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关键词： 导数   策略研究   通性通法  

摘要： 导数是高中数学的重要内容,同样是历年来高考的重点内容,特别是不等式的证明题,这类试题综合性强,具有很强的灵活性,如何能做到遇导数“不倒”呢?结合两道联考导数压轴题,对导数中的常见问题的解题策略进行研究.数学解题的最高境界必然是“无招”.数学解题中的“无招”,其实质应该是解题的“通性通法”.通性通法教学应引起广大教师的足够重视,以无招胜有招,才能让学生笑傲考场,从而做到“遇导数不倒”.

关键词： 比例型随机微分方程   高度非线性   广义Ito公式   时滞反馈控制   Lyapunov泛函  

摘要： 利用Lyapunov泛函法讨论高度非线性比例型混杂随机微分方程在时滞反馈控制下稳定所需满足的条件。当系数满足局部Lipschitz条件和Khasminskii型条件时,通过设计满足一定条件的时滞反馈控制器构造出适当的时滞量,验证受控后系统存在唯一解且稳定。通过一个算例验证了结论的有效性。

关键词： 高考命题   实数根   定义方程   衔接点   高等数学   初等数学   创新题   创新思维  

摘要： 导数是初等数学与高等数学的重要衔接点,是研究函数的单调性、极值、最值的重要工具.由于当今高考命题注重"创新意识"的考查,涉及导数应用的问题更显创新思维的活力.本文列举此类问题中的几类创新问题,供大家赏析研究.一、新定义创新题例1定义方程f(x)=f′(x)的实数根x0叫做函数f(x)的"躺平点".若函数f(x)=ln x,g(x)=x^(3)-1的"躺平点"分别为α,β,则α,β的大小关系为().

关键词： Acoustic emission (AE)   insulated gate bipolar transistor (IGBT)   stress wave   source mechanism  

摘要： Acousticemission (AE) is a fast, non-destructive and real-time detection method widely applied in the power industry. It has been reported that AE has potential application value in the condition monitoring of insulated gate bipolar transistor (IGBT). The stress wave is released at the moment when the IGBT is turned on and off, which can be measured by the AE sensor. However, due to interference from the changing electric field on the AE sensor, the pulse signal is frequently intermingled into the stress wave during measurement, making stress wave extraction difficult. In this paper, a novel stress wave extractionmethod of based on the differential AE sensor is proposed, which can decouple the pulse interferencemixed in the stress wave signal from IGBT, and the effectiveness of the method is demonstrated through experiment. Furthermore, extraction experiments of stress wave from IGBT under the conditions of various gate turn-off resistance (R-off), bus voltage (V-dc), and turn-off current (I-off) are carried out. By testing two models of IGBT from different manufacturers, similar conclusions can be obtained that the amplitude, peak-peak value and signal energy of IGBT's stress wave are all strongly related to Roff, Vdc and Ioff. In addition, the sourcemechanism of the stresswave between turn-off loss (E-off) of the IGBT and R-off, V-dc and I-off.

关键词： 不等式证明   函数   导数  

摘要： 本文以2021年全国Ⅰ卷22题为例,通过对不同解法进行分析、比较,抓住并理解问题的本质,在掌握解决这类问题的通性通法的基础上,了解一些比较常见的破解问题的技巧方法,提高数学思维的灵活性、深刻性.

关键词： 函数相关   无中生有   数学创新   导数应用   巧妙引入   巧借   妙解   研究与解决  

摘要： 导数应用一直被认为是研究与解决函数相关问题的一个“神器”,在众多的函数问题中都有导数应用的影子.在很多其他的数学创新问题中,看似与导数应用毫无联系,而结合条件特征,巧妙引入函数,借助导数应用,无中生有,往往可以优化过程,快捷处理,提高效益.

关键词： 动导数   高速风洞   试验方法   飞行器   标准化  

摘要： 飞行器动导数是其机动或受扰动飞行状态下是否具有动稳定性的一个重要判据,关系飞行安全与技战术指标的实现。高速风洞动导数试验是获取飞行器动导数的最主要的技术手段,但其系统复杂,涉及气动、机械、控制以及测量和处理等多个专业,试验预测结果的不确定因素较多。开展动导数风洞试验方法的标准化研究对于提高试验系统的精准度、可靠性具有重要的意义。本文总结了国内外高速风洞动导数试验近40年的工作经验,基于现阶段最先进技术,研究并给出了试验系统、验证标模、数据处理方法等的规范和要求,对部分重要指标进行了风洞试验验证。该标准的研究与制定将为国内外空气动力试验研究机构提供重要的行业标准与参考依据。

摘要： Motivation: Differential network inference is a fundamental and challenging problem to reveal gene interactions and regulation relationships under different conditions. Many algorithms have been developed for this problem;however, they do not consider the differences between the importance of genes, which may not fit the real-world situation. Different genes have different mutation probabilities, and the vital genes associated with basic life activities have less fault tolerance to mutation. Equally treating all genes may bias the results of differential network inference. Thus, it is necessary to consider the importance of genes in the models of differential network inference. Results: Based on the Gaussian graphical model with adaptive gene importance regularization, we develop a novel Importance-Penalized Joint Graphical Lasso method (IPJGL) for differential network inference. The presented method is validated by the simulation experiments as well as the real datasets. Furthermore, to precisely evaluate the results of differential network inference, we propose a new metric named APC2 for the differential levels of gene pairs. We apply IPJGL to analyze the TCGA colorectal and breast cancer datasets and find some candidate cancer genes with significant survival analysis results, including SOST for colorectal cancer and RBBP8 for breast cancer. We also conduct further analysis based on the interactions in the Reactome database and confirm the utility of our method.

关键词： 含参函数   一题多解   一题多变   深度学习  

摘要： 含参函数压轴问题是高考的重点,也是学生学习的难点.本文以一道试题的多解和多变为例,浅析高考试题中含参函数压轴问题的处理策略.

关键词： 相位生成载波   载波相位延迟   相位调制深度   正弦相位调制干涉仪   非线性误差  

摘要： 为消除载波相位延迟和相位调制深度波动对相位生成载波(Phase generated carrier, PGC)相位解调结果的影响,提出了一种基于互补微分相乘的PGC-Arctan相位解调改进算法。该算法通过构建一对系数相同、含待测相位的正交平方信号,再通过相除、开方和反正切运算,获得不受载波相位延迟和相位调制深度影响的相位解调结果,从而减小相位解调结果的非线性误差,使得解调结果信纳比更高、总谐波失真更小。对该算法的实现过程进行理论分析和推导,并开展了基于Matlab的算法仿真实验和基于正弦相位调制干涉仪的位移测量实验。结果表明:该算法在不同的载波相位延迟和相位调制深度下,解调结果的信纳比均大于41.50 dB,总谐波失真均不超过0.79%。该算法可有效减小PGC相位解调非线性误差,实现正弦相位调制干涉仪的精密位移测量。