查询词典 formula transformation

The main contents are as follows:(1) Derive recursive Householder transformation formula for transforming the original rectangular matrix column by column into upper triangular matrix, solve the problem of fast upper triangularization of columnvariable matrix.

主要开展的工作有：（1）、导出长方矩阵逐列上三角化的递推Householder变换公式，解决了可变列矩阵的快速上三角化问题。

It is shown that two-component Wadati-Konno-Ichikawa equation, i.e. a generalization of the wellknown WKI equation is obtained from the motion of space curves in Euclidean geometry, and it is exactly a system for the graph of the curves when the curve motion is governed by the two-component modified Korteweg-de Vries flow. At the same time, a n-component generalization to the WKI equation is obtained. Also, starting from the motion of curves, mKdV and its symmetry recursion operator is exhibited explicitly; two- and n-component mKdV systems are obtained. It is shown that WKI systems are gauge equivalent to mKdV systems. The two-component WKI equation admits an infinity number of conservation laws and a recursion formula for the conserved densities is given by considering an eigenvalue problem together with introducing an appropriate transformation.

在二维和三维欧氏空间上，我们从空间曲线运动出发，推导出了mKdV方程以及它的用以生成高阶对称的递归算子；推导出了多元mKdV方程以及二元和多元WKI方程，并证明了WKI系统和mKdV系统的规范等价性；尔后，通过考虑特征值问题，并引入一个恰当变换，给出了二元WKI方程的用以计算无穷多守恒密度的递归公式，从而证明了二元WKI方程的守恒可积性；系统地分析了两种mKdV方程的Painleve性质，并分别给出了两种不同形式的二元和n元mKdV方程的共振点出现的规律。

The main contents is: analyzing some detection method to moving target nowadays; particular studying the principle of detection moving target in SAR; analyzing SAR imaging theory and the echo model of moving target; discussing conventional SAR imaging , the movements of target cause the changes of doppler mass center and regulable frequency, and the changes cause effect the imaging result; introducing the estimation method of doppler parameter; analyzing theory of DPCA, derivating the formula needed, and validating it's validity and practicability through simulation; advancing the improved DPCA algorithm that combine the advantage of DPCA and ATI, and validating it through computer simulation; using the revision algorithm to range ambulate based on keystone transformation, and validating it through computer simulation; discussing the compensation art of SAR imaging.

主要内容有：分析了现有的一些动目标的检测方法；详细研究了SAR动目标检测的原理；分析了SAR成像理论和运动目标的回波模型；探讨常规SAR成像时，目标运动引起的多普勒质心和调频率变化，以及这些变化对成像结果的影响；介绍了多普勒参数的估计方法；分析了DPCA原理，推导所需要的基本公式，并仿真验证其有效性和实用性；提出了结合DPCA和ATI优点的改进DPCA算法，并仿真验证；探讨了SAR成像中的运动补偿技术。通过对仿真结果的分析，本文提出的方法具有一定的指导意义和参考价值。

Firstly, based on the force acting on a single-particle, establish a discriminant formula of the sand threshold, and prove that the sand threshold belongs to the cusp catastrophe. Then establish the basic equation of the cusp catastrophe using coordinate transformation and catastrophe theory. Finally, while particle Reynold number and equivalend diameter are the state variables and Shields parameter is the control variables, we can obtain the model of cusp catastrophe of sand threshold, putting those variables into the basic equations of the cusp catastrophe. The model is derived from the mathematics, which has a certain mathematical theory foundation.

首先从单颗沙粒受力分析出发，建立沙床沙粒起动条件判别公式，进而证明了风沙起动属于尖点型突变；然后通过坐标变换和突变理论建立了尖点突变的基本方程；最后本文选择颗粒雷诺数和等效粒径作为控制变量，希尔兹参数作为状态变量，并把它们代入尖点突变的基本方程，经过拓扑变换得到风沙起动的尖点突变模型，并与前人的公式及实验数据进行比较。

There are the following several points different from existing finite element eigenanalysis methods for asymptotic fields near the crack tip:(1)The jump-off that educes the formula is different.(2)The form of the element is a ad hoc element.(3)The singular transformation technique is not used in the assumption of displacement fields surrounding the wedge tip.

该方法与过去原有求解裂纹端部近似场的有限元特征分析方法有几点不同：(1)导出公式的出发点不同；(2)单元形式为高次内插单元；(3)尖劈端部邻域内的位移场假定没有采用奇异变换技术。

By means of singular model transformation technique, special Lyapunov-Krasovskii functional approach, similar Leibniz-Newton formula and linear matrix inequality concept, some new stability conditions are derived for above systems.

应用奇异模型转换技巧、特殊型Lyapunov-Krasovskii泛函数方法、相似型Leibniz-Newton公式、线性矩阵不等式观念针对上述类神经网路系统，提出新稳定测试准则。

In the third part, we study an application of stereographic projection transformation in statistics, deriving Box-Muller formula (use two independent uniform random number to generate two independent standard normal random number) and spherical symmetric distribution (a product of a positive random variable and a random vector with uniform distribution) in multivariate statistical analysis.

第3章，研究了球极投影变换在统计中的应用，通过球极投影变换获得了利用两个相互独立的均匀随机数生成两个相互独立的标准正态随机数的Box-Muller公式以及多元统计分析中的球对称分布（一个正的随机变量和一个与之相互独立的均匀分布的随机向量的乘积）。

From the formula for the field strength of a point charge,by means of the transformation of the field strength tensor in the special theory of relativity,the laws of electrostatic field and magnetic field of steady current s are derived in this paper to give the students a better understanding of the consistency of electric field and magnetic field.

从点电荷的场强公式出发，根据狭义相对论中场强张量的变换，推导出了静电场和稳恒电流磁场的诸定律，使学生对电场和磁场的统一性有了更为深刻的认识。

To a one-dimension case, the solution to the distribution of non-monotone function is given; to a two-dimension case, the transformation of random variable and the computation formula of its probability density are given when inverse transform has one value and multiple value, meanwhile, several deductive conclusions are obtained.

从一维与二维随机变量函数的分布的一般求法出发，对一维情形，给出了当随机变量函数非单调时其分布的求法；对二维情形，用随机变量变换的方法分别给出了当逆变换单值与多值时其分布密度的计算公式，并得到了若干推论。

As part of the contents of this triangle involving more to the formula, with a corresponding change it, in solving problems, how to destinations such as triangular constant transformation trigonometric function is the key to learning paper presents some problems to resolve Trigonometric function methods and techniques, hope to play a role.

由于三角这部分内容所涉及到的公式比较多，相应地变化也就多，在解题中，如何有目的地进行三角恒等变换是学好三角函数的关键。本文介绍一些解决三角问题的方法和技巧，希望能起到抛砖引玉的作用。关键词三角函数；方法；技巧

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。