关于积分中值ξ=ξ(x)的渐近性

本文对一类g(x)讨论了积分中值定理ξ=ξ(x)在x→a时的渐近性质.     

一类对称平均及其基本性质

定义了一类对称平均,并给出了它的基本性质,举例说明了它的应用。     

Sum of squares of deviations

The question is whether or not we or any student are allowed to define a measure of variability in some other way that is not written in textbooks and officially approved. We compare the sum of squares of all deviations against the usual sum of squares of deviations from the mean.     

Digital transformation solutions of entrepreneurial SMEs based on an information error-driven T-spherical fuzzy cloud algorithm

The digital transformation of enterprises has become an inevitable development trend and one of the key driving forces that promotes the sustainable development of enterprises. However, due to the many obstacles of financial burdens, technical thresholds, and talent shortages, digital transformation has become a challenging task for entrepreneurial Small and Medium-Sized Enterprises (SMEs). Additionally, many competitive digital transformation solutions on the market cause confusion when enterprises must choose one. This study drew a new information error-driven T-spherical fuzzy cloud algorithm to evaluate digital transformation solutions of entrepreneurial SMEs and support its selection. First, an evaluation index system for the digital transformation solution of entrepreneurial SMEs was established from four aspects. Then, a new concept of a T-spherical fuzzy cloud was defined to represent the evaluation information of the indicators. Additionally, a T-spherical Fuzzy Cloud Weighted Heronian Mean (T-SFCWHM) operator was used to aggregate the evaluation information. Afterward, an evaluation and selection decision framework for the digital transformation solution of entrepreneurial SMEs based on the T-SFCWHM operator was developed. Further, a practical example was given to illustrate the effectiveness of the proposed method. Finally, a discussion of the findings in our study was conducted, and the conclusions were summarized.     

微积分中若干问题的研究(Ⅱ)

对于原函数存在定理的推广,给出了另一种证明;对定积分的中值定理给出了正确的证明,而其它书中的证明是欠妥的;用定积分的定义等证明了微积分的基本公式;给出了几个旋转体的体积公式;几何级数前n项和公式的应用.     

利用小样本数据预处理技术提高效能指标精度

提出了运用熵值判别法和线性均方估计法来处理小样本数据的方法.熵值判别法是根据熵的上界对应最大的不确定度,利用所得数据的熵信息量判别数据是否含有粗大误差;线性均方估计消除粗大误差是一种采用软化的方法处理粗大误差.经过多次试验,结果表明这两种方法在处理小样本采样数据时能够有效地提高数据精度.     

平均值不等式在数学分析中的应用

在数学分析中,平均值不等式可用于判断某些数列及级数的敛散性,解决积分不等式问题,求函数极值等。本文通过实例说明平均值不等式的一些应用。     

儒家中庸思想之评述

中庸思想是儒家哲学的重要方法论,与仁爱思想共同构成了儒家思想体系的两大基石。本文剖析了儒家中庸方法论的真正内涵、不同时期对中庸的解析、以及中庸方法论与折中主义、调和论的三处差异。阐明了儒家中庸思想和所谓的折中主义、调和论有本质不同,实乃广大民众、社会所谋取的一种积极、正确,合乎事物发展规律的方法论思想。     

关于数字之和函数中的四次均值的计算

运用初等数论和组合数论等工具进行猜想、归纳和证明,解决了Smarandache F.在Only Problems,not solutions!一文中所提到的第21个未解决问题--数字之和函数的均值问题,即数字之和函数的4次均值的精确计算问题,得到了n进制数字之和函数的4次均值的精确计算公式,也为此类问题的进一步解决提供了一个较为可行的研究方法.