On Destabilization via Active Stiffness

Corless and Leitmann [2] have shown that a damped simple oscillator can be destabilized by varying the spring stiffness. The present note establishes that this result is closely related to the variational approach to absolute stability theory [1,6] both in substance and in method of proof. In particular, several key ideas employed in [2] appear in the work of Brockett [1].     

再谈W.Janous猜测的推广

首先对近年来W．Janous猜测研究的成果加以综述，在此基础上，又进一步将W．Janous猜测推广为更一般的结论。     

选尺法求解哥古猜想解答(续)

哥德巴赫猜想与古叶猜想合成哥古猜想( Goldbach -Guye's Conjecture):任何一个非零偶数(z),都可表达为两个素数(y及x)之‘和’或‘差’;即有z+=y+x,或有z=y-x.当知z+或z-时,如何求解y及x配偶成副呢?文章介绍了求解哥古猜想解答的一种选尺法(利用‘y尺’与‘x尺’间的相对位移)...     

一个极小值问题的证明

将一个与莫朗猜想等价的极小值问题转化为非线性规划问题，并利用Ｋ－Ｔ条件求解，从而证明了莫朗猜想．     

中国城市化研究的范式转型——基础方法论

对中国城市化研究不能令人满意的进展进行了坦率的剖析．指出在认识论上．没有能够正确认识城市化这样一个复杂系统性问题所对应的科学知识的属性,这导致现状研究基于本质上错误的方法论。正确的基础方法论包含不可分割的三个要点：基于猜想建构直面解决的系统性、综合性知识;通过结构把握研究的复杂系统性．实践意义和理论建构：基于对猜想的严格检验和结构引导下的累积性研究,实现可行的研究广度．深度的连续拓展和成果质量的连续提升。     

面尺法求解哥古猜想解答

哥德巴赫猜想与古叶猜想合成哥古猜想（Goldbach-Guye’s Conjecture）：任何一个非零偶数（z）,都可表达为两个素数（y及x）之＂和＂或＂差＂;即有z＋=y＋x,或有z-=y-x。当知z＋或z-时,如何求解y及x配偶成副呢？文章介绍了求解哥古猜想解答的一种面尺法（利用‘定尺’与‘动尺’间的相对位移）,并按参考文献[8]的‘提示’提出了改进措施,使缩尺法更趋完善。     

Graham's problem on shortest networks for points on a circle

Suppose a configurationX consists ofn points lying on a circle of radiusr. If at most one of the edges joining neighboring points has length strictly greater thanr, then the Steiner treeS consists of all these edges with a longest edge removed. In order to showS is, in fact, just the minimal spanning treeT, a variational approach is used to show the Steiner ratio for this configuration is at least one and equals one only ifS andT coincide. The variational approach greatly reduces the number of possible Steiner trees that need to be considered.     

Optimal Newton–Secant like methods without memory for solving nonlinear equations with its dynamics

We construct two optimal Newton–Secant like iterative methods for solving nonlinear equations. The proposed classes have convergence order four and eight and cost only three and four function evaluations per iteration, respectively. These methods support the Kung and Traub conjecture and possess a high computational efficiency. The new methods are illustrated by numerical experiments and a comparison with some existing optimal methods. We conclude with an investigation of the basins of attraction of the solutions in the complex plane.     

有限域上的不可约多项式

通过有限域上的低次本原多项式构造出了同一有限域上的高次不可约多项式。为进而构造有限域上的高阶本原多项式创造了条件。