高考题的新触角——独立性检验

一、新课标区近二年高考有关"独立性检验"考点的考情透视1.考情分析与今后预测:在2010年之前,"独立性检验"一直是新课标区高考复习的"冷僻"知识点。不过,这一考点终于在2010年以多省份多套题浮出水面.2010年的3个省份(含广东卷文、全国卷文理及     

例析二次函数的图象变换

图形的平移、轴对称、旋转常见于直线形中,在曲线形--圆中也偶有所见.然而,也有以二次函数图像为背景的图形变换,它的一些性质与直线形的图形变换有许多相通之处.     

ERM learning with unbounded sampling

The learning approach of empirical risk minimization (ERM) is taken for the regression problem in the least square framework. A standard assumption for the error analysis in the literature is the uniform boundedness of the output sampling process. In this paper we abandon this boundedness assumption and conduct error analysis for the ERM learning algorithm with unbounded sampling processes satisfying an increment condition for the moments of the output. The key novelty of our analysis is a covering number argument for estimating the sample error.     

联想让思维展翅飞翔

美国数学家波利亚在《怎样解题》一书中,提出了一个解题计划表,其中有一个重要的环节是联想.联想是我们能否顺利解决问题的桥梁,它是一种重要的思维形式.包括两种情况:一种“横向联系”,把处于不同知识块的知识联系在一起,这种思维形式有利于提高我们的思维的灵活性,也有利于我们把不同的数学知识融会贯通.联想的另一种形式,是“纵向联系”.以逻辑推理能力和运算能力为基础,将一个数学问题多次转化成另一个容易解决的数学问题,这种思维形式有利于提高思维的深刻性.横向联想,让我们的思维插上飞翔的翅膀,我们能飞得更高更远更轻盈灵活;纵向联想,能让我们的思维更加深刻,让我们的数学素养更加深厚.     

谈双曲线在生活中的应用

一、运输问题 背景材料正值施肥的旺季,小村居民合租拖拉机搬运化肥,为减少运输化肥的成本,居民派出代表陈大伯负责此事,陈大伯读书少,碰到这时还真犯了难,为了这个计划有效可行,他将这一问题拿出来和读高二的侄子我一块商量,也就有了下面的研究.     

以ZrO_2-Al_2O_3为载体Co-Mo-K耐硫变换催化剂的TPR研究

利用程序升温还原 (TPR)技术 ,研究了ZrO2 对Co/Al2 O3、Mo/Al2 O3、Mo -K/Al2 O3以及Co -Mo -K耐硫变换催化剂氧化还原性能的影响。结果表明 ,ZrO2 的引入 ,使活性组分在载体表面分散的更好 ,促进了Mo -K活性相的形成 ,使Co和Mo的还原变得容易 ,并起到抑制催化剂在反应中被重新氧化的作用。     

Global Geometry of 3-Body Motions with Vanishing Angular Momentum Ⅰ

Following Jacobi＇s geometrization of Lagrange＇s least action principle, trajectories of classical mechanics can be characterized as geodesics on the configuration space M with respect to a suitable metric which is the conformal modification of the kinematic metric by the factor （U ＋ h）, where U and h are the potential function and the total energy, respectively. In the special case of 3-body motions with zero angular momentum, the global geometry of such trajectories can be reduced to that of their moduli curves, which record the change of size and shape, in the moduli space of oriented m-triangles, whose kinematic metric is, in fact, a Riemannian cone over the shape space M^＊≌S^2 （1/2）.
In this paper, it is shown that the moduli curve of such a motion is uniquely determined by its shape curve （which only records the change of shape） in the case of h≠0, while in the special case of h = 0 it is uniquely determined up to scaling. Thus, the study of the global geometry of such motions can be further reduced to that of the shape curves, which are time-parametrized curves on the 2-sphere characterized by a third order ODE. Moreover, these curves have two remarkable properties, namely the uniqueness of parametrization and the monotonieity, that constitute a solid foundation for a systematic study of their global geometry and naturally lead to the formulation of some pertinent problems.     

无棱二面角问题的转化视角

二面角问题是立体几何三类求角问题中的难点，在求解二面角问题时，图中无两平面交线的无棱二面角更显困难，本文将以一道高考题为例，从不同的视角对此类无棱二面角的求解策略进行一些探讨。     

利用数列性质旧题新解

文[1]中应用向量的方法巧妙地将不等式的值域问题加以解决，笔者看了以后深受启发，借助特殊数列的特性对文中的几个例子加以尝试，发现也有异曲同工之妙．下面请看：     

排列组合中的“序”、“分”例析

排列组合中,经常要和有序与无序、排序与定序、分配与分组等非常易混的问题打交道,稍不慎就会出现错误.本文试对这几个问题加以辨析.