对参数假设检验中几对关系的研究

参数假设检验中存在四对密切相关的概念:原假设与备择假设、两类错误、P-值法与临界值法、区间估计与假设检验,深入了解这些概念及其原理之间的关系有利于准确把握假设检验的思想与方法。     

巧用三角代换求解一类数列极限问题

极限理论是数学分析的理论基础,正确处理极限问题尤显重要。当数列通项具有某种特殊形式时,通过实例说明,巧用三角代换能成功求解其极限问题。     

Efficient volume preserving approach for skeleton-based implicit surfaces

This paper presents an efficient way to preserve the volume of implicit surfaces generated by skeletons. Recursive subdivision is used to efficiently calculate the volume. The criterion for subdivision is obtained by using the property of density functions and treating different types of skeletons respectively to get accurate minimum and maximum distances from a cube to a skeleton. Compared with the criterion generated by other ways such as using traditional Interval Analysis, Affine Arithmetic, or Lipschitz condition, our approach is much better both in speed and accuracy.     

Abstraction and consolidation of the limit procept by means of instrumented schemes: the complementary role of three different frameworks

I investigate the contributions of three theoretical frameworks to a research process and the complementary role played by each. First, I describe the essence of each theory and then follow the analysis of their specific influence on the research process. The research process is on the conceptualization of the notion of limit by means of the discrete continuous interplay. I investigate the influence of the different perspectives on the research process and realize that the different theoretical approaches intertwine. Moreover, I realize that the research study demanded the contribution of more than one theoretical approach to the research process and that the differences between the frameworks could serve as a basis for complementarities.     

关于实数连续性的几个问题(二)

文献 [1]对实数的连续性作了深入的讨论 ,给出了Ⅰ推证Ⅱ∽Ⅶ ;Ⅱ推证Ⅰ ,Ⅲ∽Ⅶ以及Ⅲ推证Ⅰ ,Ⅱ ,Ⅳ∽Ⅶ的几个等价刻划 ,文章继续讨论类似的问题 ,并对定理的适用范畴作了归纳总结。     

关于导函数的极限的研究

探讨函数的可导性、函数的渐近线与导函数的极限之间的关系。     

最优区间估计问题的探讨

文中讨论了区间估计的最优性，并证明了最优区间估计的存在性，同时给出了一种寻求最优区间估计的方法．     

证明lim(1+1/n)~n(from n=-∞ to ∞)存在的新方法

文章利用构造不等式bn +1 -an +1b -a <(n + 1)bn(0≤a 相似文献   

MM教学方式在数列极限教学中的应用

在微积分学中，极限的教学历来被认为是教学的重点和难点。采用MM教学方式设计数列极限的教学，能使学生在轻松愉快的环境中清楚地理解与掌握数列极限的概念。     

Impact Factors and the Central Limit Theorem: Why citation averages are scale dependent

Citation averages, and Impact Factors (IFs) in particular, are sensitive to sample size. Here, we apply the Central Limit Theorem to IFs to understand their scale-dependent behavior. For a journal of n randomly selected papers from a population of all papers, we expect from the Theorem that its IF fluctuates around the population average μ, and spans a range of values proportional to $\sigma /\sqrt{n}$, where σ² is the variance of the population's citation distribution. The $1/\sqrt{n}$ dependence has profound implications for IF rankings: The larger a journal, the narrower the range around μ where its IF lies. IF rankings therefore allocate an unfair advantage to smaller journals in the high IF ranks, and to larger journals in the low IF ranks. As a result, we expect a scale-dependent stratification of journals in IF rankings, whereby small journals occupy the top, middle, and bottom ranks; mid-sized journals occupy the middle ranks; and very large journals have IFs that asymptotically approach μ. We obtain qualitative and quantitative confirmation of these predictions by analyzing (i) the complete set of 166,498 IF & journal-size data pairs in the 1997–2016 Journal Citation Reports of Clarivate Analytics, (ii) the top-cited portion of 276,000 physics papers published in 2014–2015, and (iii) the citation distributions of an arbitrarily sampled list of physics journals. We conclude that the Central Limit Theorem is a good predictor of the IF range of actual journals, while sustained deviations from its predictions are a mark of true, non-random, citation impact. IF rankings are thus misleading unless one compares like-sized journals or adjusts for these effects. We propose the Φ index, a rescaled IF that accounts for size effects, and which can be readily generalized to account also for different citation practices across research fields. Our methodology applies to other citation averages that are used to compare research fields, university departments or countries in various types of rankings.