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A wealth of superfine single-crystal hollow cuprous oxide (Cu2O) spheres with nanoholes have been prepared for the first time with glucose as the reducing agent and gelatin as a soft template. The mechanism of the formation of these hollow crystals with nanoholes has been studied, and the UV–visible absorption spectrum has been used to resolve the excitonic or interband transitions of the hollow Cu2O spheres. The band gap of the products calculated from the UV–vis spectra is as large as 2.67 eV, which is ascribed to the decrease of the overall crystal size and the hollowing of the Cu2O spheres with nanoholes.

BACKGROUND Maltose is an essential derivative of starch. To understand the processability and stability of maltose‐containing foods, material characterization of the phase and state transition from its amorphous state is required. Although the crystallization of amorphous maltose is well understood, few studies have reported the relationship between the crystallization and the glass transition temperature (Tg)‐related molecular mobility. In this study, water sorption, crystallization, Tg‐related α‐relaxation, and the corresponding time factor for amorphous maltose and maltose / whey protein isolate (WPI) mixtures are measured at various water activity (aw) levels and 25 °C. RESULTS The water‐additive principle for maltose / WPI mixtures was observed at aw ≤ 0.440 at the molecular level, whereas the crystallization of amorphous maltose occurred at high aw values (≥0.534). The crystal formation and crystallization kinetics of amorphous maltose were affected by water and WPI at aw ≥ 0.534 and 25 °C, as determined by X‐ray diffraction. The relationship between Tg and the water content was fitted by the Gordon–Taylor model, and its constant showed a compositional dependence for the maltose / WPI mixtures. The α‐relaxation temperature of the amorphous samples decreased due to water plasticization, but increased with an increase in the WPI quantity. The Strength (S) value for amorphous maltose, which was a quantitative estimate of the compositional effects on molecular mobility, was based on the William–Landel–Ferry (WLF) equation. CONCLUSION The S concept exhibits considerable potential for application in controlling the crystallization of amorphous maltose and improving the processability and stability of maltose‐containing foods. © 2020 Society of Chemical Industry

Abstract:The linear arboricity of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama et al. conjectured thatfor any simple graph G. Wu [5] proved the conjecture for a planar graph G of maximum degree = 7. It is noted here that the conjecture is also true for = 7.