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摘要： Folding-deficient mutants of solute carrier 6 (SLC6) family members have been linked to human diseases. The serotonin transporter [(SERT)/SLC6A4] is an important drug target in the treatment of depression, anxiety, and obsessive-compulsive disorders and-with structural information in several conformational states-one of the best understood transporters. Here, we surmised that thermal unfolding offered a glimpse on the folding energy landscape of SLC6 transporters. We carried out molecular dynamic (MD) simulations to understand the mechanistic basis for enhanced and reduced stability, respectively, of the thermostabilized variant SERT-Y110A/I291A/T439S, which had previously been used for crystallization of human SERT in the outward-facing state, and of the folding-deficient SERT-P601A/G602A. We also examined the hydrophobic mismatch caused by the absence of cholesterol to explore the contribution of cholesterol to protein stability. When compared with wild type SERT, the thermodynamic and kinetic stability of SERT-Y110A/I291A/T439S was enhanced. In the other instances, changes in these two components were not correlated: the mutations in SERT-P601A/G602A led to a drop in thermodynamic but an increase in kinetic stability. The divergence was even more pronounced after cholesterol depletion, which reduced thermodynamic stability but increased the kinetic stability of wild type SERT to a level comparable to that of SERT-Y110A/ I291A/T439S. We conclude that the low cholesterol content of the endoplasmic reticulum facilitates progression of the folding trajectory by reducing the energy difference between folding intermediates and the native state. SIGNIFICANCE STATEMENT Point mutations in solute carrier 6 (SLC6) family members cause folding diseases. The serotonin transporter [(SERT)/ SLC6A4] is a target for antidepressants and the best understood SLC6. This study produced molecular dynamics simulations and examined thermal unfolding of wild type and mutant SERT variants

关键词： 科研训练   科研能力   科研意识   硕士研究生培养   微分方程  

摘要： 科研训练作为硕士研究生培养过程的重要环节,是培养硕士研究生科研能力的主要途径。该研究针对当前基础数学专业微分方程方向硕士研究生科研训练的不足和现状进行分析,试图通过优化科研训练形式、提高科研训练的有效性以及完善科研训练机制和考核制度等措施,使学生积极参与各种科研训练活动,学习并掌握做科研的方法,培养科研意识,提高独立从事科研的能力。

关键词： One-sided Lipschitz condition   Commutative noise   Semi-tamed Milstein method   Strong convergence   Exponential mean square stability  

摘要： A new explicit stochastic scheme of order 1 is proposed for solving commutative stochastic differential equations (SDEs) with non-globally Lipschitz continuous coefficients. The proposed method is a semi-tamed version of Milstein scheme to solve SDEs with the drift coefficient consisting of non-Lipschitz continuous term and globally Lipschitz continuous term. It is easily implementable and achieves higher strong convergence order. A stability criterion for this method is derived, which shows that the stability condition of the numerical methods and that of the solved equations keep uniform. Compared with some widely used numerical schemes, the proposed method has better performance in inheriting the mean square stability of the exact solution of SDEs. Numerical experiments are given to illustrate the obtained convergence and stability properties. (C) 2021 Elsevier Inc. All rights reserved.

关键词： 辅助函数   构造策略   导数  

摘要： 一些不等式的证明,若能立足函数的角度,利用导数研究函数的性质(单调性或最值极值)来加以证明,就显得很有优越性.而这一思想的关键在于构造合理的辅助函数.本文精选高考经典题,以案例的形式加以分类例析,并给出了应对策略.

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关键词： 微分方程   图像去噪处理   信息传递   噪声信号   信噪比峰值  

摘要： 数字影像作为重要的信息传递媒介,为我国多个领域提供了信息传递的基础。然而,受噪声信号的干扰,图像的边缘信息存在部分缺失。基于此,提出了基于微分方程的图像去噪处理设计,通过构建全变分图像去噪模型,计算出图像的信噪比SNR,判定图像的标准;根据全变分图像中能量变化系数与噪声能量变化系数的关系,选取图像平衡点;基于微分方程的数值计算,得出图像的对偶算子值;基于图像去噪最优迭代次数与PSNR值的关系,获取图像去噪最优迭代次数;最终改进递归滤波在图像中的各向异性扩散,保护图像边缘的细节纹理信息。实验结果表明,此种图像去噪处理方法的信噪比峰值随着噪声方差的升高波动幅度较小,能够有效降低图像中的噪声信号干扰。

关键词： 地磁数据库   向下延拓   导数迭代法   滤波   高频噪声   抗噪能力  

摘要： 高精度的地磁场数据库是地磁匹配导航的基础.在构建地磁数据库时,需要将空中的航磁测量数据向下延拓至某一水平面,而向下延拓在数学上具有不适定性,通常利用迭代方法逐次逼近"适定最优解".本文针对导数迭代法在迭代过程中的噪声累积问题,提出一种改进方法,首先利用稳定的向上延拓将观测面和向上延拓、向下延拓同等高度平面上的磁场值联系起来,再通过垂向一阶导数关系构造残差项,为了抑制高频噪声的干扰,采用向上延拓算子对残差项进行低通滤波,最后更新迭代值.在不同噪声水平的仿真条件下,改进方法的延拓误差仅为导数迭代法的四分之一,表明改进方法的抗噪能力与精度远远优于导数迭代法,同时实测数据也验证了改进方法可以实现稳定的磁场向下延拓.

关键词： 数学核心素养   单元教学   定积分  

摘要： 在教学中培养学生的数学核心素养是新一轮高中数学课程改革的要求,而单元教学设计是落实核心素养的一个重要环节.本文以“定积分”单元为例,首先根据微积分发展的时间脉络,完成了单元知识点的梳理,对标了其中蕴含的核心素养;其次针对单元教学设计中的学科、学情、课标、教材、重难点等要素进行了层级递进式分析,选择教学策略;再次将历史发展主线与核心素养有机融合于单元总体目标及章节教学目标,给出了适宜的教学方式;最后顺承知识逻辑,给出了“溯源式”“探究式”“赏析式”“拓展式”的案例设计片段,使学生在学习中充分感受微积分模块的“文化积淀”“模型思想”“简洁之美”“高阶知识”,全面提升了学生的数学核心素养.

关键词： 高考试题   教材溯源   类比改编   导数  

摘要： 对2021年高考全国甲卷导数压轴题的情境来源进行教材背景的追溯,并通过对问题设置的延展和函数模型进行改编,得到一系列崭新的题目,旨在为同行在原创命题的过程中提供一些思考和借鉴.

关键词： 失分   填空题   解答题   高考选择题   防微杜渐   导数应用   举例分析   概念的理解  

摘要： 导数是研究函数的重要工具,在高考选择题、填空题和解答题中均有涉及,学生在解题时由于对一些概念的理解不透彻,结论成立的条件不充分,解题细节不完善等原因,极易出现无谓失分的情况.本文结合教学中学生常出现的几种失分情况,进行举例分析,帮助学生防微杜渐.