躺着思想,不如站起行动

在很久很久以前,有两个年轻人,一起去遥远的地方寻找幸福和快乐,一路上风餐露宿,历尽艰辛,在即将到达目的地时,遇到了一条风急浪高的大河.对于如何渡过这条河,两人有不同的意见:一个人建议砍伐附近的树造一条木船渡过河去,另一个人则认为这么高的浪,这么湍急的水流,这么宽的河面,无论造多大的船都不可能渡过这条河,与其自寻烦恼和死路,不如等这条河干了,再轻轻松松地走过去.     

形如“|x|+|y|=1”的画法及其扩展

人教版教材第二册(上)第八章第二节讲的是椭圆的简单几何性质,在对称性中有这样的描述,在曲线的方程中,如果以-y代y方程不变,那么当P(x,y)在曲线上时,它关于x轴的对称点P′(x,-y)也在曲线上,所以曲线关于x轴对称,同理如果以-x代x方程不变,那么曲线关于y轴对称,如果同时以-x代x,以     

中考数学探索题的归类及评析

近年来,数学探索题以多彩优美的格调,清新多姿的风彩,发散开放的题型,背景育人的功能,注重能力的考查,强化创新的意识,出现在全国各地的中考试卷上,并有逐年上升之势,促进了生动、活泼、主动的数学学习活动,真正起到了实施素质教育“指挥棒”的作用,本文旨对近年来中考数学探索题作些归类,并对具体实例进行评析.     

抓住小条件 解决大问题

每一道习题都有着严密的逻辑性,已知条件不可能多余,也不可能短缺,在所有条件中,抓住其最有特征性的一个,联想展开,这是解题的一种途径．许多同学在解题时,往往不去认真推敲题目中给出的已知条件,对于一些细小的似乎是不起眼的说明,便不去深入探讨,弃之一旁,熟视无睹,这是一个极大的错误．很多时候,若能紧紧抓住这些小条件,便可从这里打开缺口,解决大问题．     

共同探究,享受数学

众所周知,数学很重要,这很大层面上是由高考指挥棒决定的,学生在沉重的数学作业负担下,大多是疲于应付,很少有人真正体验到数学内在的美,学会享受数学.笔者从事高中数学多年,做了一点有益的尝试,让学生从多种角度理解数学,师生平等,教师做好组织、引领工作,充分调动学生学习数学积极性,各抒己见,经常是一个平淡的问题,往往出现多种漂亮的解法,碰撞出思维的火花,师生乐在其中,一同享受数学带给我们的快乐.现举两个案例,供大家分享.     

高盛,华尔街曾经的笑柄

第一次世界大战结束后,美国经济进入繁荣时期。伴随着经济的繁荣,美国的股市也不断攀升,一直持续着牛市行情。然而,好景不长,1929年,全球金融危机爆发,华尔街股市大崩盘,让高盛损失了92%的原始投资,公司的声誉一落千丈,濒临倒闭,沦为华尔街的笑柄、错误的代名词。     

是谁拉你走向平庸

一名长跑运动员参加一个5人小组的比赛,赛前教练对他说,据我了解,其他4人的实力不如你,于是,这名运动员轻松地跑了第一名随后教练又让他参加了一个10人小组比赛,教练把平时其他人的成绩拿给他看,他发现别人的成绩并不如自己,他又轻松跑了第一名然后,这名运动员又参加了一个20人小组的比赛,教练说,你只要战胜其中的一个人,你就能取得胜利,结果,比赛中他紧跟着教练说的那个运动员,并在最后冲刺时,又取得了第一名.     

用好轴对称性,巧解折叠型中考题

近几年来,矩形纸片的折叠问题频繁出现在全国各地的中考数学试题中,此类问题贴近同学的认知规律,能较好考查基础知识和综合运用数学知识解决问题的能力,因此,很受命题者的青睐.但是,由于矩形折叠型试题涉及知识面广,结构独特,解法灵活多样,同时融合了丰富的数学思想和方法,所以大多数同学都感到有一     

例谈数学中的一般化与特殊化

一般化与特殊化是人类认识事物的两个重要侧面,也是解题的两种基本策略,它们相辅相成,是辩证的统一.在多数场合,特殊问题简单、直观,容易认识,容易把握.但是,也有一些场合,特殊问题的个别特性可能会掩盖事物的本质属性,给解题带来困难,而直接求解相应的一般性问题,反而来得简便、明快、奇巧.     

如何激发思维灵感

我们在教学实践中感到,思维灵感往往能产生优美的方法,使问题获得巧妙的解决.这种瞬息间萌发的灵感,使得学习充满乐趣,促使学习信心倍增,但是,如何激发思维灵感,并逐渐养成学生敏而好学的习惯,却没有引起广大教者的足够重视,本文拟从例题教学的角度,谈谈激发学生思维灵感的做法和体会,期望大家都来做积极实践的有心人.     

一种基于TOPSIS思想的改进灰色关联法及其在方案评估中的应用

提出了一种基于TOPSIS思想的改进灰色关联法,方法采用了TOPSIS思想,通过标准化处理,能够将灰色关联法给出的评估结果转换为,TOPSIS方法所要用到的与最优/最劣解的距离,从而给出一个稳定的评估结果,弥补了传统灰色关联法受全局极值影响大的缺点.经实例分析证明,方法可以应用于方案评估中,并能够得出可行、稳定、科学的评估结果.     

