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.     

一类向量值映射与其边缘映射的次微分

本文研究拓扑线性空间上一类向量值映射与其边缘映射的次微分的关系。     

具变系数的二阶中立型微分方程解的振动性

本文研究具有变系数的二阶非线性中立型方程和线性中立型方程建立了方程(1)和(16)的所有有界解振动的充分条件,其条件是“sharp"的,也给出了方程(1)的线性化极限振动准则。所得结果推广了文《二阶非线性中立型微分方程解的振动准则》(钱祥征等,湖南教学年刊Vol.10No.1—2,(1990),101—108)中的结论。     

浅议黑格尔的无限观

黑格尔把无限分为两种：一种叫做“真无限”；一种叫做“坏无限”。他认为传统的无限观是形而上学的“坏无限”，无限与有限是绝对对立的。而“真无限”则认为有限和无限之间没有不可超越的界限，它是无限和有限的自身发展起来的统一。黑格尔通过对无限的划分，把真无限理解为有限和无限彼此自我否定，自我扬弃后的对立统一，进而达到他所谓的“绝对精神”。     

一类广义Liénard型方程的极限环

本文讨论广义Lienard系统(E):x+(f(x)+k(x)x)+g(x)=0,获得了系统(E)的极限环存在,至多有一个或两个的充分条件.这些条件不仅简单和易于验证,而且推广了〔5,6〕的结果.     

康托实数集合不可数证明中的四种错误探析

从逻辑、无穷观、极限论和证明的思路及具体的操作过程,分析了新发现的康托在实数集合不可数证明中所存在的四种错误,得到＂由于与现有经典无穷理论体系、经典极限论和经典数量体系密切相关的数学基础理论中所存在的缺陷,康托在这类证明中无法回避这四种很严重但却很隐蔽的错误＂的明确结论.特别是其中的逻辑错误使这样的证明无意中成了一种典型的数学魔术.     

关于收缩性逆极限的注记

在假设逆极限空间X=lim←{Xα,παβ,Λ}是λ-仿紧、投射πα为伪开映射的条件下,正规性、收缩性及次收缩性均可为其极限空间保持.为此,对逆极限保持定理的证明作了适当简化,为其他拓扑性质逆极限的简化证明提供了参考.     

基于企业生命周期理论的企业家素质SVM评价方法

基于企业生命周期理论,考察企业不同阶段对企业家素质的要求,构建企业家素质评价指标体系,并应用当今统计学习理论的新方法——支持向量机（SVM）对企业家素质进行综合评价,以克服现有企业家素质评价体系的不足,增强评价结果的有效性.     

固态继电器在全新风机组中的应用

本文介绍了应用固态继电器及可编程逻辑控制器实现的控制全新风空调机组送风温度的方法。使用这种方法设计的空调机控制系统在有效控制机组的送风温度的同时大大节约了生产成本。     

基于“三为循环法”的技校实习课堂管理模式

以技工学校电工实习为例,实施三为循环法教学比传统的实习教学取得更显著的效果,最终让学生实现自我管理、自我教育、自我发展,让学生更好地适应企业工作的要求。