一类常微分方程在奇点处解的符号算法

借助于常微分方程(或微分算子)的牛顿多边形,本文给出了一类常微分方程在奇点处解的符号算法。此算法能使我们得到方程在奇点处的精确解。     

带状非线性方程组的一种换元解法

本文对带状非线性方程组提出一种新的直接换元修正解法,得到了该算法的超线性收敛性结果及收敛阶估计,并且给出该算法与Newton法和直接弦修正算法的数值比较。     

Between Kepler and Newton: Hooke’s ‘principles of congruity and incongruity’ and the naturalization of mathematics

ABSTRACT

Robert Hooke’s development of the theory of matter-as-vibration provides coherence to a career in natural philosophy which is commonly perceived as scattered and haphazard. It also highlights aspects of his work for which he is rarely credited: besides the creative speculative imagination and practical-instrumental ingenuity for which he is known, it displays lucid and consistent theoretical thought and mathematical skills. Most generally and importantly, however, Hooke’s ‘Principles?…?of Congruity and Incongruity of bodies’ represent a uniquely powerful approach to the most pressing challenge of the New Science: legitimizing the application of mathematics to the study of nature. This challenge required reshaping the mathematical practices and procedures; an epistemological framework supporting these practices; and a metaphysics which could make sense of this epistemology. Hooke’s ‘Uniform Geometrical or Mechanical Method’ was a bold attempt to answer the three challenges together, by interweaving mathematics through physics into metaphysics and epistemology. Mathematics, in his rendition, was neither an abstract and ideal structure (as it was for Kepler), nor a wholly-flexible, artificial human tool (as it was for Newton). It drew its power from being contingent on the particularities of the material world.     

牛顿环透镜倒置和正置测干涉条纹半径的比较

在牛顿环干涉现象测透镜曲率半径实验中,分别对牛顿环透镜倒置和正置时,产生干涉的几何光路分析得到：在理论上,牛顿环透镜倒置时,比透镜正置时所测k级干涉条纹半径更准确。并且利用MATLAB软件辅助计算得到：牛顿环透镜倒置和正置时,所测k级干涉条纹半径相差微小。所以,实际实验中,牛顿环透镜既可正置也可倒置。     

岩体渗透系数反演的数值方法及其适定性

分析了渗透系数反演中的适定性问题，包括唯一性和稳定性问题，分别对直接反演法和间接反演法进行了论述，侧重研究了间接法中的正则化最小二乘法和逐个修正法，建立了两套反演数值计算方法，主要包括叠代格式的建立、Ｊａｃｏｂｉａｎ矩阵的计算、高斯一牛顿方向的修正。计算结果表明，此两种方法有较快的收敛速度和较强的稳定性。     

光滑化Newton法在网络平衡模型中的应用

建立了由制造商、分销商、顾客组成的带有竞争性的需求不确定的供应链网络平衡模型,采用收敛速度快的光滑化Newton法求解.最后通过算例说明用光滑化Newton法计算很快就能得到平衡解.     

关于求解非线性方程组的Newton法的一个改进

本文对求解非线性方程组的Ｎｅｗｔｏｎ迭代法作了改进，并给出了局部收敛性定理．计算表明，改进后的Ｎｅｗｔｏｎ法的收敛域有明显扩大．     

求解随机线性互补问题的半光滑投影牛顿算法

考虑只有有限个随机变量的随机线性互补问题,先将其转化为约束极小化问题,再利用半光滑投影牛顿算法求解该极小化问题,并给出了相应的数值实验.结果表明所给算法有效.     

一种低延迟三电平APF的方案设计及仿真研究

为实现谐波检测低延时与补偿电流跟踪控制的高实时性,以此提升三电平有源电力滤波器(active power filter,APF)的动态响应性能与稳态滤波精度。设计一种低延迟三电平APF系统方案:用移动窗积分算法降低ip-iq检测中常用二阶巴特沃斯(butterworth)低通的延迟时间;提出运用基于等距结点牛顿后差插值的瞬态重复校正预测控制方案,实现传统电压空间矢量脉调(space vector pulse width modulation,SVPWM)与无差拍算法的复合控制策略,消除传统SVPWM控制拍数的延迟。Matlab对系统方案仿真对比:三电平APF系统采用低延迟方案时启动阶段响应快且稳,负载突变后过渡响应快,稳态总谐波畸变率(total harmonic distortion,THD)为1.36%,具备明显优势。研究表明:低延迟三电平APF系统方案通过降低谐波检测延迟与电流跟踪控制延迟,提高了APF系统的滤波性能。     

Newton插值理论在金字塔型信息隐藏中的应用

研究了GF(Pn)上的Newton插值公式,且应用Newton门限方案解决了一类金字塔型 信息隐藏问题,给出了算法和算例．