变换

In chapter 2 we recall the basic facts about Riemannian manifold and some notions of the transform theory on Riemannian manifolds.

首先，利用给定流形的向量丛上联络的存在性给出流形上的不可积分布上非完整联络的存在性证明，进而证明了次黎曼联络的存在唯一性，并以此为出发点研究了次黎曼流形中仿射变换、等距变换、共形变换和射影变换下的一些不变性质，给出了相应变换下的一些不变量。

In order to realize real-time control, the paper studied two kinds of closed-loop control structures such as based on scalar quantity and double closed-loop control structure, moreover established their control structure, then simulation to the double closed-loop control structure of voltage source type matrix converter. The simulation results indicate that reach the real-time control requests, the system dynamic response performance is good, the converter input output can be adjusted in the short time.

为实现电压源型阵变换器的实时控制要求，论文对基于标量控制和双闭环的两种电压源型矩阵变换器闭环控制结构进行了研究，分别建立了这两种闭环控制的控制结构，并且对电压源型矩阵变换器的双闭环控制结构进行仿真，仿真结果表明达到了实时控制的要求，系统的动态响应性能好，变换器的输入输出能在较短的时间内达到调节。

Typical methods of the first class consist of predictive deconvolution, normal moveout interconversion stacking, f-k transformation, tau-p transformation, parabola Radon transformation and beamforming. They can be called as seismography method based on the geometry. The second class methods, mainly bases on elasticity undulatory theory, through simulation or reversal development method forecast multiple, and then match it with the original data.

比较典型的方法有预测反褶积、正常时差变换叠加、f-k变换、τ-p变换、抛物线 Radon 变换和聚束滤波等，它们可以简称为基于几何地震学方法或"几何滤波类方法"；第二类主要是基于弹性波动理论的方法，通过模拟或反演方法来预测原始数据中多次波，继而从原始数据中匹配减去所预测的多次波。

An approach to image interpolation based on local fractal similarity transformation suitablefor complex images in natural scenes is described. Similarity transformation of rectangular image blocks are added and the extremem method in the function with two variables is used to obtain the optical similarity transformation.

提出了适用于复杂自然景物图像的基于局部分形自相似变换的图像插值方法，在常用的局部分形自相似变换基础上增加了矩形图像块的自相似变换，并采用二元函数的极值方法求最佳相似变换。

This paper analysised and researched some existing algebra feature extraction method such as KL transformation, singular value decomposition、 Fisher linear discriminant and optimal discriminant transformation. On the base of this、we expound a method which named uncorrelated optimal discriminant transformation to accomplish the face recognition.Uncorrelated optimal discriminant transformation is a improvement of Fisher linear discriminant and optimal discriminant transformation.

本文对一些现有的代数特征提取方法如KL变换、奇异值分解、Fisher线性鉴别以及最佳鉴别变换做了分析和研究，在此基础上我们提出使用具有统计不相关最佳鉴别变换的投影方法来进行人脸识别，它是由Fisher线性鉴别和最佳鉴别变换改进、完善而来的。

Via generalizing the Cauchy method we obtain a new method,called the modified Cauchy method.By means of this method we establish two bilateral _3ψ_3 and _4ψ_4 series summation formulae,two four-term summation and transformation formulae for unilateral _3φ_2-series and bilateral _3ψ_3-series,and two five-term summation and transformation formulae for unilateral _3φ_2-series and bilateral _3φ_3-series,which contain many known results as their special cases,such as non-terminating q-Saalschütz summation formula,Bilateral _6ψ_6 series summation formula of Bailey,non-terminating Watson transformation formula and some transformations of _3φ_2-series etc.

通过对Cauchy方法的推广，我们得到修正的Cauchy方法，采用这个方法分别得到两个双边的_3ψ_3和_4ψ_4基本超几何级数的求和公式、单边_3φ_~(2-)级数和双边_3ψ_(3~-)级数的两个四项求和变换公式和两个五项求和变换公式，它们包括许多已有的结果为特例，如非终止的q-Saalschütz求和公式、Bailey的very-well-poised双边级数_6ψ_6求和公式、非终止的Watson变换公式和一些关于单边_3φ_(2~-)级数的变换公式等。

According to the theory of wavelet transformation, the singularities of the ECG signal are corresponding to the series of maximum-minimum pairs. The algorithm detects the onsets of Q wave at the scale 3 detail and offsets of T wave at the scale 4 detail. So the duration of QT is calculated by onset of Q wave and offset of T wave.

根据小波变换的原理，心电中的奇异点在变换后将产生一个模极大值和模极小值对，在小波变换3尺度上检测出QRS波群的起点，在小波变换4尺度上检测出T波终点，从而确定QT间期。

At the end of the chapter, the influence analysis based on ridge combined principal components estimate has been discussed. Third, based on the B-spline method, it used the Atkinson method of the transformation parameter on the bond date and compared the results.

第三章选取上交所交易的国债的一组数据，以B-样条函数为基础，利用上一章的结果以及Box-Cox变换求解变换参数的Atkinson方法，进行数据变换，比较了变换前后的结果。

The paper first discusses the programming principles of how to exploit the parallelism underlying in sequential programs with the Parallel Programming Interactive Environment, explains the designing methods of the major functions and tools integrated in the PROFPAT (the PROgramming environment for the Fortran PArallel Transformer), and demonstrates its initial application process by the practice of interactive dependence analysis, loop parallelization, array privatization and unimodular transformation.

首先，本文从理论上深入探讨了如何借助并行程序设计交互环境帮助程序员分析和利用潜藏于串行程序中的并行性的原理，详细介绍了并行程序设计环境PROFPAT中集成的主要功能和主要工具的设计实现方法，并结合交互相关性分析、交互循环并行化变换、交互数组私有化变换、交互幺模变换等程序并行化分析、变换的初步应用实践，说明了这些工具和功能的应用方法。

On the basis of the relation, we will prove some useful properties of the discrete Zak transform which lay the foundation for the computation of discrete Gabor transform.

利用连续Zak变换和离散Zak变换的关系，证明了离散Zak变换的一些性质。为进一步研究离散Gabor变换建立了数学基础。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。