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关键词： 导数几何意义   五个应用   泰勒公式   数形结合  

摘要： 导数的几何意义作为“导数概念”的几何化特征,是高考考查的重点内容.通过对近几年高考试题中导数几何意义考查的深入剖析和总结,系统性地给出了导数几何意义应用的五个方面,并引入了高等数学中泰勒公式背景下的切线放缩法,结合数形结合思想,将导数的几何意义的应用进行了提升和拓展.

关键词： Digital micromirror devices   Hyperspectral imaging   Image quality   Infrared detector arrays   Spatial light modulators   Spectral imaging  

摘要： We propose a novel, to the best of our knowledge, concept of the differential coded aperture snapshot spectral imaging (D-CASSI) technique exploiting the benefits of using a {-1,+1} random mask, which is demonstrated by a broadband single-snapshot hyperspectral camera using compressed sensing. To double the information, we encode the image with two complementary random masks, which proved to be superior to two independent patterns. We utilize dispersed and non-dispersed encoded images captured in parallel on a single detector. We explored several different approaches to processing the measured data, which demonstrates significant improvement in retrieving complex hyperspectral scenes. The experiments were completed by simulations in order to quantify the reconstruction fidelity. The concept of differential CASSI could be easily implemented also by multi-snapshot CASSI without any need for optical system modification. (C) 2022 Optica Publishing Group

关键词： 函数零点   放缩法   分析法   双变量含参不等式  

摘要： 本文中主要以构造函数、参变分离、数形结合、分析法、放缩法等基本方法,探析2021年浙江卷压轴题函数与导数的解法,并对试题难点及所考查的核心素养进行再反思和归纳,为新一轮高考复习的师生寻找一个解决这类问题的突破口,提供一个探究解法、启发教学的视角.

关键词： 导数   单调性   极值点偏移   不等式  

摘要： 利用导数研究函数的单调性和证明不等式问题是高考命题的热点.极值点偏移常作为不等式命题的切入点,以构造函数和放缩法作为主要解题策略,以压轴题形式出现,综合性强,难度大,对学生逻辑推理、数学运算等数学学科核心素养提出了更高要求,具有选拔性功能.

关键词： qMRI   Quantitative Magnetic Resonance Imaging   APOE   Apolipoprotein E   MWF   Myelin Water Fraction  

摘要： Mounting evidence indicates that myelin breakdown may represent an early phenomenon in neurodegeneration, including Alzheimer's disease (AD). Understanding the factors influencing myelin synthesis and breakdown will be essential for the development and evaluation of therapeutic interventions. In this work, we assessed associations between genetic variance in apolipoprotein E (APOE) and cerebral myelin content. Quantitative magnetic resonance imaging (qMRI) was performed on a cohort of 92 cognitively unimpaired adults ranging in age from 24 to 94 years. We measured whole-brain myelin water fraction (MWF), a direct measure of myelin content, as well as longitudinal and transverse relaxation rates (R-1 and R-2 ), sensitive measures of myelin content, in carriers of the APOE epsilon 4 or APOE epsilon 2 alleles and individuals with the epsilon 33 genotype. Automated brain mapping algorithms and statistical models were used to evaluate the relationships between MWF or relaxation rates and APOE isoforms, accounting for confounding variables including age, sex, and race, in several cerebral structures. Our results indicate that carriers of APOE epsilon 2 exhibited significantly higher myelin content, that is, higher MWF, R-1 or R-2 values, in most brain regions investigated as compared to noncarriers, while epsilon 4 carriers exhibited trends toward lower myelin content compared to noncarriers. Finally, all qMRI metrics exhibited quadratic, inverted U-shape, associations with age;attributed to the development of myelination from young to middle age followed by progressive loss of myelin afterwards. Sex and race effects on myelination were, overall, nonsignificant. These findings suggest that individual genetic background may influence cerebral myelin maintenance. Although preliminary, this work lays the foundation for further investigations to clarify the relationship between APOE genotype and myelination, which may suggest potential targets in treatment or prevention of AD

关键词： 数学分析   教学实施   反思   改进措施  

摘要： 文章作者通过针对“数学分析”课程中一个重要的知识模块“导数”,从教学设计、教学实施、学生学习效果等方面进行反思,总结出课程教学的特色和亮点,同时反思学生的实际学习效果与授课教师期望的差距,提出了今后在教学实施过程中切实可行的改进措施。

关键词： 命题者   不等式恒成立   函数与导数   解题策略   备考   函数与不等式   高考  

摘要： 函数与不等式密切联系,导数是研究函数的一个重要工具,以不等式为载体的函数与导数问题备受命题者的青睐,其中不等式恒成立问题是高考的热点和备考的难点.本文对不等式恒成立的典型问题进行分析,旨在梳理和总结相关问题的解决方法,以飨读者.

关键词： 金融科技服务   消费者反馈   合作创新   微分博弈  

摘要： 数据要素时代下,商业银行需要不断加强金融科技技术融合和应用以适应不断变化的消费者需求,与金融科技企业进行合作创新已成为主流趋势。本文立足消费者中心原则,应用微分对策理论研究商业银行和金融科技企业合作创新问题,构建基于技术创新的金融科技服务供应链动态博弈模型,比较集中式决策、无契约的分散式决策和两种合作契约的分散式决策下的均衡结果。研究表明,消费者反馈对开发商和供应商的定价策略影响不大,但会影响开发商的技术创新投入和金融科技服务内在技术先进度;消费者对价格不敏感或对技术先进度敏感时,较高的收益共享契约和较低的成本分担契约有利于稳定合作关系;在一定条件下,供应链内部成员不会同时选择同一合作契约,此时可以考虑一次性转让合同使双方决策行为一致。

关键词： 实验学校   构造函数   已知函数  

摘要： 一、结构统一,构造函数例1(2022届深圳市实验学校月考)已知函数f(x)=1/2 x^(2),g(x)=alnx。(1)若曲线y=f(x)-g(x)在x=2处的切线与直线x+3y-7=0垂直,求实数a的值.

关键词： 曲线   切线   定义   导数   题型   数学思想  

摘要： 切线问题在高中数学中十分常见,切线的定义、求解方法、常见题型是探究的重点.文章结合实例探究切线问题,开展策略总结,基于教学实践,提出几点建议.