A dynamic meshless method for the least squares problem with some noisy subdomains

The interpolation method by radial basis functions is used widely for solving scattered data approximation. However, sometimes it makes more sense to approximate the solution by least squares fit. This is especially true when the data are contaminated with noise. A meshfree method namely, meshless dynamic weighted least squares (MDWLS) method, is presented in this paper to solve least squares problems with noise. The MDWLS method by Gaussian radial basis function is proposed to fit scattered data with some noisy areas in the problem’s domain. Existence and uniqueness of a solution is proved. This method has one parameter which can adjusts the accuracy according to the size of noises. Another advantage of the developed method is that it can be applied to problems with nonregular geometrical domains. The new approach is applied for some problems in two dimensions and the obtained results confirm the accuracy and efficiency of the proposed method. The numerical experiments illustrate that our MDWLS method has better performance than the traditional least squares method in case of noisy data.     

Chebyshev pseudospectral method for computing numerical solution of convection–diffusion equation

A method for computing highly accurate numerical solutions of 1D convection–diffusion equations is proposed. In this method, the equation is first discretized with respect to the spatial variable, transforming the original problem into a set of ordinary differential equations, and then the resulting system is integrated in time by the fourth-order Runge–Kutta method. Spatial discretization is done by using the Chebyshev pseudospectral collocation method. Before describing the method, we review a finite difference-based method by Salkuyeh [D. Khojasteh Salkuyeh, On the finite difference approximation to the convection–diffusion equation, Appl. Math. Comput. 179 (2006) 79–86], and, contrary to the proposal of the author, we show that this method is not suitable for problems involving time dependent boundary conditions, which calls for revision. Stability analysis based on pseudoeigenvalues to determine the maximum time step for the proposed method is also carried out. Superiority of the proposed method over a revised version of Salkuyeh’s method is verified by numerical examples.     

Variable metric relaxation methods,part II: The ellipsoid method

The deepest, or least shallow, cut ellipsoid method is a polynomial (time and space) method which finds an ellipsoid, representable by polynomial space integers, such that the maximal ellipsoidal distance relaxation method using this fixed ellipsoid is polynomial: this is equivalent to finding a linear transforming such that the maximal distance relaxation method of Agmon, Motzkin and Schoenberg in this transformed space is polynomial. If perfect arithmetic is used, then the sequence of ellipsoids generated by the method converges to a set of ellipsoids, which share some of the properties of the classical Hessian at an optimum point of a function; and thus the ellipsoid method is quite analogous to a variable metric quasi-Newton method. This research was supported in part by the F.C.A.C. of Quebec, and the N.S.E.R.C. of Canada under Grant A 4152.     

Interactive Compromise Programming

The purpose of this paper is to introduce a solution method for multiple objective linear programming (MOLP) problems. The method, called interactive compromise programming (ICP), offers a practical solution to MOLP problems by combining judgement with an automatic optimization technique in decision-making. This is realised by using the method of compromise programming and the method of a two-person zero-sum game in an iterative way. The method is illustrated by a numerical example.     

A new symmetric linear eight-step method with fifth trigonometric order for the efficient integration of the Schrödinger equation

On the basis of a classical symmetric eight-step method, an optimized method with fifth trigonometric order for the numerical solution of the Schrödinger equation is developed in this work. The local truncation error analysis of the method proves the decrease of the maximum power of the energy in relation to the corresponding classical method, which renders the method highly efficient. This is confirmed by comparing the method to other methods from the literature while integrating the equation. The superiority of the method is strengthened by the existence of a larger interval of periodicity of the new method in comparison to the corresponding classical method.     

脉冲摄动微分系统的有界性

通过利用变分Lyapunov函数方法, 该文主要研究了脉冲摄动微分系统关于两个测度的有界性. 与以前结果相比, 不难发现变分Lyapunov函数方法是Lyapunov函数方法的推广 .     

An Improved Hybrid Method for Inverse Obstacle Scattering Problems

An improved hybrid method is introduced in this paper as a numerical method to reconstruct the scatterer by far-field pattern for just one incident direction with unknown physical properties of the scatterer. The improved hybrid method inherits the idea of the hybrid method by Kress and Serranho which is a combination of Newton and decomposition method, and it improves the hybrid method by introducing a general boundary condition. The numerical experiments show the feasibility of this method.     

STABILITY ANALYSIS OF NONLINEAR GALERKIN ＆ GALERKIN METHODS FOR NONLINEAR EVOLUTION EQUATIONS

Abstract. Ogr object in this artlcle is to describe tbe Galerkln scheme and nonlin-eax Galerkin scheme for the approximation of nonlinear evolution equations, and tostudy the stability of these schemes. Spatial discretizatlon can be pedormed by eitherGalerkln spectral method or nonlinear Galerldn spectral method; time discretizatlort isdone hy Euler sin.heine wklch is explicit or implicit in the nonlinear terms. According tothe stability analysis of the above schemes, the stability of nonllneex Galerkln methodis better than that of Galexkln method.     

An iteration method for predicting static response of nonlinear structural systems with non-deterministic parameters

Confident numerical method is a crucial issue in the field of structural health monitoring. This paper focuses on uncertainty propagation in nonlinear structural systems with non-deterministic parameters. An interval-based iteration method is proposed on the basis of interval analysis and Taylor series expansion. The proposed method aims to improve the bounds of static response calculated by the point-based iteration method. In the proposed method, the iterative interval of static response is updated by revising the lower and upper bounds, respectively, which is the essential difference in comparison with the previous point-based iteration method. In this paper, interval parameters are employed to quantify the non-deterministic parameters instead of random parameters in the case of insufficient sample data. Iterative scheme is established based on the first-order Taylor series expansion. For the implementation of interval-based iteration method, a general procedure is formulated. Moreover, the important source of the limitation of point-based iteration method is revealed profoundly, and the good performance of the proposed method is demonstrated by three numerical comparisons.