Investigation of the Effect of Four Organic Acids in Radix Isatidis on E. coli Growth by Microcalorimetry

The inhibitory effects of four organic acids (OAs) in Radix Isatidis, a traditional Chinese medicinal herb, on Escherichia coli (E. coli) growth were investigated by microcalorimetry. The power‐time curves of E. coli growth with and without OAs were acquired, meanwhile the extent and duration of inhibitory effects on the metabolism were evaluated by growth rate constants (k₁, k₂), half inhibitory ratio (IC₅₀), maximum heat output (P_max) and peak time (t_p). The values of k₁ and k₂ of E. coli growth in the presence of the four OAs decreased with the increasing concentrations of OAs. Moreover, P_max was reduced and the value of t_p increased with increasing concentrations of the four drugs. The sequence of anti‐microbial activity of the four OAs was: syringic acid>2‐amino‐benzoic acid>salicylic acid>benzoic acid. IC₅₀ of the four OAs was respectively 56 µg/mL for syringic acid, 75 µg/mL for 2‐amino‐benzoic acid, 86 µg/mL for salicylic acid and 224 µg/mL for benzoic acid. The existence of the functional groups on phenyl ring improves the anti‐microbial activity compared to benzoic acid. The functional groups methoxyl at C(3) and C(5) improve anti‐microbial activity more strongly than the other functional groups, and the functional group amino at C(2) improve anti‐microbial activity more strongly than hydroxyl at C(2) on phenyl ring.     

拟似然非线性模型中最大拟似然估计的强相合性

This paper proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of maximum quasi-likelihood estimation （MQLE） in quasi-likelihood nonlinear models （QLNM）. Our results may be regarded as a further generalization of the relevant results in Ref. [4].     

单位圆内有限级拟亚纯映射在Borel半径上的充满圆

应用覆盖曲面的几何方法,对于单位圆内有限正级的K-拟亚纯映射在其Borel半径上的性质进行了研究,用比较简单的方法证明了单位圆内有限正级K-拟亚纯映射在其Borel半径上一定存在充满圆序列,推广了Rauch A的结果.     

非局部源耦合抛物方程组中的奇性传播

讨论一个经由非局部源耦合的非线性抛物组的解的奇性传播. 给出解的4种可能的blow-up速率及相应的边界层估计. 还得到此非线性抛物组的临界指标.     

抢渡长江最优路径的讨论

给出了2003年全国大学生数学建模竞赛D题的一种求解方法.运用拉格朗日乘数法与变分法建立了水速变化时最优路径适合的方程.特别针对问题4,当水流速度线性变化时,导出了求解最优解的函数方程.     

一种特殊设计约束面的有限元网格优化问题

网格设计质量的优劣是有限元分析的关键，对一些特殊的设计约束面，网格的优化设计是建模时需要首先研究解决的问题，本文对两种材料在几何尺寸差异很大情况下的有限元网格进行了优化设计并对其进行了讨论。     

Dirichlet级数与连带级数

本文研究了右半平面内解析的Dirichlet级数的增长性,利用凸函数和一致收敛数的性质和几个引理,证明了连带级数的奇异点与原级数的增长性有关,并得到该连带级数的一些性质.