教学课程资源库 更多>>

关键词： 小学数学教育   数学分析   现状   对策  

摘要： 数学分析是小学数学教育专业的一门专业核心课程,它是提高学生的文化素质和学习有关专业知识、专门技术的重要基础和工具。它具较强的逻辑性、应用性和实践性,在社会的各行各业都具有理论实践指导作用,所以在教学中,教师要根据数学分析课程内容,结合学生所学专业,就业需求等因素进行教学,从而提高数学分析教学的有效性。

关键词： 数学运算   数学分析   算理  

摘要： 小学数学学习主要有两个方面数学运算和数学分析.数学运算是小学数学核心素养中重要的一项素养,运算能力是小学数学中最重要的一项能力,也是小数数学教学的核心所在.本文将结合笔者的教学经验来谈一下怎样在教学中落实数学运算这一核心素养.

关键词： 香蕉果醋   模糊数学   加工   工艺优化  

摘要： 香蕉果醋营养价值丰富,含有多种生物活性物质和微量元素,具有清热解毒、清肺润肠、降血压和利尿等多种药用功能,是一种食药兼备的果醋。该研究以香蕉果醋生产工艺条件为研究对象,对香蕉果醋的生产流程进行分析,建立香蕉果醋的综合感官评价标准。通过使用模糊数学矩阵方法进行分析,分别建立果醋发酵过程中的初始酒精度、接种量、发酵温度、pH值和发酵周期对香蕉果醋品质的影响,并最终选取其中3个影响最为明显的因素进行正交试验。结果表明,香蕉果醋生产工艺过程中,最佳的醋酸发酵流程为初始酒精度8%、接种量4%和发酵温度32℃技术工艺条件组合时,获得的香蕉果醋工艺综合评价为86.5分,为香蕉果醋工艺的改进提供了参考依据。

关键词： 低比转速   圆柱形叶片   数学分析   单圆弧曲线  

摘要： 圆柱形叶片广泛用于低比转速离心叶轮。在叶片进出口处边界条件一定的情况下,尽管有多种曲线可供选择作为叶片表面的平面投影,但单圆弧是一种使用历史较长、具有较明显几何优势的常用曲线。通过数学分析,课题组导出了这种曲线两种满足给定约束的绘形新方法及其包角计算式,这些方法为叶片设计人员提供了快速绘形叶片的新途径,丰富了水泵的系统设计理论。

关键词： Cauchy inverse problem   Elasticity equation   Steklov-Poincare operator   Fixed point theory   Degree of Leray-Schauder   Boundary elements method  

摘要： In this work, an inverse problem in linear elasticity is considered, it is about reconstructing the unknown boundary conditions on a part of the boundary based on the other boundaries. A methodology based on the domain decomposition operating mode is opted by constructing a Steklov-Poincare kind's operator. This allows us to reformulate our inverse problem into a fixed point one involving a Steklov kind's operator, the existence of the fixed point problem is shown using the topological degree of Leray-Schauder. The proposed approach offers the opportunity to exploit domain decomposition methods for solving this inverse problem. Finally, a numerical study of this problem using the boundary element method is presented. The obtained numerical results show the efficiency of the proposed approach. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： Co-infection model   Existence results   Numerical simulations   GABMM method  

摘要： The current research study is devoted to analyze the fractional order co-infection disease epidemic model endowed with Caputo fractional derivative. We also investigate the qualitative analysis of the Caputo coinfection model via using classical fixed point theory. Moreover, the stability results regarding the Ulam-Hyers type are also investigated for the proposed model. Apart from this, to simulate the model, the fractional Adam-Bashforth Moulten (ABM) method is utilized to handle the required results. By using Matlab, graphical presentation against various fractional orders are given.

关键词： Complex fluids   thermodynamic consistency   stability  

摘要： The goal of this paper is to derive governing equations for complex fluids in a thermodynamically consistent way so that the conservation of energy and the increase of entropy is guaranteed. The model is a system of first-order partial differential equations on density, velocity, energy (or equivalently temperature), and conformation tensor. A barotropic model is also derived. In the one-dimensional case, we express the barotropic model in the form of hyperbolic balance laws, and show that it satisfies the stability condition. Consequently, the global existence of solutions around equilibrium states is proved and the convergence rates is obtained.

关键词： Plasmon resonance   Curved nanorod   Anisotropic geometry   Neumann-Poincare operator  

摘要： Y We investigate plasmon resonances for curved nanorods which present anisotropic geometries. We analyze quantitative properties of the plasmon resonance and its relationship to the metamaterial configurations and the anisotropic geometries of the nanorods. Based on delicate and subtle asymptotic and spectral analysis of the layer potential operators, particularly the Neumann-Poincare operators, associated with anisotropic geometries, we derive sharp asymptotic formulae of the corresponding scattering field in the quasi-static regime. By carefully analyzing the asymptotic formulae, we establish sharp conditions that can ensure the occurrence of the plasmonic resonance. The resonance conditions couple the metamaterial parameters, the wave frequency and the nanorod geometry in an intricate but elegant manner. We provide thorough resonance analysis by studying the wave fields both inside and outside the nanorod. Furthermore, our quantitative analysis indicates that different parts of the nanorod induce varying degrees of resonance. Specifically, the resonant strength at the two end-parts of the curved nanorod is more outstanding than that of the facade-part of the nanorod. (C) 2021 Elsevier Masson SAS. All rights reserved.

关键词： banana fiber   E-glass fiber   hybrid composite   mathematical model   tensile strength  

摘要： This article presents a mathematical model to predict the tensile strength of banana/glass hybrid polymer composites. Equivalent fiber surface efficiency factor and fiber waviness factor have been introduced in the proposed model and their effects on tensile strength have been discussed. The hybrid composites were fabricated with the different proportions of volume fraction of each of the glass fibers and banana fibers keeping the total volume fraction (V-F) of combined fibers from 20% to 50%. The tensile test of hybrid composites was carried out as per ASTM D3039. The proposed model has been tested versus experimental results as well as the literature results, which shows quite good approximation of tensile strength. The proposed model is generalized and can be applied to any hybrid reinforced composites with the combination of low-elongated and high-elongated fibers with varying fiber loading.

关键词： Topological spread model   Random spread model   Transition model   Spread rate   n-Spread    rate  

摘要： This paper models the spread of the pandemic with mathematical analysis to provide predictions for different classes of individuals. We consider the spread by using a branching process and a substitution dynamical system as random and deterministic models, respectively, to approximate the pandemic outbreak. Both approaches are based on the assumption of Markov processing. The deterministic model provides an explicit estimate for the proportion of individuals of a certain type in the particular generation given any initial condition, where a generation means a unit of observation time. The proportion relates to the matrix derived from the Markov setting. In addition, the methodology reveals the efficiency of epidemic control policies, such as vaccine injections or quarantine, by the relative spread rate that is used for the prediction of the number of individuals of a certain type. On the other hand, the stochastic approximation has more of an empirical impact than the deterministic one does. Our investigation explicitly exhibits the spread rate of a certain type with respect to an initial condition of any type. After estimating the average spread rate, the effect of adopting a particular policy can be evaluated. The novelty of this elucidation lies in connecting these two models and introducing the idea of the transition spread model between two topological spread models to capture the change of the spread patterns, which is a real-world phenomenon during the epidemic periods due to changes in the environment or changes in disease control policies. Roughly speaking, the deterministic model is a special case of the stochastic model under some particular probability. Most importantly, with the help of the stochastic model, we establish the transition processing of two deterministic models, which is called a transition model. In other words, any stochastic model is "bounded" by two deterministic models. Moreover, a computable way has been established to predict the lon