Isaac Newton and Augustan Anglo-Latin poetry

Although many historians of science acknowledge the extent to which Greek and Roman ideals framed eighteenth-century thought, many classical references in the texts they study remain obscure. Poems played an important role not only in spreading ideas about natural philosophy, but also in changing people’s perceptions of its value; they contributed to Newton’s swelling reputation as an English hero. By writing about Latin poetry, we focus on the intersection of two literary genres that were significant for eighteenth-century natural philosophy, but seem alien to modern science. We classify Augustan Latinate scientific poetry by considering the audiences for whom the poems were intended. We distinguish three broad categories. One type of poetry was circulated amongst gentlemanly scholars (we look particularly at Tripos verses, and laments for Queen Caroline). A second group comprised poetry written specifically to promote or criticise Newton and his books, particularly the Principia (we look at versions of Pope’s epitaph, and Halley’s Lucretian poem). After Newton’s death, a third type of poetry became increasingly significant, included in collections of poems rather than in texts of natural philosophy. Overall, we show how the classical past was vital for creating the scientific future.     

一类稀疏非线性方程组的换元解法

对具有带状稀疏Jacobi阵的非线性方程组提出一种两步换元解法,其目的是在每迭代步中,减少函数值的运算,同时也减少线性方程组求解的计算量。进一步,对三对角、五对角Jacohi阵的情形分别给出计算公式并计算其效能指标。     

求解非线性最优化问题的Newton算法研究

本文概述了非线性规划中Newton算法的基本原理和发展,阐述了Newton算法与其他算法的混合算法,并探讨了Newton算法的超线性收敛性,从而进一步阐明了此算法的研究方向。     

度量空间中某类泛函极小的局部有界性

主要研究了牛顿空间中泛函F(u,u)=∫f(u,gu)dμ的极小问题,其中对某常数c>0,泛函满足条件gup-c|u|p≤f(u,gu)≤gpu+c|u|p.牛顿空间是Soolev空间在度量空间中的推广,具有更一般的性质.在该空间中研究偏微分方程,对建立更一般的偏微分方程理论具有指导和开拓意义.本文利用De Giorgi迭代的方法验证了该泛函极小的局部有界性,而这一性质的成立为我们今后进一步研究该泛函极小的正则性奠定了基础.     

SAR距离-多普勒成像算法中的距离徙动及校正

在SAR距离-多普勒成像算法中,距离徙动会使距离向和方位向发生耦合,成像质量下降.典型的距离徙动校正插值算法有：最近邻插值、牛顿插值、辛格插值等.但以上算法的光滑性和收敛性不好,而三次样条函数具有连续的二阶导数,且可采用分段函数的形式,具有很好的光滑性和收敛性.作者用三次样条函数插值进行距离徙动校正,进行了点目标SAR仿真成像,得到了满意的仿真结果.     

基于交替修正牛顿法的分布式传感器定位算法

为了克服锚节点位置误差影响定位精度这一问题,提出了一种基于交替修正牛顿法的分布式定位算法。首先,将无线传感器网络表示的无向图划分成多个部分重叠的子图,建立可独立求解的子图内定位问题,子图内未知节点根据不准确的锚节点位置和测距信息采用修正牛顿法得到初步估计位置,再融合求平均得到估计位置;其次,根据第一步结果和测距信息采用修正牛顿法更新锚节点位置,使其位置更为精准;最后,未知节点再根据相对准确的锚节点位置更新估计位置。实验结果表明,与现有的分布式算法相比,所提算法具有更好的定位性能和扩展性,能够应用于较大规模的无线传感器网络。     

热电偶冷端软件补偿算法分析

针对目前常用热电偶冷端温度补偿方法中,硬件调校复杂,转换计算繁琐等问题,笔者提出一种硬件简单,不必查表,而采用牛顿迭代法实现热电偶冷端软件补偿的方法－ 其通用性强,成本低,精度高,适合于各种计算机温度测量与控制系统     

基于试飞数据的固定翼飞机盘旋性能仿真分析技术

针对飞行试验过程中的盘旋性能分析问题,提出一种以试飞数据为基础的盘旋性能仿真分析方法。首先依据拉依达准则识别试飞数据中的异常值,并根据提出的移动基准区间牛顿插值方法对异常值修正;然后建立飞机盘旋运动的动力学计算模型,采用欧拉角法通过坐标变换矩阵求解飞机盘旋动力学方程,计算结果应用中心插值算法进行平滑处理。最后基于某型固定翼飞机实际飞行试验中记录的试飞数据进行算例分析,依据能量机动理论绘制完整的盘旋性能飞行包线,将理论计算结果与仿真结果进行对比表明了所建模型与仿真分析方法的有效性与正确性,为飞机的反馈设计及飞行性能的改进提供方法及依据,在工程实际应用上具有一定的可行性。     

From centripetal forces to conic orbits: a path through the early sections of Newton’s Principia

In this study, we test the security of a crucial plank in the Principia’s mathematical foundation, namely Newton’s path leading to his solution of the famous Inverse Kepler Problem: a body attracted toward an immovable center by a centripetal force inversely proportional to the square of the distance from the center must move on a conic having a focus in that center. This path begins with his definitions of centripetal and motive force, moves through the second law of motion, then traverses Propositions I, II, and VI, before coming to an end with Propositions XI, XII, XIII and this trio’s first corollary. To test the security of this path, we answer the following questions. How far is Newton’s path from being truly rigorous? What would it take to clarify his ambiguous definitions and laws, supply missing details, and close logical gaps? In short, what would it take to make Newton’s route to the Inverse Kepler Problem completely convincing? The answer is very surprising: it takes far less than one might have expected, given that Newton carved this path in 1687.     

一类竞赛试题的统一解法

本文主要利用Cauchy不等式的取等条件对一类特殊方程组的求解问题提出了一种新的解法,并与传统解法进行对比,突出其优越性。