课程文献中心 更多>>

关键词： 代数推理   图象生成   反比例函数  

摘要： 以苏科版初中数学“反比例函数的图象与性质”教学实践为例,针对学生存在的图象绘制机械化与性质分析表面化两大认知困境,提出“代数推理与图象生成双向建构”的教学策略.通过“问题引领—实践探究—类比总结”的教学流程,引导学生从函数表达式出发分析定义域、符号关系及增减性,推理图象特征(渐近性、象限分布),再通过描点法画图验证,并结合几何画板动态演示突破“折线”认知误区,形成对双曲线平滑性与连续性的深刻理解.教学中强调数形结合的双重表征,以代数推理预测几何特征,以图象生成反哺性质归纳,并借助技术工具突破传统边界.实践表明,该策略能有效促进学生认知重构,搭建函数研究的基本框架并培养核心素养,为后续学习奠定思维基础.

关键词： 四维欧氏空间   直纹面   结构函数   平均曲率向量场   特殊曲线  

摘要： 在四维欧氏空间中,利用腰曲线的定义,提出直纹面的结构函数,将三维欧氏空间中的不可展直纹面及其标准方程推广到四维欧氏空间。通过直纹面的结构函数来研究曲面自身的性质,得到4类特殊伴随直纹面的结构函数、导线和腰曲线之间的关系,并对这些直纹面进行分类。最后给出导线是Mannheim曲线和第三型斜角螺线时结构函数的具体表达式,并计算此时伴随直纹面的平均曲率向量场。

关键词： 土壤厚度   滴水   水文类型   水化学   元素/Ca比值  

摘要： 岩溶地区的复杂性加大了洞穴滴水研究的难度,土壤厚度状况对洞穴滴水水文类型和水化学特征有重要影响。本研究对遵义市清江洞内6个滴水点开展了一个水文年监测,采用Smart-Friendrich分类系统进行滴水分类,探讨土壤厚度对水文、水化学特征及先期方解石沉淀(PCP)的影响。结果表明:(1)清江洞滴水点可分为渗流、包气带流和季节流三种滴水类型,滴速与土壤含水量密切相关,呈现出雨季大旱季小的变化特征,上覆土壤较薄的渗流类滴水点滴速全年稳定性较好,不易断流;(2)滴水水化学季节变化明显,其中二氧化碳分压(pCO_(2))、电导率(EC)、Ca^(2+)存在较明显的空间差异,渗流类滴水点因上覆土壤较薄而数值最小,另外两类滴水点因上覆土壤较厚,水化学数值和变幅较大;(3)滴水点稳定碳同位素(δ^(13)C_(DIC))与水化学特征变化类似,渗流类滴水点因上覆土壤较薄,其δ^(13)C_(DIC)更偏正,包气带流和季节流类滴水点δ^(13)C_(DIC)则相反;(4)土壤厚度影响滴水点的干湿状况和水化学特征,进而也对PCP过程产生重要影响。这些发现证明了土壤厚度是影响滴水水文、水化学和δ^(13)C_(DIC)的重要因素。

关键词： 主体地位   概念教学   实效性  

摘要： 随着新课程改革的推进,高中数学教学开始注重转变传统的应试教育模式,强调学生的主体性,致力于培育学生的数学学科核心素养.数学概念不仅是学生学习数学的根基,更是培养学生数学学科核心素养的基石.在高中数学概念教学中,教师应重视对概念本质的深入理解,引导学生亲历概念的形成过程,及时给予关键性的点拨和讲解,帮助他们深刻地掌握概念,从而提升概念教学的实效性,发展学生的数学学科核心素养.

关键词： 文会图   宋代服饰   宴饮生活   文化内涵  

摘要： 中国饮食自古多茶酒相伴,饮茶品酒更是文人之好,尤其在尚雅崇文的宋代,庭园宴饮之事盛行。文章以《文会图》为蓝本,辅以宋代其他画作及文字史料,通过服饰形制、色彩和面料等要素对画作进行观物、考证和取意,得出《文会图》可以作为考证宋代宴饮生活及审美意趣的代表画作,其中的服饰形、色和质均体现了宋人的生活和处世观。

