关于不定方程x3-1=749y2

利用同余式、平方剩余、Pell方程的解的性质、递归序列证明了:不定方程x³-1=749y²仅有整数解(x,y)=(1,0).     

Biosynthesis of Pd/MnO2 nanocomposite using Solanum melongena plant extract and its application for the one‐pot synthesis of 5‐substituted 1H‐tetrazoles from aryl halides

In this work, for the first time, Solanum melongena plant extract was used for the green synthesis of Pd/MnO₂ nanocomposite via reduction osf Pd(II) ions to Pd(0) and their immobilization on the surface of manganese dioxide (MnO₂) nanoparticles (NPs) as an effective support. The synthesized nanocomposite were characterized by various analytical techniques such as Fourier transform infrared (FT‐IR), X‐ray diffraction (XRD), transmission electron microscopy (TEM), field emission scanning electron microscopy (FESEM), energy dispersive X‐ray spectroscopy (EDS) and UV–Vis spectroscopy. The catalytic activity of Pd/MnO₂ nanocomposite was used as a heterogeneous catalyst for the one‐pot synthesis of 5‐substituted 1H‐tetrazoles from aryl halides containing various electron‐donating or electron‐withdrawing groups in the presence of K ₄ [Fe (CN) ₆ ] as non‐toxic cyanide source and sodium azide. The products were obtained in good yields via a simple methodology and easy work‐up. The nanocatalyst can be recycled and reused several times with no remarkable loss of activity.     

两种群相互竞争的具有脉冲接种的SEIR传染病模型

研究了一类两种群相互竞争的具有脉冲接种的SEIR传染病模型,讨论了系统周期解的存在性,并利用Floquet定理证明,在满足一定条件下,周期解是局部渐近稳定的。     

Travelling wave mathematical analysis and efficient numerical resolution for a one-dimensional model of solid propellant combustion

We investigate a model of solid propellant combustion involving surface pyrolysis coupled to finite activation energy gas-phase combustion. Existence and uniqueness of a travelling wave solution are established by extending dynamical system tools classically used for premixed flames, dealing with the additional difficulty arising from the surface regression and pyrolysis. An efficient shooting method allows to solve the problem in phase space without resorting to space discretisation nor fixed-point Newton iterations. The results are compared to solutions from a CFD code developed at ONERA, assessing the efficiency and potential of the method, and the impact of the modelling assumptions is evaluated through parametric studies.     

超临界水中硫酸钠结晶动力学的分子动力学模拟

在超临界水反应器中，硫酸钠是易造成堵塞的一种常见无机盐，研究其结晶动力学对于防盐沉积反应器的设计具有重要意义.本文采用LAMMPS分子动力学模拟软件研究硫酸钠在超临界水中的微观结晶过程，其中水分子采用SPC/E模型，离子-离子、离子-水分子相互作用采用Coulumb和Lennard-Jones联合势能函数.结果表明：水对离子的静电屏蔽作用随温度升高而增强、随密度减小而减弱；增大超临界水的温度和密度有利于离子扩散，进而促进离子相互碰撞、成核；在模拟的超临界水参数范围内，其成核速率的数量级为10²⁹cm^-3·s^-1，生长速率为(19.8~25.8) m·s^-1.     

一般三阶非线性常微分方程的正周期解

用锥上的不动点指数理论,考虑一般三阶常微分方程■正2π-周期解的存在性,其中:■是三阶常微分算子;■连续,f(t,x,y,z)关于t以2π为周期.在非线性项f满足一些易验证的不等式条件下,允许f(t,x,y,z)关于x,y,z满足超线性或次线性增长,得到了该方程正2π-周期解的存在性结果.     

三类包含Euler函数的方程

讨论了三类包含Euler函数的方程x-ψ(x)=2~(ω(x)),x-ψ(ψ(x))=2~(ω(x))与ψ(x~k)=2~(ω(x~k))的可解性,利用初等方法给出这三类方程的所有正整数解,其中ψ(x)为Euler函数,ω(x)为x的相异素因子个数.     

Comparison of plasma pharmacokinetics of Tanreqing solution between intratracheal aerosolization and intravenous injection in rats

A rapid ultra high performance liquid chromatography tandem mass spectrometry method was developed for the simultaneous analysis of baicalin, oroxylin A‐7‐O‐β‐d ‐glucoronide and chlorogenic acid in rats plasma, and applied to comparison of pharmacokinetics of Tanreqing solution between intratracheal aerosolization and intravenous injection. Results of the analytical method validation assay showed high sensitivity, accuracy and suitable recovery. Results of pharmacokinetics showed similar decline phases for baicalin, oroxylin A‐7‐O‐β‐d ‐glucoronide and chlorogenic acid in two different delivery routes. The half‐lives of intratracheal aerosolization and intravenous injection were 0.90 and 1.22 h for baicalin, 0.47 and 0.17 h for oroxylin A‐7‐O‐β‐d ‐glucoronide and 0.22 and 0.13 h for chlorogenic acid, and this implies that compounds were retained in the lung for a relatively short time. This study was the first to provide important pharmacokinetics information for traditional Chinese medicine delivery to the lung.     

地下水脆弱性风险预警和评估的区间三角模糊多属性决策模型

应用基于逼近理想解排序法的区间三角模糊多属性决策模型,对三江平原六大分区地下水脆弱性进行了风险预警和评估.评估结果与前人吻合,可为有关决策部门采取相应降低环境风险的措施提供参考.实例验证表明,模型具有更高的计算精度和更好的评价效果,为有关环境风险决策部门对地下水风险预警和评估提供了新的思路和方法.     

一类变号(k,n-k)共轭边值问题正解的存在性

通过构造一个特殊的锥,利用范数形式的锥拉伸锥压缩不动点定理,在允许非线性项变号无下界且没有任何单调性假设的条件下,得出了一类高阶(k,n-k)共轭两点边值问题方程组正解的存在性结论.