Analysis and modeling of radiometric error caused by imaging blur in optical remote sensing systems

Imaging blur changes the digital output values of imaging systems. It leads to radiometric errors when the system is used for measurement. In this paper, we focus on the radiometric error due to imaging blur in remote sensing imaging systems. First, in accordance with the radiometric response calibration of imaging systems, we provide a theoretical analysis on the evaluation standard of radiometric errors caused by imaging blur. Then, we build a radiometric error model for imaging blur based on the natural stochastic fractal characteristics of remote sensing images. Finally, we verify the model by simulations and physical defocus experiments. The simulation results show that the modeling estimation result approaches to the simulation computation. The maximum difference of relative MSE (Mean Squared Error) between simulation computation and modeling estimation can achieve 1.6%. The physical experimental results show that the maximum difference of relative MSE between experimental results and modeling estimation is only 1.29% under experimental conditions. Simulations and experiments demonstrate that the proposed model is correct, which can be used to estimate the radiometric error caused by imaging blur in remote sensing images. This research is of great importance for radiometric measurement system evaluation and application.     

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.     

On cohomological dimension and depth under linkage

Some relations between cohomological dimensions and depths of linked ideals are investigated and discussed by various examples.     

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.     

On noncommutative piecewise Noetherian rings

We extend the definition of a piecewise Noetherian ring to the noncommutative case, and investigate various properties of such rings. In particular, we show that a ring with Krull dimension is piecewise Noetherian. Certain fully bounded piecewise Noetherian rings have Gabriel dimension and exhibit the Gabriel correspondence between prime ideals and indecomposable injective modules.     

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.     

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%.     

Hlder Norm Estimate for a Hilbert Transform in Hermitean Clifford Analysis

A Hilbert transform for Hlder continuous circulant (2 × 2) matrix functions, on the d-summable (or fractal) boundary Γ of a Jordan domain Ω in R2n , has recently been introduced within the framework of Hermitean Clifford analysis. The main goal of the present paper is to estimate the Hlder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the Hlder exponents, the diameter of Γ and a specific d-sum (d d) of the Whitney decomposition of Ω. The result is shown to include the case of a more standard Hilbert transform for domains with left Ahlfors-David regular boundary.     

电化学沉积金属铜的分形枝晶生长控制与性能

 以CuSO_{4/sub>为前驱体,HCl为添加剂,采用电化学沉积方法,在室温条件下制得了μm级、面心立方结构分形铜的枝状晶体,研究了铜离子浓度、硫酸浓度、电流密度、沉积时间、氯离子浓度等实验参数对分形枝状铜晶体尺寸、结构的影响。结果表明：硫酸的浓度对铜沉积物结构无明显影响;随着Cu^{2+/sup>浓度的不断增大,铜沉积物的分形效果越来越明显;增大电流密度（0.4～1.6 A·cm-2/sup>）,铜沉积物由致密向多分枝的开放型转变;延长沉积时间（大于等于5 min）,可获得含大量次级分枝铜的晶体;适当增加盐酸用量（0.05～0.20 mol/L）,铜沉积物枝晶尺寸显著减小。最后讨论了分形枝晶铜在碱性条件下氧化甲醇的电化学性能。}}     

矩阵奇异值分解及其在高维数据处理中的应用

矩阵奇异值分解能够实现对高维数据的局部特征提取及维数约减,在智能信息处理和模式识别研究领域具有十分重要的应用价值.首先分析了高维数据处理所面临的困境,并对常用的降维算法进行简单的归纳总结;然后阐述了矩阵奇异值分解的基本原理及其在维数约减和数据压缩中的物理意义;接着通过分析两种建立在奇异值分解基础上的PCA与LSA降维算法的数学导出过程,进一步给出了两者的等价性证明;最后总结了矩阵奇异值分解的优缺点,并且预测了高维数据处理技术未来的发展趋势.