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关键词： Mathematica程序   数学分析   数学实验  

摘要： 探讨了在数学分析课堂中引入计算机程序辅助开展教学的必要性,并介绍了几个经典知识点的程序设计和教学策略,包括利用Mathematica的数据帮助学生发现数列极限规律,剖析函数列不一致收敛的原因;利用Mathematica图像帮助学生提高空间想象能力,阐述二元函数的稳定点和极值点的关系以及利用定义进行定积分的数值模拟计算.教学实践表明,使用Mathematica程序辅助数学分析的教学,有助于突破教学难点,提高教学效率.

关键词： 微积分   数学分析   实变函数   度量理论   积分函数   微分函数  

摘要： 本文定义了微分函数的概念.微分函数是标准积分的被积函数,标准积分的积分函数则是一个绝对连续函数.在度量理论的意义下,积分是积分函数的函数值,微分是特定条件下微分函数的函数值.

关键词： 误区   泰勒公式   四则运算  

摘要： 对泰勒公式和函数极限的四则运算法则运用上出现的常见易错点进行分析．通过相应的例题说明，使数学分析学习者可以避免进入这些误区。

关键词： 数学分析   数学思想   数学能力  

摘要： 本文主要是基于数学分析习题课的教学探讨以促进学生应用能力的培养的研究。在习题课教学中,教师要有意识、有目的地结合数学分析课程的实际,引导学生积极地参与到整个解题思维过程,培养学生形成活用数学方法的能力、探究问题的能力、概括总结的能力。

关键词： bioeconomic model   Hamilton-Jacobi-Bellman equation   inland fishery   optimal control  

摘要： This short paper presents an optimal control model for cost-effective and ecologically conscious management of released fish. Finding an optimal management strategy reduces to solving a Hamilton-Jacobi-Bellman equation having a solution by separation of variables. This paper analyzes the behavior of the solution and the associated optimal management strategy. The latter is verified with an actual strategy for Plecoglossus altivelis in Japan.

关键词： boundary layer theories   through flow   Net solute removal rate   forced convection   mathematical analysis   Drug Liberation  

摘要： This paper applies boundary layer theory to the process of drug dissolution in the USP (United States Pharmacopeia) Flow Through Apparatus. The mass transfer rate from the vertical planar surface of a compact within the device is examined. The theoretical results obtained are then compared with those of experiment. The paper also examines the effect on the dissolution process caused by the interaction between natural and forced convection within the apparatus and the introduction of additional boundaries.

关键词： Co-infection   Mathematical model   Backward bifurcation   Global statbility   Sensitivity and uncertainty analysis  

摘要： The re-emergence of syphilis has become a global public health issue, and more persons are getting infected, especially in developing countries. This has also led to an increase in the incidence of human immunodeficiency virus (HIV) infections as some studies have shown in the recent decade. This paper investigates the synergistic interaction between HIV and syphilis using a mathematical model that assesses the impact of syphilis treatment on the dynamics of syphilis and HIV co-infection in a human population where HIV treatment is not readily available or accessible to HIV-infected individuals. In the absence of HIV, the syphilis-only model undergoes the phenomenon of backward bifurcation when the associated reproduction number () is less than unity, due to susceptibility to syphilis reinfection after recovery from a previous infection. The complete syphilis-HIV co-infection model also undergoes the phenomenon of backward bifurcation when the associated effective reproduction number () is less than unity for the same reason as the syphilis-only model. When susceptibility to syphilis reinfection after treatment is insignificant, the disease-free equilibrium of the syphilis-only model is shown to be globally asymptotically stable whenever the associated reproduction number () is less than unity. Sensitivity and uncertainty analysis show that the top three parameters that drive the syphilis infection (with respect to the associated response function, ) are the contact rate (), modification parameter that accounts for the increased infectiousness of syphilis-infected individuals in the secondary stage of the infection () and treatment rate for syphilis-only infected individuals in the primary stage of the infection (). The co-infection model was numerically simulated to investigate the impact of various treatment strategies for primary and secondary syphilis, in both singly and dually infected individuals, on the dynamics of the co-infection of syphilis and HIV. It is

关键词： Human evaluation   Association   Mathematical analysis   Arch forms  

摘要： Objectives: To evaluate the relationship between human evaluation of the dental-arch form, to complete a mathematical analysis via two different methods in quantifying the arch form, and to establish agreement with the fourth-order polynomial equation. Materials and methods: This study included 64 sets of digitised maxilla and mandible dental casts obtained from a sample of dental arch with normal occlusion. For human evaluation, a convenient sample of orthodontic practitioners ranked the photo images of dental cast from the most tapered to the less tapered (square). In the mathematical analysis, dental arches were interpolated using the fourth-order polynomial equation with millimetric acetate paper and AutoCAD software. Finally, the relations between human evaluation and mathematical objective analyses were evaluated. Results: Human evaluations were found to be generally in agreement, but only at the extremes of tapered and square arch forms;this indicated general human error and observer bias. The two methods used to plot the arch form were comparable. Conclusion: The use of fourth-order polynomial equation may be facilitative in obtaining a smooth curve, which can produce a template for individual arch that represents all potential tooth positions for the dental arch. (C) 2018 CEO. Published by Elsevier Masson SAS. All rights reserved

关键词： Pine Wilt Disease (PWD)   Stability analysis   Reproduction number   Global stability   Numerical results  

摘要： The present paper describes the dynamics of the Pine Wilt disease with variable population size. The basic mathematical results for the model are presented. The stability analysis of both the disease-free and endemic cases are presented whenever R-0 lesser or greater than one, respectively. Further, an optimal control problem is formulated and the necessarily involved results are presented. Moreover, the numerical simulation of the optimal control problem with suggested control strategies for the possible eliminations of the infection in the pine trees population is presented. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Crossover   Dual mutation   Genetic algorithms   Schema   Schema survival  

摘要： Genetic algorithms are widely used in the field of optimization. Schema theory forms the foundational basis for the success of genetic algorithms. Traditional genetic algorithms involve only a single mutation phase per iteration of the algorithm. In this paper, a novel concept of genetic algorithms involving two mutation steps per iteration is proposed. The purpose of adding a second mutation phase is to improve the explorative power of the genetic algorithms. All the possible cases regarding the working of the proposed variant of the genetic algorithms are explored. After a meticulous analysis of all these cases, three lemmas are proposed regarding the survival of a schema after the application of the dual mutation. Based on these three lemmas, a theorem is proved, and a mathematical expression representing the probability of survival of a schema after the application of the crossover and dual mutation is derived. This expression provides a new insight about the penetration of a schema for such scenario and improves our understanding of the functioning of this modified form of the genetic algorithm. [ABSTRACT FROM AUTHOR]