Tensor method for optimal control problems constrained by fractional three-dimensional elliptic operator with variable coefficients

We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional two- (2D) and three-dimensional (3D) elliptic operators with variable coefficients. We solve the governing equation for the control function which includes a sum of the fractional operator and its inverse, both discretized over large 3D $n\times n\times n$ spacial grids. Using the diagonalization of the arising matrix-valued functions in the eigenbasis of the one-dimensional Sturm–Liouville operators, we construct the rank-structured tensor approximation with controllable precision for the discretized fractional elliptic operators and the respective preconditioner. The right-hand side in the constraining equation (the optimal design function) is supposed to be represented in a form of a low-rank canonical tensor. Then the equation for the control function is solved in a tensor structured format by using preconditioned CG iteration with the adaptive rank truncation procedure that also ensures the accuracy of calculations, given an $\epsilon$-threshold. This method reduces the numerical cost for solving the control problem to $O(n\log n)$ (plus the quadratic term $O(n^2)$ with a small weight), which outperforms traditional approaches with $O(n^3\log n)$ complexity in the 3D case. The storage for the representation of all 3D nonlocal operators and functions involved is also estimated by $O(n\log n)$. This essentially outperforms the traditional methods operating with fully populated $n^3\times n^3$ matrices and vectors in ${?}^{n^3}$. Numerical tests for 2D/3D control problems indicate the almost linear complexity scaling of the rank truncated preconditioned conjugate gradient iteration in the univariate grid size n.     

中空MOFs材料制备及电催化应用的研究进展

水分裂、金属-空气电池和燃料电池等能源转换技术对解决未来的能源危机和环境问题至关重要.氧还原反应(ORR)、氧析出反应(OER)和氢析出反应(HER)作为其核心反应,存在反应动力学速率较慢的问题,因此,开发研制高效的非贵金属电催化剂具有重要意义.金属有机骨架(MOFs)材料因具有高度可调的组成和多孔晶体结构,在不同的应用领域引起了越来越多的关注.中空MOFs纳米材料具有MOFs材料高度可调的组成和结构优势,又具有中空结构纳米材料的优点(如更快的物质传输、更丰富的孔隙率、灵活多变的活性组分、更多的暴露活性位点及对苛刻条件的更好相容性等),在电催化领域显现出巨大的应用潜力.本文对近几年来基于中空结构MOFs材料的制备及在电催化方面应用的研究进展进行了综合评述,并对该领域面临的挑战和发展前景进行了总结和展望.     

高比能锂离子电池层状富锂正极材料改性策略研究进展

层状富锂材料具有超过250 mAh∙g⁻¹的高可逆比容量,被认为是下一代高比能锂离子电池最具商业化前景的正极材料之一。然而,层状富锂材料在实际应用之前仍需解决诸多挑战,如高电压氧释放、层状到岩盐相的结构变化、过渡金属离子迁移等结构劣化,并由此带来了较低的初始库伦效率、电压/容量的衰减以及循环寿命的不足。针对以上问题,进行层状富锂材料改性无疑是一种行之有效的方法。本综述全面介绍了层状富锂材料的结构、组分以及电化学性能,在此基础上对材料改性策略进行了系统阐述,详细介绍了体相掺杂、表面包覆、缺陷设计、离子交换和微结构调控等一系列改性策略的现状以及发展趋势,最终提出了高容量和长循环层状富锂材料和高比能锂离子电池的设计思路。     

Desirability functions as response in a d‐optimal design for evaluating the extraction and purification steps of six tranquillizers and an anti‐adrenergic by liquid chromatography‐tandem mass spectrometry

