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关键词： 数学分析   一流本科专业建设   教学改革  

摘要： 数学分析课程是数学类专业最重要的专业基础课之一,对数学类专业后续课程的学习具有重要意义。基于国家级一流本科专业建设的背景,对数学分析课程的课程目标、教学内容、教学手段、考核评价等方面进行了有益探索,为构建数学类专业课程高质量教学和助推国家级一流本科专业建设提供参考。

关键词： 辅助函数   微分中值定理   不等式证明   计算极限  

摘要： 构造辅助函数是数学中常用的解题技巧之一,在解答一些条件与结论的逻辑关系并不直接的问题时起着重要的作用.在本文中,我们主要归纳总结几类需要通过构造辅助函数解答的题型,并针对相应的题型介绍一些辅助函数的构造方法.

关键词： 思政元素   数学分析   概念  

摘要： 本文从数学史、数学思想、数学建模思想、哲学思想四个方面出发,挖掘其与数学分析概念的若干课程思政案例,为后续数学分析的课程思政改革提供支撑。

关键词： 数学分析   课程改革   技术革新   应用导向  

摘要： 近年来本科生的知识结构与水平已发生显著改变,国家的科技发展战略也逐步调整.现行的数学分析课程内容与教学方案已不能完全满足新时代人才的培养需求.本文深入剖析了数学分析课程的内容设置与课堂教学的现状,指出了当前面临的知识衔接不足、教学方式单一、重理论轻应用等方面的突出问题,阐述了数学分析课程改革的必要性和迫切性.依循我国高等教育课程的改革趋势,有针对性地提出了整合资源、创新手段、交叉融合、面向应用的建设思路;实现课程知识完备化、差异化,内容的立体化、应用化,教学资源可视化、互动化.并结合具体案例阐述了各种措施的特点、作用和可行性,旨在探索本科数学分析课程改革的优化方案,打造顺应时代发展的数学分析课程.

关键词： 《工科数学分析》   学习兴趣   教学内容   教学方式  

摘要： 随着科技技术的不断发展与日新月异,现代高等教育对大学数学的教育也提出了更多、更高的要求,《工科数学分析》作为各高校对微积分基础要求更高的理工科专业本科生必修的一门重要基础课,该课程的教学具有很大的难度与压力。本文首先阐述了大学数学学习的重要意义,随后结合作者的教学实践重点讲述了该课程教学的一些探索与思考:1) 教学内容探索;2) 教学方式探索。

关键词： Tumor invasion   Density dependent diffusion   Global existence   Stability  

摘要： This work studies an outstanding reaction-diffusion system modeling tumor invasion, with interactions among tumor tissue, acid concentration and normal tissue. This model has very different features from the models extensively studied in the mathematics literature. The most challenge issue for mathematical analysis of the present model is the existence of classical solution, since the diffusion of tumor tissue is influenced by the density of normal cells and diffusion degeneracy arises when normal cells are at the carrying capacity. A rigorous proof of global existence and uniqueness of classical solutions is presented. Moreover, we study global dynamics of the solution, and show asymptotic stability of the four possible constant equilibria under various scenarios. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Inverters   Neurons   Artificial neural networks   Memristors   Sensitivity   Training   Integrated circuit modeling   Memristive neural networks   circuit elements' non-idealities   mathematical analysis   sensitivity term  

摘要： In this paper, the sensitivity of the neural network (NN) outputs to device parameter uncertainties (non-idealities) in inverter-based memristor (IM) crossbar neuromorphic circuits is mathematically modeled and verified using exhaustive circuit and system-level simulations. The NN sensitivity is obtained by modeling the sensitivity of the IM neuron output to the non-idealities of its circuit elements. The analysis reveals a higher sensitivity of the output voltage of the IM neuron to the non-idealities of the inverters compared to the conductance variation of the memristors. Among the inverter non-idealities, horizontal shift of the inverters voltage transfer characteristic (VTC) shows the highest impact on the output voltage of the neuron. To reduce the accuracy loss due to the variations, a training approach which includes a sensitivity term in the cost function of the training phase, is suggested. The achievable improvements through the said NN training approach are evaluated. In the evaluation, the California Housing, MNIST, and Fashion MNIST datasets are employed. The results show up to 50% reduction in the NN output variations in the presence of circuit elements' non-idealities.

关键词： sports   fairness   shootout   prouhet-thue-morse sequence  

摘要： A shootout is a popular mechanism to identify a winner of a match between two teams. It consists of rounds in which each team gets, sequentially, an opportunity to score a point. It has been shown empirically that shooting first or shooting second in a round has an impact on the scoring probability. This raises a fairness question: is it possible to specify a sequence such that identical teams have equal chance of winning? We show that, for a sudden death, no repetitive sequence can be fair. In addition, we show that the so-called Prohuet-Thue-Morse sequence is not fair. There is, however, an algorithm that outputs a fair sequence whenever one exists. We also analyze the popular best-of-k shootouts and show that no fair sequence exists in this situation. In addition, we find explicit expressions for the degree of unfairness in a best-of-k shootout;this allows sports administrators to asses the effect of the length of the shootout on the degree of unfairness.

关键词： Memristor emulator   Fractional-order memristor   Cubic model   Intersection points  

摘要： Cubic model of flux-controlled memristor model is presented in this work and the model is analyzed at various fractional orders. Analytic computations with a sinusoidal source shows that the v - i loop can have up to two more additional intersection points aside from the origin and are located in the 1st and 3rd quadrants respectively. The locations of the intersection points and the area of the v - i loops are both dependent on the excitation signal frequency and fractional orders. Floating and Grounded emulator circuits for the cubic models are designed incorporating a fractional order integrator designed from the 2nd-order rational approximation of s(-alpha). PSPICE simulations verify the correctness of the numerical analysis and calculations. An application example shows that the fractional-order cubic model can generate chaos in Chua's circuit and produced an increase in the system dynamics. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.