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关键词： 数学分析   验证性证明   引用性证明   构造性证明   反证法  

摘要： 命题证明是数学分析教学中的难点。文章对数学分析中的几种证明方法进行了深入分析，并通过例证加以说明。

关键词： 数学分析   知识结构   课程特点   自主学习  

摘要： 不同课程的知识结构、课程特点和学习目标各有不同,所以针对不同的课程开展自主学习的方法也各有不同。本文针对数学分析课程,从如何端正学生的学习态度、提高学生的听课效率到学生对概念的理解、对定理的学习、知识点的联结等方面,进行深入的探讨,阐述了在数学分析的学习中,学生该如何有效地开展自主学习。

关键词： 传统能源   TMT行业   主成分分析  

摘要： 传统能源行业与新兴的TMT行业是目前备受关注的两个重要行业,理清二者之间的关系有助于调整我国产业转型的步伐。本文以上市公司股票指数为切入点,运用主成分分析、多元线性回归等数学方法,对二者的关系给出定量的描述,并结合现实加以分析。

关键词： 数学教学   合情推理   推理策略   小数除法   整数   除数   小学教学   数学分析  

摘要： 《小学教学（数学版）》2017年第7-8期《数学教学中合情推理策略的使用：挑战与机遇》一文，以“讨论吧”话题“我的想法错在哪里”为案例，从数学分析、认知分析和教学分析三个方面对数学教学中合情推理策略的使用进行了深入的研究，反复阅读之后，我受益匪浅。正如文中所说，合情推理是人类常见的一种思维方式。教师应抓住其有利的方面为教学所用。

关键词： 风景园林学   数学分析方法   实际操作应用  

摘要： 随着我国经济的飞速发展,越来越多的人们在温饱这个大问题上已经得到了解决,转而开始向生活享受这方面靠拢;这其中最具有代表性的就是城市中风景园林的建设。在当代我国的许多大城市中,为了保证城市中的绿地面积以及确保城市中环境的整体质量,风景园林的建设也就应运而生,这给居住在城市中的人们带来了很多的好处。但如何修建风景园林,以及运用什么样的方法来修建风景园林使其作用发挥到最大是风景园林学中较为重要的一点——只有将其琢磨透,将其书本上的理论应用到实际生活中才是风景园林学最终的目的。因此在这里,为了让我们在以后的实际应用中将风景园林学的作用发挥到极致,我们就以风景园林学中常用的数学分析方法为例进行相应的研究与探讨。

关键词： 教学方式   自主学习   习题选择   高效课堂  

摘要： 习题课是"数学分析"课程教学的重要环节,是课堂教学的延伸与提高,它能使学生进一步掌握并拓展知识、提升思维能力。本文从多个方面提出优化"数学分析"课程习题课教学的策略。

关键词： linear viscoelasticity   dynamic moduli   relaxation spectrum   i-Rheo   Laplace and Fourier transforms  

摘要： This paper is focused on mathematical analysis related with problems of linear viscoelastic identification such as intrinsic errors of conventional test methods, conversion between data of various viscoelastic functions, resolution and informativeness of viscoelastic functions and new test methods which are faster than dynamic test and more accurate than static tests. This paper provides various mathematical and numerical tools: Some of them are newly introduced here and the others are described for the reviewing previous works in this field.

关键词： Nucleotides   DNA   Terminator Codon   Strands   Translation   Codons   maximum length   DNA strand   Triplets   Stop   Reading Frames   mathematical analysis  

摘要： A mathematical analysis was performed, which shows that the maximum length of DNA in which translation is possible for at least one of three reading frames for any DNA strand is 10 nucleotides. In the case of any nonstandard stop codon triplet, this number can only decrease. Moreover, for any DNA consisting of at most 11 nucleotides, two and more genes overlaps in plus and minus strands are possible. The probability that a stop codon triplet chosen at random belongs to the group of stop codon triplets with these properties is less than 0.06.

关键词： Soil organic carbon dynamics   reaction-diffusion-advection system   positive weak solutions   periodic weak solutions  

摘要： The aim of this paper is to study the mathematical properties of a new model of soil carbon dynamics which is a reaction-diffusion-advection system with a quadratic reaction term. This is a spatial version of Modeling Organic changes by Micro-Organisms of Soil model, recently introduced by M. Pansu and his group. We show here that for any nonnegative initial condition, there exists a unique nonnegative weak solution. Moreover, if we assume time periodicity of model entries, taking into account seasonal effects, we prove existence of a minimal and a maximal periodic weak solution. In a particular case, these two solutions coincide and they become a global attractor of any bounded solution of the periodic system.

关键词： H1N1 model   Delays   Stability analysis   Sensitivity analysis  

摘要： Recently, a large number of mathematical models that are described by delay differential equations (DDEs) have appeared in the life sciences. In this paper, we present a delay differential model to describe influenza A (H1N1) dynamics. We begin by presenting the model with a brief discussion, followed by proving the positivity and boundedness of the model solution. We establish sufficient conditions for the global stability of the equilibria (the infection free equilibrium and the infected equilibrium), these conditions are obtained by means of the Lyapunov LaSalle invariance principle of the system. Also we have carried out bifurcation analysis along with an estimated length of delay to preserve the stability behavior. In particular, we show the threshold dynamics in the sense that if (reproduction number) R-0 < 1 the infectious population disappear so the disease dies out, while if R-0 > 1 the infectious population persist. Sensitivity analysis of the influenza A (H1N1) model reveals which parameter values have a major impact on the model dynamics. Numerical simulations with application to H1N1 infection are given to verify the analytical results. (C) 2017 Elsevier B.V. All rights reserved.