氮掺杂碳量子点荧光猝灭法测定柠檬黄

以甘氨酸和乙二胺为前驱物,采用水热法一步合成了氮掺杂碳量子点(N-CQDs)。该量子点近乎球形,分散性好,稳定性高。在pH=5的B-R缓冲溶液中,柠檬黄对N-CQDs的荧光强度有明显猝灭作用,且其猝灭程度与柠檬黄浓度具有良好线性关系,基于此构建了荧光传感体系,建立了柠檬黄检测新方法。方法线性范围为0.16～20.0μmol·L~(-1),检出限为0.076μmol·L~(-1),应用于饮料和枸杞酒中柠檬黄的测定,加标回收率为92.3%～103.5%。光谱分析和荧光寿命测量结果表明柠檬黄对量子点的荧光猝灭为内滤效应和荧光共振能量转移协同作用的结果。     

碳点增强的Ru纳米颗粒复合材料用于碱性条件下高效电解水析氢

In the 21st century, hydrogen energy is a novel energy source. Its use is expected to mitigate the problems of environmental pollution and global warming caused by the excessive use of conventional fossil fuels. The hydrogen evolution reaction (HER) for water splitting has attracted considerable attention because of its environmental friendliness. To improve electrocatalyst performance and reduce operation cost, carbon-based metal hybrid materials exhibiting high efficiency and catalytic activity have been developed. Among them, carbon dots (CDs) have garnered significant research attention and have been widely applied in biosensing, bioimaging, and energy conversion/storage because of their facile synthesis, biocompatibility, tunable photoluminescence, excellent stability, and good electronic properties. CDs are widely used as carriers in the construction of electrocatalysts prepared from carbon-based metal hybrid materials. At present, it is believed that CDs exhibit excellent confinement effects, which can effectively inhibit the growth and agglomeration of metal nanoparticles, thereby preparing well-distributed carbon-based metal hybrid materials with a uniform and controllable size. However, the formation process of the small-molecule raw materials of CDs has not been elucidated. In this study, CDs and small-molecule raw materials from synthetic CDs were used as precursors to prepare nitrogen-doped CD-supported ruthenium nanoparticle (Ru@CDs) and small-molecule-supported ruthenium nanoparticle (Ru@Molecule) hybrid materials, respectively. The interaction between the small molecules and Ru in the process of CD formation and the effect on HER performance were explored. Moreover, we prepared different carriers such as metal organic frameworks(MOF), carbon nanotubes (CNTs), and graphene (GO)-supported ruthenium nanoparticle hybrid materials. Among them, Ru@CDs exhibited controllable size and excellent dispersibility and exhibited outstanding HER activity and good stability. Ru@CDs were found to require a low overpotential of 22 mV to reach a current density of 10 mA·cm⁻². Moreover, we observed the presence of an intermediate state between the molecules and CDs and demonstrated that the intermediate state exhibits no confinement effect. Furthermore, we found that with increasing calcination temperature, the intermediate state gradually changes to CDs. The unique spatial confinement between CDs and metal ions is key to the formation of monodisperse Ru nanoparticles. Our results confirmed that Ru@CDs serve as excellent HER catalyst supports. This work not only reveals the effect of the unique spatial confinement of CDs on the supported metals and their promoting effect on electrocatalytic activity but also provides guides the future development of CD-based metal hybrid electrocatalysts.     

聚苯胺纳米点阵列的制备和库仑台阶现象

本文制备了PANI纳米点阵列, 利用导电原子力显微镜(C-AFM)表征了其形貌和导电性能, 在室温下观察到PANI纳米点的库仑台阶(Coulomb staircase)现象, 并利用库仑阻塞效应的理论进行了初步的分析.     

一个多元校正的稳健诊断新方法

提出一种新的稳健诊断方法，与最小二乘估计结合进行混合物光谱中非线性点的诊断。文中探讨了该方法的性能，用计算机数字模拟及实际多组分光谱体系夺其进行检验，展示了此诊断方法在分析化学计量学中实际应用的可行性。     

速解一类双零点求参数范围问题

<正>一、问题的提出函数是高中数学的重要组成部分,零点作为函数的基本要素之一,与函数、方程、函数的图象等知识点联系紧密,所以函数的零点和导数相结合的综合性问题一直是高考的热点之一,与函数零点个数有关的试题更是层出不穷.下面的试题是2013年高考江苏卷第20题的改编题,我们先来考虑这道经典的双零点求参数范围问题.     

