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关键词： 小学生   数学分析能力   数学思维  

摘要： 当前阶段,小学数学教学工作已经越来越受到教育界的关注和重视。作为一门逻辑性与探索性极强的基础学科,小学生若想有效掌握各项数学知识,就必须拥有一定的数学分析能力。鉴于此,作者在文章中针对当前阶段如何有效提高小学生的数学分析的能力进行了一定探究,并且提出了一些合理的建议,以供参考。

关键词： 数学分析   概率论   相互关系   应用  

摘要： 数学分析与概率论是互相渗透与相互依存的关系,两者共同发展,互相影响。数学分析作为一门基础性的学科,经过多年的发展与研究已经形成了一套较为完备的理论体系,并且对概率论的发展起到了良好的促进作用。反之,概率论的计算方法以及解题思路也可以把一些复杂的数学分析问题进行简化,实现确定性问题与随机性问题之间的有效转化,使得数学分析问题得以高效解决。

关键词： 微课翻转   定积分   数学分析  

摘要： 数学分析授课时,学生普遍觉得概念抽象难懂,证明过程抽象难以掌握。针对这一问题,教师有必要对学生的课前学习进行加强,利用信息化技术,借助微课翻转对数学分析中定积分的概念进行教学设计,教学效果较好。

关键词： 思政元素   数学分析   教学  

摘要： 本文通过分析思政元素与数学分析结合的可能性,探讨了思政元素在数学分析中的几点应用,从而得出思政元素可以自然融入数学分析的教学,拓展教学新方法的结论。

关键词： nanosecond pulse shaper   step-recovery diode   diode's model of switching   differential equations to describe the multiloop circuits  

摘要： This paper describes mathematically an expanded circuit additionally containing parasitic capacitors and inductors for the pulser circuit on two SRDs, which allows a relatively wide range to vary the output pulse duration with a rise time and fall time of less than a nanosecond. Resolving a system of differential equations, we acquire a possibility of analyzing the influence of the circuit elements on the output pulse parameters and to select the optimum value. The calculation results are compared with experimental data.

关键词： Spatial heterogeneity   Cell-to-cell infection   Basic reproduction number   Global dynamics  

摘要： We propose a general model to investigate the joint impact of viral diffusion and cell-to-cell transmission on viral dynamics. The mathematical challenge lies in the fact that the model system is partially degenerate and the solution map is not compact. While the simpler cases with only indirect transmission mode or weak cell-to-cell transmission mode have been extensively studied in the literature, it remains an open problem to understand the local and global dynamics of fully coupled viral infection model with partial degeneracy. In this paper, we identify the basic reproduction number as the spectral radius of the sum of two linear operators corresponding to direct and indirect transmission modes. It is well-known that viral mobility may induce infection in low-risk regions. However, as diffusion coefficient increases, we prove that the basic reproduction number actually decreases, which indicates that faster viral movements may result in a lower level of viral infection. By an innovative construction of Lyapunov functionals, we further demonstrate that the basic reproduction number is the threshold parameter which determines global picture of viral dynamics. In addition to the traditional dichonomy results of extinction and persistence as obtained in earlier works for many simpler models, we are able to prove global asymptotic stability of infection-free steady state and global attractiveness (as well as uniqueness) of chronic-infection steady state, depending on whether the basic reproduction number is smaller or greater than one. Numerical simulation supports our theoretical results and suggests an interesting phenomenon: boundary layer and internal layer may occur when the diffusion parameter tends to zero. (C) 2020 Elsevier Masson SAS. All rights reserved.

摘要： Modeling of infectious diseases is essential to comprehend dynamic behavior for the transmission of an epidemic. This research study consists of a newly proposed mathematical system for transmission dynamics of the measles epidemic. The measles system is based upon mass action principle wherein human population is divided into five mutually disjoint compartments: susceptible S(t)-vaccinated V(t)-exposed E(t)-infectious I(t)-recovered R(t). Using real measles cases reported from January 2019 to October 2019 in Pakistan, the system has been validated. Two unique equilibria called measles-free and endemic (measles-present) are shown to be locally asymptotically stable for basic reproductive number R-0 < 1 and R-0 > 1, respectively. While using Lyapunov functions, the equilibria are found to be globally asymptotically stable under the former conditions on R-0. However, backward bifurcation shows coexistence of stable endemic equilibrium with a stable measles-free equilibrium for R-0<1. A strategy for measles control based on herd immunity is presented. The forward sensitivity indices for R-0 are also computed with respect to the estimated and fitted biological parameters. Finally, numerical simulations exhibit dynamical behavior of the measles system under influence of its parameters which further suggest improvement in both the vaccine efficacy and its coverage rate for substantial reduction in the measles epidemic.

关键词： Malaria   Quarantine   Basic reproduction number   Standard incidence   Bilinear incidence   Backward bifurcation  

摘要： People infected with malaria may receive less mosquito bites when they are treated in well-equipped hospitals or follow doctors' advice for reducing exposure to mosquitoes at home. This quarantine-like intervention measure is especially feasible in countries and areas approaching malaria elimination. Motivated by mathematical models with quarantine for directly transmitted diseases, we develop a mosquito-borne disease model where imperfect quarantine is considered to mitigate the disease transmission from infected humans to susceptible mosquitoes. The basic reproduction number R0 is computed and the model equilibria and their stabilities are analyzed when the incidence rate is standard or bilinear. In particular, the model system may undergo a subcritical (backward) bifurcation at R0=1 when standard incidence is adopted, whereas the disease-free equilibrium is globally asymptotically stable as R0 <= 1 and the unique endemic equilibrium is locally asymptotically stable as R0>1 when the infection incidence is bilinear. Numerical simulations suggest that the quarantine strategy can play an important role in decreasing malaria transmission. The success of quarantine mainly relies on the reduction of bites on quarantined individuals.