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关键词： Backward bifurcation   Mass action incidence   Stability   Standard incidence   Vaccine   Lyapunov function  

摘要： In this paper, we develop a new disease-resistant mathematical model with a fraction of the susceptible class under imperfect vaccine and treatment of both the symptomatic and quarantine classes. With standard incidence when the associated reproduction threshold is less than unity, the model exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium. It is then proved that this phenomenon vanishes either when the vaccine is assumed to be 100% potent and perfect or the Standard Incidence is replaced with a Mass Action Incidence in the model development. Furthermore, the model has a unique endemic and disease-free equilibria. Using a suitable Lyapunov function, the endemic equilibrium and disease free equilibrium are proved to be globally-asymptotically stable depending on whether the control reproduction number is less or greater than unity. Some numerical simulations are presented to validate the analytic results.

关键词： COVID-19   Disease dynamics   Mexico   Effective daily reproduction ratio   Sensitivity analysis  

摘要： We propose an SEIARD mathematical model to investigate the current outbreak of coronavirus disease (COVID-19) in Mexico. Our model incorporates the asymptomatic infected individuals, who represent the majority of the infected population (with symptoms or not) and could play an important role in spreading the virus without any knowledge. We calculate the basic reproduction number (R-0) via the next-generation matrix method and estimate the per day infection, death and recovery rates. The local stability of the disease-free equilibrium is established in terms of R-0 . A sensibility analysis is performed to determine the relative importance of the model parameters to the disease transmission. We calibrate the parameters of the SEIARD model to the reported number of infected cases, fatalities and recovered cases for several states in Mexico by minimizing the sum of squared errors and attempt to forecast the evolution of the outbreak until November 2020. (c) 2020 Elsevier Ltd. All rights reserved.

关键词： 小学数学   数学分析能力   逻辑思维  

摘要： 在小学阶段,对于学生而言难以理解和掌握的学科之一就是数学学科,相较于其他语言类学科而言,其具有更强的学科逻辑性,并对学生的数学分析能力及运用能力要求较高。所以数学教师需要对数学教学方法和手段加强改进和创新,采用适当方式对学生的数学分析能力进行有效培养,使学生能够顺利找到问题的解决方法和途径。目前新课标的深入实施,进一步明确了小学数学的教学目标和方向,除了进行基础数学知识的传授外,还需要使学生能够对所学的数学知识加深理解,并应以学生对数学学习方法的有效掌握为教学重点,对其数学思维能力加强培养,从而对学生的全面发展起到有效促进作用。本文就小学数学教学,围绕学生数学分析能力培养及提高的有效途径进行分析和探讨。

关键词： 数学分析思想   高中数学   应用  

摘要： 高中数学是一门综合性较强的学科,在学习的过程中,不仅要求学生具有良好的逻辑分析能力,同时还有拥有严谨的学习态度。教师在授课过程中不仅要引导学生掌握正确的解题方法,同时还要促使他们拥有合理的数学分析能力。为此本文笔者结合实际教学经验,就数学分析思想在高中数学解题中的具体 应用策略展开分析。

关键词： Radon mitigation   Vapor intrusion mitigation   Active soil depressurization   Subslab venting   Radius of influence   Mass flux  

摘要： Volatile organic compounds (VOCs) and radon progeny pose potential health risks to occupants of certain buildings via subsurface vapor intrusion (VI) to indoor air. VI mitigation is usually performed using systems that extract gas from below the building, and the system performance is typically evaluated by measuring the distribution of applied vacuum below the floor. This article provides a new approach to assessing the radius of influence (ROI) for subslab venting systems based on mass flux instead of static vacuum distribution and includes an analyses of 121 pneumatic tests performed at 65 different suction points in 16 different buildings. The mathematical model represents a two-layer system with horizontal radial flow through transmissive material below the floor slab and vertical flow through discontinuities in the floor slab (which is simplified to approximate an equivalent porous medium). The analysis includes comparisons of the flux-based ROI to values calculated using the two-layer model for 1) vacuum, 2) velocity, and 3) travel time, which may be useful as alternative performance metrics for mitigation systems. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Mathematical analytic solution procedure   Inventory model   Retailer's optimal replenishment policy   Economic order quantities (EOQ)   Trade credits   Cash discounts   Permissible delay in payment   Cash discount  

