MULTILINEAR CALDER(O)N-ZYGMUND OPERATOR ON MORREY TYPE SPACES——In Memory of Professor Yongsheng Sun

In this paper, the authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey and generalized Morrey spaces, respectively. As their special cases, the corresponding results of multilinear Calderón-Zygmund operator can be obtained.     

高中化学优质教学案例中教材分析的现状研究及分析模型建构*

以核心期刊《化学教育》2018-2021年高中化学教学设计及实施类文献为研究对象,在较完备的教材分析视角指引下,采用内容分析法研究优质教学案例中教材分析的现状及特点,在此基础上构建教材分析模型,探索优质教学案例的设计路径。     

Analytical analysis of anisotropic thermophoresis of a charged spheroidal colloid in aqueous media for extremely thin EDL cases

Thermophoresis of charged spheroids has been widely applied in biology and medical science. In this work, we report an analysis of the anisotropic thermophoresis of diluted spheroidal colloids in aqueous media for extremely thin EDL cases. Under the boundary layer approximation, we formulate the thermophoretic velocity, the thermophoretic force, and the thermodiffusion coefficient of a randomly dispersed spheroid. The parametric studies show that under the aforementioned conditions, the thermophoresis is anisotropic and its thermodiffusion coefficient should be considered as a vector, D _T. The thermodiffusion coefficient values and directions of D _T are strongly related to the aspect ratio and the angle θ between the externally applied temperature gradient and the particle's axis of revolution: The increasing aspect ratio enlarges the thermodiffusion coefficient value D_T of prolate (oblate) spheroids to a constant value when θ < 60° (θ > 45°), and it reduces D_T of prolate (oblate) spheroids to a constant value when θ > 60° (θ < 45°). The thermodiffusion coefficient direction of both prolate and oblate spheroids deviates slightly from −∇T_∞ for a small aspect ratio, and such deviation becomes serious for a large aspect ratio.     

自适应结构多工况下强度控制的研究

对自适应超静定桁架结构的强度控制问题进行了研究，把模型从单一工况推广到了多工况，实现了理论的完整性，定义了结构工作状态系数， 分析了作动器的联入对结构强度的影响，利用超静定桁架的耦合特性和作动器的调节功能，把强度控制问题转化为数学规划问题，方法简单有效。     

连续体结构拓扑优化应力约束凝聚化的ICM方法

为克服应力约束下拓扑优化问题约束数目多、应力敏度计算量大的困难，提出 了应力约束化凝聚化的ICM方法. 在利用Mises强度理论将应力约束转换成应变能约束后， 提出了应力约束凝聚化的两条途径：其一为应力全局化的方法，其二为应力约束集成化的方 法. 由此建立了多工况下以重量为目标、以凝聚化应变能为约束的连续体结构优化模型，并 利用对偶理论对优化模型进行了求解. 4个数值算例表明：该方法具有较高的计算效率，得 到的拓扑结构比较合理，不仅适用于二维连续体结构，也适用于三维连续体结构.     

A critical investigation of smoothed particle hydrodynamics applied to problems with free‐surfaces

In this paper, an in‐depth study of SPH method, in its original weakly compressible version, is achieved on dedicated 2D and 3D free‐surface flow test cases. These rather critical prototype problems shall constitute suitable test cases to get through when building a free‐surface SPH model. The present work aims at investigating various numerical aspects of this method, often little mentioned in literature. In particular, a great care is paid to the dynamic part of the solution, which is critical to the local hydrodynamic load prediction. The role of numerical errors in the development of acoustic frequencies in the pressure signals is discussed, as well as the influence of the choice of the sound velocity. On the shown test problems, it is also evidenced that some numerical tools are crucial to ensure the robustness and accuracy of the standard SPH method. The convergence of our model is heuristically proved on these nonlinear prototype tests, showing at the same time the very satisfactory level of accuracy reached. Through these tests, some other numerical specificities of the SPH method are discussed, such as the self‐redistribution of the particles occurring during the Lagrangian evolution. A higher order model is also proposed, and its advantages and drawbacks are discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

贝叶斯公式的几个应用

介绍了贝叶斯公式的一些应用实例及分析,以使在教学中能帮助学生更深入地理解该公式.     

Nonlinear approximation with general wave packets

We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete characterization of the approximation spaces is derived.     

多工况下结构鲁棒性拓扑优化设计

针对工程中存在多个随机不确定工况载荷作用的情况, 将鲁棒性设计思想引入到连续体结构拓扑优化设计, 发展和完善不确定性优化理论和计算方法. 基于概率模型和SIMP方法,提出以结构柔顺度标准差最小化为目标、具有体积约束的连续体鲁棒性拓扑优化数学模型.通过对目标函数及其灵敏度计算公式的推导, 采用数学规划法实现优化问题的求解. 数值算例验证了所提优化模型的正确性及算法的有效性, 并通过与确定性优化结果的比较,证明鲁棒性拓扑优化能够给出结构柔顺性变异更小的材料分布.      

真实情境与化学学科核心素养的发展——基于《普通高中化学课程标准(2017年版)》的解读

《普通高中化学课程标准（2017年版）》构建了化学学科核心素养的内容体系及其发展水平框架,重视开展“素养为本”的教学,重视真实情境的创设。在分析教学情境的内涵与功能的基础上,解读了新课标中课程内容、实施建议和命题原则中对真实情境创设与应用的要求,讨论了真实情境在发展学生化学学科核心素养中的教育价值。通过对具体教学案例的分析,探讨了基于学生化学学科核心素养发展的教学情境设计的策略。