《高等几何》“立体式”教学模式的探索

所谓立体式教学模式,就是将一门课程的预习、讲授、课堂交流、课后答疑、作业设计、考试考查等各个教学环节;将本课程的教学内容与其它课程或学科;将教师与每个学生个体构建成一个有机联系的立体网络,最大限度地提高课程教学效率.进行《高等几何》立体式教学模式的措施有:精心组织材料,上好第一次课;引导学生自学,养成预习习惯;拓展课堂内容,联系相关学科;师生互动交流,拓展教学效果.     

均布载荷作用下厚矩形板的弯曲

推广应用功的互等定理法(RTM)于求解基于Reissner理论的厚矩形板的弯曲问题，给出了二对边简支另两边固定厚矩形板在均布载荷作用下弯曲的精确解析解，并分析了解的数值结果．     

圆面探测器对圆面源（非同轴）的几何因子的蒙特卡罗计算

用基本Monte Carlo方法计算了圆面探测器对均匀平行圆面源（两圆面中心轴线间距离为C）的几何因子，并且与圆面探测器对均匀同轴圆面源的几何因子进行了比较，探讨了两圆面中心轴线间距离C对几何因子的影响；为了检验本文方法及所编程序的好坏，选取C=0时的数据与多边形近似法进行了比较。并根据讨论的结果，提出了对实验操作的要求。     

Wavy film flow along periodic wall under monochromatic-frequency flowrate perturbation

Surface wave dynamics of falling film on the surface of periodic rectangular wall under monochromatic-frequency flowrate forcing disturbances is studied via numerical simulation. Waveforms formed on the periodic rectangular wall are different from those on the flat plate. At low frequency, the perturbation introduced at the inlet first undergoes a steady flow region and then develops into solitary waves. When the frequency becomes higher, solitary waves disappear. Film deformations in the steady flow region and characteristics of solitary waves are studied as the film travels down. There are circulations at the depression of periodic wall which are dependent on the local film characteristics and geometry of the corrugation. Moreover, the flow rate and geometry of the corrugations can also affect the evolvement of the monochromatic perturbation.     

高师《初等几何研究》教学现状调查思考

《初等几何研究》是高师院校培养中学数学师资所特有的课程。目前《初等几何研究》教学现状不容乐观。基于此,对山西省高师数学系《初等几何研究》教学现状进行了调查和分析,发现《初等几何研究》课程存在诸多问题。因此,需要提高学生对《初等几何研究》课程重要性的认识,激发其学习兴趣;与时俱进改革教学内容,满足学生的发展需求;提倡多样化的教学方法,贯穿启发式的教学思想;掌握现代化的教学手段,提高教学效果;建立多元化的考核评价机制,培养学生的研究能力和创新精神。     

关于笛卡尔解析几何的哲学背景

分析笛卡尔数学创造工作中的心灵直观因素与笛卡尔知识论核心的"直观—演绎"原则如何在他的数学工作"解析几何"的建立中的具体体现,说明笛卡尔的数学工作和他的哲学思想的结合.     

几何证明题的认知分解及其对教学的启示——基于ACT-R对几何证明题解题过程的模拟

文章基于ACT-R对几何证明题解题过程的模拟,提出了一种对几何证明题解题进行认知分解方法,该方法能有效地将几何证明题的解题过程分解成单一、可训练的认知动作,并将解题过程所需要的全部知识都挖掘出来。这种分解使得学生能够通过对认知动作的训练和对知识的记忆有效的掌握几何证明题的解题方法。     

基于“几何画板”绘制双曲线

几何画板是一个优秀的专业学科平台软件,代表了当代专业工具平台类教学软件的发展方向。主要介绍使用几何画板画双曲线的几种作法:双曲线第一定义、双曲线第二定义、直角坐标方程、参数方程、极坐标方程,并给出每种作法的详细制作步骤。     

Experimental measurement of the quantum geometric tensor using coupled qubits in diamond

Geometry and topology are fundamental concepts, which underlie a wide range of fascinating physical phenomena such as topological states of matter and topological defects. In quantum mechanics, the geometry of quantum states is fully captured by the quantum geometric tensor. Using a qubit formed by an NV center in diamond, we perform the first experimental measurement of the complete quantum geometric tensor. Our approach builds on a strong connection between coherent Rabi oscillations upon parametric modulations and the quantum geometry of the underlying states. We then apply our method to a system of two interacting qubits, by exploiting the coupling between the NV center spin and a neighboring ¹³C nuclear spin. Our results establish coherent dynamical responses as a versatile probe for quantum geometry, and they pave the way for the detection of novel topological phenomena in solid state.     

Mechanical behaviour of cross-country ski racing poles during double poling

The purpose of this study was to evaluate the behaviour of cross-country ski poles during double poling on a treadmill using three-dimensional kinematics. The results were compared with standard laboratory tests of the pole manufacturers. A total of 18 skiers were analysed at two speeds (85% and 95% of the maximal speed) at grades of 1.5% and 7%. Variables describing cycle characteristics, bending stiffness, bending behaviour, and trajectories of the pole markers were analysed. Triangular-shaped poles demonstrated the greatest stiffness and lowest variability in maximal bending. Softer poles demonstrated greater variability in bending behaviour and lost ground contact at high skiing speeds, which for some skiers resulted in failure to complete high-speed tests. Considerable variations in pole behaviour for similar poles between skiers were observed, which might be attributed to differences in technique, indicating that mechanical properties of the poles did not exclusively determine pole behaviour in the dynamic situation. The greatest magnitude of pole bending was in the middle part of the pole, which differed from the standard static pole analysis of the manufacturer. Increases in grade demonstrated the greatest effect on pole bending. Distinct differences from the pole manufacturers' laboratory measures were apparent, suggesting that basic pole testing might be adapted.