黎曼流形上不变集的分形维数估计

本文利用整体Lyapunov指数给出了光滑黎曼流形上C1-映射不变集的分形维数的上界.     

a-Si:H簿膜的晶化与分形结构的形成

利用透射电子显微镜(TEM)观测a-Si:H 薄膜在不同温度下生长的分形结构。实验方法为原位动态技术。对分形结构的TEM形貌像用Sandbox方法计算了其分形维数。450℃时,形成具有类似分叉状的分形结构,分形线数d_f=1.69;800℃时,形成岛状分形结构,分形维数d_f=1.76。实验结果表明,分形结构的形成与薄膜物性的变化相联系。文中还对分形结构与a =Si:H 薄膜晶化的关系进行了讨论。     

Strkuctured-light Image Compression Based on Fractal Theory

The method of fractal image compression is introduced which is applied to compress the line structured-light image.Based on the self-similarity of the structured-light image, we attain satisfactory compression ratio and higher peak signal-to-noise ratio (PSNR).The experimental results indicate that this method can achieve high performance.     

自相似曲线与Whitney型临界集

本文讨论一类（包括Ｋｏｃｈ曲线在内的）自相似曲线，证明了其上的简单曲线是Ｗｈｉｔｎｅｙ型临界集，并在微小扰动下仍是简单曲线．     

Representation of discrete sequences with high-dimensional iterated function systems

Iterated Function System (IFS) models have been used to represent discrete sequences where the attractor of the IFS is self-affine or piece-wise self-affine in R ² or R ³ (R is the set of real numbers). In this paper, the piece-wise hidden-variable fractal model is extended from R ³ to R ⁿ (n is an integer greater than 3), which is called the high-dimensional piece-wise hidden-variable fractal model. This new model uses a “mapping partial derivative” and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the hidden variables. Therefore, the result is very general.     

川藏公路培龙沟路段堆积物的分形特征及其地质意义

川藏公路培龙沟路段有多种不同类型的堆积物。本文应用分形理论,探讨了培龙沟路段泥石流堆积物、冰碛堆积物、冲洪积堆积物以及坡积或者残坡积物的分形特征。通过粒度分析法计算出不同类型堆积物的粒度分维,得到泥石流堆积物分维最大,冰碛堆积物分维较大,坡积或者残坡积堆积物较小,冲积物或者洪积物分维最小的规律。最后系统论述了堆积物粒度分维的地质意义,认为堆积物粒度分维是对堆积物物质组成的复杂性和自组织性、堆积物形成过程和形成时间以及泥石流、冰川、河流和洪水等搬运能力和运动过程的反映和度量。该研究为野外不同类型堆积物的区分、成因、形成过程等研究提供了一种新的方法,具有一定参考价值。     

Reduced reference image quality assessment using regularity of phase congruency

In this paper, a reduced-reference image quality assessment metric is proposed, which measures the difference of the regularity of the phase congruency (PC) between the reference image and the distorted image. The proposed model adopts a three-stage approach. The PC of the image is first extracted, then the fractal dimensions are computed on PC as the image features that characterize the image structures from the view of the spatial distribution. Finally the image features are pooled as the quality score using ℓ₁ distance. The proposed approach is evaluated on seven public benchmark databases. Experimental results have demonstrated the excellent performance of the proposed approach.     

Synthesis and gas sensing behavior of nanostructured V2O5 thin films prepared by spray pyrolysis

Nanocrystalline vanadium pentoxide (V₂O₅) thin films have been deposited by a spray pyrolysis technique on preheated glass substrates. The substrate temperature was changed between 300 and 500 °C. The structural and morphological properties of the films were investigated by means of X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM), and atomic force microscopy (AFM). The influence of different substrate temperatures on ethanol response of V₂O₅ has also been investigated. XRD revealed that the films deposited at T_pyr=300 °C have low peak intensities, but the degree of crystallinity improved when the temperature was increased to 500 °C and films had orthorhombic structures with preferential orientations along the (0 0 1) direction. The fractal analysis showed a decreasing trend versus the pyrolysis temperature. Sensing properties of the samples were studied in the presence of ethanol vapor. The operating temperature of the sensor was optimized for the best gas response. The response increased linearly with different ethanol concentrations. It was found that films deposited at the lowest substrate temperature (300 °C) had the highest sensing response to ethanol.     

Special fractal growth of dendrite copper using a hydrothermal method

Special fractal dendrite Cu nanostructures have been synthesized through a simple hydrothermal method, and the effects of the volume ratio between glycerol and water and the concentration of H₃PO₃ on the morphologies of dendrite Cu have been studied in detail. The Field emission scanning electron microscopy (FESEM), Transmission electron microscopy (TEM) and X-ray diffraction (XRD) have been used to characterize these Cu products. The results indicate that rhombic diamond and different morphologies of fractal dendrite were prepared because of the accumulation of Cu nuclei based on the diffusion-limited aggregation (DLA) and the nucleation-limited aggregation (NLA) model. Fortunately, symmetrical leaf-like dendrite Cu nanostructures different from Cu dendrites reported before have been obtained. Additionally, an explanation for the growth of fractal dendrite Cu has been discussed carefully.     

Bessel sequences of exponentials on fractal measures

Jorgensen and Pedersen have proven that a certain fractal measure ν has no infinite set of complex exponentials which form an orthonormal set in L²(ν). We prove that any fractal measure μ obtained from an affine iterated function system possesses a sequence of complex exponentials which forms a Riesz basic sequence, or more generally a Bessel sequence, in L²(μ) such that the frequencies have positive Beurling dimension.