微元法是分析解决物理问题的常用方法,是一种从部分到整体的思维方法,通过将问题分解为众多微小的“元过程”,运用熟悉的物理规律解决问题,从而使问题简单化。微元法中“元”的寻找是解决问题的关键,对一些特殊的积分区域,如圆柱面,圆柱...微元法是分析解决物理问题的常用方法,是一种从部分到整体的思维方法,通过将问题分解为众多微小的“元过程”,运用熟悉的物理规律解决问题,从而使问题简单化。微元法中“元”的寻找是解决问题的关键,对一些特殊的积分区域,如圆柱面,圆柱体,球体,本文打破常规的微元分割,找到灵活的“微元(——弧棒,柱壳,球壳)”,实现积分运算的简化。The differential element method is a commonly used method for analyzing and solving physical problems. It is a way of thinking that moves from part to whole by breaking down problems into numerous small “element processes” and applying familiar physical laws to solve them, simplifying the problem. The search for “elements” in the differential element method is the key to solving problems. For some special integration regions, such as cylindrical surfaces, cylinders, and spheres, this article breaks away from conventional finite element segmentation and finds flexible “differential elements” (arc rods, cylindrical shells, spherical shells) to simplify integration operations.展开更多
通过研究非自治传染病SIRS模型解的存在性和建立迭代算法,分析模型的特殊性质,引入特殊性质的函数,将模型转换为积分系统,并构造所需的迭代序列,证明这个序列收敛于模型的解。可以证明,在一定时间内,SIRS模型具有唯一解,解和近似解之间...通过研究非自治传染病SIRS模型解的存在性和建立迭代算法,分析模型的特殊性质,引入特殊性质的函数,将模型转换为积分系统,并构造所需的迭代序列,证明这个序列收敛于模型的解。可以证明,在一定时间内,SIRS模型具有唯一解,解和近似解之间能进行误差估计。该算法克服模型中非线性项可取负值和不满足Lipschitz条件的困难,证明了SIRS模型解存在,且可使用迭代算法求出和进行误差估计。This paper studies the existence and iterative algorithms of solutions to the SIRS model of non- autonomous infectious diseases. By analyzing the special properties of the model and introducing the function with special properties, the SIRS model is changed to an integral system, and the required iterative sequence is constructed. It is proved that this sequence converges to the solution of the model. It is proved that the SIRS model has a unique solution within a certain period of time, and the error estimations between the exact solution and the approximate solution are established. By overcoming the difficulties that the nonlinear terms in the model may take negative values and do not satisfy the Lipschitz condition, it is proved that the solution of the SIRS model can be obtained by an iterative method, and the error estimation can be performed.展开更多
传统Pearson相关系数计算公式具有不稳健性,离群值的存在会导致计算结果与实际不符。针对此问题,文章给出了一种稳健估计方法。在模拟样本量分别为20、50、100、200,污染率分别为1%、5%、10%情形下,比较传统相关系数值与稳健相关系数值...传统Pearson相关系数计算公式具有不稳健性,离群值的存在会导致计算结果与实际不符。针对此问题,文章给出了一种稳健估计方法。在模拟样本量分别为20、50、100、200,污染率分别为1%、5%、10%情形下,比较传统相关系数值与稳健相关系数值,发现:稳健相关系数公式正确率均显著高于传统相关系数。在实例分析中进一步验证了稳健相关系数的可行性和有效性。文章研究结论可用于含离群值变量的相关系数稳健估计。The traditional Pearson correlation coefficient calculation formula is not robust, and the existence of outliers will cause the calculation results to be inconsistent with reality. To solve this problem, this paper presents a robust estimation method. When the simulated sample size is 20, 50, 100 and 200 respectively, the pollution rate is 1%, 5% and 10% respectively, it is found that the accuracy of the robust correlation coefficient formula is significantly higher than that of the traditional correlation coefficient. The feasibility and effectiveness of a robust correlation coefficient are further verified in the example analysis. The conclusions of this paper can be used for robust estimation of correlation coefficients with outlier variables.展开更多
在质量过程控制中,不合格品率小漂移的检测会受到样本的误分类以及小样本量的影响而产生严重的质量误判。本文首先针对样本的分类误差建立误分类修正数据模型实现样本观测值误分类修正,再结合DEWMA p控制图对参数小漂移的敏感性和对样...在质量过程控制中,不合格品率小漂移的检测会受到样本的误分类以及小样本量的影响而产生严重的质量误判。本文首先针对样本的分类误差建立误分类修正数据模型实现样本观测值误分类修正,再结合DEWMA p控制图对参数小漂移的敏感性和对样本量的宽容特性,开发了带有误分类修正的DEWMA p控制图(MisC-DEWMA p)。实验结果表明,在对不合格品率的检测,特别是基于小样本的相应检测中,MisC-DEWMA p控制图对不合格品率小而持久的漂移具有更高的敏感性和精确性。In the quality process control, the monitoring of potential small shift at nonconforming proportion will suffer from misclassification and the small-size of sampled observations and thus present kind of a misjudge. In this paper, a data-modified model is firstly established to correct the sample data carrying misclassification, and then DEWMA p Control Chart with Misclassification Correction (MisC-DEWMA p) is proposed, equipped with the strong small-shift-sensitivity and small-sample-kindness of DEWMA p control chart. The numerical and real data experiment results show that, for a process with small persistent shift of nonconforming proportion, MisC-DEWMA p control chart provides a higher sensitivity and accuracy.展开更多
本文探讨了将MATLAB软件应用于线性代数教学的重要性,并对其在教学过程中可能遇到的挑战进行了分析。通过三个具体的线性代数应用案例,展示了MATLAB软件在实际教学中的有效性,为如何在线性代数教学中更好地利用MATLAB提供了参考。This a...本文探讨了将MATLAB软件应用于线性代数教学的重要性,并对其在教学过程中可能遇到的挑战进行了分析。通过三个具体的线性代数应用案例,展示了MATLAB软件在实际教学中的有效性,为如何在线性代数教学中更好地利用MATLAB提供了参考。This article discusses the importance of applying MATLAB software to the teaching of linear algebra and analyzes the challenges that may be encountered in the teaching process. Through three specific cases of linear algebra applications, it demonstrates the effectiveness of MATLAB software in teaching, providing a reference for how to better utilize MATLAB in the teaching of linear algebra.展开更多
文摘微元法是分析解决物理问题的常用方法,是一种从部分到整体的思维方法,通过将问题分解为众多微小的“元过程”,运用熟悉的物理规律解决问题,从而使问题简单化。微元法中“元”的寻找是解决问题的关键,对一些特殊的积分区域,如圆柱面,圆柱体,球体,本文打破常规的微元分割,找到灵活的“微元(——弧棒,柱壳,球壳)”,实现积分运算的简化。The differential element method is a commonly used method for analyzing and solving physical problems. It is a way of thinking that moves from part to whole by breaking down problems into numerous small “element processes” and applying familiar physical laws to solve them, simplifying the problem. The search for “elements” in the differential element method is the key to solving problems. For some special integration regions, such as cylindrical surfaces, cylinders, and spheres, this article breaks away from conventional finite element segmentation and finds flexible “differential elements” (arc rods, cylindrical shells, spherical shells) to simplify integration operations.
