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关键词： 压轴题   双变量   思维能力   高考试卷   求解策略   导数   常考题型   学生解题  

摘要： 以导数为背景的二元不等式问题是近年高考的常考题型.此类问题题型丰富、思维能力要求高、方法灵活,备受命题人青睐,在高考试卷中常以把关题或压轴题的形式出现,成为学生解题中难点问题.此类问题虽然变化性强,但并非无规律可循.本文从双变量的属性入手,分类例析、总结问题的求解方略.

关键词： 不等式问题   高考真题   模拟试题   导数及其应用   函数的单调性   工具性   热点问题  

摘要： 导数是强有效的解题利器,在研究函数的单调性、最值(极值)、零点及生活中的优化等问题中都有着重要的应用,此外,利用导数来研究不等式问题,也很能突显其工具性。下面,我们从近年的高考真题及模拟试题来探究:导数及其应用的热点问题。

关键词： 图像问题   微分思想   电磁感应   数形结合   物理建模   物理学科核心素养   物理观念   科学思维  

摘要： 电磁感应中的图像问题能够很好地考查学生物理建模、推理运算、数形结合等综合处理物理问题的能力,集中反映学生的物理观念、科学思维等物理学科核心素养,已经成为近些年高考考查的热门内容.本文以电磁感应问题中经常出现的三种模型为例,详细讨论微分思想在处理图像问题中的应用.

关键词： 脉冲微分混沌系统   数值模拟   相图   分岔图   Poincare截面  

摘要： 由于脉冲微分混沌系统具有复杂的性态,在理论分析时具有一定的难度,而数值分析在一定程度上可以提供一些指导,所以数值模拟方法成为脉冲微分混沌系统研究的重要手段.该文设计了脉冲微分混沌系统的动力学分析算法,并将数值解以可视化的形式展现,绘制出方程组解的相图、分岔图、Poincare截面.以具有Holling type-Ⅱ功能反应函数的Gompertz病毒传染病模型为例验证算法的可行性,进行了数值模拟,得到了一些有意义的结论.

关键词： 一线教师   导数压轴题   函数不等式   具体函数   中学  

摘要： 导数压轴题往往以常见的函数不等式为载体,通过与具体函数结合来呈现给学生.作为中学一线教师,如果能够在解题时利用好函数不等式,总结函数不等式的衍生与创新,深挖问题的根源,就能快速解开问题的症结,从而对于相应问题认识得更全面,更透彻.下面就一道导数压轴题与大家探讨.

摘要： Mitochondrial amidoxime-reducing component (mARC) enzymes are molybdenum-containing proteins that metabolize a number of endobiotics and xenobiotics. The interindividual variability and differential tissue abundance of mARC1 and mARC2 were quanti-fied using targeted proteomics in three types of tissue fractions: 1) pediatric liver tissue homogenates, 2) total membrane fraction of the paired liver and kidney samples from pediatric and adult donors, and 3) pooled S9 fractions of the liver, intestine, kidney, lung, and heart. The absolute levels of mARC1 and mARC2 in the pediatric liver homogenate were 40.08 +/- 4.26 and 24.58 +/- 4.02 pmol/mg homogenate protein, respectively, and were independent of age and sex. In the total membrane fraction of the paired liver and kidney samples, the abundance of hepatic mARC1 and mARC2 was comparable, whereas mARC2 abundance in the kidney was approximately 9-fold higher in comparison with mARC1. The analy-sis of the third set of samples (i.e., S9 fraction) revealed that mARC1 abundance in the kidney, intestine, and lung was 5-to 13 -fold lower than the liver S9 abundance, whereas mARC2 abun-dance was approximately 3-and 16-fold lower in the intestine and lung than the liver S9, respectively. In contrast, the kidney mARC2 abundance in the S9 fraction was approximately 2.5-fold higher as compared with the hepatic mARC2 abundance. The abundance of mARC enzymes in the heart was below the limit of quantification (similar to 0.6 pmol/mg protein). The mARC enzyme abundance data pre-sented here can be used to develop physiologically based pharma-cokinetic models for the prediction of in vivo pharmacokinetics of mARC substrates. SIGNIFICANCE STATEMENT A precise targeted quantitative proteomics method was developed and applied to quantify newly discovered drug-metabolizing enzymes, mARC1 and mARC2, in pediatric and adult tissue sam-ples. The data suggest that mARC enzymes are ubiquitously expressed in an isoform-specific manner in the human

