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.     

闭区间[0,1]上的分形插值函数的分数阶积分

介绍了分形插值函数和迭代函数系统以及v阶黎曼-刘准尔分数阶积分的概念及相关定理.利用这些概念及定理讨论了分形插值函数的分数阶积分在[0,1]上连续性及判定[0,1]上的分形插值函数的分数阶积分也是[0,1]上的分形插值函数,并给予了证明.     

处理污泥焦颗粒内部孔结构在燃烧过程中变化

在管式炉反应器中进行了1种污泥定温燃烧试验,进行了5个不同燃烬率样品的液氮静态容量法等温物理吸附试验.发现不同燃烬率的污泥样品孔分布特性相似,其孔系统可能主要是由一端封闭的不透气的孔构成;随着燃烬率的增加,比表面积、平均孔径和孔体积等参数变化不同;样品颗粒内孔表面分形维数随燃烬率的增长呈先降低再升高的趋势.     

An Exploratory Study on the Complexity and Machine Learning Predictability of Stock Market Data

This paper shows if and how the predictability and complexity of stock market data changed over the last half-century and what influence the M1 money supply has. We use three different machine learning algorithms, i.e., a stochastic gradient descent linear regression, a lasso regression, and an XGBoost tree regression, to test the predictability of two stock market indices, the Dow Jones Industrial Average and the NASDAQ (National Association of Securities Dealers Automated Quotations) Composite. In addition, all data under study are discussed in the context of a variety of measures of signal complexity. The results of this complexity analysis are then linked with the machine learning results to discover trends and correlations between predictability and complexity. Our results show a decrease in predictability and an increase in complexity for more recent years. We find a correlation between approximate entropy, sample entropy, and the predictability of the employed machine learning algorithms on the data under study. This link between the predictability of machine learning algorithms and the mentioned entropy measures has not been shown before. It should be considered when analyzing and predicting complex time series data, e.g., stock market data, to e.g., identify regions of increased predictability.     

Morphology Development in Multi‐Component Polymer Blends: I Composition Effect on Phase Morphology in PP/PET Polymer Blends

The relationship of the phase morphology of polypropylene/polyethylene‐terephthalate (PP/PET) blends and their corresponding compatibilized blends with composition was investigated using digital image analysis. A diameter, d _g , was defined and calculated to discuss the phase morphology of this polymer blend system. A figure‐estimation method was introduced to determine the width of the distribution of d _g . Based on the method, it is proven that the distribution of d _g obeys a log‐normal distribution and consequently, the distribution width, σ was calculated. Further, a fractal dimension, D _f , was introduced to describe the distribution of main sizes of the particles of the dispersed phase. The results showed that, while d _g increased with the concentration of the dispersed phase, σ and D _f show different dependence relations on composition;σ increases monotonously but D _f shows a maximum at a PET content of 30%, indicating that, even though the whole size distribution is much broader, the distribution of the main body of size becomes more uniform when the content of PET is less than 30%.     

纹理高阶分形特征在海面舰船目标检测中的应用

针对复杂海面环境下的舰船目标检测，分析了高阶分形特征缝隙在纹理分类中的应用，提出了一种基于分形维与缝隙的目标检测新方法，并利用该方法对海面舰船目标进行了检测。实验结果表明利用纹理分形维与缝隙特征进行海面舰船目标检测，可以取得较单一分形维检测更高的准确率。     

The fractal measurement of experimental images of supersonic turbulent mixing layer

Flow visualization of supersonic mixing layer has been studied based on the high spatiotemporal resolution Nano-based Planar Laser Scattering(NPLS) method in SML-1 wind tunnel. The corresponding images distinctly reproduced the flow structure of laminar,transitional and turbulent region,with which the fractal measurement can be implemented. Two methods of measuring fractal dimension were introduced and compared. The fractal dimension of the transitional region and the fully developing turbulence region of supersonic mixing layer were measured based on the box-counting method. In the transitional region,the fractal dimension will increase with turbulent intensity. In the fully developing turbulent region,the fractal dimension will not vary apparently for different flow structures,which em-bodies the self-similarity of supersonic turbulence.     

Scale-Invariant Branch Distribution from a Soluble Stochastic Model

We consider a general model of branch competition that automatically leads to a critical branching configuration. This model is inspired by the 4– expansion of the dielectric breakdown model, but the mechanism of arriving at the critical point may be of relevance to other branching systems as well, such as fractures. The exact solution of this model clarifies the direct renormalization procedure used for the dielectric breakdown model, and demonstrates nonperturbatively the existence of additional irrelevant operators with complex scaling dimensions leading to discrete scale invariance. The anomalous exponents are shown to depend upon the details of branch interaction; we contrast with the branched growth model in which these exponents are universal to lowest order in 1–, and show that the branched growth model includes an inherent branch interaction different from that found in the dielectric breakdown model. We consider stationary and non-stationary regimes, corresponding to different growth geometries in the dielectric-breakdown model.     

电解沉积的分形维数与ZnSO_4溶液浓度的关系

用电沉积方法得到了不同浓度硫酸锌电解液的分形凝聚图像;进行图像处理,得到了其分形维数与浓度的关系曲线;用粒子扩散限制凝聚模型解释了此关系