查询词典 singular conic

This article takes the teaching of conic sections as an example. By designing worksheets, teachers can introduce the historical material about conic sections to students. By way of using Apollonius' definition of parabola, ellipse and hyperbola, teachers can introduce the geometric aspect of "conic section" to students. By using the concept of " latus rectum " in Conics , we can connect "conic sections"-- representation of geometrical aspect, with "the equation of conic sections"-- representation of algebraic aspect to improving insufficiency of text books.

同时本文也试著从历史文本中寻找材料，简单举例说明数学教师可以如何应用这些史料在几何单元教学上，例如三角函数的正余弦定理，最后再以圆锥曲线的正焦弦为例，说明如何利用数学史料於此单元的教学，尤其是阿波罗尼斯的《锥线论》中对圆锥曲线的3个命题，将此3个命题的内容与意涵，尤其是正焦弦在圆锥曲线的几何意义上所扮演的角色，将其适当地融入教学中，将可使学生真正学习圆锥曲线的几何知识，而不再只是代数形式的几何知识。

An image conic can be the projection of either a planar conic or silhouette of a conicoid. We show that at least three images, taken from the same position with different camera orientations, of two planar conics, or two conicoids, or one conic and one conicoid, are needed for the calibration, and a closed-form solution can be obtained. Our new conic based calibration technique requires no knowledge of camera's orientations, and relies solely on image correspondences.

在不同的方位拍摄三幅或三幅以上图像，每幅图像至少包含两个空间平面二次曲线、或两个二次曲面、或一个平面二次曲线与一个二次曲面的投影，利用图像之间的二次曲线对应关系，可以确定摄像机的内参数矩阵，同时可以获得摄像机不同方位之间的旋转矩阵。

Chapter Five shows the case study of the beauty of math in high school teaching. Conic section is taken as an example to unearth the beauty of mathematics in from the following three aspects: 1. the language beauty of conic section reveals the external formal beauty; 2. the methodological beauty and the logical beauty of conic section reflect the internal rational beauty; 3. the beauty of mathematics in conic section reveals the new value in internal knowledge structure of textbooks. Moreover, the application of the beauty of mathematics in high school math teaching is also discussed from the following four points of view: the pursuit of conciseness, the construction of symmetry, the utilization of unity and the discovery of uniqueness.

首先，以圆锥曲线教学为案例来挖掘中学数学教学中的数学美，具体从三个层次探讨①圆锥曲线语言之美，是数学美的外在形式美具体展现；②圆锥曲线方法美、逻辑美，是深层次数学美的内在理性美的反映；③在圆锥曲线的教学过程中，利用其数学美处理教材，揭示内在知识结构的新价值；其次，提出数学美在中学数学学习中的具体案例运用，并具体从追求简洁性、构造对称性、利用统一性和发现奇异性四个方面来举例探讨。

Using algebraic methods which include extended Tanh-method,some new solitary solutions to the DBM and Log-DBM equation,such as singular solitary solutions,double singular peakon solitary wave solutions,double solitary wave solution with peakon and singular periodic solitary wave solutions are obtained..With the aid of an auxilitary function combined with the elliptic integral of the first kind,periodic solitary solution,singular and periodic singular solitary solutions can be obtained.

第三章利用扩展的Jacobi椭圆函数展开法研究了方程，并给出ZK-MEW方程的Jacobi椭圆函数解，特别的，当模数m→0和m→1时，其中一部分解退化为三角函数解和孤立波解；其次使用sn-cn拟设法，研究了K(k，s，1)方程，得到了k=s=3时的新的精确解，并在模数m→0和m→1时得到了丰富的三角函数和孤立波解。

By means of analyzing the noise error, it is proposed to use an algorithm of singular value decomposition total least squares to conduct the interharmonics estimation, namely taking the noise interference at both sides of the matrix equation into account simultaneously and solving the minimum norm problem by least square method under such condition. In the proposed algorithm by means of singular value decomposition of a new augmented matrix and by use of a simple and practical method to determine the number of principal singular value related to signal to noise ratio, the storage calculation of right singular matrix is performed, thus a more accurate frequency estimation of interharmonics can be obtained.

