First Exit Times for Ordinary and Compound Poisson Processes with Non-linear Boundaries

Distributions of the first-exit times from a region with concave upper boundary are discussed for ordinary and compound Poisson processes. Explicit formulae are developed for the case of ordinary Poisson processes. Recursive formulae are given for the compound Poisson case, where the jumps are positive, having discrete or continuous distributions with finite means. Applications to sequential point estimation and insurance are illustrated.      

Cu-W薄膜表面形貌的分形表征与电阻率

磁控溅射制备铜钨薄膜，用原子力显微镜和功率谱密度法分析薄膜生长表面形貌的分形维数，发现频段的选择基本不影响分形维数与溅射时间的关系.随溅射时间延长，薄膜厚度增加，分形维数增大，电阻率随分形维数的增大而升高.分析分形维数与电阻率的关系，认为对同一物质的导电薄膜，其表面形貌与电阻率存在对应关系. 关键词： Cu-W薄膜 分形维数 功率谱密度 电阻率     

一个分段连续系统中的胖奇异集激变

报道一种有特色的激变.这种激变是在一类分段连续力场作用下的受击转子模型中观察到的.描述系统的二维映象定义域中的函数不连续边界随离散时间发展振荡，从而使这个边界的向前象集构成一个承载混沌运动的胖分形.在控制参数的一个阈值下，一个椭圆周期轨道突然出现在此胖混沌奇异集中，使得迭代向它逃逸，胖混沌奇异集因此突然变为一个胖瞬态集.在这种情况下，有可能根据椭圆周期轨道逃逸孔洞，以及胖分形奇异集的测度随参数变化的规律，估算迭代在奇异集中的平均生存时间所遵循的标度规律.直接数值计算和由此估算所得标度因子值可以很好地互相印证. 关键词： 激变 胖分形 分段连续系统 标度律     

The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces

This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length ξ and the roughness exponent α, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with α= 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.     

含有理想导体的准分形结构光子晶体的能带

用时域有限差分方法计算了一组具有相似几何结构且包含理想金属材料的准分形光子晶体的能带.数值计算结果表明，这种准分形结构光子晶体具有绝对带隙，且带隙的宽度会 随着分形级数的增大而增大.同时，随着级数的增大，其能带在整体地趋向于高频端的同时，能带会被快速拉直而形成孤立的能级. 关键词： 光子晶体 带隙 分形     

Boundary integrability of nonlinear sigma models

We describe recent work on the classical integrability of the principal chiral model and general sigma models with boundaries in (compact) symmetric spaces.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 322–328, February, 2005.     

Dynamics of the Action of a CAT(0) Group on the Boundary

The main theorem here gives a geometric condition on the fixed point sets of two hyperbolic isometries of a CAT(0) group which guarantees that the subgroup generated by the two elements contains a free subgroup. A result in section 3 shows that an element extends to the identity on the boundary if and only if the element is virtually central in the CAT(0) group. Finally, the two dimensional case is considered in the last section of the paper and there it is shown that powers of two hyperbolic isometries commute if and only if a geometric condition on the fixed point sets is satisfied.     

煤多相燃烧分形增长模型的初步研究

本文运用分形理论对煤的多相燃烧过程进行了探索性研究。根据分形动力学的概念认为；煤的多相燃烧中，反应面积的分形增长有DLC模式和KLC模式，一般情况是这两种模式的迭加。模型还引入了孔洞的合并及煤种的影响因素，初步提出了较有通用意义的燃烧模型。该模型把对碳焦的表面分形与燃烧速率的计算结合起来初步揭示了碳焦结构对燃烧过程的影响。     

INERTIAL FRACTAL SET AND FRACTAL STRUCTURE OF ATTRACTORS FOR THE GINZBURG-LANDAN EQUATION

1.IntroductionTheGinzburg-Landanequationsgovernthefiniteamplitudeevolutionofinstabilitywavesinalargevarietyofdissipativesystemswhichareclosetocriticallty.VariousformsoftheGinzburg-Landanequationariseinhydrodynamicinstabilitytheory:thedevelopmentofTolllnieu-SchlichtingwavesinplanePoiseuilleflows,thenonlineargrowthofconvectionrollsintheRayleigh-Benardproblem,andtheappearanceofTaylorvorticesintheflowbetweencounterrotatingcircularcylinders(see[7--9]).Theekistenceofattractorsandaninertialmanifo…     

基于自适应多尺度时频熵的遥测振动信号异常检测方法

针对遥测振动信号频域成份复杂、非平稳非线性和强噪声特性,提出一种基于自适应多尺度时频熵的遥测振动信号异常检测方法;首先对采集到的遥测振动信号进行零漂修正和趋势项消除,然后采用自适应分解方法对信号进行多尺度分解,得到若干分量,利用相关系数剔除虚假分量;接下来用筛选出的分量作时频分布,对时频分布进行多层多尺度划分,计算相应尺度频段内信号的分形维数,依据分形维数的大小自适应地确定各频段的时频划分尺度;最后计算时频平面的自适应多尺度时频熵,通过时频熵的变化情况对遥测振动信号进行异常检测;实测数据验证了该方法的有效性。