In this research, a simple and rapid method for the separation and preconcentration of trace amounts of crystal violet (CV) from aqueous sample solutions by modified magnetic nano-particles (MNPs) has been developed. The modification of magnetite nanoparticles was conducted by tetra ethoxysilane (TEOS) followed by micelles of anionic surfactant (SDS) to enhance the preconcentration of CV. To characterize the shape and structure of the nanoadsorbent, FT-IR and XRD procedures were used. Also, the average size of the synthesized nanoparticles was achieved between 30 and 40 nm by TEM technique. The effects of some important parameters such as: aqueous solution pH, adsorbent dosage, contact time, temperature and desorption conditions on the separation and concentration of CV were investigated. So, under optimal experimental conditions: aqueous solution pH 6, solution temperature = 20 °C, 7 mg of adsorbent, 1 mL of eluent (0.8 mL of acetonitrile + 0.2 mL of acetic acid), the recovery of CV from river water samples was achieved 98.32 ± 0.056% (n = 5) in two short periods of time for extraction (5 min) and elution (2 min). The maximum sorption capacity of the nano-composite was determined to be 16.37 mg/g. Also linear dynamic range and limit of detection were calculated to be 10-2500 ppb and 1.82 ppb, respectively. Finally, the proposed method was successfully applied for the separation and concentration of CV from the real water samples and the results were satisfied.

Many studies have recently been conducted on the evaluation of system performance with a two‐stage network structure in data envelopment analysis (DEA) literature. One of the topics of interest to researchers has been the mitigation of undesirable products or nondiscretionary factors into their corresponding possible production set (PPS) and their impact on overall efficiency calculations. Determination of decision‐making units (DMUs) with Pareto–Koopmans efficiency status is decisive in identifying benchmark units. The calculated overall efficiency status is compromised when both undesirable products and nondiscretionary factors are present. This work utilizes an axiomatic approach. A novel PPS for a two‐stage network in presence of undesirable intermediate products and nondiscretionary exogenous inputs is introduced. Based on this PPS and by focusing on the principle of mathematical dominance, new models for evaluating overall and divisional efficiencies are presented. In addition, by proposing a two‐step network DEA approach, a necessary and sufficient condition for detection of DMUs with Pareto–Koopmans efficiency status is provided. And by introducing a two‐step algorithm, a novel technique for determining overall efficiency conditions is produced. Finally, the proposed technology is applied to a practical example, and outcomes are discussed.

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