查询词典 laplace transform

It is shown that many of the existing integral transforms (including their logically equivalents) such as chirplet transform, dispersion transform, wavelet transform, chirp-Fourier transform, short-time Fourier transform, Gabor transform, Fourier transform, cosine transform, sine transform, Hartley transform, Laplace transform, z transform, Mellin transform, Hilbert transform, autocorrelation function, cross-correlation function, and the energy and mean of a signal, can each be considered as a special case of the FMmlet transform with specific parameters. In fact, an inventory of subspaces of FMmlet transform runs into countless numbers. The subspaces mentioned above are merely a few among a zoo of subspaces. They are essentially obtained by cutting the transform space of FMmlet transform at different positions, and can be likened to the computed tomography in medical diagnosis. Through these subspaces we actually see different slices or profiles of the FMmlet transform.

将现有诸多变换置于统一的 FMmlet 变换中加以审视，发现 chirplet 变换、频散变换、小波变换、 chirp-Fourier 变换、短时 Fourier 变换、 Gabor 变换、 Fourier 变换、余弦变换、正弦变换、 Hartley 变换、 Laplace 变换、变换、 Mellin 变换、 Hilbert 变换、自相关函数、互相关函数、能量和均值等，均为 FMmlet 变换在其参数取特定值时的特例；上述诸变换之间的差别，主要在于变换空间的维数有别，以及在不同空间维上取值的不同；这些变换有如医学诊断中的 CT，均由压缩 FMmlet 变换域空间所致，可以说我们通过这些变换看到的，是 FMmlet 变换的不同剖面。

The Laplace Transform; The Region of Convergence for Laplace Transforms; The Inverse Laplace Transform; Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot; Properties of the Laplace Transform; Analysis and Characterization of LTI Systems Using the Laplace Transform; System Function Algebra and Block Diagram Representations; The Unilateral Laplace Transform..

教学内容：拉普拉斯变换；拉普拉斯变换收敛域；拉普拉斯反变换；由零极点图对傅立叶变换进行几何求值；拉普拉斯变换性质；常用拉普拉斯变换对；用拉普拉斯变换分析和表征线性时不变系统；系统函数的代数属性与方框图表示；单边拉普拉斯变换。

The Laplace Transform; The Region of Convergence for Laplace Transforms; The Inverse Laplace Transform; Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot; Properties of the Laplace Transform; Analysis and Characterization of LTI Systems Using the Laplace Transform; System Function Algebra and Block Diagram Representations; The Unilateral Laplace Transform.;Roth rule ;Signal Flow Graphs.

教学内容：拉普拉斯变换；拉普拉斯变换收敛域；拉普拉斯反变换；由零极点图对傅立叶变换进行几何求值；拉普拉斯变换性质；常用拉普拉斯变换对；用拉普拉斯变换分析和表征线性时不变系统；系统函数的代数属性与方框图表示；单边拉普拉斯变换；罗斯准则；信号流图。

Mastery: The Laplace Transform, The Region of Convergence for Laplace Transforms, The Inverse Laplace Transform, Properties of the Laplace Transform, Some Laplace Transform Pairs; Analysis and Characterization of LTI Systems Using the Laplace Transform, System Function Algebra and Block Diagram

基本要求：掌握拉普拉斯变换定义，拉普拉斯变换收敛域，拉普拉斯反变换，拉普拉斯变换性质，用拉普拉斯变换分析和表征线性时不变系统，系统函数的代数属性与方框图表示；熟悉常用拉普拉斯变换对，单边拉普拉斯变换；了解由零极点图对傅立叶变换进行几何求值。

Mastery: The Laplace Transform, The Region of Convergence for Laplace Transforms, The Inverse Laplace Transform, Properties of the Laplace Transform, Some Laplace Transform Pairs; Analysis and Characterization of LTI Systems Using the Laplace Transform, System Function Algebra and Block Diagram Representations;Roth Criterion;Mason Equation of the Signal Flow Graphs.

基本要求：掌握拉普拉斯变换定义，拉普拉斯变换收敛域，拉普拉斯反变换，拉普拉斯变换性质，用拉普拉斯变换分析和表征线性时不变系统，系统函数的代数属性与方框图表示，罗斯判别，信号流图的梅森公式；熟悉常用拉普拉斯变换对，单边拉普拉斯变换；了解由零极点图对傅立叶变换进行几何求值。

Applying the De Caen"s inequality of sum of the squares of the degree and Cauchy"s inequality, we obtain a strict lower bound and a strict upper bound of the largest Laplace eigenvalues only in terms of vertex number of a unicycle graph. Applying the Laplace matrix theorem of trees, we obtain an upper bound of the second smallest Laplace eigenvalues of a unicycle. Extremal graph whose second smallest Laplace eigenvalues reach the obtained upper bound is determined. We also obtain an upper bound of the second largest Laplace eigenvalues in terms of vertex number of the largest connected branch of unicycle graph, and obtain a theoretical method to calculate the second largest Laplace eigenvalues of unicycle graph. We obtain an upper bound of any Laplace eigenvalues in terms of vertex number of a unicycle graph. We also obtain the distribution of Laplace eigenvalues in the inter [0,n] in terms of the matching number.

