Relaciones implicativas entre las estrategias empleadas en la resolución de situaciones lineales y no lineales

Este estudio analiza las relaciones implicativas entre las estrategias usadas por 136 estudiantes de primer curso de educación secundaria en la resolución de problemas lineales y no lineales. En primer lugar, se describen las estrategias ocupadas por los alumnos y después, empleando el software CHIC, se identifican sus relaciones implicativas. Los resultados muestran que es importante que los estudiantes comprendan la idea de razón para que sean capaces de identificar las situaciones lineales; de igual manera, aportan información sobre los posibles precursores del desarrollo del razonamiento proporcional en los estudiantes de educación secundaria.

Determination of cyclic and linear siloxanes in wastewater samples by ultrasound-assisted dispersive liquid-liquid microextraction followed by gas chromatography-mass spectrometry

A fast, simple and environmentally friendly ultrasound-assisted dispersive liquid-liquid microextraction (USA-DLLME) procedure has been developed to preconcentrate eight cyclic and linear siloxanes from wastewater samples prior to quantification by gas chromatography-mass spectrometry (GC-MS). A two-stage multivariate optimization approach has been developed employing a Plackett-Burman design for screening and selecting the significant factors involved in the USA-DLLME procedure, which was later optimized by means of a circumscribed central composite design. The optimum conditions were: extractant solvent volume, 13 µL; solvent type, chlorobenzene; sample volume, 13 mL; centrifugation speed, 2300 rpm; centrifugation time, 5 min; and sonication time, 2 min. Under the optimized experimental conditions the method gave levels of repeatability with coefficients of variation between 10 and 24% (n=7). Limits of detection were between 0.002 and 1.4 µg L−1. Calculated calibration curves gave high levels of linearity with correlation coefficient values between 0.991 and 0.9997. Finally, the proposed method was applied for the analysis of wastewater samples. Relative recovery values ranged between 71–116% showing that the matrix had a negligible effect upon extraction. To our knowledge, this is the first time that combines LLME and GC-MS for the analysis of methylsiloxanes in wastewater samples.

Screen-printed electrode-based electrochemical detector coupled with in-situ ionic-liquid-assisted dispersive liquid–liquid microextraction for determination of 2,4,6-trinitrotoluene

A novel method is reported, whereby screen-printed electrodes (SPELs) are combined with dispersive liquid–liquid microextraction. In-situ ionic liquid (IL) formation was used as an extractant phase in the microextraction technique and proved to be a simple, fast and inexpensive analytical method. This approach uses miniaturized systems both in sample preparation and in the detection stage, helping to develop environmentally friendly analytical methods and portable devices to enable rapid and onsite measurement. The microextraction method is based on a simple metathesis reaction, in which a water-immiscible IL (1-hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide, [Hmim][NTf2]) is formed from a water-miscible IL (1-hexyl-3-methylimidazolium chloride, [Hmim][Cl]) and an ion-exchange reagent (lithium bis[(trifluoromethyl)sulfonyl]imide, LiNTf2) in sample solutions. The explosive 2,4,6-trinitrotoluene (TNT) was used as a model analyte to develop the method. The electrochemical behavior of TNT in [Hmim][NTf2] has been studied in SPELs. The extraction method was first optimized by use of a two-step multivariate optimization strategy, using Plackett–Burman and central composite designs. The method was then evaluated under optimum conditions and a good level of linearity was obtained, with a correlation coefficient of 0.9990. Limits of detection and quantification were 7 μg L−1 and 9 μg L−1, respectively. The repeatability of the proposed method was evaluated at two different spiking levels (20 and 50 μg L−1), and coefficients of variation of 7 % and 5 % (n = 5) were obtained. Tap water and industrial wastewater were selected as real-world water samples to assess the applicability of the method.

Primal Attainment in Convex Infinite Optimization Duality

This article provides results guarateeing that the optimal value of a given convex infinite optimization problem and its corresponding surrogate Lagrangian dual coincide and the primal optimal value is attainable. The conditions ensuring converse strong Lagrangian (in short, minsup) duality involve the weakly-inf-(locally) compactness of suitable functions and the linearity or relative closedness of some sets depending on the data. Applications are given to different areas of convex optimization, including an extension of the Clark-Duffin Theorem for ordinary convex programs.

Tungsten coil atomic emission spectrometry combined with dispersive liquid–liquid microextraction: A synergistic association for chromium determination in water samples

A novel and environment friendly analytical method is reported for total chromium determination and chromium speciation in water samples, whereby tungsten coil atomic emission spectrometry (WCAES) is combined with in situ ionic liquid formation dispersive liquid–liquid microextraction (in situ IL-DLLME). A two stage multivariate optimization approach has been developed employing a Plackett–Burman design for screening and selection of the significant factor involved in the in situ IL-DLLME procedure, which was later optimized by means of a circumscribed central composite design. The optimum conditions were complexant concentration: 0.5% (or 0.1%); complexant type: DDTC; IL anion: View the MathML sourcePF6−; [Hmim][Cl] IL amount: 60 mg; ionic strength: 0% NaCl; pH: 5 (or 2); centrifugation time: 10 min; and centrifugation speed: 1000 rpm. Under the optimized experimental conditions the method was evaluated and proper linearity was obtained with a correlation coefficient of 0.991 (5 calibration standards). Limits of detection and quantification for both chromium species were 3 and 10 µg L−1, respectively. This is a 233-fold improvement when compared with chromium determination by WCAES without using preconcentration. The repeatability of the proposed method was evaluated at two different spiking levels (10 and 50 µg L−1) obtaining coefficients of variation of 11.4% and 3.6% (n=3), respectively. A certified reference material (SRM-1643e NIST) was analyzed in order to determine the accuracy of the method for total chromium determination and 112.3% and 2.5 µg L−1 were the recovery (trueness) and standard deviation values, respectively. Tap, bottled mineral and natural mineral water samples were analyzed at 60 µg L−1 spiking level of total Cr content at two Cr(VI)/Cr(III) ratios, and relative recovery values ranged between 88% and 112% showing that the matrix has a negligible effect. To our knowledge, this is the first time that combines in situ IL-DLLME and WCAES.

Mercury determination in urine samples by gold nanostructured screen-printed carbon electrodes after vortex-assisted ionic liquid dispersive liquid–liquid microextraction

A novel approach is presented to determine mercury in urine samples, employing vortex-assisted ionic liquid dispersive liquid–liquid microextraction and microvolume back-extraction to prepare samples, and screen-printed electrodes modified with gold nanoparticles for voltammetric analysis. Mercury was extracted directly from non-digested urine samples in a water-immiscible ionic liquid, being back-extracted into an acidic aqueous solution. Subsequently, it was determined using gold nanoparticle-modified screen-printed electrodes. Under optimized microextraction conditions, standard addition calibration was applied to urine samples containing 5, 10 and 15 μg L−1 of mercury. Standard addition calibration curves using standards between 0 and 20 μg L−1 gave a high level of linearity with correlation coefficients ranging from 0.990 to 0.999 (N = 5). The limit of detection was empirical and statistically evaluated, obtaining values that ranged from 0.5 to 1.5 μg L−1, and from 1.1 to 1.3 μg L−1, respectively, which are significantly lower than the threshold level established by the World Health Organization for normal mercury content in urine (i.e., 10–20 μg L−1). A certified reference material (REC-8848/Level II) was analyzed to assess method accuracy finding 87% and 3 μg L−1 as the recovery (trueness) and standard deviation values, respectively. Finally, the method was used to analyze spiked urine samples, obtaining good agreement between spiked and found concentrations (recovery ranged from 97 to 100%).