以形助数,把握概念本质——“认识小数”教学实践与思考

从整数到小数,是数系的一次扩充,也标志着学生的数概念从具有离散性的整数向具有稠密性的有理数发展.充分挖掘小数中的直观成分,利用生动、形象的图形能将抽象的数学知识直观化,进而引导学生进行探索,把握概念的本质.     

具有离散性的连续性模型映射

为了实现在连续性空间中的离散分段问题,采用解决离散性问题的方法虚拟构造连续性集合,将连续性问题映射为分段的离散问题,根据集合中元素的离散特性实现连续性模型的分段求解.通过数据结构的设计与压缩路径的算法证实,模型的映射能够解决实际问题的分段求解.     

Thermodynamic Performance Characteristics of a Brownian Microscopic Heat Engine Driven by Discrete and Periodic Temperature Field

A Brownian microscopic heat engine with a particle hopping on a one-dimensional lattice driven by a discrete and periodic temperature field in a periodic sawtooth potential is investigated. In order to clarify the underlying physical pictures of the heat engine, the heat flow via the potential energy and the kinetic energy of the particles are considered simultaneously. Based on describing the jumps among the three states, the expressions of the efficiency and power output of the heat engine are derived analytically. The general performance characteristic curves are plotted by numerical calculation. It is found that the power output-efficiency curve is a loop-shaped one, which is similar to one for a real irreversible heat engine. The influence of the ratio of the temperature of the hot and cold reservoirs and the sawtooth potential on the maximum efficiency and power output is analyzed for some given parameters. When the heat flows via the kinetic energy is neglected, the power output-efficiency curve is an open-shaped one, which is similar to one for an endroeversible heat engine.     

表面张力实验装置的改进

本针对拉脱法测量液体表面张力实验中仪器误差较大,测量结果不理想的情况,对该实验装置进行了改进,使测量数据离散性小、精度高。     

具有无穷多个不连续点Sturm-Liouville算子谱的离散性

研究了一类内部具有无穷多个不连续点的Sturm Liouville问题,即内部具有无穷多个转移条件的Sturm Liouville问题.首先建立了新Hilbert空间,在新的空间中定义了与转移条件相关联的最小算子C_(min)和最大算子C_(max),并给出了它们的性质.之后利用算子分解法得到了最小算子C_(min)自共轭扩张谱是离散的充分条件.     

线性随机结构的平稳随机响应

对于不仅结构参数具有随机性,而且外载是平稳随机激励的问题,给出了随机响应变异系数的计算方法。应用虚拟激励法先将随机荷载转化为确定性的简谐荷载,使双随机问题得以精确地转化为单随机问题进行分析。求解过程显著简化,而且包含了二种随机因素之间的耦合效应。用数值模拟法对方法的精度作了估计。     

辩证运用方法解决数列问题

数列的特征（离散性、函数性等）提醒我们：在解决数列问题时，应注意常用方法的辩证运用．     

核电工程地质(四)

核电工程地质(四)古迅(中国科学院地质研究所北京100029)6地基的勘察、试验和稳定性评价在核安全法规和有关的核安全导则中“, 核电厂的地基包括了基础结构、工程支撑结构和下卧的岩上材料(地基材料)三个部分。     

上海光源首批波荡器永磁块研制

介绍了上海光源2台混合型真空室内波荡器IVU25用636件Sm2Co17永磁块(规格为65 mm×25 mm×8.965 mm)和1台APPLE-Ⅱ型椭圆极化波荡器EPU100用668件NdFeB永磁块(规格为35 mm×35 mm×25 mm)的研制情况。指出了影响剩磁离散性、磁化偏角、机械尺寸精度等技术要求的基本因素,并对其原理进行了分析。研制的Sm2Co17和NdFeB永磁块的磁性能、磁场品质、机械尺寸精度等满足了上海光源首批波荡器插入件技术要求。     

A Boussinesq model with alleviated nonlinearity and dispersion

The classical Boussinesq equation is a weakly nonlinear and weakly dispersive equation, which has been widely applied to simulate wave propagation in off-coast shallow waters. A new form of the Boussinesq model for an uneven bottoms is derived in this paper. In the new model, nonlinearity is reduced without increasing the order of the highest derivative in the differential equations. Dispersion relationship of the model is improved to the order of Pade （2,2） by adjusting a parameter in the model based on the long wave approximation. Analysis of the linear dispersion, linear shoaling and nonlinearity of the present model shows that the performances in terms of nonlinearity, dispersion and shoaling of this model are improved. Numerical results obtained with the present model are in agreement with experimental data.