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.     

Determinaton of Three Kinds of Organic Acids in the Leaves of Elaeagnus angustifolia L. from Different Regions and Different Growth Stages in Xinjiang Province by Using High-Performance Thin-Layer Chromatography

JPC – Journal of Planar Chromatography – Modern TLC - High-performance thin-layer chromatography, which is a quick qualitative and quantitative method, was used to determine 3 kinds of...     

Mechanically strong and stiff supramolecular polymers enabled by fiber reinforced long-chain alkane matrix

Fiber-reinforced-concrete (FRC) mechanism refers short discrete fibers that are uniformly distributed and randomly oriented, which offers an effective way to improve the mechanical performance of concrete. In the design of supramolecular polymers, an analogous concept of FRC appears to have been considered very rarely-although fibrous structure has been frequently observed/generated during the supramolecular polymerization. In this work, we apply the alkane thermosets, octadecane (C₁₈H₃₈) and tetracosane (C₂₄H₅₀), taking the role of “concrete”, and the low-molecular-weight monomer with long alkyl chains as the essential “fiber” component, to fabricate the “fiber reinforced supramolecular polymer”. Very much like FRC mechanism in material science, the resulting fiber reinforced supramolecular polymer thus exhibit unusually high mechanical strength and stiffness, which is unprecedented in the conventional supramolecular strategy.     

MIL-101(Cr) Microporous Nanocrystals Intercalating Graphene Oxide Membrane for Efficient Hydrogen Purification

Graphene oxide (GO) is a promising two-dimensional building block for fabricating high-performance gas separation membranes. Whereas the tortuous transport pathway may increase the transport distance and lead to a low gas permeation rate, introducing spacers into GO laminates is an effective strategy to enlarge the interlayer channel for enhanced gas permeance. Herein, we propose to intercalate CO₂-philic MIL-101(Cr) metal-organic framework nanocrystals into the GO laminates to construct a 2D/3D hybrid structure for gas separation. The interlayer channels were partially opened up to accelerate gas permeation. Meanwhile, the intrinsic pores of MIL-101 provided additional transport pathways, and the affinity of MIL-101 to CO₂ molecules resulted in higher H₂/CO₂ diffusion selectivity, leading to a simultaneous enhancement in gas permeance and separation selectivity. The MIL-101(Cr)/GO membrane with optimal structures exhibited outstanding and stable mixed-gas separation performance with H₂ permeance of 67.5 GPU and H₂/CO₂ selectivity of 30.3 during the 120-h continuous test, demonstrating its potential in H₂ purification application.     

Ultrafast synthesis of near-infrared-emitting aqueous CdTe/CdS quantum dots with high fluorescence

The traditional aqueous route to synthesis CdTe/CdS Core/shell (c/s) quantum dots (QDs) via decomposition of Cd-thiol complexes is usually time consuming. Herein, an ultrafast and facile aqueous synthetic approach under atmospheric pressure for CdTe/CdS c/s QDs with emission from the green to the near-infrared window (535–820 nm) is reported. With purified CdTe core QDs diluted in solution of Cd-3-mercaptopropionic acid (MPA) complexes, CdTe/CdS c/s QDs with emission wavelengths at 700 and 800 nm can be obtained within 20- and 45-min refluxing under the optimized experimental conditions, respectively. This is the most rapid way to prepare CdTe/CdS c/s QDs in aqueous phase, and the obtained QDs were highly luminescent without postsynthesis treatment. The influences of various experimental factors, including Cd²⁺ concentration, MPA-to-Cd ratio, pH value, and dilution ratio on the growth rate and luminescent properties of the obtained CdTe/CdS c/s QDs, have been taken into consideration. The three processes “purification-dilution-addition” ensure the synthesis environment with high pH value and low core concentration and have a marked impact on the rapid synthesis rate and the resulting high fluorescence of CdTe/CdS c/s QDs.     

旋转压电纳米梁的振动分析

本文基于非局部弹性理论，对旋转压电纳米梁模型的振动进行了分析．首先由哈密顿原理导出旋转压电纳米梁的动力学控制方程及相应的边界条件；再通过微分求积法对控制方程和两类边界条件进行离散；最后通过数值计算分析振动特性．通过改变旋转角速度、轮毂半径、非局部参数以及外部电压分析它们对压电纳米梁振动频率的影响关系．数值结果表明这些参数对压电纳米梁固有频率有不可忽略的影响，本文进一步讨论了旋转角速度对结构模态的影响．     

Re‐Appearance of Cooperativity in Ultra‐Small Spin‐Crossover [Fe(pz){Ni(CN)4}] Nanoparticles

A reverse nanoemulsion technique was used for the elaboration of [Fe(pz){Ni(CN)₄}] nanoparticles. Low‐temperature micellar exchange made it possible to elaborate ultra‐small nanoparticles with sizes down to 2 nm. When decreasing the size of the particles from 110 to 12 nm the spin transition shifts to lower temperatures, becomes gradual, and the hysteresis shrinks. On the other hand, a re‐opening of the hysteresis was observed for smaller (2 nm) particles. A detailed ⁵⁷Fe Mössbauer spectroscopy analysis was used to correlate this unusual phenomenon to the modification of the stiffness of the nanoparticles thanks to the determination of their Debye temperature.     

Discovery of a new nontoxic cuprate superconducting system Ga-Ba-Ca-Cu-O

Superconductivity is observed in a new nontoxic cuprate system Ga-Ba-Ca-Cu-O,with T_c=82 K for Ga Ba_2Ca_5Cu_6O_(14+δ)(Ga-1256)and T_c=116 K probably for Ga Ba_2Ca_3Cu_4O_(10+δ)(Ga-1234)or Ga Ba_2Ca_2Cu_3O_(8+δ)(Ga-1223),respectively.All compounds are fabricated by solid state reaction method under high pressure and high temperature.Samples are characterized by resistivity,magnetization and X-ray diffraction(XRD)measurements.The temperature dependence of magnetization measured in both zero-field-cooled and field-cooled processes on one sample(S1)shows two superconducting transitions at about 82 K and113 K.The estimated shielding fraction for the phase with T_cof 82 K is about 67%,while the fraction for another phase with T_(c )of 113 K is quite small.The XRD Rietveld refinement for S1 indicates two main phases existing in the sample,Ga-1256 with fraction of about 58%and non-superconducting Ca_(0.85)Cu O_2with fraction of about 42%respectively.Thus,we can conclude the superconducting phase with transition temperature of 82 K is due to Ga-1256.The resistivity measurement also confirms the superconductivity for S1,and the resistivity reaches zero at about 82 K.The temperature dependence of magnetization for another sample(S2)shows much higher superconducting shielding fraction for the phase with T_cof 116 K,which may be a promising prospective for the synthesis of Ga-1234 or Ga-1223 phase.     

利用自由基引发的1,2-炔基迁移实现非活性烯烃的炔膦酰化

研究了1,4-烯炔衍生物与二芳基膦氧化物在银介导下发生的炔酰化反应.该反应利用自由基引发的1,2-炔基迁移策略合成了一系列γ-酮膦氧化物,产率适中.该反应机理可能涉及膦中心自由基与乙烯基的加成、3-exo-dig环化和1,2-炔基迁移等连续的过程,一步形成了C-P、C-C键等化学键,实现了非活性烯烃的双官能化.