比较两数大小的方法

比较两数大小的题目题型虽小,但技巧性、综合性都比较强,且解法灵活,涉及的知识面较广,一般不易观察直接获解,需要根据题意寻找适当的方法.如何比较两数大小,下面作一些归纳、总结、探析,以飨读者.1 作商比较两数大小我们知道,若A＞0,B＞0,则当A/B＞1时,有A＞B;当A/B=1时,有A=B;当A/B＜1时,有A＜B.例1 已知a＞0,b＞0,且2011a=2012b,试比较2011a与2012b的大小,并说明理由.     

欣赏两个指数函数的性质

以无理数e=2.71828…为底的指数函数y=ex,是中学数学乃至大学数学研究的重点,与其相关的问题也是高考命题的热点,故值得我们深入研究,为此,本文介绍由y=ex简单     

MPCK视角下的指数函数的单调性

MPCK(Mathematics Pedagogical Content Knowledge)是近几年数学教育研究的热点问题[1-4].发展MPCK不仅是教师组织、教师教育工作者和教育研究人员的诉求,而且是学者,政府乃至全社会不约而同的呼声.按照香港中文大学     

On multifractal of Cantor dust

We consider quasi-self-similar measures with respect to all real numbers on a Cantor dust. We define a local index function on the real numbers for each quasi-self-similar measure at each point in a Cantor dust, The value of the local index function at the real number zero for all the quasi-self-similar measures at each point is the weak local dimension of the point. We also define transformed measures of a quasi-self-similar measure which are closely related to the local index function. We compute the local dimensions of transformed measures of a quasi-self-similar measure to find the multifractal spectrum of the quasi-self-similar measure, Furthermore we give an essential example for the theorem of local dimension of transformed measure. In fact, our result is an ultimate generalization of that of a self- similar measure on a self-similar Cantor set. Furthermore the results also explain the recent results about weak local dimensions on a Cantor dust.     

关于常系数齐次线性微分方程组的解法研究

利用凯莱-哈密顿定理给出矩阵指数函数eAt的简洁计算方法;同时利用约当标准形推导出求常系数齐次线性微分方程组通解的循环公式.     

几对易错函数图象的交点问题

在初中,学习了一次函数、反比例函数与二次函数．在高中,又学习了指数函数、对数函数与三角函数等．对这些常见的函数的图象的交点个数是值得探究的．但是在教学中发现,对其中几对函数的图象的交点情况,有些同学仅凭直观就作出判断,往往得出错误的结论,兹列举如下．     

The Fractal Dimensions of Complex Networks

It is shown that many real complex networks share distinctive features, such as the small-world effect and the heterogeneous property of connectivity of vertices, which are different from random networks and regular lattices. Although these features capture the important characteristics of complex networks, their applicability depends on the style of networks. To unravel the universal characteristics many complex networks have in common, we study the fractal dimensions of complex networks using the method introduced by Shanker. We find that the average ＇density＇ （p（r ） ） of complex networks follows a better power-law function as a function of distance r with the exponent dl, which is defined as the fractal dimension, in some real complex networks. Furthermore, we study the relation between df and the shortcuts Nadd in small-world networks and the size N in regular lattices. Our present work provides a new perspective to understand the dependence of the fractal dimension df on the complex network structure.     

Exact Penalty Function and Asymptotic Strong Nonlinear Duality in Integer Programming

In this paper,a logarithmic-exponential penalty function with two parameters for integer program-ming is discussed.We obtain the exact penalty properties and then establish the asymptotic strong nonlinearduality in the corresponding logarithmic-exponential dual formulation by using the obtained exact penaltyproperties.The discussion is based on the logarithmic-exponential nonlinear dual formulation proposed in [6].     

指数函数与一次函数的大小关系

探究了指数函数y=ax与一次函数y=ax b(a>0且a≠1)的大小关系