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The research presented in this paper investigates the adsorption of cation surfactantsscetyltrimethylammonium bromide (CTAB) and cetylpyridinium chloride (CPC)sonto magnetic nanoparticles and the application of this mixed hemimicelles solidphase extraction (SPE) method for the preconcentration of several typical phenolic compoundssbisphenol A (BPA), 4-tertoctylphenol (4-OP), and 4-n-nonylphenol (4-NP)sfrom environmental water samples. In this novel SPE method, the charged surfactants CTAB and CPC form mixed hemimicelles on Fe 3 O 4 nanoparticles (Fe 3 O 4 NPs), which causes retention of analytes by strong hydrophobic and electrostatic interactions. The SPE method combines the advantages of mixed hemimicelles and magnetic nanoparticles. In order to provide guidelines for the mixed hemimicelles SPE method development, surfactant adsorption isotherms and -potential isotherms were also investigated. The main factors affecting the adsolubilization of analytes, such as the amount of Fe 3 O 4 NPs and surfactants, the type of surfactants, the solution pH, the sample loading volume, and the desorption conditions, were investigated and optimized. A concentration factor of 800 was achieved by the extraction of 800 mL of several environmental water samples using this SPE method. Under the selected conditions, detection limits obtained for BPA, 4-OP, and 4-NP were 12, 29, 34 ng/L, respectively. The accuracy of the method was evaluated by recovery measurements on spiked samples, and good recoveries (68-104%) with low relative standard deviations from 2 to 7% were achieved. The advantages of this new SPE method include high extraction yields, high breakthrough volumes, short analysis times, and easy preparation of sorbents. To the best of our knowledge, this is the first time that a mixed hemimicelles SPE method based on magnetic separation and nanoparticles has been used for the pretreatment of environmental water samples.

By an undirected rigid formation of mobile autonomous agents is meant a formation based on graph rigidity in which each pair of "neighboring" agents is responsible for maintaining a prescribed target distance between them. In a recent paper a systematic method was proposed for devising gradient control laws for asymptotically stabilizing a large class of rigid, undirected formations in two-dimensional space assuming all agents are described by kinematic point models. The aim of this paper is to explain what happens to such formations if neighboring agents have slightly different understandings of what the desired distance between them is supposed to be or equivalently if neighboring agents have differing estimates of what the actual distance between them is. In either case, what one would expect would be a gradual distortion of the formation from its target shape as discrepancies in desired or sensed distances increase. While this is observed for the gradient laws in question, something else quite unexpected happens at the same time. It is shown that for any rigidity-based, undirected formation of this type which is comprised of three or more agents, that if some neighboring agents have slightly different understandings of what the desired distances between them are suppose to be, then almost for certain, the trajectory of the resulting distorted but rigid formation will converge exponentially fast to a closed circular orbit in two-dimensional space which is traversed periodically at a constant angular speed.

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