用于留数算术中的数值／留数／数值的转换

介绍用光学方法完成留数算术中的数值/留数/数值的转换,并附有实验结果。     

Assessment of linear finite‐difference Poisson–Boltzmann solvers

CPU time and memory usage are two vital issues that any numerical solvers for the Poisson–Boltzmann equation have to face in biomolecular applications. In this study, we systematically analyzed the CPU time and memory usage of five commonly used finite‐difference solvers with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient solvers, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson–Boltzmann equation. It turns out that the time‐limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical solvers for the Poisson–Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

改进的非线性整数规划算法

通过对LUUS随机搜索算法的分析，本文首次提出了一种改进的随机定向搜索法（MRDISA）通过实例计算，说明该算法的优点是最优解的可靠性不受初始值X^(0)和初始搜索范围R^(0)的影响，并可用于求解高维约束非线性整数规划问题。     

森林病虫害模型的数值模拟

讨论森林病虫害的离散模型.根据森林病虫害传播的特征,针对各分块区域之间已感病树不互相转移的情况,建立差分方程模型;讨论系统的平衡点,并对无病平衡点和地方病平衡点进行稳定性分析,得到地方病平衡点稳定的充分条件;用Matlab进行多种情况的数值模拟,验证了理论结果.     

相干光脉冲位置调制信道容量及传信率最大化研究

分析了相干光脉冲位置调制的信道容量及传信率最大化条件.通过分析光外差接收的脉冲位置调制信号具有的概率分布特性,推导出采用最大似然检测的相干脉冲位置调制信道具有的转移概率矩阵和信道容量,证明在检测器散粒噪声极限假设下,信道容量只取决于接收脉冲能量和脉冲位置调制阶数.利用Jensen不等式化简信道容量得到其下限,该下限能够近似实际通信链路的信道容量.基于此估计出达到最高传信率时的脉冲位置调制阶数同粒子数反转的重建时间之间的关系,给出了二者在一定范围内的一般映射.数值仿真表明,在接收能量使信道误码率优于10-2时,估箅出的脉冲位置调制阶数能够使传信率接近最大值.     

Introduction to integral calculus at high school through calculating area and volume with spreadsheets

This paper gives an account of an experiment in which 33 high school students of age 16–19 acquired the principles of the integral calculus through applying the rectangle method in spreadsheet to calculate the area of a planar figure bounded by the graph of a function and the volume of a body created by the rotation of the graph. A questionnaire survey was carried out to find out whether the students found the lesson interesting, contributing to their mathematical and technological knowledge and motivating to continue with more complicated tasks.     

一种静电像管优化设计方法的设想

从数值计算出发,以实例计算静电像管的均方根半径值,给出系统在最佳像面及其各附加像面处的均方根值,验证了理论分析的正确性,并从理论上提出了一种关于静电像管优化设计方法的设想。     

薄板弯曲问题的复合傅里叶级数方法

解析方法与数值方法有效融合是提高计算效能的重要途径．提出薄板弯曲问题的复合傅里叶级数方法．它以解析方法为融合基体,数值方法为融合增强相,是一种新的融合模式．在这种新的融合模式中,傅里叶级数解析解作为变形场的连续表现形式,摆脱了载荷形式和边界条件的强烈依赖性,表现出良好的收敛性态．     

酸度分布-吸收光谱法用于灰色体系中食用色素的定量分析

利用合成色素随ｐＨ变化的人分布分数曲线和吸收光谱构成两维波谱信息,建立了灰色体系中色素的定量分析方法。约束背景双线性分解法（ＣＢＢＬ）结合数值遗传算法（ＮＧＡ）用于两维矩阵的数据处理。推导了型体总数与两维矩阵的有效秩之间的关系。吸光度矩阵的主成分数根据残余矩阵的残差平方和噪声水平相比较 确定,对标准样品及模拟灰色体系样品的研究表明该法确定的主成分数与理论值一致。对胭脂红、日落黄和柠檬黄的模拟灰色休