Some results on the behavior and estimation of the fractal dimensions of distributions on attractors

The strong interest in recent years in analyzing chaotic dynamical systems according to their asymptotic behavior has led to various definitions of fractal dimension and corresponding methods of statistical estimation. In this paper we first provide a rigorous mathematical framework for the study of dimension, focusing on pointwise dimension(x) and the generalized Renyi dimensionsD(q), and give a rigorous proof of inequalities first derived by Grassberger and Procaccia and Hentschel and Procaccia. We then specialize to the problem of statistical estimation of the correlation dimension and information dimension. It has been recognized for some time that the error estimates accompanying the usual procedures (which generally involve least squares methods and nearest neighbor calculations) grossly underestimate the true statistical error involved. In least squares analyses of and we identify sources of error not previously discussed in the literature and address the problem of obtaining accurate error estimates. We then develop an estimation procedure for which corrects for an important bias term (the local measure density) and provides confidence intervals for. The general applicability of this method is illustrated with various numerical examples.     

PP/PS共混体系相结构形成与演变

以连续共混过程中间歇出料法研究了聚丙烯(PP)/聚苯乙烯(PS)体系共混过程中的扫描电镜图样演化过程,利用小角激光散射(SALS)证明了PP/苯乙烯-乙烯-丙烯嵌段共聚物(SEP)/PS体系的部分相容性,同时说明SALS研究聚合物熔体动态过程的有效性.针对扫描电镜图样,用重心粒径dg这一结构参数研究了PP/PS体系共混过程,利用分布函数求取了分散相PP分形维数,对共混过程中相分散进行了研究.     

Studies of heterogeneity properties of selected high-temperature superconductor surfaces

Nitrogen adsorption measured at 77 K was used to characterize the surface heterogeneity of high-temperature superconductor surfaces. Properties relating to adsorption and porosity of the solids (adsorption capacity, specific surface area, radii and volume of the pores, pore-size distribution function) were determined from nitrogen adsorption–desorption isotherms and atomic force microscopy (AFM) for a series of oxide superconductors. It is shown that the adsorption isotherms of all samples are S-shaped and belong to type II according to the IUPAC classification. On the basis of the nitrogen adsorption isotherms and AFM data, fractal dimensions were determined and correlations found with adsorption and porosity parameters.     

测量圆盘转动惯量产生误差的曲线研究

结合三线摆实验的基本过程,进行实验数据的采集。利用投影法来测量圆盘的转角大小,借助于matlab的cftool工具箱,对数据进行曲线拟合,对测出来的二组数据拟合,得到转角与百分差曲线图。通过误差的大小比较,得出圆盘转动惯量测量值与理论值的百分差随转角变化最接近于三次曲线。     

Bounds for the fundamental solutions of elliptic and parabolic equations

It is shown that any elloptic or parabolic operator in nondivergence form with measurable coefficients has a global fundamental solution verifying certain pointwise bounds.     

Dimension polynomials of difference local algebras

We extend the concept of the difference dimension polynomial of a difference field extension to difference local algebras. The main theorem of the paper establishes the existence and form of the dimension polynomial associated with the localization of a finitely generated well-mixed difference algebra at a prime reflexive difference ideal.     

Some Remarks on One-dimensional Functions and Their Riemann–Liouville Fractional Calculus

A one-dimensional continuous function of unbounded variation on [0,1] has been constructed.The length of its graph is infnite,while part of this function displays fractal features.The Box dimension of its Riemann–Liouville fractional integral has been calculated.     

基于PLC的三维调整机同步控制系统设计与实现

针对三维调整机难以实现多台同步工作，设计了基于PLC的同步控制方案。在同步控制系统方案中，采用西门子PLC通过工业无线以太网进行同步控制，由各维度油缸的位移传感器来保证同步控制的精确性。经实验，证实了此系统的精度满足设计要求，实现了同步控制的效果。     

Surface influence on the rotational and translational dynamics of molecules confined inside a mesoporous carbon xerogel

Low-field nuclear magnetic resonance techniques are employed to extract information about the effects introduced by the interaction with the surface on the rotational and translational dynamics of molecules confined inside a mesoporous carbon xerogel. The molecules under study were water, cyclohexane, and hexane. They were chosen due to their different interaction strength with the carbonaceous matrix. Frequency dependent longitudinal relaxation measurements, using the fast field cycling technique, allowed extraction of the fractal dimension of the carbon xerogel surface. It was observed that the measured value is influenced by the molecule affinity to the surface. Diffusion measurements, using the pulse field gradient technique, have revealed that the stronger interaction with the surface of cyclohexane and hexane molecules leads to an increased diffusive tortuosity, as compared with water.     

“多角度欣赏面心立方晶胞”教学设计*

尝试利用“火花学院”App等在线交互资源,引导学生从立体几何及密置层堆积模型视角,观察、描述、绘制面心立方晶胞的正四面体填隙、正八面体填隙、三视图和沿体对角线投影图像,加深学生对以面心立方晶胞结构为基础的CaF₂→金刚石晶胞、NaCl→钙钛矿晶胞结构的理解;再结合新型材料透明镁铝尖晶石晶体结构的探讨,了解晶体制备中的掺杂改性等常用方法,发展学生的微观探析能力和科学创新意识。