Conceptualizing and organizing content for teaching and learning in selected Chinese, Japanese and US mathematics textbooks: the case of fraction division

In this study, selected Chinese, Japanese and US mathematics textbooks were examined in terms of their ways of conceptualizing and organizing content for the teaching and learning of fraction division. Three Chinese mathematics textbook series, three Japanese textbook series, and four US textbook series were selected and examined to locate the content instruction of fraction division. Textbook organization of fraction division and other content topics were described. Further analyses were then conducted to specify how the content topic of fraction division was conceptualized and introduced. Specific attention was also given to the textbooks’ uses of content constructs including examples, representations, and exercise problems in order to show their approaches for the teaching and learning of fraction division. The results provide a glimpse of the metaphors of mathematics teaching and learning that have been employed in Chinese, Japanese, and US textbooks. In particular, the results from the textbook analyses demonstrate how conceptual underpinnings were developed while targeting procedures and operations. Implications of the study are then discussed.     

Effect of radiation-induced mean wavelength shift in optical fibers on the scale factor of interferometric fiber optic gyroscope at a wavelength of 1300 nm

In order to analyze the effect of wavelength-dependent radiation-induced attenuation (RIA) on the mean transmission wavelength in optical fiber and the scale factor of interferometric fiber optic gyroscopes (IFOGs), three types of polarization-maintaining (PM) fibers is tested by using a ⁶⁰Co γ -radiation source. The observed different mean wavelength shift (MWS) behaviors for different fibers are interpreted by color-center theory involving dose rate-dependent absorption bands in ultraviolet and visible range and total dose-dependent near infrared absorption bands. To evaluate the mean wavelength variation in fiber coil and the induced scale factor change for space-borne IFOG under low radiation dose in space environment, the influence of dose rate on the mean wavelength is investigated by testing four germanium (Ge) doped fibers and two germanium-phosphorus (Ge-P) codoped fibers irradiated at different dose rates. Experimental results indicate that the Ge-doped fibers show the least mean wavelength shift during irradiation and their mean wavelength of optical signal transmitting in fibers will shift to shorter wavelength in low-dose-rate radiation environment. Finally, the change in the scale factor of IFOG resulting from the mean wavelength shift is estimated and tested, and it is found that the significant radiation-induced scale factor variation must be considered during the design of space-borne IFOG.     

Removing paint from a metal substrate using a flattened top laser

In this paper,we investigate laser cleaning using a flattened top laser to remove paint coating from a metal substrate.Under the irradiation of a flattened top laser,the coating paint of the metal substrate can be removed efficiently by laser induced ablation,stress,and displacement force.The temperature distribution,stress,and displacement are calculated in the coating layer and substrate using finite element analysis.The effects of a Gaussian laser and a flattened top laser and the results of different diameters of laser spot are compared.The investigation shows that the flattened top laser can reduce the substrate damage and enhance the cleaning efficiency.This method meets the need of large area industrial cleaning applications by optimizing the flattened top laser parameters.     

循环跃迁的Δ 型三能级系统中的无反转激光

研究了在引入非相干抽运的情况下,循环跃迁的Δ型共振三能级系统中产生的无反转激光.利用主方程的方法, 导出了缀饰态中强相干场极限下布居数项和相干项的稳态近似解析解以及产生无反转激光所需要满足的条件;并利用数值模拟的方法讨论了布居数分布、 系统增益对探测场和相干场拉比频率的依赖性以及随时间的演化规律. 结果表明:无论各个参量取何值,共振Δ型三能级系统总是处于无粒子数反转的状态; 只要探测场或相干场之中有一个为强场,便可产生无反转激光; 当其中任意一个场远强于另一个场时,系统的无反转增益将不再依赖于任何一个场的拉比频率.     

卷绕式螺旋形薄膜介质脉冲形成线设计

采用模块化结构,设计了一种卷绕式螺旋形薄膜介质脉冲形成线,并且对绝缘材料、电极材料的选择依据进行了分析。基于模块化卷绕式脉冲形成线,研制的重复频率脉冲方波产生器采用4个开关同步触发四级形成线模块,从而实现多模块的电压串联叠加,以达到产生高压的目的。开关采用气体火花间隙开关,每级开关及充放电采用电感隔离。研制的脉冲产生器输出电压220 kV,脉冲宽度182 ns,前沿50 ns,可10 Hz重复频率稳定运行。     

相对论返波管振荡器齿状阴极

研究了一种齿状阴极的电子束产生传输过程以及对相对论返波管振荡器产生高功率微波的影响。基于SINUS881加速器,利用束流轰击金属靶观测齿状阴极产生电子束在不同轴向位置上的角向分布,并开展了基于环形阴极和齿状阴极的X波段相对论返波管振荡器的实验研究。对不同齿数及尺寸对电子束流特性、器件输出微波功率和脉冲宽度的影响进行了分析。实验结果表明:当阴极的齿数增加到一定数量时,电子束的横向运动使得电子束在径向逐渐趋于分布均匀;与均匀环形阴极的打靶结果近似,此时,电子束对于相对论返波管振荡器产生微波的功率和脉宽影响不大。     

氘氘中子产额铟活化诊断方法

提出了活化法测量DD中子产额的实验方法,该方法可提高DD中子产额测量的精度。方法基于铟同位素115In与DD中子的非弹性散射反应,活化反应释放的射线被HPGe探测器记录,根据活化系统标定灵敏度推算出中子产额。分析了探测器记录的活化射线数与中子产额间的关系。介绍了一套活化测量的系统设计。通过蒙特卡罗方法模拟了活化样品出射的射线数与样品厚度的关系,模拟结果表明:样品厚度取为1 cm可兼顾活化效率和测量精度。在加速器上对铟活化样品进行了标定实验,实验结果表明:在聚变中子产额大于2109的实验中可使用铟活化诊断方法,中子产额测量的相对标准误差在10%以内。随着聚变中子产额的不断提高,铟活化测量中子产额的精度可进一步提高。     

Recursion relations for the constrained multi-component KP hierarchy

In this paper, we define a new constrained multi-component KP(cMKP) hierarchy which contains the constrained KP(cKP) hierarchy as a special case. We derive the recursion operator of the constrained multi-component KP hierarchy. As a special example, we also give the recursion operator of the constrained two-component KP hierarchy.