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关键词： 高考数学试题   研究   视角  

摘要： 文章以2021年新高考全国Ⅰ卷第22题为例,对试题进行简评与溯源、多角度分析和多方法解答,并对试题进行推广与变式,同时给出对研究高考数学试题的思考。

关键词： 分类   完整解析   拉球进洞   微分方程   运动轨迹  

摘要： 在粗糙斜面上收绳将小球缓慢拉进小洞,是竞赛题中常见的物理情景。本文首先推导极坐标系下小球的运动轨迹微分方程,较通常文献更简捷地证明了μ=tanα时的运动轨迹是半圆周,然后研究了尚未见文献研究的μ>tanα(斜面较粗糙)和μ>tanα(斜面较光滑)的两种情形,均得到相应运动轨迹的解析表达式。最后用数学软件绘制出三种情形相对应的运动轨迹曲线,从而形成该问题完整而直观的认识,可供在物理教学和竞赛辅导中参考。

关键词： 甲型H1N1流感   传染病传播   甲型H1N1病毒   微分方程   SIE   数学模型   疾病  

摘要： 传染病是如今世界最严重的疾病之一,建立相应的数学模型具有重要价值。本文以甲型H1N1流感为例,阐述微分方程在传染病传播中如何应用,并对SIEIR模型进行优化。其对甲型H1N1流感防控工作具有一定意义,为避免此类高传染型疾病的再次蔓延提供一些可行的启发。

关键词： 伺服控制   跟踪微分器   微分器   Simulink  

摘要： 目的解决跟踪微分器(TD)的参数设计问题。方法对TD的工作原理、参数进行解释,提出其参数R与工作频率上限的关系,建立扫频仿真模型,通过扫频仿真获得TD的频率特性。通过不同输入幅值仿真研究其频率特性的非线性,通过添加白噪声,研究TD的抗噪声能力。结果仿真表明,对于输入幅值为1的情况,由R计算的频率上限确实反映了TD的工作频率范围。在该范围内,TD跟踪信号的幅值、相位良好;频率超出范围后,幅值、相位很快变差。输出幅值变小时,频率上限扩展。时域仿真的波形展示了与频率特性一致的结果。与平滑滤波器对比仿真显示,一般情况下,TD的跟踪信号、微分信号优于平滑滤波器,但是信噪比很差时,平滑滤波器反而优于TD。结论解决了TD参数R的定量设计问题,仿真展示了TD的时域、频域特性,为TD的应用提供了参考。

关键词： 导数证明   设计明暗线   问题   方法  

摘要： 数学证明的真谛不在于能证明命题真假,而在于它能启发人们对命题有更深刻的理解,并能促进新发现,这就突破了传统教学中对数学证明的观念.根据这样的认识,我们认为对数学学习来说,数学证明的教育价值主要体现在帮助学生学会学习、培养学生思维能力、提升学生核心素养等几个方面.

关键词： 区域综合能源系统   伊藤积分   随机微分   可再生能源   调度优化  

摘要： 区域综合能源系统在调度过程中面临着可再生能源出力的不确定因素,会给系统的安全稳定运行带来一定的风险。考虑可再生能源出力在时间上的连续性和随机性,建立了带有伊藤积分的区域综合能源系统连续随机调度优化模型。该模型聚合了以热电联产机组、燃气锅炉、风电机组、电储能和热储能的能源集线器作为供能单元,向区域内部的电热负荷供能。采用真实的算例对模型进行验证分析,算例结果表明:该模型能够给出一组连续的最优调度方案,从而为调度人员的正确决策提供有效支持。该方法能够快速得到目标函数区间,相比于蒙特卡洛模拟,大大提高了计算效率。

关键词： 零点   最小值   导数   实数根  

摘要： 从四个不同的角度去解透一道简洁优美的导数题,从中可以窥视其内在本质.

关键词： HIV-1   N-glycans   O-glycans   porous graphitized carbon   vaccine   virus-like particles  

摘要： Human immunodeficiency virus 1 (HIV-1) virus-like particles (VLPs) are nanostructures derived from the self-assembly and cell budding of Gag polyprotein. Mimicking the native structure of the virus and being noninfectious, they represent promising candidates for the development of new vaccines as they elicit a strong immune response. In addition to this, the bounding membrane can be functionalized with exogenous antigens to target different diseases. Protein glycosylation depends strictly on the production platform and expression system used and the displayed glycosylation patterns may influence downstream processing as well as the immune response. One of the main challenges for the development of Gag VLP production bioprocess is the separation of VLPs and coproduced extracellular vesicles (EVs). In this study, porous graphitized carbon separation method coupled with mass spectrometry was used to characterize the N- and O- glycosylation profiles of Gag VLPs produced in HEK293 cells. We identified differential glycan signatures between VLPs and EVs that could pave the way for further separation and purification strategies to optimize downstream processing and move forward in VLP-based vaccine production technology.

关键词： Social network   Friendship relationship   Shared interest   Ordinary differential equation   Information diffusion  

摘要： Nowadays, online social networks such as Twitter, Digg, and so on have become extremely popular thanks to the provision of unprecedented quantities of data to network users. This event has encouraged many studies of information diffusion in online social networks, especially in the mechanism and dynamics of the information diffusion process over such networks. Many previous studies of information diffusion in social networks have been based on experimental analyses or differential equations with temporal dimensions. Some recent studies have developed the information diffusion process using the heat transfer equations, the reaction-diffusion equations, or the hydrodynamic equations. This paper proposes a model called Ordinary Differential Information Diffusion or ODID to study both temporal and spatial patterns of the information diffusion process in online social networks. By using the formulation of ordinary differential equations, this model is constructed with friendship, relationships, and interactions between network users without quite relying on geometric linkages of the underlying network. The model is validated by the Digg data set whereby it is confirmed that with 95% confidence the ODID computations are not significantly different from the actual data and the average prediction accuracy of the model is about 98.78%. (C) 2022 The Author(s). Published by Elsevier Inc.