l⁻¹ level and sodium(I), potassium(I), magnesium(II), calcium(II) and aluminium(III) at the 1000 μg l⁻¹ level did not interfere. A high enrichment factor, 200, was obtained. The detection limit (3σ) of copper was 0.34 μg l⁻¹. The precision of the method, evaluated by seven replicate analyses of solutions containing 5 μg of copper was satisfactory and the relative standard deviation was 1.7%. The adsorption of copper onto Ambersorb 572 can formally be described by a Langmuir equation with a maximum adsorption capacity of 14.3 mg g⁻¹ and a binding constant of 0.00444 l mg⁻¹. The accuracy of the method is confirmed by analysing tomatoes leaves (NIST 1573a) and lead base alloy (NBS 53e). The results demonstrated good agreement with the certified values. This procedure was applied to the determination of copper in waters (tap, river and thermal waters), aluminium foil and tea samples.     

The Semi-Infinite q-Boson System with Boundary Interaction

Upon introducing a one-parameter quadratic deformation of the q-boson algebra and a diagonal perturbation at the end point, we arrive at a semi-infinite q-boson system with a two-parameter boundary interaction. The eigenfunctions are shown to be given by Macdonald’s hyperoctahedral Hall–Littlewood functions of type BC. It follows that the n-particle spectrum is bounded and absolutely continuous and that the corresponding scattering matrix factorizes as a product of two-particle bulk and one-particle boundary scattering matrices.     

An approach to best proximity points results via simulation functions

In this paper, we investigate of the existence of the best proximity points of certain mapping defined via simulation functions in the frame of complete metric spaces. We consider the uniqueness criteria for such mappings. The obtained results unify a number of the existing results on the topic in the literature.     

Artificial neural network combined with principal component analysis for resolution of complex pharmaceutical formulations

A chemometric approach based on the combined use of the principal component analysis (PCA) and artificial neural network (ANN) was developed for the multicomponent determination of caffeine (CAF), mepyramine (MEP), phenylpropanolamine (PPA) and pheniramine (PNA) in their pharmaceutical preparations without any chemical separation. The predictive ability of the ANN method was compared with the classical linear regression method Partial Least Squares 2 (PLS2). The UV spectral data between 220 and 300 nm of a training set of sixteen quaternary mixtures were processed by PCA to reduce the dimensions of input data and eliminate the noise coming from instrumentation. Several spectral ranges and different numbers of principal components (PCs) were tested to find the PCA-ANN and PLS2 models reaching the best determination results. A two layer ANN, using the first four PCs, was used with log-sigmoid transfer function in first hidden layer and linear transfer function in output layer. Standard error of prediction (SEP) was adopted to assess the predictive accuracy of the models when subjected to external validation. PCA-ANN showed better prediction ability in the determination of PPA and PNA in synthetic samples with added excipients and pharmaceutical formulations. Since both components are characterized by low absorptivity, the better performance of PCA-ANN was ascribed to the ability in considering all non-linear information from noise or interfering excipients.     

A New Chemometric Strategy in Electrochemical Method Optimization for the Quantification of Cefdinir in Tablets,Effervescent Tablets and Suspension Samples

A new voltammetric method, based on the use of single‐use pencil graphite electrode, was developed for the quantitative determination of cefdinir by square wave voltammetry. Chemometric optimization strategy was used to select the suitable values for three experimental parameters (pH of the supporting electrolyte, frequency and square wave amplitude) by applying a 3³ full factorial design model. The optimal voltammetric conditions were found to be pH 5.0 for supporting electrolyte (Britton‐Robinson buffer), 43 mV for square wave amplitude and 108 Hz for frequency. Square wave voltammograms of calibration, validation and unknown samples were recorded between 0.0–1400 mV under the optimized voltammetric conditions. Linear regression equation was computed in the linear working range of 0.5–20 μg/mL by using the relationship between the concentration and peak current at 600 mV. The optimized voltammetric method was validated by assessing the analysis results of validation samples. Then the proposed method was applied for the quantitative determination of cefdinir in three different pharmaceutical preparations, namely film‐coated tablets, effervescent tablets and powder for oral suspension. It was concluded that the proposed voltammetric method was suitable for the quantitative analysis of commercial pharmaceutical preparations containing cefdinir.     

Spectrum and Eigenfunctions of the Lattice Hyperbolic Ruijsenaars–Schneider System with Exponential Morse Term

We place the hyperbolic quantum Ruijsenaars–Schneider system with an exponential Morse term on a lattice and diagonalize the resulting n-particle model by means of multivariate continuous dual q-Hahn polynomials that arise as a parameter reduction of the Macdonald–Koornwinder polynomials. This allows to compute the n-particle scattering operator, to identify the bispectral dual system, and to confirm the quantum integrability in a Hilbert space setup.