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关键词： 不等式   导数   构造  

摘要： 基于解决一类与对数及指数有关的不等式问题,提升学生多视角思考问题、解决问题的能力.归纳了解决此类不等式的经典方法,如作差、作商以及等价转化等.本节课选取了利用导数解决一类不等式问题的小切口,提升学生核心素养的着力点多,对学生的综合能力要求较高.

关键词： 函数的微分   认知心理学   微分概念的教学设计  

摘要： 从认知心理学的角度,通过剖析学生的认知结构,揭示了微分概念的“同化固定点”——高阶无穷小概念理解的不透彻和高阶无穷小近似代替思想的缺乏是造成微分理解困难的深层原因,为此,基于学习理论构建了融合概念形成和概念同构两种概念获得方式的数学概念教学模式,并在此模式下进行了微分概念的教学设计.

关键词： 奇点   稳定性   极限环   多项式系统  

摘要： 本文结合微分方程奇点稳定和极限环的概念与相关定理,利用MATLAB软件对现有的二次系统、三次系统,三维系统的奇点与极限环的研究结果进行了数值模拟,并间接验证其结论的正确性,对非线性微分方程的奇点的深入研究具有重要参考价值.

关键词： 高中数学   导数   知识图谱   CNKI文献数据库  

摘要： 运用Bicomb2.0和SPSS26.0软件,对中国知网收录的与高中数学导数教学有关的350篇文献绘制研究热点的可视化图谱,分析高中数学导数教学的研究热点领域,预测高中数学导数教学的未来发展趋势。

关键词： 核心素养   综合考查   初等函数   数学抽象   数学建模   恒成立   思维的灵活性   函数模型  

摘要： 导数的综合应用问题是高考的必选题,基本上出现在第20或21题,难度较大,能拉开区分度.这类考题一般围绕y=e^(x),y=lnx与其他初等函数,综合考查函数的单调性、最值、零点、极值点、恒成立等,技巧性高、综合性强,更能充分考查学生的数学抽象、直观想象、逻辑推理、数学建模等核心素养,彰显学生思维的灵活性及多样性.近5年来高考全国卷的14份考卷中有10份涉及ex或lnx函数模型,下面结合几道典型的高考题说明这类导数综合应用问题的解决策略.

关键词： 代数重数   几何重数   向量积   微分  

摘要： 关于方阵特征值的代数重数大于等于几何重数这一结论,许多教材利用线性代数的知识已经给出证明,本文借助微分的观点证明了该结论.此外,利用微分证明了一个关于线性变换和向量积的恒等式,从而展示了微分在代数中应用的两个案例.

关键词： Soil structure interactions  

摘要： The role of spatially variable soil stiffness and strength on structural performance has been increasingly recognized with the rapid development of geotechnical reliability-based design tools. Performance criteria linked to the angular distortion between foundations and the probability of exceeding certain limit states as a function of linear-elastic soil property autocorrelation have shed light on the link between foundation soils and potential structural damage. However, the role of soil-structure interaction (SSI), especially considering nonlinearity in soil and structural elements, to redistribute shear and flexure within structures that result from differential foundation movements, has been largely neglected. This study presents a critical examination of the effect of nonlinear SSI to redistribute flexural demands within a steel structure founded in soils exhibiting spatial variability and the corresponding differential settlements through a comparison of uncoupled and coupled Monte Carlo simulations (MCS). This study shows that the differential settlement, Delta s, computed using coupled (i.e., SSI) analyses are significantly smaller than those derived from the uncoupled analyses for the random field models (RFMs) used to simulate soil spatial variability. The effect of SSI is to substantially reduce the probability of exceeding selected limit state criteria due to differential movements that vary in magnitude with the level of stringency of the limit state criteria;the most significant reduction corresponds to the structural ultimate limit state (ULS). Furthermore, the effect of SSI on structural performance and the critical scale of fluctuation, S alt , becomes more apparent and beneficial as the severity of differential movement increases. Smaller and/or "allowable" angular distortions are governed by the local footing-to-footing distance, whereas the probability of exceeding the ULS (i.e., yielding of beams) is controlled by the entire structure working t

关键词： 高阶微分算子   转移条件   J-自伴   C-正交  

摘要： 本文研究了一类具有转移条件的高阶复系数微分算子的J-自伴性,利用J-对称微分算式的拉格朗日双线性型、J-自伴算子的定义及矩阵表示的方法,证明了这类微分算子是J-自伴的,且对应于不同特征值的特征向量和特征子空间都是C-正交的.

关键词： 分数阶微分方程   双参数   奇摄动  

摘要： 讨论了一类奇摄动分数阶微分方程边值问题。在适当假设条件下,先求出该问题的外部解,再运用双参数展开理论构造出边界层矫正项,得到解的形式渐近展开式,最后运用极值原理进行余项估计。

关键词： correlated differential privacy   multiparty data release   machine learning  

摘要： Differential privacy(DP)is widely employed for the private data release in the single-party *** utility could be degraded with noise generated by ubiquitous data correlation,and it is often addressed by sensitivity reduction with correlation ***,increasing multiparty data release applications present new challenges for existing *** this paper,we propose a novel correlated differential privacy of the multiparty data release(MP-CRDP).It effectively reduces the merged dataset's dimensionality and correlated sensitivity in two steps to optimize the *** also propose a multiparty correlation analysis *** on the prior knowledge of multiparty data,a more reasonable and rigorous standard is designed to measure the correlated degree,reducing correlated sensitivity,and thus improve the data ***,by adding noise to the weights of machine learning algorithms and query noise to the release data,MP-CRDP provides the release technology for both low-noise private data and private machine learning *** experiments demonstrate the effectiveness and practicability of the proposed method on the utilized Adult and Breast Cancer datasets.