一类非线性复微分方程的超越亚纯解北大核心CSCD

本文主要研究非线性复微分方程f^(4)+a(z)ff^((k))=p_(1)(z)e^(α_(1)(z))+p_(2)(z)e^(α_(2)(z))的超越亚纯解,其中a,p_(1),p_(2)是非零的有理函数,α_(1),α_(2)是非常数的多项式.进一步地,考虑当亚纯解存在时,α_(1),α_(2),p_(1)和p_(2)所满足的条件.另外,还讨论了非线性复微分方程f^(3)+a(z)f’=p_(1)(z)e^(ν(z))+p_(2)(z)e^(-ν(z))的亚纯解的存在性,其中a,p_(1),p_(2)是非零的有理函数,ν是非常数的多项式.所得的结果直接推广了一些已知的结果.     

A Space-Time Polynomial Collocation Method for Solving 3D Burgers Equations北大核心CSCD

Burgers方程是一类应用广泛的非线性偏微分方程,方程中的非线性项难以处理。该文提出一种新的时空多项式配点法——多项式特解法求解三维Burgers方程。求解过程分为两步:第一步,对三维Burgers方程中的线性导数项(包括时间导数项),求出相应的多项式特解。第二步,将求出的多项式特解作为基函数,对三维Burgers方程中剩余的非线性项进行迭代求解。与时空多项式函数作为基函数对三维Burgers方程进行直接求解相比,该算法简单易行,得到的近似解精度非常高,算法极其稳定,对于教学过程中提高学生的编程能力,加深对高维Burgers方程的理解能力以及Burgers方程的实际应用具有重要意义。     

Elastic Analysis of Anisotropic Functionally Graded Rotating Disks With Non-Uniform Thicknesses北大核心CSCD

研究了任意梯度变化的变厚度各向异性转动圆盘的弹性问题.假设圆盘绕刚性轴匀速转动,其材料性能和厚度沿径向任意梯度变化.考虑圆盘在中心转轴处受位移约束,外侧自由,根据各向异性转动圆盘的平衡微分方程,得到关于径向应力的Fredholm积分方程,继而通过对Fredholm积分方程进行数值求解,得到结构的位移场和应力场.对具体梯度变化情况仅需代入相应梯度变化进行求解即可.数值算例部分,通过假设厚度、弹性模量等参数为特殊的幂函数形式,将由Fredholm积分方程求出的数值解与对应的精确解进行对比,以及针对常见的Voigt模型,将由该方法算得的数值解和ANSYS有限元计算结果进行对比,验证了该方法的准确性和精度.其次,针对Voigt模型,重点分析了厚度变化、材料性能梯度参数、各向异性度等对应力场和位移场的影响.提出了针对材料性能和厚度沿径向呈任意梯度变化的圆盘结构弹性分析方法,将为优化功能梯度圆盘的结构和材料参数、有效调整构件应力分布、提高结构安全性,提供强有力的工具;算例分析结果对功能梯度圆盘在复杂条件下的结构安全设计有重要的理论指导意义.     

聚焦“三点共线”模型破解线段最值问题——以2022年全国各地中考数学试题为例

线段最值问题是历年全国各地中考热点问题,这类问题通常以等腰三角形、直角三角形、矩形、菱形、圆等具有特殊性质的图形为基本图形,以动点或动线段为背景,以线段(或线段之和)的最值为问题情境,主要考查学生综合运用所学知识分析问题和解决问题的能力.解决这类问题的关键是利用转化思想将线段最值问题转化为常见的几何模型,将动态几何问题转化为静态几何问题,然后利用基本图形的性质解决问题.文章以等腰三角形、正方形、矩形等基本图形为例,说明“三点共线”模型在解决线段最小值问题中的应用.     

含引发机制A2＋Aa型缩聚反应体系高分子矩研究

利用概率分析的方法研究了含引发机制的Ａ２＋Ａａ型缩聚反应体系的高分子矩，得到了高分子矩满足的递推公式，给出了该体系０次矩、１次矩和２次矩的明显表达式，讨论了高分子矩在凝胶点附近的临界表示式及其满足的标度律。