通过分析噪声误差，提出采用奇异值总体最小二乘(singular value decomposition total least squares，SVDTLS)算法进行间谐波频率估计，即同时考虑矩阵方程两边的噪声干扰，采用SVDTLS算法求解该情况下的最小范数解，通过对增广矩阵进行奇异值分解(singular value decomposition，SVD)，采用简单实用的与信噪比相关的主奇异值个数确定方法对分解的右奇异矩阵进行存储计算，得到了较精确的间谐波频率估计结果。

The problem of a curved rigid line or crack crossing the interface of the circular inclusion are studied by the principal part analysis method of Cauchy type integral equation. The singular stress index at the intersection and the singular stress at the angular regions near the intersection are obtained. The singular stress coefficients of rigid line at intersection and the stress intensity factors of crack at intersection are defined by using the singular stress.

利用Cauchy型奇异积分方程的主部分析方法对曲线型刚性线和曲线裂纹和圆夹杂界面的相交问题进行了研究，得出刚性线以及裂纹和界面交点处的奇性应力指数以及交点处角形域内的奇性应力，并利用奇性应力分别定义了刚性线在交点处的应力奇异因子和裂纹在交点处的应力强度因子。

In order to find a stable approximate solution of linear compact operator equation, the article introduces general theories about ill-posed problems, it bases on spectral theory of self-adjiont compact operators and the singular value decomposition for compact operators, avails singular system to give expression of the solution, and explains ill-posedness of compact operator equation roots in the property that the singular values trends to zero. Thereout, it is provided with theoretic support of building up regularization method by inducting regularization filter to weaken or filtrate the influence that the nature of the singular value being very close to zero has on the solutions stability.

为了得到线性紧算子方程稳定的近似解，介绍了不适定问题正则化的一般理论，以自伴紧算子的谱分析与紧算子奇异值分解为理论基础，利用奇异系给出了解的表达式，说明了紧算子方程不适定性的根源在于紧算子的奇异值趋于零的性质，由此通过引入正则化滤子函数来减弱或滤掉奇异值趋于零的性质对解的稳定性的影响，构造正则算子，从而提供了建立正则化方法的理论依据。

If singular value curve is convex in the coordinates 'k' of maximum peak of curvature spectrum, then the number of effective singular values is k; if singular value curve is concave in the coordinates 'k', then the number of effective singular values is k-1, and this rule is tested by the signal processing examples.

如果奇异值曲线在曲率谱最大峰值的位置坐标k处是凸出的，则有效奇异值的个数为k；如果奇异值曲线在k处是凹进的，则有效奇异值的个数为k-1，通过信号处理实例证实了这种结论。

Based on this result,the intrinsic reasons that singular value vector-based recognition methods have the low recognition accauracy are follows: singular value vectors of arbitrary two face images have not the equivalent basis space in general;there is no one-to-one correspondence between singular value vector and face image;singular value vectors are not separated.

进一步研究发现，导致基于奇异值向量人脸识别算法识别率低的根本原因是：不同人脸图像对应的奇异值向量所在的基空间不一致、奇异值向量与人脸图像之间并不存在一一对应关系、奇异值向量具有不可分割性。

Seeing image as a matrix, the method applied singular value decomposition on image matrix to decompose image information to a series of sub-spaces correspond to singular value and singular value vector, and then by reconstruction of image matrix using effective singular value to remove noising.

从矩阵的角度出发，通过对图像矩阵进行奇异值分解，将包含图像信息的矩阵分解到一系列奇异值和奇异值矢量对应的子空间中，然后通过有效奇异值重构图像矩阵达到去噪目的。

He became prime minister in 1997 and won international acclaim for his role in the Northern Ireland peace process.

他在1997年成为总理，并且因为在北爱尔兰的和平进程中发挥的作用受到国际社会的赞许。

Mixed Page Sorting Method Using the cuttable user model, this thesis proposes a mixed page sorting method by using cutted user model in server-side and complete user model in client-side.

隐私分级利用的混合式页面排序方法针对个性化搜索中搜索结果排序的问题，本文利用隐私可控开放的用户偏好模型，提出一个在客户端和服务器端分步进行的隐私分级利用的混合式页面排序方法。