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关键词： 数学分析   不等式   证明方法  

摘要： 不等式证明是数学分析中经常遇到且较难理解和掌握的证明问题之一。文章主要对不等式证明的几种常见方法进行梳理,以培养学生不等式证明的发散思维。

关键词： 经济数学   定义   数学分析  

摘要： 本文主要针对经济数学中学生感到比较枯燥无味的定义,如何让学生正确认识到它们的重要性,并对它们感兴趣,同时能够掌握和运用它们展开研究。

关键词： 微分   微元法   Stokes公式  

摘要： '微分'这个概念是数学分析中非常重要的概念,但是学生普遍反映这个概念不好理解,抓不到要义,云里雾里,也不会使用。为了帮助学生更好地理解这个概念,本文将从概念的引入、概念的质疑以及一些重要应用三个方面来探讨这个概念的教学。

关键词： 数学分析   精品在线开放课程   课程建设   教学改革  

摘要： 对《数学分析》精品在线开放课程建设的目标、建设的思路与教学设计、教学内容与网上资源、教学活动与学习评价等进行探究,总结了实施课程建设的教学效果与影响,提出了完善课程建设的思路与设想.

关键词： 教材   剥离   类比   发散  

摘要： 本文围绕小学数学教材资源的开发和发掘,阐述了在小学数学课堂教学中,通过捋顺条件、强化表述、抓住关键、小组交流几个方面,培养学生的数学分析能力。

摘要： In this work, we analyze a nonlinear partial differential equation (PDE) model for the total value adjustment on European options in the presence of a counterparty risk. We transform the nonlinear PDE into an equivalent one, involving a sectorial operator, and prove the existence and uniqueness of a solution. (C) 2019 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

关键词： Heat and mass transfer   Modeling   Thermal analysis   Solidus temperature   Steel   Phase transformation  

摘要： An approximate analytical model has been developed to obtain simultaneous solutions for nonlinear solute- and heat-transfer equations for multi-component alloy steels;in this model, a linear relation between the solid fraction and the temperature in the mushy zone was assumed. This model predicts important parameters, such as the solidus temperature for the multi-component steel materials that have not been well confirmed by the reliable measurement in a real process. The predicted temperature, solidification constants, and effective partition ratios of solutes were in good agreement with both the reported measurements and generally accepted values. The predicted solidus temperatures were also in reasonable agreement with the reported zero ductile temperature of Fe-C-Mn steel and the thermo-analytically measured solidus temperatures of steels of various grades. The solutions were also in good agreement with those separately performed numerical thermal analysis. The model involves the solution for Fe-C binary alloy which is consistent with the Neumann's solution in the low carbon range. Thus, this model provides approximate analytical solutions that can reduce the computational load, saving time and cost. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Basic Reproductive Number   Sensitivity Analysis   Ordinary Differential Equations  

摘要： In this work we formulate a mathematical model to assess the importance of sexual transmission during the Zika virus outbreak that occurred in Rio de Janeiro, Brazil, in 2015. To this end, we deduce from the model an analytical expression of the basic reproduction number of Zika, R-0, in terms of the vectorial and sexual transmissions, and we use the estimations given in Ref. 1 [Villela DAM, Bastos LS, de Carvalho LM, Cruz OG, Gomes MFC, Durovni B, Lemos MC, Saraceni V, Coelho FC, Codeco CT, Zika in Rio de Janeiro: Assessment of basic reproduction number and comparison with dengue outbreaks, Epidemiol Infect 145(8): 1649-1657, 2017] for the R-0 values of Zika virus and dengue virus epidemics in Rio de Janeiro to evaluate the contribution of sexual transmission of Zika virus. According to the obtained results, sexual transmission (pure plus mediated by vector transmission) contributes from 23% to 46% for the R-0 increment. Also, an asymmetric sexual transmission between men and women can explain the fact that the incidence of Zika virus in women was 60% higher than in man during the 2015 epidemics. We also carry out a sensitivity analysis using R-0 as the output parameter. The results of this analysis have shown that the transmission rate between human and mosquito populations, the mosquito mortality rate, and the human infectious period are the parameters that contribute more to the R-0 variation, highlighting the importance of vector control to halt disease transmission.