[en] Based on the bosonization approach, the supersymmetric Burgers (SB) system is transformed to a coupled bosonic system. By solving the bosonized SB (BSB) equation, the difficulties caused by the anticommutative fermionic field of the SB equation can be avoided. The nonlocal symmetry for the BSB equation is obtained by the truncated Painlevé method. By introducing multiple new fields, the finite symmetry transformation for the BSB equation is derived by solving the first Lie’s principle of the prolonged systems. Some group invariant solutions are obtained with the similarity reductions related by the nonlocal symmetry. (paper)

[en] Two long Schiff base ligands H₂L¹ and H₂L² that have flexible long-chain backbones were used to synthesize 8- and 12-metal Zn-Ln nanoclusters [Zn₄Eu₄(L¹)₂(OAc)₁₀(NO₃)₂(OH)₄] (1) and [Zn₈Yb₄(L²)₈(OAc)₈](OH)₄ (2), respectively. The crystal structures of 1 and 2 show that their molecular sizes are about 9 × 10 × 11 Å and 9 × 19 × 28 Å, respectively. Both clusters display typical emission bands of lanthanide ions. Interestingly, the Zn–Yb cluster 2 exhibits NIR luminescent response to metal cations, especially to Co²⁺ and Cu²⁺ at the ppm level.

[en] Graphical abstract: - Highlights: • We develop a new DGT device for in situ sampling Cr (VI) in water. • Polyquaternary ammonium salt (PQAS) was used as binding agent of DGT device. • Cr (VI) can be accumulated in the PQAS binding phase whereas Cr (III) cannot. • The DGT performance was independent of pH 3–12 and ionic strength 1 × 10⁻³–1 mol L⁻¹. - Abstract: A diffusive gradients in thin films (DGT) device with polyquaternary ammonium salt (PQAS) as a novel binding agent (PQAS DGT) combined with graphite furnace atomic absorption spectrometry (GFAAS) was developed for the selective sampling and measurement of Cr (VI) in water. The performance of PQAS DGT was independent of pH 3–12 and ionic strength from 1 × 10⁻³ to 1 mol L⁻¹. DGT validation experiments showed that Cr (VI) was measured accurately as well as selectively by PQAS DGT, whereas Cr (III) was not determined quantitatively. Compared with diphenylcarbazide spectrophotometric method (DPC), the measurement of Cr (VI) with PQAS DGT was agreement with that of DPC method in the industrial wastewater. PQAS-DGT device had been successfully deployed in local freshwater. The concentrations of Cr (VI) determined by PQAS DGT coupled with GFAAS in Nuer River, Ling River and North Lake were 0.73 ± 0.09 μg L⁻¹, 0.50 ± 0.07 μg L⁻¹ and 0.61 ± 0.07 μg L⁻¹, respectively. The results indicate that PQAS DGT device can be used for the selective sampling and measurement Cr (VI) in water and its detection limit is lower than that of DPC method