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Firstly, we consider the problem of the representation formula for the transition probability density of a right process under Girsanov transform. Secondly,we consider the problem of the MEMMs (minimal entropy martingale measure)for Markov switching Levy processes, and justify that the minimal entropy martingale measure is obtained by some regime switching Esscher transform. At last,we consider the problem of the invariant measure and the ergodic property of recurrent right processes. This paper includes 5 chapters.

首先，我们考虑了满足一定条件的右过程在Girsanov变换下的转移概率密度的表达式问题；其次，我们考虑了由Markov调制的Lévy过程的最小相对熵鞅测度的问题，证明了其最小相对熵鞅测度是某个状态转换Esscher变换；最后，我们考虑了右过程的不变测度及其遍历性的问题。

The main results are as follows:(1) Based on the basic ideas of Hough transform and random Hough transform, a new method for the detection of general quadric curves was proposed, which used the representation of a family of quadric curves passing through four random selected points.

取得的主要结果如下：（1）基于Hough变换和随机Hough变换的主要思想，利用过四点的二次曲线簇表示，提出了一种一般二次曲线的检测方法。

The application of Fourier transform and wavelet transform to signal fault diagnosis was mainly concerned.

研究了傅里叶变换与小波变换在信号故障诊断中的应用。

Number Theoretic Transform; Integer transform; Fermat number transforms; Discrete Image data

数论变换；整型变换； Fermat数变换；离散图象数据

This paper analyzes the property of FNT, the characteristics of Kernel Matrixes and the relationship between Kernel Matrixes of two-dimensional Fermat number transform whose modulus are odd prime and image data, and presents and proves the deduction of the theorem which demonstrates the relationship among different transform matrixes corresponding to different roots of unity under the same odd prime modulus of FNT, and reveals the essence of FNT whose modulus are odd prime.

分析二维Fermat数变换性质、正反变换核的特点、二维模为奇素数的二维Fermat数变换正反变换核以及与图像数据的关系，提出了不同单位根对应变换矩阵间的关系定理的推论，证明了该推论中模为奇素数的二维Fermat数变换的不同单位根对应的变换矩阵之间的关系，揭示了模为奇素数的二维Fermat数变换的本质，在构造离散图象数据Fermat数变换时为单位根的选择奠定了理论基础。

On one hand, it overcomes Fourier Transform that is not equal to analyzing unsteady signal and transient signal; On the other hand, it overcomes Fourier Transform that the scale of window of time domain and frequency domain is fixedness.

因此，本文通过运用小波分析对这些特征信息进行分析提取，结果表明利用暂态过程中含有的高频信息，能够有效实现故障选线。

Duplicate Layer and transform it with Edit ?Transform ?Flip Horizontal.

做法是找一幅竹子的大图，使用矩形选区工具选出合适大小，复制并粘贴到新的图层内。

This thesis discusstion these contents, optics of lens characteristic, Fourier transform lens's performance index,design characteristic, structure type, etc. especially, do a lot work in quadruplet full symmetrical double far distance fourer transform lens aspect.

论文对光学透镜的傅里叶变换特性，傅里叶变换透镜的性能指标、设计特点、结构类型等作了研究，尤其是在四组元全对称双远距傅里叶变换透镜方面做了大量的工作。

The use of Fourier transform and analysis, as well as introduce the principle of Fourier transform.

详细说明：傅立叶变换的运用与分析，以及对傅立叶变换的原理介绍。

Detailed analysis and Fourier Transform on the principle and the fast Fourier transform analysis and method introduced.

详细分析和讲解傅立叶变换的原理和快速傅立叶变换的分析与实现方法介绍。

Pachomius manual labour was organized as an essential part of the monastic life; and since it is a principle of the monks as distinguished from the mendicants, that the body shall be self-supporting, external work of one sort or another has been an inevitable part of the life ever since.

根据圣pachomius体力劳动组织作为一个重要组成部分寺院生活；以来，这是一个原则的和尚，作为有别于乞丐，该机构应自支撑，对外工作的这种或那种已一个必然的一部分，生活至今。

In order to study the effects of parametrical rolling on the ship movement and tilts, in allusion to ship's navigating in regular following waves, the equation of ship rolling motion is transformed into normal Mathieu equation by proper variable replacement when strong parametrical excitation in restoring moment varied according to sine or cosine wave.

为研究参数横摇对船舶运动和倾覆的影响，通过对船在规则波上随浪航行时，恢复力矩中出现的1个以正余弦规律变化的强参数激励项进行适当的变量置换，将船舶的横摇运动方程转换成标准形式的Mathieu方程。