小波变换特征提取的复合材料损伤检测

论述了小波变换及其快速算法，基于小波变换的波形模量极大点来构造全局的相似性度量，并将此应用于复合材料损伤类型的检测     

中国股市行业板块的动态相关性建模——基于DCC—MVGARCH模型

相关性的讨论是现代金融分析的重要内容,行业板块的相关分析是组合投资的关键步骤。基于能刻画动态相关的DCC-MVGARCH模型对我国波动剧烈的六个股市行业板块进行了相关性研究,结果表明：十个板块相关性序列可看成常量,Pearson相关系数仍能刻画其相对大小,这为机构投资者按Pearson相关系数进行组合构建提供了实证依据;五个动态相关性序列是宽平稳而非严平稳的,适合采用随机过程建模以实现预测,另外动态相关性与时变波动率存在一定的关系,当波动率增强时,相关性有随之增大的趋势。     

一类微分-差分方程组的内禀对称和等价群变换

研究一类微分-差分方程组的对称和等价群变换.采取内禀的无穷小算子方法,给出了方程组的内禀对称和等价群变换.为结合抽象Lie代数结构,给方程完全分类提供了理论基础.     

基于数据变换的GM(1,1)残差修正模型在交通量预测中的应用

首先提出了一种变换,该变换既可以提高序列的光滑度,而且逆变换后相对误差保持不变,然后针对模拟残差时正时负的现象,又给出了一种变换,该变换可以将任意摆动序列变换为单调递增序列,最后给出了基于残差修正的GM(1,1)模型.将模型应用于实际,预测效果比较满意.     

极分解与广义*-Aluthge变换

首先给出了Hilbert空间上有界线性算子极分解的的若干性质.其次指出广义的*-Aluthge变换与*-Aluthge变换具有许多相似性质;例如,T_(α,β)^((*))=U|T_(α,β)((*))=U|T_(α,β)^((*))|当且仅当T是双正规的,即[|T|,|T*|]=0,其中对任意两个算子A和B,[A,B]=AB-BA.     

巧用图形变换 妙求路线极值

引例:(2012年四川凉山州卷)在学习轴对称的时候,老师让同学们思考课本中的探究题:如图1所示,要在燃气管道l上修建一个泵站,分别向A、B两镇供气.泵站修在管道的什么地方,可使所用的输气管线最短?你可以在l上找几个点试一试,能发现什么规律?     

傅里叶变换轮廓术中滤波窗方位选择研究

在傅里叶变换轮廓术频域滤波过程中通常采用不对称的汉宁窗滤波窗来提取基频信号,当投影呈二维变化的光栅条纹时,采用的滤波窗长短轴方向和载频方向不吻合,会导致被测物体的部分高频信息丢失,从而影响相位展开的难易程度和系统测量的精度。分析比较物体高度的分布与频谱的关系,通过旋转滤波窗使其短轴方向与载频方向一致,可以保留物体的高频信息,降低相位展开的复杂度,提高测量的精确度。计算机模拟和实物实验结果表明滤波窗旋转滤波可以避免相位展开在物体高度突变处的出错,有效地提高测量精度。     

Calculation of the photoelectron spectra under a scaling transform

By solving the time-dependent Schro¨dinger equation, the dependence of photoelectron energy spectra on the binding energy of targets, wavelength and the intensity of laser pulse is exhibited and a scaling law of kinetic energy spectra of both the direct and the rescattered photoelectrons is concluded. The scaling law provides a convenient tool to determine the equivalent photoionization process of various atoms or molecules in various laser fields. The verification of the scaling law by independent methods provides incontestable support to the validity of the scaling law.     

Extraction and verification of coherent structures in near-wall turbulence

According to the characteristics of coherent structures in near-wall turbulence, an accurate extraction and verification method is developed based on wavelet transform (WT) and correlation analysis in this paper. At first, the fluid field of a turbulent boundary layer is measured precisely in a gravitational low-speed water tunnel. On the basis of the distribution of the coherent structures, velocity data of three test points are selected and analyzed, whose dimensionless heights are 20.8, 33.5, and 42.6. According to the frequency range of power spectrum density (PSD), coherent and incoherent structures are both extracted from the original signals using continuous and orthogonal wavelet transforms. To confirm the validity of the extracted signals, the probability density function (PDF) of each extracted signal is calculated. The result demonstrates that the incoherent structures obey the Gaussian distribution, while the coherent structures deviate from the Gaussian distribution. The PDFs of the coherent structures and the original signals are similar, which shows that the coherent structures make most contributions to the turbulence. For further verification, a correlation parameter between coherent and incoherent structures is defined, which evidently proves the validity of the extraction method in this paper.     

Exact solutions of （3＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations

The symmetries and the exact solutions of the (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations, which describe atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space-time translations. Three types of symmetry reduction equations and similar solutions for the (3+1)-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space-time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the (3+1)-dimensional INHB system.