All‐in‐one solid‐phase microextraction: Development of a selective solid‐phase microextraction fiber assembly for the simultaneous and efficient extraction of analytes with different polarities

In the present work, for the first time, an all‐in‐one solid‐phase microextraction technique was developed for the simultaneous and efficient extraction of analytes within a vast polarity range. A novel fiber assembly composed of two different steel components each coated with different coatings (polydimethylsiloxane and polyethylene glycol) in terms of polarity by sol–gel technology was employed for the extraction of model compounds of different polarity in a single run followed by gas chromatography with mass spectrometry. Effective parameters in the extraction step and gas chromatography with mass spectrometry analysis were optimized for all model compounds. The detection limits of the developed method for model compounds were below 0.2 ng/L. The repeatability and reproducibility of the proposed method, explained by relative standard deviation, varied between 7.22 and 9.15% and between 7.95 and 14.90 (n = 5), respectively. Results showed that, under random conditions, compared to separate extractions performed by two other differently end‐coated components that had not been assembled as the final dual fiber, as two individual fibers; simultaneous, efficient and relatively selective extraction of all model compounds was obtained in a single run by the proposed all‐in‐one technique. Finally, the optimized procedure was applied to extraction and determination of the model compounds in spiked water samples.     

Active Constraint Set Invariancy Sensitivity Analysis in Linear Optimization

Active constraint set invariancy sensitivity analysis is concerned with finding the range of parameter variation so that the perturbed problem has still an optimal solution with the same support set that the given optimal solution of the unperturbed problem has. However, in an optimization problem with inequality constraints, active constraint set invariancy sensitivity analysis aims to find the range of parameter variation, where the active constraints in a given optimal solution remains invariant.For the sake of simplicity, we consider the primal problem in standard form and consequently its dual may have an optimal solution with some active constraints. In this paper, the following question is answered: “what is the range of the parameter, where for each parameter value in this range, a dual optimal solution exists with exactly the same set of positive slack variables as for the current dual optimal solution?”. The differences of the results between the linear and convex quadratic optimization problems are highlighted too.