关键词： Force   Accelerometers   Micromechanical devices   Resonant frequency   Silicon   Frequency measurement   Structural engineering   MEMS accelerometer   scale factor   DETF   nonlinearity  

摘要： The scale factor nonlinearity of MEMS differential silicon resonant accelerometer(DSRA) structure is mainly due to the force-frequency nonlinear characteristic of DETF. This paper presents a detailed analysis of the relationship between the structural parameters, measurement range and the scale factor nonlinearity, which will provide a reference for the parameter design of DETF and overall structure. The inherent force-frequency nonlinearity of DETFs is analyzed, and the effects of structural parameters of DETF and axial force on nonlinearity of frequency variation are revealed. Combining the working principle of MEMS DSRA introduced first, the scale factor nonlinearity is studied. The results show that the structural parameters of the proof mass (determines the conversion between acceleration and inertial force), the support mechanism and the lever mechanism (determines the transfer coefficient of inertial force), and the DETF (determines the inherent force-frequency nonlinearity and affect the transfer coefficient of inertial force), as well as the measurement range, can all affect the scale factor nonlinearity. Moreover, the scale factor nonlinearity is directly proportional to the square of the measurement range and the square of the nominal scale factor, and inversely proportional to the square of the natural frequency of DETF. The finite element simulation is carried out, and the simulation results are in good agreement with the theoretical analysis values. Finally, the experiment on the scale factor nonlinearity of a prototype is carried out. The measured scale factor nonlinearity of the prototype is 1994.09ppm, which is consistent with the theoretical analysis value of 1737.30ppm.

关键词： 高考   导数   教学   思考  

摘要： 导数及其应用是高考的重要考点之一.导数题能综合考查学生多方面的学科素养、关键能力和必备知识,渗透多种数学思想方法,其要求之高,难度之大,让广大考生心有余悸.文章以一道高考导数题教学为例,谈谈此类题的教学过程、设计意图及教学思考.

关键词： 数学建模   数学抽象   数学方法   数学思维   综合实践活动   类比联想   发现和提出问题   数学概念  

摘要： 《普通高中数学课程标准(2017年版)》指出,数学建模是对现实问题进行数学抽象,用数学语言表达问题、用数学方法构建模型解决问题的素养[1].数学建模主要表现为:发现和提出问题,建立和求解模型,检验和完善模型,分析和解决问题[1].数学建模活动是基于数学思维运用模型解决实际问题的一类综合实践活动,是高中阶段数学课程的重要内容.解题中的建模是依据题目中的条件和结论的特征,类比联想相关数学概念、公式、定理、证明,构造出新的数学模型.

关键词： Customer order scheduling   Production sequencing   Assembly scheduling problems   Total completion time   Metaheuristics  

摘要： Although the customer order scheduling problem to minimize the total completion time has received a lot of attention from researchers, the literature has not considered so far the case where there are sequence-dependent setups between jobs belonging to different orders, a case that may occurs in real-life scenarios. For this NP-hard problem we develop a novel efficient approximate solution procedure. More specifically, we develop an innovative discrete differential evolution algorithm where differential mutations are performed directly in the permutation space and that uses a novel, parameter-free, restart procedure. The so-obtained solutions are improved by two proposed local search mechanisms that employ problem-specific, heuristic dominance relations. We carry out an extensive computational experience with randomly generated test instances to compare our proposal with existing algorithms from related problems. In these experiments, the proposed algorithm obtains the best results in terms of their average relative percentage deviation and success rate. Furthermore, an analysis of variance test, followed by a Tukey's test, confirms the excellent performance of the algorithm proposed.