文摘通过研究非自治传染病SIRS模型解的存在性和建立迭代算法,分析模型的特殊性质,引入特殊性质的函数,将模型转换为积分系统,并构造所需的迭代序列,证明这个序列收敛于模型的解。可以证明,在一定时间内,SIRS模型具有唯一解,解和近似解之间能进行误差估计。该算法克服模型中非线性项可取负值和不满足Lipschitz条件的困难,证明了SIRS模型解存在,且可使用迭代算法求出和进行误差估计。This paper studies the existence and iterative algorithms of solutions to the SIRS model of non- autonomous infectious diseases. By analyzing the special properties of the model and introducing the function with special properties, the SIRS model is changed to an integral system, and the required iterative sequence is constructed. It is proved that this sequence converges to the solution of the model. It is proved that the SIRS model has a unique solution within a certain period of time, and the error estimations between the exact solution and the approximate solution are established. By overcoming the difficulties that the nonlinear terms in the model may take negative values and do not satisfy the Lipschitz condition, it is proved that the solution of the SIRS model can be obtained by an iterative method, and the error estimation can be performed.
文摘传统Pearson相关系数计算公式具有不稳健性,离群值的存在会导致计算结果与实际不符。针对此问题,文章给出了一种稳健估计方法。在模拟样本量分别为20、50、100、200,污染率分别为1%、5%、10%情形下,比较传统相关系数值与稳健相关系数值,发现:稳健相关系数公式正确率均显著高于传统相关系数。在实例分析中进一步验证了稳健相关系数的可行性和有效性。文章研究结论可用于含离群值变量的相关系数稳健估计。The traditional Pearson correlation coefficient calculation formula is not robust, and the existence of outliers will cause the calculation results to be inconsistent with reality. To solve this problem, this paper presents a robust estimation method. When the simulated sample size is 20, 50, 100 and 200 respectively, the pollution rate is 1%, 5% and 10% respectively, it is found that the accuracy of the robust correlation coefficient formula is significantly higher than that of the traditional correlation coefficient. The feasibility and effectiveness of a robust correlation coefficient are further verified in the example analysis. The conclusions of this paper can be used for robust estimation of correlation coefficients with outlier variables.
文摘在质量过程控制中,不合格品率小漂移的检测会受到样本的误分类以及小样本量的影响而产生严重的质量误判。本文首先针对样本的分类误差建立误分类修正数据模型实现样本观测值误分类修正,再结合DEWMA p控制图对参数小漂移的敏感性和对样本量的宽容特性,开发了带有误分类修正的DEWMA p控制图(MisC-DEWMA p)。实验结果表明,在对不合格品率的检测,特别是基于小样本的相应检测中,MisC-DEWMA p控制图对不合格品率小而持久的漂移具有更高的敏感性和精确性。In the quality process control, the monitoring of potential small shift at nonconforming proportion will suffer from misclassification and the small-size of sampled observations and thus present kind of a misjudge. In this paper, a data-modified model is firstly established to correct the sample data carrying misclassification, and then DEWMA p Control Chart with Misclassification Correction (MisC-DEWMA p) is proposed, equipped with the strong small-shift-sensitivity and small-sample-kindness of DEWMA p control chart. The numerical and real data experiment results show that, for a process with small persistent shift of nonconforming proportion, MisC-DEWMA p control chart provides a higher sensitivity and accuracy.
文摘本文探讨了将MATLAB软件应用于线性代数教学的重要性,并对其在教学过程中可能遇到的挑战进行了分析。通过三个具体的线性代数应用案例,展示了MATLAB软件在实际教学中的有效性,为如何在线性代数教学中更好地利用MATLAB提供了参考。This article discusses the importance of applying MATLAB software to the teaching of linear algebra and analyzes the challenges that may be encountered in the teaching process. Through three specific cases of linear algebra applications, it demonstrates the effectiveness of MATLAB software in teaching, providing a reference for how to better utilize MATLAB in the teaching of linear algebra.
