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.     

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．     

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.     

Controllable Construction of Amino-Functionalized Dynamic Covalent Porous Polymers for High-Efficiency CO2 Capture from Flue Gas

The design of high-efficiency CO₂ adsorbents with low cost, high capacity, and easy desorption is of high significance for reducing carbon emissions, which yet remains a great challenge. This work proposes a facile construction strategy of amino-functional dynamic covalent materials for effective CO₂ capture from flue gas. Upon the dynamic imine assembly of N-site rich motif and aldehyde-based spacers, nanospheres and hollow nanotubes with spongy pores were constructed spontaneously at room temperature. A commercial amino-functional molecule tetraethylenepentamine could be facilely introduced into the dynamic covalent materials by virtue of the dynamic nature of imine assembly, thus inducing a high CO₂ capacity (1.27 mmol·g⁻¹) from simulated flue gas at 75 °C. This dynamic imine assembly strategy endowed the dynamic covalent materials with facile preparation, low cost, excellent CO₂ capacity, and outstanding cyclic stability, providing a mild and controllable approach for the development of competitive CO₂ adsorbents.     

水波聚焦的研究

利用水波槽装置观察到了水波聚焦现象,并利用流体力学中的表面波理论,借用光学中对折射率的定义,推出了与光线通过薄透镜聚焦完全对应的水波聚焦理论公式,以及焦距随水深变化的关系曲线,从而将水波的几何特性与光波的几何特性统一起来。     

生物电化学系统降解多环芳烃萘及微生物群落研究

采用单室空气阴极微生物燃料电池(MFC)反应器构型, 以不同浓度萘为基底物质, 考察MFC的产电性能、 萘降解率、 化学需氧量(COD)和总有机碳含量(TOC)降解率及MFC阴阳极微生物活性和多样性. 结果表明, 循环伏安曲线受不同浓度萘的影响变化较为明显, 随着萘浓度的增大, 最大功率密度呈下降趋势, 且萘对MFC的阴极电极电势影响较大; 当萘的浓度为15 mg/L时, MFC最大功率密度可达(645.841±28.08) mW/m ²; 对萘的降解率高达100%, 且MFC对COD和TOC的降解率随着萘浓度的提高而增大, 但是增大的速率逐渐减小. 对MFC阳极微生物膜进行高通量测序发现, Geobacter是优势菌属, 相对丰度达81%, 阴极主要以Aquamicrobium为主.     

Synthesis of arylstannanes by palladium-catalyzed desulfitative coupling reaction of sodium arylsulfinates with distannanes

A novel Pd-catalyzed desulfitative cross-coupling reaction of sodium arylsulfinates with hexaalkyl distannanes is realized, allowing the facile synthesis of functionalized arylstannanes with moderate to excellent yields. The successful implement of gram-scale synthesis and tandem Stille coupling reaction demonstrates the potential applications of this method in organic synthesis.     

Dip-Pen Nanolithography(DPN): from Micro/Nano-patterns to Biosensing

Dip-pen nanolithography is an emerging and attractive surface modification technique that has the capacity to directly and controllably write micro/nano-array patterns on diverse substrates. The superior throughput, resolution, and registration enable DPN an outstanding candidate for biological detection from the molecular level to the cellular level. Herein, we overview the technological evolution of DPN in terms of its advanced derivatives and DPN-enabled versatile sensing patterns featuring multiple compositions and structures for biosensing. Benefitting from uniform, reproducible, and large-area array patterns, DPN-based biosensors have shown high sensitivity, excellent selectivity, and fast response in target analyte detection and specific cellular recognition. We anticipate that DPN-based technologies could offer great potential opportunities to fabricate multiplexed, programmable, and commercial array-based sensing biochips.     

Disentanglement Dynamics in Nonequilibrium Environments

We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.     

Functional Polythioamides Derived from Thiocarbonyl Fluoride**

Polythioamide is a unique type of sulfur-containing polymer with advanced functionalities. Nonetheless, the elemental sulfur commonly used in their synthesis tends to react readily with unsaturated functional groups, thereby limiting the scope of eligible substrates. Inspired by the highly efficient sulfur-fluoride exchange ( SuFEx ) polymerization through discrete hubs, we present herein a pioneering and versatile approach to the synthesis of polythioamides from diboronic acids, secondary diamines, and thiocarbonyl fluoride as the central connective hub. Well-defined structures, including previously inaccessible unsaturated substrates, were realized. These newly devised polythioamides can efficiently and selectively bind to metal ions and were applied in precious-metal recovery. Further development resulted in Pd^II-crosslinked single-chain nanoparticles serving as recyclable homogeneous catalysts, thus demonstrating the vast potential of these unprecedented polythioamides. We anticipate that thiocarbonyl fluoride could emerge as a potent hub for facilitating the intricate synthesis of sulfur-containing polymers.