关键词： Importance sampling  

摘要： Continual learning (CL) has emerged as a crucial paradigm for learning from sequential data while retaining previous knowledge. Continual graph learning (CGL), characterized by dynamically evolving graphs from streaming data, presents distinct challenges that demand efficient algorithms to prevent catastrophic forgetting. The first challenge stems from the interdependencies between different graph data, in which previous graphs influence new data distributions. The second challenge is handling large graphs in an efficient manner. To address these challenges, we propose an efficient continual graph learner (E-CGL) in this paper. We address the interdependence issue by demonstrating the effectiveness of replay strategies and introducing a combined sampling approach that considers both node importance and diversity. To improve efficiency, E-CGL leverages a simple yet effective multilayer perceptron (MLP) model that shares weights with a graph neural network (GNN) during training, thereby accelerating computation by circumventing the expensive message-passing process. Our method achieves state-of-the-art results on four CGL datasets under two settings, while significantly lowering the catastrophic forgetting value to an average of −1.1%. Additionally, E-CGL achieves the training and inference speedup by an average of 15.83× and 4.89×, respectively, across four datasets. These results indicate that E-CGL not only effectively manages correlations between different graph data during continual training but also enhances efficiency in large-scale CGL. © Zhejiang University Press 2025.

关键词： Prisms  

摘要： A single-camera, dual-prism panoramic three-dimensional digital image correlation (3D-DIC) method was developed to enable full 360° measurement of internal surface deformation and to evaluate its effectiveness for internal morphology characterization of circular pipes and pipeline defect detection. A single camera in conjunction with a double-prism optical arrangement is employed to reproduce a stereoscopic (dual-camera) imaging effect by refracting light through two prisms oriented at a prescribed angle, allowing simultaneous capture of left and right views. Panoramic observation of the entire inner surface is achieved via reflection from a convex mirror, providing continuous 360° coverage. Subsequent digital image correlation processing and coordinate transformation are performed on the acquired images to reconstruct the three-dimensional displacement field and strain distribution. Morphology experiments indicate a maximum absolute error of 0.4 mm, with the majority of measurement points exhibiting errors within 0.1 mm. Deformation tests show a maximum relative error of 3.86% in comparison with strain gauge measurements. The proposed system demonstrates high accuracy and practicality, achieves simplified hardware through optical design, and enables high-precision measurement of inner pipe-surface deformation. © 2025 Chinese Academy of Sciences. All rights reserved.

关键词： Strain measurement  

摘要： With the rapid expansion of the flexible display industry, represented by foldable smartphones, simultaneous measurement of deformation and stress distribution across multiple structural layers under bending has become a critical challenge for structural design and performance evaluation. A color multichannel optical measurement system, integrating multi-channel Digital Image Correlation (DIC) with fluorescent labeling and the screen’s own display, is presented to enable, for the first time, synchronous measurement of deformation and strain fields in multiple structural layers of a foldable screen during dynamic bending. The display layer produces red speckle patterns via intrinsic luminescence, while the surface protective layer is endowed with blue fluorescent speckles by spray-coating a UV-excited powder, enabling non-destructive speckle application compatible with mass-produced flexible screens. Incorporation of green fluorescent powder into intermediate structural layers during manufacturing further permits synchronous measurement of additional layers. Color-speckle images are captured simultaneously by a color camera system and spectrally separated. Full-field deformation and strain distributions for each structural layer are then computed independently using DIC algorithms. The system attains in-plane and out-of-plane deformation measurement accuracies of 1 μm and 5 μm, respectively, satisfying the high-precision requirements of multilayer material characterization in flexible-screen design and testing. Experimental results confirm that the proposed method accurately and synchronously retrieves deformation and strain fields for each layer of a flexible display, offering an innovative, non-destructive testing tool for reliability assessment of flexible displays. © 2025 Chinese Academy of Sciences. All rights reserved.

关键词： 无人平台建图   任务相关性   交叉注意力   信息瓶颈   预训练  

摘要： 在自动驾驶、无人作战等领域发展需求驱动下，任务相关性建图成为提升地面无人平台决策精度与效率的关键。从四个方面系统归纳和评述了任务相关性建图研究现状和主要进展。聚焦感知信息相关性过滤，分析了信息瓶颈理论或交叉注意力机制技术细节；聚焦先验信息相关性过滤，分析了规则先验类、神经参数类和测绘地理类先验数据的融合过滤方法；聚焦地图模型的任务相关性设计，分析了嵌入用户层、任务推理层和决策层等地图模型设计方式；聚焦地图建模的任务相关性方法，分析了预训练建图和空间感知引擎构建等任务驱动的建图方法。以全面评述为基础，提出了任务相关性建图指标体系，为任务相关性建图提供标准化衡量指标，并对现有高精地图、3DSG建图和Active SLAM建图等工作进行比较分析。提出了任务相关性建图的未来发展方向，包括多维度分层地图模型、多模态细粒度感知算法、多源数据深度融合及任务驱动实时建模引擎等。