On Napoleon's theorem in the isotropic plane]{On Napoleon's theorem in the isotropic plane

Summary Napoleon's original theorem refers to arbitrary triangles in the Euclidean plane. If equilateral triangles are externally erected on the sides of a given triangle, then their three corresponding circumcenters form an equilateral triangle. We present some analogous theorems and related statements for the isotropic (Galilean) plane.     

电控径向双折射滤波器的横向超分辨与轴向扩展焦深

提出利用电控径向双折射光瞳滤波器实现横向超分辨性能参量的调制与轴向扩展焦深。该光瞳滤波器由两个平行偏光镜,一个电光晶体与一个径向对称双折射晶体组成。分析了电光晶体与径向双折射元件对光偏振态的空间调制作用,通过控制电光晶体的相位延迟实现径向中心处初始偏振态的控制,与径向双折射元件横向偏振态调制结合,实现了庞加莱球上偏振态演变路径与阶段的控制,从而对焦点附近偏振态进行空间调制以实现光强的重新分布。研究结果表明,外加电场调制可以实现横向上超分辨性能的调控以及轴向上焦深的扩展,并可得到相应的电光相位延迟范围。     

二维恒定各向同性介质渗透系数反演的遗传算法

给出了利用遗传算法求解二维恒定各项同性介质渗透系数反演的一种新方法,该方法把参数反演问题转化为优化问题通过遗传算法求解.数值模拟结果表明:该方法具有精度高、收敛速度快、编程简单、易于计算机实现等优点,值得在实际工作采用.     

Nd~(3 ):YAG激光器基横模选择的实验研究

阐述了谐振腔与横模选择的原理、分析选横模的方法,研究了如何在YAG脉冲激光器上抑制高阶模.从而得到波长为1.06μm的单一基模激光束输出,并通过实验验证倾斜反射镜选模的效果.     

猫眼激光谐振腔横模选择特性研究

将猫眼逆向器作为激光谐振腔的一个腔镜组成猫眼谐振腔。介绍了猫眼逆向器的结构,阐述了猫眼逆向器中凸透镜和凹面镜的间距改变时猫眼曲率半径的相应变化,并通过有效地控制该间距来选择激光横模,从而保证基横模输出。在激光谐振腔衍射积分方程的基础上,运用牛顿柯特斯数学方法,对不同参量下的猫眼激光谐振腔的横模状况进行分析,得出了各阶横模对应的特征值和功率损耗,计算出保证基横模输出的参量,并与实验对比,得到了一致的结论,为激光器的横模选择和控制提供了一种简便易行的新方法。     

多元Sobolev关于L_(qp)(R~d)下的平均线性宽度

得到了两种多元 Sobloev类于 Lqp( Rd )下平均线性宽度的弱渐进估计 .     

A penny-shaped crack in a transversely isotropic piezoelectric solid: Modes II and III problems

An exact analysis of the modes II and III problems of a pennyshaped crack in a transversely isotropic piezoelectric medium is performed in this paper. The potential theory method is employed based on the general solution of three-dimensional piezoelasticity and the four harmonics involved are represented by one complex potential. Previous results in potential theory are then utilized to obtain the exact solution that is expressed in terms of elementary functions. Comparison is made between the current results with those published and good agreement is obtained. The project supported by the National Natural Science Foundation of China (No. 19872060)     

Kink Surfaces in a Directionally Reinforced neo-Hookean Material under Plane Deformation: I. Mechanical Equilibrium

Stationary kinks (elastostatic shocks) are examined in the context of a base neo-Hookean response augmented with unidirectional reinforcing that is characterized by a single additional constitutive parameter for the additional fiber reinforcing stiffness. Previous work has shown that such a transversely isotropic material can lose ellipticity in plane deformation if the reinforcing is sufficiently large and the fiber direction is sufficiently compressed. Here we show that the same reinforcing levels can give rise to piecewise smooth plane deformations separated by a plane stationary kink. Attention is restricted to deformations in which, on one side of the kink, the load axis is aligned with the fiber axis. Then the fiber stretch on this side of the kink is a natural load parameter. It is found that such a deformation can support a planar kink for a certain range of this load parameter. This range is dependent on the reinforcing parameter, and can even involve fiber extension if the reinforcing is sufficiently large. The set of all deformation states on the other side of the kink is precisely characterized in terms of a one-parameter family of (kink orientation, kink strength)-pairs. The results are interpreted in terms of the associated fiber alignment discontinuity and fiber stretch discontinuity.     

粒子的横向运动对环形质谱仪性能的影响

 分析了粒子的横向运动对环形质谱仪的分辨本领及测量精度的影响，给出了计算这些影响的方法。     

The fundamental matrix of the system of linear elastodynamics in hexagonal media. Solution to the problem of conical refraction

An explicit integral representation by single definite integralsof the fundamental matrix (Green's tensor) of the time-dependentsystem of hexagonal elastic media is derived. Thereby the problemof internal conical refraction in such media is solved.