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A criterion is proposed that determines the moment when the growth pattern of the monotonic numerical sequence varies from the linear to the parabolic one. The criterion is based on the comparison of squares of errors for the linear and the incomplete quadratic approximation. The approximating functions are constructed locally, only at those points that are located near a possible change in nature of the increase in the sequence. [ABSTRACT FROM AUTHOR]

The nanocomposite PbSnF4@SWNT was obtained by capillary technique for the first time. This nanocomposite was investigated using X-ray diffraction phase analysis (XRD), high-resolution transmission electron microscopy (HRTEM) and scanning transmission electron microscopy (STEM), energy-dispersive X-ray spectroscopy (EDX). SWNT diameter is ~2 nm. Lead tetrafluorostannate (PbSnF4) monoclinic modification (space group P2/n) was identified by XRD analysis. The periodicity of the crystal plane (201) along the tube axis is ~3.2Å. The distortion of plane is 11° with respect to the nanotube axis. The model of PbSnF4 single crystal contains ~168 atoms. The structure of 1D PbSnF4@SWNT nanocomposite and HREM image were modelled. [ABSTRACT FROM AUTHOR]