有趣的数字

假设地球是半径为R米的完整球体，若用绳子从北极开始绕一圈，其长度为2πR米．如果我们把绕地球一周的绳子增加1米，则绳子变为2πR＋1米、现用此长度的绳子重新绕地球一周，就会在绳和地面之间产生缝隙，问猫是否可以从这个缝隙钻过去呢？     

AGSM光束在自由空间中的传输

 用矩阵方法研究了有扭曲的各向异性高斯-尔模型（AGSM）光束通过自由空间的传输。给出了光束参数的解析传输公式和详细数值计算结果，说明AGSM光束的传输特性以及扭曲因子和空间相关长度的影响。     

叠砖平衡的一种简单解法

 叠砖的平衡问题(见图1)是一个有趣的力学平衡问题,本文利用质点系质心的定义,介绍一种较为简单的解法。为保持本文的完整性,不妨重述叠砖的平衡问题:N块完全相同的砖块以图1所示方式叠放在一起并保持平衡,每个砖块的长度为l,质量为m,求砖块突出部分的最大长度Lmax。图1考察平衡时,前i-1块砖、第i块砖和第i+1块砖之间的关系。设第i块砖相对于第i+1块砖探出的长度为di。     

两亲性嵌段聚合物的同步辐射小角x射线散射研究

应用同步辐射小角x射线散射(SAXS)方法研究了不同聚合条件下苯乙烯对乙烯基苯甲酸两亲性嵌段聚合物的聚集行为,结果发现该聚合物在选择性溶液中自组装形成胶束.胶束的形态和结构取决于嵌段聚合物的组成、浓度以及溶剂的性质等因素 关键词： 小角x射线散射 两亲性嵌段聚合物 分形维数 粒径     

高功率固体激光器光学元件位相误差滤波

不同频段的位相误差对输出光束将产生不同的影响，低频段主要影响远场焦斑主斑的能量分布，中高频段影响光的散射或者可能出现的较大的强度峰值调制，高频段影响光的散射，导致能量的损失。研究光学元件引入的位相误差与输出光束之间的定性、定量关系，首先必须对位相误差进行相应的滤波处理，反映光学元件面形的细微误差。     

Self-assembly behaviour of amphiphilic diblock copolymer in selective solvents studied by synchrotron small-angle x-ray scattering

The aggregation behaviour of styrene-vinyl benzoic acid (PSm-b-PVBAn) amphiphilic diblock copolymers in selective solvents with different m and n was investigated by synchrotron small-angle x-ray scattering (SAXS). We have carried out a detailed analysis of scattering intensity, dimension, shape and microstructure of the diblock copolymers of narrow distribution in water, methanol, ethanol and isopropanol selective solvents, respectively. We have found that the aggregation behaviour of the copolymer depends on the nature of the solvent and the micelle forms fiat disc objects with the ratio of radius ω=0.4. The average radius gyration Rg of the copolymer decreases as solvents change from isopropanol to ethanol and to methanol, and increases with increasing pH in aqueous solution, but decreases with the addition of COCl2 in ethanol solvent. The scattering intensity of diblock copolymer micelle follows I(h) ∝ h^-α in different selective solutions, suggesting that the PSm-b-PVBAn coils have self-similar structure behaviour or a fractal structure in the selective solvents. All of these revealed that the aggregation behaviour of the diblock copolymer changes dramatically with experimental condition in the selective solvent. The increase of mass fractal dimension (Dm) from 2.12 to 2.47 indicates that the copolymer chain changes from a swollen coil to a rather compact disc in the course of changing solvents, decreasing surface fractal dimension (Ds) from 2.98 to 2.58 indicates that the copolymer micelle change from a rather rough surface to a smooth form in the course of increasing pH in aqueous solutions, and increasing Dm and Ds from 2.29 to 2.35 and 2.70 to 2.90, respectively, indicates the shrinkage of copolymer micelle to a rather compact and rough disc form by adding COCl2 in ethanol solvents.     

激光与材料参数对瞬态SBS 诱导的激光超声破坏效果的影响

 通过数值求解一维瞬态受激布里渊散射（SBS）声光耦合波方程，从理论上分析了泵浦激光参数及光学材料参数对SBS过程发生阈值的影响。以SBS过程中建立起来的应力场抗拉（压）强度和散射场的反射率为判据，分析了激光脉宽及作用区域长度对激光超声破坏材料效果的影响，探讨了短脉冲激光（约ns）引起的激光超声对材料的破坏机理；讨论了通过参数配置有效遏制SBS过程激光超声对光学材料的破坏问题。     

AR箭图一类连通分支的结构

给出了代数闭域上基连通有限维代数A的AR箭图中带有方向圈及不含有DT_r周期模且除投射-内射模外所含元均是左稳定模的一类连通分支的结构。