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关键词： compressible Navier-Stokes-Fourier system   fluid-particle interaction   maximal regularity   R-sectorial operators   strong solutions  

摘要： We study an initial and boundary value problem modelling the motion of a rigid body in a heat conducting gas. The solid is supposed to be a perfect thermal insulator. The gas is described by the compressible Navier-Stokes-Fourier equations, whereas the motion of the solid is governed by Newton's laws. The main results assert the existence of strong solutions, in an Lp-Lq setting, both locally in time and globally in time for small data. The proof is essentially using the maximal regularity property of associated linear systems. This property is checked by proving the R-sectoriality of the corresponding operators, which in turn is obtained by a perturbation method.

关键词： Nonlocal-nonsingular derivative   Fractional HIV/AIDS system   Numerical simulations   Finite difference method   Stability analysis  

摘要： An epidemic system of HIV/AIDS transmission is examined in this paper. The classical time derivative is modelled with the Atangana-Baleanu nonlocal and nonsingular fractional operator in the Caputo sense. Mathematical analysis which shows that both the disease free equilibrium state and endemic equilibrium are locally asymptotically stable. A viable numerical approximation technique of Atangana-Baleanu operator is also given. Some numerical simulation results obtained for different instances of fractional order gamma are reported to justify the theoretical results. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： 数学建模   数学分析   案例设计  

摘要： 根据数学分析的特点,结合传统模式数学教学与案例教学的实际情况,对二者进行比较研究。对启发式案例教学、数学式案例教学、专题式案例教学等方面进行探索,对其引入数学模型,数学分析的知识点等,通过具体的数据分析实例探索和实践得出一套适用于学生的教学方案,从而实现学生自主学习,提高学生数学知识应用水平,达到良好的教学效果。本文以高校数学分析课里面的数学模型引进为切入点,对相关案例设计进行分析研究,得出结论并提高学生对数学知识的认识水平,让他们感受到数学的魅力。

关键词： Optical waveguide   guided waves   inverse spectral problem   ill-posed problem   regularized iterative method  

摘要： Y We analyse mathematically the problem of determining refractive index profiles from some desired/measured guided waves propagating in optical fibres. We establish the uniqueness of the solution of this inverse spectral problem assuming that only one guided mode is known. We then propose an iterative computational procedure for solving numerically the considered inverse spectral problem. Numerical results are presented to illustrate the potential of the proposed regularized Newton algorithm to efficiently and accurately retrieve the refractive index profiles even when the guided mode measurements are highly noisy.

关键词： 数学师范专业   专业基础课程   教师发展   数学分析  

摘要： 专业基础课程的学习是培养教师专业知识发展的重要途径.数学分析是数学类专业最重要的基础课程之一,是联系初等数学与现代数学的纽带,是后续课程学习的基础.当前,师范专业的基础课程的教与学面临多方面的挑战,从教师教育的视角考虑,通过分析数学分析课程与初等数学的联系,以及学习过程中表现出来的学生基础差异和教育转型等方面的问题,寻找适合师范院校一线教师的解决对策,对数学师范专业的基础课程的教学发展具有重要的理论和现实意义.

关键词： 欧拉积分   贝塔函数   伽马函数  

摘要： 欧拉积分在多个领域有广泛应用。本文首先介绍数学分析教材中给出的两种欧拉积分:贝塔函数和伽玛函数,并介绍了它们的性质。然后详细讨论了欧拉积分在计算定积分、多重积分以及概率论中的应用。在欧拉积分的教学中,拓展本部分的内容可以增加学生知识面。

关键词： 小学数学   解决问题能力   培养  

摘要： 在小学数学课堂教学中,做好对学生分析和解决问题能力的组成及培养策略研究,能够为实现小学数学学科的素质教育目标带来支持。文章先对小学数学学生分析和解决问题能力组成要素进行简述,之后对小学数学学生分析和解决问题能力培养策略予以探讨,希望能够为推动小学数学教学水平进步带来支持。带来支持。

关键词： 高中   数学分析   解决问题能力   逻辑思维能力   数学建模能力  

摘要： 本文主要针对高中数学分析与解决问题能力的培养展开分析,首先介绍了提升该能力需要注重的两个要点,其次提出了深入教材了解内涵、采用通性通法学习模式、以应用题提升识别能力、通过开放题与新型题拓展知识面、记录错题本五点建议,希望能够真正形成问题分析、解决能力,提高数学综合素质与学习水平.

关键词： 多元化评价   数学分析   教学模式  

摘要： 多元化评价是现代教育评价理论所提倡的,在大学数学类课程教学中讨论如何有效实现多元化评价是一个重要课题。本文提出新的数学分析课程教学模式,并对该教学模式中的多元化评价进行探索,为大学数学类课程实现多元化评价提供一种有效方式。

关键词： Global stability   Geometric approach   Harmonic mean type incidence rate   Optimal control  

摘要： This article deals with qualitative analysis of a smoking model and provides parametric conditions for controlling diseases under the influence of smoking. The model is obtained by taking into account a novel uptake function, which relates the incidence of potential smoker with occasional smoker, of harmonic mean type for the potential and occasional smokers. Introducing a new type of incidence rate, the local as well as global stabilities for the proposed model are discussed at its steady-states. Minimizing the number of individuals involved in a substance abuse in any community is very difficult task, therefore we have introduced four control variables in the controlled system. Pontrygin's maximum principal is used to derive optimality system. Finally, the obtained results are illustrated numerically and graphically. (C) 2019 Elsevier Inc. All rights reserved.