本文得到了以下几个方面的结果： 1、利用图度平方和的De Caen不等式和Cauchy不等式给出单圈图的最大Laplace特征值仅依赖于顶点数的严格的上下界；利用树的Laplace理论给出了单圈图次小Laplace特征值的一个上界，并刻画了达到该上界的极图；利用子图的连通分支的顶点个数给出了单圈图次大Laplace特征值的一个上界，并给出了单圈图次大Laplace特征值一个理论上的一个求法；利用单圈图的阶数给出了其一般Laplace特征值的一个上界；利用单圈图的匹配数给出其Laplace矩阵谱在区间[0，n]上的分布情况。

The Laplace Transform; The Region of Convergence for Laplace Transforms; The Inverse Laplace Transform; Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot; Properties of the Laplace Transform; Analysis and Characterization of LTI Systems Using the Laplace Transform; System Function

教学内容：拉普拉斯变换；拉普拉斯变换收敛域；拉普拉斯反变换；由零极点图对傅立叶变换进行几何求值；拉普拉斯变换性质；常用拉普拉斯变换对；用拉普拉斯变换分析和表征线性时不变系统；系统函数的代数属性与方框图表示；单边拉普拉斯变换。

In the ***, all types and fundamental principles of Radon transform are summarized systematacially. This *** starts from the general linear Radon transform, and then researches how to use the damped least square method to find the solution of the forward transform. However, the least squares smoothing effect will lead to a certain degree of trails in the data of Radon domain, which led to the application\'s limitations. After that the implementation in Radon domain and relative merits of linear Radon transform, parabolic Radon transform and polynomial Radon transform which have time invariance are introduced, the conjugate gradient method that can solve numerical solution is also given. And then the high resolution Randon transform is discussed, it introduces the regularization theory and Bayes principle into inversion, which successfully remove the negative affect caused by discrete Radon transform. Finally, we introduce the optimal weighting similar coefficient Radon transform, which adapt to the time variant quality of hyperbolic Radon transform.

本文系统总结了Radon变换的各种类型及其基本原理，从τ- p变换(即一般线性Radon变换)出发，研究利用阻尼最小二乘平方法求解其正变换，但是最小平方法的平滑作用会导致Radon域数据存在一定程度的拖尾效应，给这种方法的应用带来了很大的局限性；然后先容了具有时不变性的线性、抛物和多项式Radon变换在频率域的实现及其优缺点，给出了求解其数值解的共轭梯度算法；接着讨论了高分辨率Radon变换，它把正则化思想和贝叶斯原理引进到了反演中，很好的克服了离散Radon变换产生的截断效应对结果的不利影响；最后先容了适应双曲Radon变换时变性质的高分辨率最优相似系数加权Radon变换。

Laplace transform has broad application of space, Laplace transform the complex function addressed in practical applications are very important, LaPlace integral transformation in pure mathematics and applied mathematics are in a powerful tool.

拉普拉斯变换有着广阔的应用空间，拉普拉斯变换在复变函数论及实际应用中都很重要，拉普拉斯积分变换在纯数学以及应用数学中都是一个有力的工具。

Since Leptokurtosis, skewness and fat-tail are always used to depict market risk, this paper introduces the improved Laplace distribution to risk management of stock portfolio. Empirical results show, improved Laplace distribution and asymmetric Laplace distribution are similar for estimating Leptokurtosis, while improved Laplace distribution is better for estimating skewness.In order to analyze the correlation between return distribution and volatility, the thesis uses ARCH-M Models to simulate the return series of China's Stock Market and developed markets ao as to discover the relation between investment return and time-varying risk.

对尖峰、厚尾、偏态的刻画有助于正确估计市场风险，本文将改进型Laplace分布引入到股票组合的风险管理中，实证结果发现，改进型Laplace分布和非对称Laplace分布对尖峰、厚尾的刻画效果接近；而非对称Laplace分布对负偏性考察不足，改进型Laplace分布的拟合结果能够准确地反映股指收益的负偏态，这也正是改进型Laplace分布相对于传统的非对称Laplace分布的优势所在。

In the chapter 2, the theoretic knowledge about the photosensitive resin and the grinding tools was firstly introduced.

第二章阐述了光固化树脂结合剂磨具的相关理论研究。

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