Internal standards can be added at different stages of an analytical procedure. When they are added at the beginning of a multiresidue method and their behavior is not exactly the same as that of the analytes, the intended correction for small variations within the analytical process could not be achieved. Because of this, in the present work, the use of d ‐optimal designs together with desirability functions is proposed to state the experimental response under study. The overall desirability function used relates two analytical criteria: to assess a similar chemical behavior of each analyte in relation to its internal standard and to avoid a significant reduction of the absolute peak area of the internal standards. This strategy has been applied to the analysis of the effect of four factors related to the extraction and purification steps of six tranquillizers and a β‐blocker from pig muscle analyzed by liquid chromatography–tandem mass spectrometry. The effect of those factors has been evaluated by means of an ad hoc d ‐optimal design consisting of only 11 experiments. The resulting levels of the four factors that enable to achieve the greatest overall desirability have also been compared with those obtained when either the standardized or absolute peak area has been considered as response. Differences in both the significant factors and their optimum levels have been observed. It is noticeable that the experimental effort necessary to study the effect of the factors has been reduced by more than 50% thanks to the d ‐optimal design. Copyright © 2015 John Wiley & Sons, Ltd.     

大学有机化学“五维度”教学新策略——以“芳烃的亲电取代和亲核取代反应”为例

介绍了大学有机化学“强理念、重思维、活课堂、共育人、乐钻研”五维度教学新策略的内涵与实践。以线下教学为主,腾讯会议和慕课为辅助,践行“有机化学是科学也是艺术”的教学理念;采用多循环“疑探式”教学方式,辨析亲电试剂和亲核试剂的多样性;注重培养学生多种科学思维的综合运用;强化“文献预习”“练习讲解”“综合作业”“师生互动”等多个教学环节,加深学生对知识的理解与应用,提升学生在课堂中的参与度,着重培养学生的科学思维和人文素养、自主学习与团队合作精神。     

提升化学学科核心素养的高中化学教学——以“金属的防护”为例

针对人教版选修1《化学反应原理》第4章第3节“金属的腐蚀与防护”课时2“金属的防护”进行教学实践探索,融合STEM教育理念促进知识与社会生活结合。选用任务情境“家用电热水器碳钢内胆防腐”,通过实验探究构建起电化学防护的认知模型,再将模型应用于实际生产生活问题的解决,进行热水器内胆的防腐设计。在真实情境问题的解决中,将知识、方法、应用等3者融合,培养学生的问题意识和创新思维,逐步内化并表现出化学学科核心素养。     

国内外近30年“电化学”主题概念测查研究进展*

梳理了国内外1990-2020年核心期刊文献中对学生电化学主题概念测评的实证研究,主要涵盖学生电化学概念理解水平以及影响因素等方面。据此探讨其对化学教师教学实施以及国内外化学教育实证研究的启示,以期为中学化学教学及后续研究提供有益参考。     

国内外“物质的量”主题教学研究现状述评

分别以“Web of Science”与“中国知网”数据库为检索源,对2000—2020年间国内外“物质的量”主题研究论文进行检索,根据论文的研究内容进行分类归纳。研究表明:目前“物质的量”主题教学研究主要涉及:概念历史考量、教材研究、教师发展、学生认知与教学策略研究等5个方面。通过探析国内外的相关研究成果,以期为国内相关研究与实践提供有益借鉴。     

金属草酸盐基负极材料——离子电池储能材料的新选择

商业化锂离子电池石墨负极和锂盐过渡金属氧化物正极材料的储锂容量都已接近各自的理论值,探索下一代高能量密度电极材料是解决现阶段锂离子电池容量限制的关键。近年来,新型金属草酸基负极材料,借助其在金属离子电池中多元化储能机制诱发的较高储能效应在碱金属离子电池绿色储能材料领域备受关注。本文就金属草酸基材料在锂、钠、钾金属离子电池方面的最新研究进行了综述,着重介绍了材料的晶型结构、多元化储能机制及储能过程中的动力学特征,简单阐述了材料在电化学储能中存在的问题,分析了金属草酸基负极材料在形貌晶型控制、界面碳复合改性和金属元素掺杂方面的改性策略。最后,预测了金属草酸基负极材料在碱金属离子电池体系的发展方向。