一类数列极限的计算

极限计算是高等数学中的基本计算,虽然计算极限的方法有很多种,但是却不能解决所有的极限问题.在十几年的高等数学教学过程中,我们经常帮助考研的学生解决一些问题,在解决问题的过程中,我们发现有一类数列极限的计算有着共同的特点,本文中我们对这类数列极限的计算方法进行了总结,并给出定理及证明.     

随机取向群聚椭球粒子光散射特性研究

利用离散偶极子近似方法,考虑单元粒子之间的电磁相互作用,数值计算了随机取向的不同尺度参数、不同纵横比的群聚椭球粒子的缪勒矩阵元素,给出了各个缪勒矩阵元素的角分布曲线,探讨了随机取向的群聚椭球粒子的尺度参数、纵横比、基本粒子相对位置对其缪勒矩阵元素的影响。并将随机取向群聚椭球粒子的光散射特性与单个等效球形粒子的数值结果进行了比较。结果表明,随机取向群聚椭球粒子的光散射特性与等效球形粒子的光散射特性存在很大差别,基本粒子的形状越偏离球形,这种差别就越大; 随机取向群聚椭球粒子中椭球粒子的纵横比和相对位置对整个群聚粒子的缪勒矩阵元素存在不同程度的影响,并且此影响随着粒子尺度参数的增大而变得更加显著。     

随机取向群聚椭球粒子光散射特性研究

利用离散偶极子近似方法,考虑单元粒子之间的电磁相互作用,数值计算了随机取向的不同尺度参数、不同纵横比的群聚椭球粒子的缪勒矩阵元素,给出了各个缪勒矩阵元素的角分布曲线,探讨了随机取向的群聚椭球粒子的尺度参数、纵横比、基本粒子相对位置对其缪勒矩阵元素的影响。并将随机取向群聚椭球粒子的光散射特性与单个等效球形粒子的数值结果进行了比较。结果表明,随机取向群聚椭球粒子的光散射特性与等效球形粒子的光散射特性存在很大差别,基本粒子的形状越偏离球形,这种差别就越大; 随机取向群聚椭球粒子中椭球粒子的纵横比和相对位置对整个群聚粒子的缪勒矩阵元素存在不同程度的影响,并且此影响随着粒子尺度参数的增大而变得更加显著。     

Free vibration of functionally graded beams based on both classical and first-order shear deformation beam theories

The free vibration of functionally graded material （FGM） beams is studied based on both the classical and the first-order shear deformation beam theories. The equations of motion for the FGM beams are derived by considering the shear deforma- tion and the axial, transversal, rotational, and axial-rotational coupling inertia forces on the assumption that the material properties vary arbitrarily in the thickness direction. By using the numerical shooting method to solve the eigenvalue problem of the coupled ordinary differential equations with different boundary conditions, the natural frequen- cies of the FGM Timoshenko beams are obtained numerically. In a special case of the classical beam theory, a proportional transformation between the natural frequencies of the FGM and the reference homogenous beams is obtained by using the mathematical similarity between the mathematical formulations. This formula provides a simple and useful approach to evaluate the natural frequencies of the FGM beams without dealing with the tension-bending coupling problem. Approximately, this analogous transition can also be extended to predict the frequencies of the FGM Timoshenko beams. The numerical results obtained by the shooting method and those obtained by the analogous transformation are presented to show the effects of the material gradient, the slenderness ratio, and the boundary conditions on the natural frequencies in detail.     

Fe/Cr超晶格电子结构和磁性质的理论研究(英文)

应用密度泛函全势线性缀加平面波方法研究了Fe3/Cr3超晶格的电子结构和磁性质.结果表明,这种体系的基态相邻铁原子层间存在铁磁耦合,内禀自旋波波长大约2层厚的长度.