Investigating the effect of flexible constraints on the accuracy of self‐modeling curve resolution methods in the presence of perturbations

Self‐modeling curve resolution methods have continuously been improved during recent years. Many efforts have been made on curve resolution methods to reduce the rotational ambiguity by means of different types of constraints. Choosing proper constraints and cost functions is critically important for the reduction of the rotational ambiguity because the constraints have a direct influence on the accuracy of the area of feasible solution (AFS). In this work, we introduce a new improved cost function, which serves to apply nonnegativity, unimodality, equality, and closure constraints. We also investigate the reduction of the AFS under hard and soft constraints. Another point of this work is to evaluate the accuracy and precision of the reduced AFS in the presence of noise and perturbations, under hard and soft implementation of nonnegativity, unimodality, equality, and closure constraints. A comparison is given between the reduced AFS with soft constraints (small deviations from constraints are accepted) and the reduced AFS under hard constraints (restrictedly forced constraints). A graphical visualization of this comparison is presented for various model problems. The results show that an AFS computation with soft constraints provides more reliable results, especially in the presence of noise. The test problems substantiate significant advantages of soft constraints over hard constraints because the obtained profiles are closer to the potentially true noisy profiles, which contain small deviations from ideal responses. Using tunable parameters ϵ,γ,ω,δ is one of the advantages of soft constrained cost function that allows the small deviations from ideal responses. Ultimately, soft constraints can help to reduce the lack‐of‐fit, and they are a proper instrument to handle the effect of noise on the AFS. Copyright © 2016 John Wiley & Sons, Ltd.     

Steady vortical flow around a finite plate

An explicit solution for a layer of fluid with constant vorticitysurrounding a thin plate of finite length is obtained usingelementary conformal mapping methods. In the limit of largeplate length the behaviour of the solution near the ends ofthe plate tends to that of the previously known solution fora semi-infinite plate. Contour dynamics is used to investigatethe stability of the steady solutions.     

Chemometrics assisted dispersive liquid–liquid microextraction for quantification of seven UV filters in urine samples by HPLC‐DAD

In the present study, dispersive liquid–liquid microextraction followed by high performance liquid chromatography‐diode array detection has been developed as simple, rapid, accurate, and efficient sample preparation method for simultaneous determination of seven organic UV filters in urine samples. The influence of the main effects as well as their interactions was studied through a 2^(6–2) fractional factorial design. The candidate parameters were: type and volume of dispersant and extraction solvents, sample pH, and salt concentration. Under final optimal conditions, the analytes were extracted from 5 mL of samples by addition of 0.5 mL of acetonitrile (dispersing solvent) containing 70 μL of carbon tetrachloride (extraction solvent), without modifying the pH of the solution and applying the (+1) level of salt concentration (10% w/v NaCl). The assay was linear (R² > 0.997), relative recoveries ranged from 86.9 up to 97.3% and the LOQs between 3 and 45 ng mL^?1 were obtained. The intra‐ and interday RSDs were lower than 5 and 8% at the middle point of the linear range, respectively. The proposed method was successfully applied to different volunteer urine samples and it was shown that the extraction efficiency was not affected by the type of urine samples.     

Nonlinear optical characterization of phosphate glasses based on ZnO using the Z-scan technique

The nonlinear optical properties of a phosphate vitreous system [(ZnO)_x-(MgO)_30-x-(P₂ O₅)₇₀], where x=8, 10, 15, 18, and 20 mol% synthesized through the melt-quenching technique have been investigated by using the Z-scan technique. In the experiment, a continuous-wave laser with a wavelength of 405 nm was utilized to determine the sign and value of the nonlinear refractive (NLR) index and the absorption coefficient with closed and opened apertures of the Z-scan setup. The NLR index was found to increase with the ZnO concentration in the glass samples by an order of 10^-10 cm²·W^-1. The real and imaginary parts of the third-order nonlinear susceptibility were calculated by referring to the NLR index (n₂) and absorption coefficient (β) of the samples. The value of the third-order nonlinear susceptibility was presented by nonlinear refractive or absorptive behavior of phosphate glasses for proper utilization in nonlinear optical devices. Based on the measurement, the positive sign of the NLR index shows a self-focusing phenomenon. The figures of merit for each sample were calculated to judge the potential of phosphate glasses for application in optical switching.     

Fast liquid chromatography-diode array detection assisted by chemometrics for quantification of seven ultraviolet filters in effluent wastewater

A fast chromatographic method is presented for simultaneous quantification of seven organic ultraviolet (UV) filters (benzophenone-3,4-methylbenzilidene camphor, octocrylene, 1-(4-tert-butylphenyl)-3-(4-methyoxyphenyl)1,3-propanedione), ethylhexyl methoxy cinnamate, ethylhexyl salicylate and homosalate) in effluent wastewater samples. The UV filters were pre-concentrated by Bond Elut-ENV cartridges and separated on an ODS column (15 cm × 0.46 cm, 5 μm) in less than 2.5 min using a non-aqueous mobile phase of methanol-acetonitrile (50:50, v/v) with flow-rate of 1.5 mL min⁻¹. Appropriate baseline correction through asymmetric least squares was applied to reduce the matrix of background signals in three way data. Then, second-order calibration based on multivariate curve resolution-alternating least squares (MCR-ALS) was implemented on the unfolded three-way data obtained from liquid chromatography with diode array detection (LC-DAD) through standard addition calibration method for handling co-eluted peaks, systematic and proportional errors. Recoveries ranging from 76% to 130% and %RSD values less than 11.2 for all UV filter shows the accuracy and precision of the proposed method in wastewater samples. In addition, statistical t-test as well as computed elliptical joint confidence region (EJCR) confirms the accuracy of the proposed method and indicates the absence of both constant and proportional errors in the predicted concentrations. This study demonstrates that coupling of the fast HPLC-DAD method with powerful algorithm of MCR-ALS can be considered as an efficient method for quantification of UV filters in highly contaminated samples of wastewaters where both time and cost per each analysis can be reduced significantly.