天体运行轨道的背景介质理论导引与自相似分形测度计算的分维微积分基础

通过讨论天体运行背景介质理论的连续轨道及离散轨道这二个研究方向的基础假设,介绍了天体运行轨道的具体方程形式及理论框架概要;进一步地通过讨论天体运行轨道Binet方程的一般形式及其行星近日点进动角的解,给出了连续轨道理论与Newton理论及Einstein广义相对论的联系与区别;通过讨论天体运行轨道的分维扩展方程,给出了包括太阳系行星、天王星卫星、地球卫星、绕月航天器等在内的离散轨道（稳定性轨道）方程及其预言数据.特别地,作为对天体在较为广泛区域作用曲线的初步探讨推论,指出仅由天体引力难以形成质量密度趋于无穷大的理想黑洞.通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设,进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式,给出分维导数与分数阶导数的区别,随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式,给出了其与目前Hausdorff测度方法（覆盖方法）的区别,并对包括三分Cantor集合、Koch曲线、Sierpinski垫片及正交十字星形等自相似分形在内的测度进行了计算分析.     

量子理论中一个定理的随机推广

随机情况下的量子理论有着更广泛的实际应用,所以利用数学期望将量子理论中的一个重要定理在随栅隋况下作了推广,证得这个定理对随机自相似集也成立,这对进一步研究随机自相似集的量子维数和量子误差提供了理论依据,丰富了量子理论．     

龙陵—瑞丽走滑体系中段自相似结构与热液成矿定位

龙陵－瑞丽走滑体系是滇西三江构造带中腾冲地块与邦地块交界线南段的大规模右旋平移走滑带。剖面上它是一个自相似的花状构造体系;平面上则是一个由强应变带与弱应变域交织复合的自相似的网眼构造,表现为大尺度的“网眼构造”套叠小尺度的“网眼构造”的复杂图像,热液蚀变主要集中在不同尺度的弱应变域的下列三个部位：（１）弱应变域消失部斜面朝向与走滑运动方向一致的一侧。（２）强烈错位部;（３）角砾化透镜体中。走滑带的     

The problem of scaling in grid-related hydrological process modelling

This article shows some important scaling aspects that exist in hydrological process grid modelling with GIS, with respect to selecting the optimal grid width. Hydrologically relevant space parameter fields should often be regarded as self-similar fractals for which certain invariance characteristics are applied. These characteristics are especially important if there is an extensive change in the model grid width. The self-similarity generates simple scaling laws, which can be used for rescaling procedures. © 1997 John Wiley & Sons, Ltd.     

Some Distinctions Between Self-Similar and Self-Affine Estimates of Fractal Dimension with Case History

Compass, power-spectral, and roughness-length estimates of fractal dimension are widely used to evaluate the fractal characteristics of geological and geophysical variables. These techniques reveal self-similar or self-affine fractal characteristics and are uniquely suited for certain analysis. Compass measurements establish the self-similarity of profile and can be used to classify profiles based on variations of profile length with scale. Power spectral and roughness-length methods provide scale-invariant self-affine measures of relief variation and are useful in the classification of profiles based on relative variation of profile relief with scale. Profile magnification can be employed to reduce differences between the compass and power-spectral dimensions; however, the process of magnification invalidates estimates of profile length or shortening made from the results. The power-spectral estimate of fractal dimension is invariant to magnification, but is generally subject to significant error from edge effects and nonstationarity. The roughness-length estimate is also invariant to magnification and in addition is less sensitive to edge effects and nonstationarity. Analysis of structural cross sections using these methods highlight differences between self-similar and self-affine evaluations. Shortening estimates can be made from the compass walk analysis that includes shortening contributions from predicted small-scale structure. Roughness-length analysis reveals systematic structural changes that, however, cannot be easily related to strain. Power-spectral analysis failed to extract useful structural information from the sections.     

A self-similar flow behind a shock wave in a gravitating or non-gravitating gas with heat conduction and radiation heat-flux

The propagation of a spherical shock wave in an ideal gas with heat conduction and radiation heat-flux, and with or without self-gravitational effects, is investigated. The initial density of the gas is assumed to obey a power law. The heat conduction is expressed in terms of Fourier’s law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density, and the total energy of the wave to vary with time. Similarity solutions are obtained and the effects of variation of the heat transfer parameters, the variation of initial density and the presence of self-gravitational field are investigated.     

Perfect Fluid Lrs Bianchi I With Time Varying Constants

It is investigated the behaviour of the “constants” G, c and Λ in the framework of a perfect fluid LRS Bianchi I cosmological model. It has been taken into account the effects of a c-variable into the curvature tensor. Two exact cosmological solutions are investigated, arriving t the conclusion that if q < 0 (deceleration parameter) then G, c are growing functions on time t while Λ is a negative decreasing function on time.     

用一维时间序列确定吸引子维数应注意的两个问题

该文给出了严格自相似和统计自相似的区别，并由此讨论了用一维时间序列确定吸引子维数应注意的两个问题，即维数计算公式中的标度范围及比例系数问题和双对数图与Ｄ－ｍ图的关系问题。     

Self-similar cataclasis in the formation of fault gouge

Particle-size distributions have been determined for gouge formed by the fresh fracture of granodiorite from the Sierra Nevada batholith, for Pelona schist from the San Andreas fault zone in southern California, and for Berea sandstone from Berea, Ohio, under a variety of triaxial stress states. The finer fractions of the gouge derived from granodiorite and schist are consistent with either a self-similar or a logarithmic normal distribution, whereas the gouge from sandstone is not. Sandstone gouges are texturally similar to the disaggregated protolith, with comminution limited to the polycrystalline fragments and dominantly calcite cement. All three rock types produced significantly less gouge at higher confining pressures, but only the granodiorite showed a significant reduction in particle size with increased confining pressure. Comparison with natural gouges showed that gouges in crystalline rocks from the San Andreas fault zone also tend to be described by either a self-similar or log-normal particle distribution, with a significant reduction in particle size with increased confining pressure (depth). Natural gouges formed in porous sandstone do not follow either a self-similar or a log-normal distribution. Rather, these are represented by mixed log-normal distributions. These textural characteristics are interpreted in terms of the suppression of axial microfracturing by confining pressure and the accommodation of finite strain by scale-independent comminution.     

土壤水力特性分形特征的研究进展

从土壤结构特征的描述、土壤水力特性的研究等方面,综合评述了80年代以来国内外应用分形理论描述土壤水力特性参数及分形特征的研究进展,并探讨了其发展方向和前景。