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     

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.     

Low dimensional modules over quantum complete intersections in two variables

We classify all the indecomposable modules of dimension ≤ 5 over the quantum exterior algebra k(x, y)/(x^2, y^2, xy + qyx) in two variables, and all the indecomposable modules of dimension ≤3 over the quantum complete intersection k(x,y)/(x^m,y^n,xy + qyx) in two variables, where m or n ≥3, by giving explicitly their diagram presentations.     

论怀疑

现代世界,资讯发达,我们常常会听到一些匪夷所思的事情.这些传闻可信么?的确,大千世界,无奇不有,好像什么事情都可能发生,但我们也不能听到什么都相信我们要有怀疑精神,要独立思考,对该事件发生的可能性大小作一些分析,有助于我们作出理性判断.也就是说,我们要作出理性判断,要以怀疑精神作为前提,以概率分析为辅助.下面,就让我们从怀疑谈起.     

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.     

本期特约编委简介

杨仁宽,男,湖北恩施市人,湖北大学毕业.广东省数学特级教师,广东省南粤优秀教师,广东省名师工作室主持人,广州市名教师,教育部"国培研修员",省教育厅"南粤名师大讲堂"主讲、主评,广东省示范性高中广州市从化中学教研主任,从化市十大科技杰出人才,从化市劳动模范,《数学大世界》执行编委,国家级优秀(核心)期刊《高中数理化》特邀编委,广州市教育局第十三届特约教研员,主持教育部规划课题的子课题结题,主持广州市教育局资助课题在研,核心期刊《中学数学》2006年第10期     

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.     

品鸭脖赏小题——武汉市中考数学选择压轴题赏析

武汉鸭脖名扬天下,鸭脖虽小,品之有趣:一在麻劲够劲,二在慢啃细嚼之间回味无穷.同样,武汉人出的中考数学题也匠心独运,特色鲜明,出现在“脖颈”处的小题,带着股明显的鸭脖味儿,初品辣火呛口,但只要解题者细细品味、慢慢咀嚼,总会嚼出“香气”,唇齿留香.     

相似三角形等积式问题证明“三部曲”

等积式证明问题是初中平面几何的重要内容,它涉及的知识内容广泛,有利于培养学生综合运用知识的能力.等积问题综合性强,类型繁多,涉及面广,难度大,加之许多学生由于基础知识不牢,不善于归纳总结,结果在解决等积问题时不能灵活运用,感觉问题的分析困难,甚至是无从下手,望而生畏.为此,     

IMGS方法对于,H -矩阵的若干令人满意的改进

该文给出线性方程组改进的Gauss-Seidel迭代法（被称之为IMGS方法）对于H -矩阵的收敛性定理,并且对其参数a_i与SOR迭代法的参数ω的取值范围进行了比较. 所用方法及所得结论优于近年来相关结论,并且表明这种IMGS方法对,H -矩阵是有效的.     

CUTTING CORNERS PRESERVES LIPSCHITZ CONTINUITY

ＣＵＴＴＩＮＧＣＯＲＮＥＲＳＰＲＥＳＥＲＶＥＳＬＩＰＳＣＨＩＴＺＣＯＮＴＩＮＵＩＴＹ￥ＦＥＮＧＹＵＹＵ（Ｄｅｐｔ．ｏｆＭａｔｈ．ＵＳＴＣ，Ｈｅｆｅｉ，２３００２６，Ｐ．Ｒ．Ｃｈｉｎａ）ＪＥＲＮＥＪＫＯＺＡＫ（Ｄｅｐｔ．ｏｆＭａｔｈ．Ｕｎｉｖｅｒｓｉｔ...     

A generalized Fourier transform and convolution on time scales

In this paper, we develop some important Fourier analysis tools in the context of time scales. In particular, we present a generalized Fourier transform in this context as well as a critical inversion result. This leads directly to a convolution for signals on two (possibly distinct) time scales as well as several natural classes of time scales which arise in this setting: dilated, closed under addition, and additively idempotent. We explore the properties of these time scales and demonstrate the utility of these concepts in discrete convolution, Mellin convolution, and transformations of a random variable.     

平面上点的表示系统

利用矩阵作为基底和有限个点作为表示系数构造出了平面上点的表示系统，并讨论了这种表示系统的性质，还找出了平面上所有点和所有坐标为整数的点能够表示的条件。     

一类多维0-1背包问题的约束归并方法

提出一种新的关于多维背包(Multi-dimensions Knapsack Problem,MKP)的约束替代问题,MKP是NP-完全问题,称这种约束替代方法为不等式单约束平面生成法.叙述了单约束不等平面生成算法的基本思想,证明了此方法的一些性质及化简问题后所得到的新问题MKPS与原问题MKP的等价性.最后用实例证实了这种化简方法及其有效性。     

Asymptotic behaviour for the 3-D Schrödinger-Poisson System in the attractive case with positive energy

In this paper, we study the asymptotic behaviour of solutions to the three-dimensional Schrödinger-Poisson system in the attractive case with positive energy. In this case, it is proved that for a real initial condition, the solutions expand unboundedly as time goes to infinity. The proof of this result is based on the derivation of a dispersive equation relating density and linear momentum, as well as on optimal bounds for the kinetic energy.     

Multipliers on matrix ordered operator spaces and some K-groups

Matrix ordered operator spaces are ‘non-commutative Banach spaces equipped with a non-commutative order’. Examples include C*-algebras as well as their duals. In this article, we define and intrinsically characterize the multiplier algebra for this class of spaces and briefly tackle the problem of extending K-theory to this context.     

GENERALIZED MATRIX MULTISPLITTING RELAXATION METHODS AND THEIR CONVERGENCE

In this paper, we set up a general framework of parallel matrix mullisplitting relaxation methods for solving large scale system of linear equations. We investigate the convergence properties of this framework and give several sufficient conditions ensuring it to converge as well as diverge. At last, we conclude a necessary and sufficient condition for the convergence of this framework when the coefficient matrix is an L-matrix.     

A curve-fitting genetic algorithm for a styling application

Fitting curves in computer-aided geometric design is generally regarded as an optimisation problem. Depending on the application, the conditions to be satisfied can make the problem difficult to solve using classic methods, and for this reason, stochastic methods, such as genetic algorithms appear to be appropriate. This article considers a curve fitting problem, with the objective of generating shapes with specific curvature variations for use in the design of car bodies. To this end, a particular curve model was developed and implemented within a genetic algorithm. The main characteristics of this algorithm are described and its promising results are presented. The conclusion will show that this technique can be used as an alternative method in the design of car bodies.