摘要： Recently, Huang and Hsu (J Oper Res Soc Jpn 50:1-13, 2007) investigated the retailer's optimal replenishment policy with non-instantaneous receipt under trade credit and cash discount. Basically, their inventory model is correct and interesting. However, they ignored explorations of interrelations of functional behaviors of the annual total cost to locate the optimal solutions so much so that the accuracy and reliability of the process of the proof of their solution procedure are questionable. The main purpose of this paper is to provide accurate and reliable mathematical analytic solution procedures to improve the findings in the aforementioned work of Huang and Hsu (J Oper Res Soc Jpn 50:1-13, 2007). Some related recent works on the subject-matter of this investigation are also cited with a view to providing incentive and motivation for making further advances along the lines of the supply chain management and associated inventory problems which we have discussed in this article.

摘要： Ebola virus disease (EVD) is one of the deadliest viral infections that has caused a serious global health problem in the known human history. It was first transmitted to humans through domestic and wild animals, and then, the spread was through direct and indirect contacts among individuals. To control this spread is one of the most challenging aspects of epidemic studies carried out so far. The aim of this paper is to propose a transmission model called Susceptible-Vaccinated-Exposed-Infected-Recovered (SVEIR) by incorporating an additional class of vaccinated individuals. We investigate the rate of spread of EVD in population when the voluntary vaccination is introduced at the level of its susceptibility. Our proposed model helps in better understanding of the dynamical behavior of EVD and explains its stability pattern. We present two main equilibrium points and their stability analysis. It is proven that disease-free equilibrium (DFE) F0 is both locally and globally stable when the value of threshold parameter R0 we obtain through our model is strictly less than one. Moreover, for R0>1, F0 is not stable, and the endemic equilibrium (EE) F1 is locally and globally stable. Hence, EVD spreads uniformly among individuals. We also study the effect of threshold parameter R0 at different vaccination coverage levels to validate our conclusions in this paper. The theory of Lyapunov functions is employed to study global stabilities at both levels. We use Runge-Kutta method of order 4 (RK4) and Non-Standard Finite Difference (NSFD) scheme for the proposed model to confirm our obtained theoretical results through numerical simulations. Furthermore, the discretized SVEIR model obtained by applying NSFD scheme is dynamically consistent with the continuous model for any step size h thus used. A quantitative analysis of an epidemic model for different vaccination coverage levels is also presented. It is concluded that eradication of Ebola virus is possible if a human populatio

关键词： 数学分析   连续   一致连续  

摘要： 本文用辨析的方式剖析连续与一致连续这两个概念,以求厘清差别,深刻理解“一致”的含义.

关键词： 数学分析   课程思政   教学案例  

摘要： 针对数学与应用数学专业本科生教材《数学分析(上册)》,从数学哲学、数学美学、数学创新和数学人文四个角度,给出若干课程思政案例,通过这些案例把思想政治工作贯穿到高校教育教学的全过程,在传授专业知识的同时,提高大学生的思想政治觉悟,使其形成正确的世界观、人生观、价值观,达到教书和育人的和谐统一。

关键词： 复变函数   数学物理方程   应用数学专业   知识框架   数学分析   《复变函数与积分变换》   泛函分析   解析函数  

摘要： 复变函数作为应用数学专业以及数学的主要基础课程,后续课程中包含了数学物理方程以及泛函分析等。复变函数作为以上内容的基础,提供了解析函数的具体方法。在复变函数的应用方面不仅限于数学中,更被广泛应用在其他领域中。在复变函数的学习中,通过学习《复变函数与积分变换》充分掌握复变函数的重点以及难点。复变函数与其他学科之间也存在着衔接的关系,是数学分析的延展,无论在知识框架还是理论体系方面,都需要注意与数学分析进行衔接,同时也需要注意复变函数与其他学科的衔接。