矩阵的扩充与紧支撑正交小波

从矩阵的扩充出发给出了尺度因子a=4时紧支撑正交小波的一种构造方法，同时说明了补空间Wj在a=4时可以进一步分解为三个子空间的正交直和，实现Wj的细致化．     

凸规划的内椭球法与原始-对偶仿射尺度算法

对线性约束的凸规划问题给出了一个原始-对偶仿射尺度算法，比较了这种方法与“内椭球法”两种算法的关系，并证明了该算法的迭代复杂性是O(nL^2)。     

广义正交小波包

本给出一种任意伸缩矩阵正交小波包构造方法．该小波包是以频域形式给出的，献[1]所给小波包仅是其一特例．这样所得的小波包使得L^2(R^s)中小波基的选择更灵活，最后给出算例．     

基于专用芯片的高速实时FFT系统实现研究

研究了基于专用芯片的高速实时ＦＦＴ系统的点数和精度问题，分析了统一的ＦＦＴ算法与ＦＦＴ专用芯片的级联问题；定标算法与ＦＦＴ专用芯片的精度问题，提出了一种高速实时ＦＦＴ系统的实现方案和性能测试方法，并根据实测数据讨论了ＦＦＴ系统的精度。     

框架多分辨分析谱的研究

首先给出了一个可测集是框架多分辨分析(FMRA)谱的充分和必要条件,然后用一种新的方法刻画了包含于给定多分辨分析(MRA)的框架多分辨分析(FMRA)的谱.这是对H.O.Kim等人研究的改进.     

来自多尺度分析的R iesz基

不采用正交化方法,给出了来自多尺度分析的R iesz小波基的具体形式以及小波基母函数ψ(x)与尺度函数φ(x)的关系.建立了基于这种R iesz基的分解与重构算法.     

多晶Co膜退火前后磁滞标度行为研究

研究了多晶Co薄膜制备态与退火态的磁滞回线与标度行为，结果表明：对易轴方向A∝A0＋H^（0.67-1.00）Ω^0.90，对难轴方向A∝A0＋H^（1.75-2.50）Ω^（1.45-0.95），与理论计算（α=0．95，β=0．28（Heisenberg模型））作比较，A与H的关系符合的较好，A与Ω的指数关系有些差异，这种差异还有待进一步研究。     

Comments on scaling effect of reciprocity in BRDF study

Reciprocity principle is a common theory in electromagnetics and optics. It is also one of the general principles of the radiation transformation theory. However, in many remote sensing studies, this principle cannot be always supported by experimental data, especially when the scaling effect of the remote sensing image pixel is considered. The debate over the issue of whether the reciprocity principle can be used as a fundamental standard in evaluating the effectiveness of remote sensing observations has lasted for years. Using geometrical optics model, Li and Wan proved the existence of the scaling effect in applying the reciprocity principle to a remote sensing image pixel in 1998. In 2002, Snyder challenged Li's proof, and attempted to prove that reciprocity principle is universally valid without any scale limitation. In this paper, we will argue with Snyder's theory and point out that Snyder's theory had neglected an important condition used in Li's proof and, as a result, drawn the wrong conclusion. Here we will restate Li's condition in his demonstration and offer a further proof to verify that reciprocity principle cannot be applied unconditionally to the study of bi-directional reflectance distribution function (BRDF) of land surfaces in field or satellite remote sensing observation scale.     

Simple scaling relations in geodynamics： the role of pressure in mantle convection and plume formation

Scaling relations are important in extrapolating laboratory experiments to the Earth‘s mantle. In planetary interiors, compression becomes an important parameter and it is useful to explore scalings that involve volume. I use simple volume scaling relations that allow one to extrapolate laboratory experiments and upper mantle behavior, in a thermodynamically self-consistent way, to predict lower mantle behavior. The relations are similar to the quasi-har-monic approximation. Slabs and plates have characteristic dimensions of hundreds of kilometers and time constants of 100 million years, but the volume scalings predict order of magnitude higher values in the deep mantle. The scaling relations imply that the deep mantle is a sluggish system with ancient features. They imply irreversible chemical stratification and do not favor the plume hypothesis.