Annealing behavior of gel‐spun polyethylene fibers at temperatures lower than needed for significant shrinkage

The annealing at 373 K of ultrastrong, gel‐spun polyethylene (PE) has been studied. At this temperature, the fibers show no significant shrinkage. Still, a significant decrease in the mechanical properties is observed. The fibers have been analyzed with differential scanning calorimetry (DSC), temperature‐modulated differential scanning calorimetry (TMDSC), atomic force microscopy (AFM), and small‐angle X‐ray scattering (SAXS). During the annealing, the glass transition of the intermediate phase is exceeded, as shown by DSC. When split for structure analysis by AFM, the annealed fibers undergo plastic deformation around the base fibrils instead of brittle fracture. The quasi‐isothermal TMDSC experiments are compared to the minor structural changes seen with SAXS and AFM. The loss of performance of the PE fibers at 373 K is suggested to be caused by the oriented intermediate phase, and not by major changes in the structure or morphology. The overall metastable, semicrystalline structure is shown by TMDSC to posses local regions that can melt reversibly. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 403–417, 2003     

一类SierPinski地毯的Hausdorff测度的初等证明

在平面上以直径为d(d>0)的正M边形为基本集(M≥3为整数),构造压缩比为1∶k(k为不小于M的实数)的广义Sierpinski地毯,并用初等方法计算出它的Hausdorff测度为ds,其中s=logkM.     

Bush连续不可微函数的分形性质

本文对用递推关系确定的Bush连续不可微函数,找出了迭代函数系(IFS),从而得到它的级数表达式和所具有的自仿射分形的有关性质.最后还计算出函数图象的Hausdorff 维数的准确值.     

Dynamic fractal unifying interaction confirmed with magnetospheric behavior and orbital data

The solar wind makes the magnetosphere to expand and contract as indicated by the expansions and contractions of the auroral oval due to balancing of the dynamic pressure of the ambient space plasma at inner and outer magnetic lines. This self‐similar magnetospheric behavior elucidates the controversial magnetic storm‐substorm relationship and reveals the 3D‐spiral structure of magnetic interaction. The found self‐similarly evolving structure of one seen as fundamental interaction suggests dynamic fractal unifying interaction that builds a firework universe having 3D‐spiral code. The unifying interaction is described with equation drawn in new fundamental dynamic fractal framework. The equation of unifying interaction converges to the inverse square laws and the principle of uncertainty at laboratory scales. The dynamic fractal fundamental framework is made of one 3D‐spirally‐faster‐inward contracting and expanding, oscillating, basic matter. It simply accounts for observed constant speed of light and for the creation of bright and dark bands on a screen behind a tiny slit. The dynamic fractal framework is quantitatively confirmed with the orbital data for the Milky Way Galaxy, the Sun, the Earth, and the triple asteroid system 87 Sylvia. Many testable predictions are also made. The presented new fundamental dynamic fractal framework allows qualitative and quantitative modeling and simplification. © 2007 Wiley Periodicals, Inc. Complexity 12: 61–76, 2007     

A multifractal decomposition according to rate of returns

For one‐dimensional simple symmetric random walk, the Hausdorff and packing dimensions of sets of sample paths with prescribed rate of returns to the origin are determined. This gives a multifractal decomposition of the underlying sample space. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

单模光纤中皮秒啁啾脉冲压缩

对单模光纤正群速色散区秒啁啾脉冲的非线性传进行了近似的解析分析和定量的数值计算。结果表明，负啁啾脉冲在传输过程中能得到有效压缩。压缩比与脉冲初始峰值功率和初始啁啾程度有关。初始峰值功率一定的脉冲，其压缩比随初始啁啾程度的增大面大，初始啁啾程度一定的脉冲，压缩比随初始峰值功率的增大而减小，表明自相位调制效应导致脉冲压缩效果变差。计算结果还表明，在脉冲时域宽度得到压缩的同时，光谱宽度也能得到同步压缩。     

产生特殊聚焦图形的二元光学元件

通过面积编码将伽博（Gabor)波带片的透过率函数的余弦分布等效为二元分布，研制了能产生各种特殊聚焦图形的二元光学元件。根据透镜聚焦的物理原理制作的二元振幅型波带片可以方便地产生多种聚焦线，给出了相应的实验结果，并讨论了改善聚焦效果的优化条件。     

微裂纹扩展中的分形现象及其计算机仿真

本文探讨了采用仿真技术研究微裂纹连接过程和生成分形断口表面的可行性，发展了用于仿真微裂纹随机生长行为的ＧＯ模型的基本构相，并进行了计算机仿真实验，由此得出了一此有的结论。     

Lipschitz classes on local fields

The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on the Euclidean space R~n and the local field K are compared,so that one may interpret the essential differences between the analyses on R~n and K.Finally,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m＜(ln 2/ln 3).     

有限分形介质中分数阶反应扩散方程及其解析解

建立了有限分形介质中具有吸附效应的分数阶反应扩散积分方程.利用Lap lace变换、广义有限H ankel变换及其相应的逆变换得到了以M ittag-Leffler函数为主要形式的解析解,并研究了解的渐近性态.