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关键词： 民族院校   数学分析课程   教学现状分析   教学对策  

摘要： 数学与应用数学(藏汉双语)专业学生在数学分析课程学习中存在问题较多,教学效果不佳,导致问题的原因是多方面的.从数学基础、价值认识、学习兴趣、教学方式方法、学习方法、双语基础水平和双语教学、教材内容、考评体系与方式等8个方面进行了教学现状调查分析,针对存在的问题进行教学改进,应该从以下几个方面入手:强化预备知识教学,巩固提高数学基础;加强课程重要性引导,明确价值认识;渗透数学文化,提升学习兴趣;丰富教学方式,改进教学方法;更新教学理念,改进学习方法;加强双语基础水平达标,提高双语教学效果;优化教学内容,增强教材实用性;改进考评体系和方式,调动学习积极性.

关键词： 数学分析   教学改革   核心课程   实验班教学  

摘要： 数学分析课程是数学及相关专业如数学与应用数学、信息与计算科学、统计学、理工科等的核心专业课,是实变函数、复变函数、泛函分析、常微分方程、概率论与数理统计、拓扑学、微分几何等大学后续课程的基石。结合近年来数学分析课程教学的实践,针对实验班数学分析课程的教学体会与经验共享于同行。

关键词： 数学分析   教学改革   教学实践  

摘要： 针对安徽农业大学信息与计算科学专业和统计学专业的生源特点,剖析了该专业基础课程数学分析教学中存在的问题,分别从课程的教学目的、内容、方法和考核等方面给出了相应的解决策略。

关键词： Visceral leishmaniasis model   Stability   Time-delay   Hopf bifurcation   Numerical simulation  

摘要： In this paper, we discuss some of the dynamical characteristics of a visceral leishmaniasis (VL) model with time delay. We have derived sufficient conditions to ensure the stability of the considered delayed VL model at the steady states. Taking the time delay as a bifurcation parameter, we have established a criteria for the existence of Hopf bifurcation of the considered model. Moreover, conditions for global stability of the steady states are also presented. Finally, some numerical simulations are given to show the effectiveness of our theoretical results.

关键词： Kinetic-fluid theory   Nonlocal diffusion   Nonlinear cross-diffusion   Nonlinear Galerkin method   Asymptotic-preserving scheme   Pattern formation   Finite-volume method   Finite-element method  

摘要： In this article we propose a nonlocal cross-diffusion-fluid system describing the dynamics of multiple interacting populations living in a Newtonian fluid. First, we derive our non- local cross-diffusion-fluid system from a nonlocal kinetic-fluid model by the micro-macro decomposition method. Second, we prove the existence of weak solutions for the proposed system by applying the nonlinear Galerkin method with a priori estimates and compactness arguments. On the basis of micro-macro decomposition, we propose and develop an asymptotic-preserving numerical scheme. Finally, we discuss the computational results for the proposed system. (C) 2019 Elsevier Inc. All rights reserved.

ISBN: (纸本)9787040534436

关键词： Calculator effect   Spreadsheets   Drill environments   Algebra calculators  

摘要： The paper investigates the possibility of getting the answer and solution of arithmetic and algebra tasks from outside pieces of software when the intended solution environment is paper and pencil or some teacher-controlled software system. We consider spreadsheets, lightweight drill environments, programs with step by step dialog and "algebra calculators". For spreadsheets the paper describes several cases of mathematically incorrect calculations. For drill environments we ascertain that they do not create a major risk of cheating. However, "algebra calculators" provide answers and solution steps for most of the common elementary algebra task types (usually for a licence fee). The conclusion is that addition of detailed solutions to computer algebra systems does not change the situation with homework cheating substantially.

关键词： Adobe clay brick   Optimization   Plasticity   Drying sensitivity  

摘要： This research studies the effects of composition and granulometry analysis of 139 heavy clays on the important characteristics of wet and adobe clay bricks. ANN models were obtained with high prediction accuracy in training cycles (r(2)): 0.580-0.907. Standard score analysis (SS) is performed to evaluate the optimal content of raw materials to gain adobe bricks. Optimal macro-oxides content was 53-66% SiO2, 4.6-7.5% Fe2O3, 12.5-18.2% Al2O3, 0.9-8.8% CaO, 1.2-3.6% MgO. The optimal quantity of alevrolite-sized particles varied between 46 and 65%, and clay-sized particles contents ranged from 20.4 to 40.6%. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： 极限思想   数学分析   教学研究  

摘要： 极限是数学分析中最重要的概念,贯穿于整个数学分析的教学,是理工科学生必须要学习的最重要的一个知识点在现代数学分析中,几乎所有的基本概念(连续、微分、积分)都是建立在极限概念的基础之上,本文主要讲述了极限的产生发展及在数学分析教学中如何把握和理解极限进行了阐述,并同时注重传授极限思想,培养学生的数学思维。

关键词： Malaria dynamics   Reinfection   Relapse   Lyapunov stability   Pontryagin's maximum principle   Cost-effective intervention  

摘要： Recurrent malaria constitutes one of the greatest setbacks to the realization of malaria disease elimination from the population. In this paper, a deterministic model governed by a system of nonlinear differential equations is developed to assess the effects of recurrent malaria - reinfection and relapse on the transmission dynamics of the disease. The model is distributed into autonomous and non-autonomous systems. Analysis of the autonomous model shows that reinfection, which is the recurrence of malaria symptoms due to new parasites infection, has the potential to trigger the existence of two endemic equilibrium points when the basic reproduction number is below unity. Consequently without reinfection, global asymptotic dynamics of the autonomous model is established in the presence of relapse with the aid of carefully constructed Lyapunov functions for both the disease-free and endemic equilibria. The non-autonomous model with time-dependent control strategies is analyzed using Pontryagin's Maximum Principle to find the optimal solutions to the malaria control problem. Cost-effectiveness analysis is conducted to buttress the results of the optimal control problem by using the average cost-effectiveness ratio (ACER) and incremental cost-effectiveness ratio (ICER) methods. Finally, numerical simulations are demonstrated to enhance the theoretical results. (C) 2020 Elsevier Inc. All rights reserved.