变换点

In the geometry of matrices, the points of the associated space are a certain kind of matrices, there is an arithmetic distance of two points in this space, and there is a transformation group acting on this space. Two distinct points is said to be adjacent if their arithmetic distance is one or minimal.

在矩阵几何中，空间中的点是某一类矩阵，两点间存在一种算术距离，还有一个变换群作用在这个空间上，两个不同的点间的算术距离为1或最小时称这两点是粘切的。

We introduce the general sigma point selection framework, and give two kinds of efficient methods: a reducing the computing complexity by decreasing the number of the sigma point; b scaling the sigma points to influence the effects of the higher order moments, then improve the accuracy of the UT; c Convergence analysis of the UKF, when used as an observer for nonlinear deterministic discrete-time system, is presented. Based on the UKF that captures the posterior mean and covariance accurately to the second or third order term (in terms of Taylor series expansion) for any form of nonlinearity, sufficient conditions to ensure local asymptotic convergence are established.

论文介绍了sigma点的一般选取规则，并给出了两种有效的方法：a通过减少sigma点集合的元素的数目来减少计算复杂度，b通过增加参数来逼近泰勒展开的高阶项，从而提高UT变换的精度；c论文研究了UKF算法应用于非线性确定性离散时间系统时的收敛性问题。

So the conformal transformation model for the image rectification is taken as a beginning to deduce the relation between the accuracy of an arbitrary point and the accuracy of control points, besides, according to such relation, the inverse distance power method is used to give the spatial interpolation for the image rectification accuracy, which also achieved the interpolation value in x or y directions.

并以相似变换作为影像纠正的基本模型，推导了纠正后任意点精度与控制点精度的关系，基於此选择采用空间插值方法，插值影像纠正后任意点不同方向上的点位的精度。

In order to solve the problem,We proposed a simple formula for computing paraxial travel time of single-way wave operator. The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential manifold. The travel time are expressed as polynomials of the horizontal offset between the two points, and the single-square-root operator in frequency-wavenumber domain are expressed as polynomials of wavenumber. Coefficients of travel time polynomials and that of single-square-root operator are related each other and calculated by Lie algebraic integrand, exponential map and the saddle-point method.

针对此，基于时间空间域到频率波数域和向量场到指数流形上的正反变换，提出了计算单程波算子旁轴走时的简便公式，将走时表示成空间变量(地面点到地下相点的水平距离)的多项式，将频率波数域单平方根算子表示成波数的多项式，运用Lie代数积分、指数映射和鞍点法将走时多项式的系数与单平方根算子的系数联系起来，运用单平方根算子的系数计算走时多项式的系数。

In order to solve the problem, We proposed a simple formula for computing paraxial travel time of single-way wave operator. The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential as polynomials of wavenumber. Coefficients of travel time polynomials and that of single-square-root operator are related each other and calculated by Lie algebraic integrand, exponential map and the saddlepoint method.

针对此，基于时间空间域到频率波数域和向量场到指数流形上的正反变换，提出了计算单程波算子旁轴走时的简便公式，将走时表示成空间变量（地面点到地下相点的水平距离）的多项式，将频率波数域单平方根算子表示成波数的多项式，运用Lie代数积分、指数映射和鞍点法将走时多项式的系数与单平方根算子的系数联系起来，运用单平方根算子的系数计算走时多项式的系数。

By employing the Jordan-Wigner transformation and a modified mean field method, we are able to determine its ground-state quantum phase diagram approximately. The chapter IV is the main part of this Thesis. It contains the main innovations in our work. We propose and study in detail a S=1 Ising chain with the interplay of single-ion anisotropy and dimerization. The main results and innovations are the following: We show that the total number of the zero-component of spins at each site is a conserved quantity. This quantity, which may intuitively called as hole's quantum number, is hidden in the system. We show further that the hole's number in the ground-state is zero; By using the Jordan-Wigner transformation, we map this model onto a series of subsystems described by the spin 1/2 dimerized transverse Ising model. We solve the subsystems exactly, by presenting the exact wave functions and spectra;We show that this system exhibits a series of quantum phase transitions by varying the dimerization strength. We determine the quantum critical points exactly. We also show that the criticality is the same as that of the uniform S = 1/2 transverse Ising chain.

