数学建模对高中生构建数学底层思维的作用及其教学实施建议

数学底层思维即用数学的眼光观察世界、用数学的思维分析世界以及用数学的语言表达世界,是人们面对自然和社会中纷繁多样的现象和问题时,所展现的自发的、不依赖监督的、融汇数学学科核心素养的思维方式.作为国家高中新课程标准中数学六大核心素养之一的数学建模,是培养学生数学底层思维的良好载体,对人才培养和社会发展均起到良好的促进作用.本文主要阐述了数学建模对高中生构建数学底层思维的作用,并结合教学实例给出教学实施建议.     

Strong π-π stacking interactions led to the mis-assignment of dimer emissions to the monomers of 1-acetylpyrene

Both experimental and computational studies showed owing to strong π-π stacking interactions, 1-acetylpyrene mainly exists in dimers and molecular aggregates even at low concentrations, which led to the mis-assignment of its monomer emission peaks.     

Supercubooctahedron (Cs6Cl)2Cs5[Ga15Ge9Se48] Exhibiting Both Cation and Anion Exchange

A novel type of supertetrahedral connectivity is exhibited by the 72‐atom discrete supercubooctahedron in (Cs₆Cl)₂Cs₅[Ga₁₅Ge₉Se₄₈] ( 1 ), which undergoes both cation and anion exchange, as revealed by unambiguous single‐crystal X‐ray diffraction data. Electronic‐structure studies helped to understand the Ge/Ga distribution.     

Luminescent Ag6Au6 Heterometallic Ethisterone Cluster and Probe for Estrogen Receptor α

A heterometallic cluster [Ag₆Au₆(ethisterone)₁₂] of an unprecedented topology was synthesized and characterized. A sensitive and specific probe for estrogen receptor α (ERα) has been developed for the first time based on the enhancement of the Ag₆Au₆ luminescence.     

Multilayered 2D Cesium-Based Hybrid Perovskite with Strong Polarization Sensitivity: Dimensional Reduction of CsPbBr3

3D perovskite CsPbBr₃ has recently taken a blooming position for optoelectronic applications. However, due to the lack of natural anisotropy of optical attributes, it is a great challenge to fulfil polarization-sensitive photodetection. Here, for the first time, we exploited dimensionality reduction of CsPbBr₃ to tailor a 2D-multilayered hybrid perovskite, (TRA)₂CsPb₂Br₇ ( 1 , in which TRA is (carboxy)cyclohexylmethylammonium), serving as a potential polarized-light detecting candidate. Its unique quantum-confined 2D structure results in intrinsic anisotropy of electrical conductivity, optical absorbance, and polarization-dependent responses. Particularly, it exhibits remarkable dichroism with the photocurrent ratio (I_pc/I_pa) of ≈2.1, being much higher than that of the isotropic CsPbBr₃ crystal and reported CH₃NH₃PbI₃ nanowire (≈1.3), which reveals its great potentials for polarization-sensitive photodetection. Further, crystal-based detectors of 1 show fascinating responses to the polarized light, including high detectivity (>10¹⁰ Jones), fast responding time (≈300 μs), and sizeable on/off current ratios (>10⁴). To our best knowledge, this is the first study on 2D Cs-based hybrid perovskite exhibiting strong polarization-sensitivity. The work highlights an effective pathway to explore new polarization sensitive candidates for hybrid perovskites and promotes their future electronic applications.     

Growth of Hydrophilic CuS Nanowires via DNA‐Mediated Self‐Assembly Process and Their Use in Fabricating Smart Hybrid Films for Adjustable Chemical Release

Facile growth of CuS nanowires through self‐assembly and their application as building blocks for near‐infrared light‐responsive functional films have been demonstrated. It is found that DNA is a key factor in preparing the CuS material with defined nanostructure. An exclusive oriented self‐aggregate growth mechanism is proposed for the growth of the nanowires, which might have important implications for preparing advanced, sophisticated nanostructures based on DNA nanotechnology. By employing the hydrophilic CuS nanowire as an optical absorber and thermosensitive nanogel as guest reservoir inside alginate film, a new platform for the release of functional molecules has been set up. In vitro studies have shown that the hybrid film possesses excellent biocompatibility and the release rate of chemical molecules from the film could be controlled with high spatial and temporal precision. Our novel approach and the resulting outstanding combination of properties may advance both the fields of DNA nanotechnology and light‐responsive devices.     

Synthesis of a Nine-atom Germanium Cluster K_(0.5)[K(18-crown-6)]_(1.5)Ge_9·1.5en with Unprecedented “up” and “down” Chain Arrangement of Unit [-(Ge_9-K-Ge_9)~(3-)-]

A new complex K0.5[K(18-crown-6)]1.5Ge9·1.5en(1) which contains unprecedented "up" and "down" chain arrangement of unit [-(Ge-9-K-Ge9)3-] has been prepared by the reaction of K4Ge9 with HgS in ethylenediamine(en) in the presence of 18-crown-6(1,4,7,10,13,16-hexaoxacyclooctadecane), and characterized by X-ray structure analysis. The color of the title crystals(black), which is darker than that of the reported three compounds with chains of germanium clusters, may result from the naked K+ and their interactions with the chain. And the structure differences between 1 and the reported three compounds with chains of germanium have also been discussed.     

Growth and spectral properties of Yb:Ca0.28Ba0.72Nb2O6 disordered crystal

The growth, XRD patterns, spectral properties, and fluorescence decays of Yb:Ca_0.28Ba_0.72Nb₂O₆ (Yb:CBN) with doping concentration of 1 at.% and 5 at.% were studied. The peak absorption cross-section and the emission cross-section were calculated. Larger Stark splitting of Yb:CBN offers the prospect of the quasi-four level laser operation.