查询词典 spectral analysis

Firstly, a quantitative relation about finite deformation and geometrical parameters which exhibit variation of laser spectral image was introduced. And then, particular emphasis was put on some important computer processing steps related to the analysis of spectral image, such as digitizing, segmentation, feature extraction and analytical algorithms. Lastly, some examples about an experiment of a ring subject to large diametral compression were given.

文中首先给出了有限应变和平均整旋角与反映频谱图像变化的几何参数之间的定量关系，然后着重介绍了与频谱图像分析有关的数字化、分割、特征提取和分析算法等重要的图像处理过程，最后给出圆环受径向荷载大变形实验的分析实例。

The stability and convergence for spectral methods and spectral element methods are presented, with the aid of the knowledge of functional analysis and calculus and with the help of the theorem of Lax-Milagram, the stability and convergence for steady problems, evolution equations and Navier-Stokes Equations are analyzed in detail.

利用泛函分析和微积分的基本知识，运用Lax-Milagram定理等，从理论上比较详细地分析了谱方法和谱元方法在定常问题、非定常问题以及求解Navier-Stokes方程方面的稳定性和收敛性问题，得出了Navier-Stokes方程谱近似的稳定性条件和收敛性准则。

This retrospective study included three medical institutes and fifty-nine patients of Alzheimer's disease. Based on spectral analysis, we calculated and presented spectral profile、power ratio、interhemispheric alpha coherence and intrahemispheric alpha coherence of individual EEG.

本研究收集三个专科医疗机构、59 位阿兹海默病患的数位脑波资料，利用频谱分析计算并呈现 spectral profile、power ratio、interhemispheric alpha coherence 和 intrahemispheric alpha coherence 等指标。

The main contents include: Some preliminary theory (introduction to Sobolev spaces and variational formulations for differential equations); finite element methods for one-dimensional elliptic problems; the construction methods for general finite elements; error estimates for interpolation operators and inverse inequalities for finite element spaces; a priori and a posteriori error estimates for the finite element method for high-dimensional elliptic problems; some typical spectral methods for partial differential equations; error analysis for the spectral approximation for some linear and nonlinear partial differential equations.

主要内容有：准备知识（Sobolev空间的基本概念和主要结果，微分方程的变分描述）；一维椭圆型方程有限元方法；一般有限元的构造；插值算子误差估计和逆不等式；高维椭圆型方程的先验、后验误差估计；求解偏微分方程的几类谱方法；线性与非线性问题谱逼近的误差分析等。

In order to find a powerful assistant computation tool for further analysis and design of multilayer optical coatings,an analytical model is mathematically established for accurate calculation of the first and second derivatives of the spectral coefficients of multilayer optical coatings with respect to layer parameters like thickness,real refractive index and extinction coefficient. It is based on the matrix theory of calculating the spectral coefficients of multilayer optical coatings and is achieved by perfectly using the trace operation of matrix.

为了寻找一种膜系深入分析与设计的有力辅助计算工具，从光学薄膜光谱系数的矩阵计算理论出发，基于对矩阵求迹运算的巧妙运用，从数学上建立了准确计算膜系光谱系数关于膜层几何厚度、实际折射率和消光系数等膜层参数的一阶和二阶偏导数的解析模型。

Missirlis in article [1]. At the same time, a sufficient condition for convergence of the PSD method is given to be compared when the coefficient matrix A of the linear system Ax = b is a symmetric, positively defective matrix. In §3.2, an example is given to state that the range of our sufficient condition is wider than theorem 3.3 of article [1]. On the other hand, following a.n analogous approach of [14] and starting the functional relationshipwe have a perfect analysis for the PSD method to converge and optimum valves for the involved parameters under different conditions.Under the assumptions that A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are real,we get necessary and sufficient conditions for the PSD method to convergence.The result is equal to theorem 1 of article [9].Under the same condition, we can see the optimal parameter and of corresponding spectral radius of thePSD method in [8]:(2)When A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are imaginary or zero,we get necessary and sufficient conditions for the PSD method to convergence.In chapter 3, the optimal parameter and of corresponding spectral radius of the PSD method are given by table 3.3. Moreover, under the assumption 0