第四章是本文的重点及主要创新内容，我们具体研究了自旋为1的在横向单离子晶格场中的一维二聚化Ising链，我们得到的主要结果和创新之处是：(1)证明了这一模型具有一种隐藏的对称性，即自旋第三分量为零的格点数目是一个守恒量，并证明基态出现在空穴数目为零的子空间中；(2)利用Jordan-Wigner 变换将此模型变换到一系列自旋为1/2的横磁场中的二聚化Ising 模型，并给出了相应严格的波函数及能谱；(3)我们发现系统的基态随着二聚化强度的变化将呈现出一系列量子相变，我们得到了量子临界点的精确位置，并证明其临界性质与自旋为1/2的横磁场中的均匀Ising 链中的临界行为属于同一普适类。

First of all two-dimensional bar code of the positioning and segmentation algorithm using Hough Transform and Sobel edge detection of the bar code images collected from the original image to effectively separate and then analyzes the barcode image through the optical system of the noise model, put forward a Calculation of point spread function of standard deviation of the algorithm uses Flourier transform adaptively select the threshold to remove noise caused by invalid border, bar code and thus be the basic module.

首先探讨了二维条码的定位与分割算法，利用Hough变换与Sobel边缘检测把条码图像从原始采集的图像中有效地分割出来然后分析了条码图像经过光学系统的噪声模型，提出了一种计算点扩展函数标准方差的算法采用Flourier变换自适应地选取阈值去除噪声导致的无效边界，从而得到条码的基本模块。

The phase conversion process has been discussed on the basis of three working ways of inductance loading in TEM-Ⅱtransmitter, and then several problems have been put forward.

分析了IGBT全桥变换电路实现功率变换时感性负载上电压、电流的瞬态变化规律及无功功率的释放回路，对TEM-Ⅱ型瞬变电磁法发射机阻感性负载三种工作方式的换相过程作了深入全面的讨论，进而提出几点注意事项。

Presence of multiples leads to poor quality in main stages of offshore seismic data processing, such as velocity analysis, stacking and imaging. Three basic multiple attenuating methods are reviewed; and a more effective multiple attenuator is achieved by joining them. As the first step, shot or receiver records are extrapolated by wave-equation datum algorithms. The extrapolation will establish a model of waterbottom multiples. Waterbotton multiples will then be removed by subtracting the extrapolated records from the original records. After that, predictive deconvolution is used to attenuate the multiples created by source ghost. Finaly, RADON transformation is adopted to separate peg-leg multiples and residual water-bottom multiples from the original data in the τ-p domain.

地震勘探尤其是海上地震勘探中存在着各类多次波，由于多次波的存在严重影响了速度分析、叠加、偏移成像等地震资料处理，海上多次波主要有全程多次波和层间多次两大类，为了压制海上不同类型的多次波，本文首先分析波场外推、预测反褶积和拉东变换衰减不同多次波的理论基础，然后联合采用这些方法，分别衰减全程多次波和层间多次波；即：首先对炮记录或者接收点记录进行波场外推，建立海底多次波模型，预测并减去全程多次波，然后利用预测反褶积衰减掉周期性明显的多次波，最后将数据转换到τ-p 域，用拉冬变换根据同一时间多次波和有效波在速度等方面的差异，进一步分离层间多次波和剩余的全程多次波，并在该域中切除分离出的多次波，从而实现联合多次波衰减处理。

The power electronic converter topologies for power point tracking and voltage conversion are studied in this paper.

论文研究了电力电子变换器拓扑技术在最大功率点跟踪及电压变换方面的应用。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。