基于F-B函数的牛顿法解一般约束优化规划问题

文章给出了一个解决一般约束最优化问题的含调节参数型的牛顿算法.算法有两个重要特征,首先,算法借助Lagrange函数和NcP中的F-B函数,通过构造等价于点条件的线性方程组采处理一般约束优化问题,其次,利用F-B函数的光滑性质,定义了调节参数,从而弱化了K-T点条件.文章在适当的条件下,证明了该算法具有全局收敛性.数值实验表明算法有效.     

Newton’s notion and practice of unification

In this paper I deal with a neglected topic with respect to unification in Newton’s Principia. I will clarify Newton’s notion (as can be found in Newton’s utterances on unification) and practice of unification (its actual occurrence in his scientific work). In order to do so, I will use the recent theories on unification as tools of analysis (Kitcher, Salmon and Schurz). I will argue, after showing that neither Kitcher’s nor Schurz’s account aptly capture Newton’s notion and practice of unification, that Salmon’s later work is a good starting point for analysing this notion and its practice in the Principia. Finally, I will supplement Salmon’s account in order to answer the question at stake.     

Early eighteenth-century Newtonianism: the Huguenot contribution

John Theophilus Desaguliers’s allegorical poem The Newtonian system of the world, the best model of government (1728) crystallizes the contribution of several important French Protestant exiles to the construction of early Newtonianism. In the context of diverging interpretations of Newton’s scientific achievement in terms of natural religion, writers such as Des Maizeaux, Coste, Le Clerc and others actively disseminated a version of Newtonianism which was close to Newton’s own intention. Through public experiments, translations, correspondence, reviews and books, they managed to convey a vision of Newtonian science which coincided with their propaganda of English liberties in Church and State. Therefore their effort on behalf of Newtonianism can be interpreted as part of a wider strategy of assimilation into English society at a time when most exiled Huguenots had given up hope of ever recreating a French Reformed Church at home.     

古巴比伦人求算术平方根的探究

分析了古巴比伦人求算术平方根的算法，证明了其正确性。然后将其算法推广到求n次算术根，并证明了其正确性。     

基于Origin的牛顿环实验数据处理方法

用Origin软件对牛顿环实验的数据进行线性拟合与作图,拟合的结果与所作图形均与传统的最小二乘法进行数据处理的结果相吻合.实验表明：利用软件处理的实验数据与作图,具有简洁、快捷与直观等特点,避免了人为因素所造成的误差.     

Newton and action at a distance between bodies—A response to Andrew Janiak's “Three concepts of causation in Newton”

This article responds to Professor Andrew Janiak's recent attempt to defend the proposition that Isaac Newton did not believe in action at a distance between bodies (or any other kind of substance) (Janiak, 2013). His argument rests on a distinction between “three concepts of causation in Newton”, which leads him to conclude that although Newton did not believe in action at a distance between bodies, he was able to accept that gravity was a “distant action”. I critically examine Janiak's arguments here, and the historical evidence he brings to bear upon it, and argue that Professor Janiak's latest claims do nothing to undermine the view to which he is opposed, namely, that Newton did believe in the possibility of action at a distance between bodies.     

3000m障碍跑场地设计的一种新方案——牛顿迭代法在场地设计中的应用

本文用牛顿迭代法求得3000m障碍跑第二弯道所需设计线应对圆心角的弧度和圆的半径,给障碍跑场地的设计和测画提供了理论依据。     

牛顿引力平方反比定律的发现

本文回溯了牛顿早期动力学思想发展的主要线索及其研究的具体过程，深入探究牛顿有关引力平方反比定律发现的认识论根源，指出：牛顿“跨越”离心力定律，应用自己的“（１／２）Ｒ公式”和推广的伽利ｔ２定律，并结合开普勒周期定律，在１６６９年前得到圆轨道上的意向力平方反比关系；牛顿在１６７９年才认识到开普勒面积定律的物理意义，在成文于１６８０年的《论椭圆轨道》原始手稿中解决开普勒命题，即证明椭圆轨道上的引力平方反比定律。     

Newton迭代双侧逼近序列一般构造方法

求方程近似解的Newton迭代法构造的序列是单侧逼近精确解的，这给误差分析带来很大的困难。本文提出了构造Newton迭代双侧逼近序列一般方法，精确解介于两个序列之间，这样可通过两个近似解来估计逼近精确解的程度。     

Newton type methods for solving nonsmooth equations

1.INTRODUCTION Thenonsmoothequationsproblemplaysanimportant roleinengineering,systemanalysis,management scienceandetc.Manypublicationsdealtwiththe methodsforsolutionofnonsmoothequations,see Refs.[1～4].Letusconsiderthesystemofnons moothequations F(x)=0(1)whereF∶Rn→RmislocallyLipschitzian.NewtonmethodsforsolvingthenonsmoothEq.(1)aregiven asfollows xk+1=xk-V-1kF(xk)(2)whereVkisanelementofvarioussubdifferentialsof Fatxk,forinstance,Clarkesubdifferential[1],B differential[2],b differen…