Missirlis在文献[1]中定理3.3的不准确，同时给出了当线性方程组Ax=b的系数矩阵A为对称正定阵时，PSD迭代法收敛的一个充分条件与之比较，并且在§2.3中用实例说明了对于一部分矩阵而言本文得到的充分条件广于[1]中定理3.3的充分条件；另一方面，按照文献[14]的方法，我们从PSD迭代法的特征值λ与其Jacobi迭代矩阵B的特征值μ的关系式：出发，在不同条件下对PSD迭代法的收敛性和最优参数以及最优谱半径进行了完整的分析：(1)在系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为实数的条件下，给出了PSD迭代法收敛的充分必要条件，此结果与[9]中的定理1等价，此时最优参数及最优谱半径由[8]得：(2)第三章表3.3中给出了，当系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为纯虚数或零时的PSD迭代法的收敛范围和最优参数，并且我们可以得到当0

This thesis is divided into six parts. The first chapter is preface, the current status of research in the inverse problems for parabolic partial differential equations is reported; the second chapter is "regularization methods for numerical differentiation and their applications ", in this chapter we investigate many regularization methods from a viewpoint of regularization theory and algorithm, some applications in the inverse problems for parabolic partial differential equations are given; the third chapter is "spectral regularization methods". Based on Fourier analysis, within the framework of regularization theory, we apply the spectral methods to some ill-posed problems. Many numerical experiments are done in order to show the validity of the methods; the fourth chapter is devoted to wavelet dual least squares method and a revised wavelet method; in the fifth chapter,we combine finite difference method with method of lines and apply it to the backward heat conduction problem in time; in the sixth chapter "identification problems for unknown source ", the essence and the degree of two problems related to source identification are pointed out, at the same time, some numerical methods are reported.

本文分为六个部分，第一章前言简要分析了国内外抛物型偏微分方程反问题的研究现状；第二章数值微分的正则化及其应用从正则化理论和算法的角度出发，考察了许多正则化方法，还给出了数值微分在抛物型偏微分方程反问题的一些应用；第三章谱正则化方法是在Fourier分析的基础上，在一般正则化理论的框架下，给出了这种方法在各种不适定问题中的应用，数值实验表明谱方法是有效的；第四章研究了小波对偶最小二乘方法和改进的小波方法；第五章主要研究了有限差分方法结合线方法在时间反向热传导问题中的应用；第六章是未知源识别问题，主要指出了两类未知源问题的不适定程度和不适定本质，同时报告了一些数值方法。

Wavelength calibration coefficients were calculated through regression analysis after several ordinal numbers of CCD's pixels corresponding to Mercury-Argon Lamp's spectral lines were measured. The residuals of certain spectral lines were computed using the coefficients measured and the ones from factory, the degree of fitting for regression equation was estimated using the new coefficients. The final results validated the wavelength calibration model.

在测量了多条光谱线对应的CCD像元的序数之后，使用回归分析得到波长定标的系数，连同光谱仪出厂时的波长定标系数，计算出了两组定标系数在给定的一些谱线位置处的残差，并利用实验所得的系数对回归方程进行了拟合优度检验，结果表明波长定标模型是有效的。

According to the computational stability analysis conducted to the linear term time difference scheme in simple harmonic motion equation, one new semi-implicit integration scheme also is designed. By adopting a kind of revised time-explicitdifference scheme to these linear terms still included in spectral model governing equations, this defect of spectral model only partly used in semi-implicit integrating scheme, can be overcome to some degree.

以简谐振动方程中线性项时间差分格式对其计算稳定性影响为理论依据，本文设计了一种新谱模式半隐式时间积分方案，此方案通过对一般谱模式求解框架中那些隐含的线性项采用了一种显式修正的差分格式，可有效克服其国际谱模式半隐式时间求积方案实质上只是部分应用了半隐式差分格式的问题。

The analysis of deformation series, of spectral response function and of spectral density in the frequency domain.

8在变形序列的频域分析中，主要对表征序列的频时域特性函数一频谱响应函数和频谱密度进行分析。

Through comparing with the results by simulation to study the effects of theprojectile"s final velocity, the angle of rotation and the ballistic trajectory"s migration withdifferent projectile"s rotating speeds, different target"s moving speeds and differentpenetration angles.

通过比较数值模拟的结果来研究不同弹头转速、目标速度、侵彻角对侵彻过程中弹头最终速度、翻转角度和弹道偏移的影响。

I love stationery and all the accoutrement of writing.

我爱文具以及所有的书写的工具装备。