调和共轭

The numerical algorithm based on theories of projecting and Laguerre,such as homology,circular points and ω of absolute conic is established,an iterative elimination method is applied to boost the nonlinear problem solving.

通过调和射影及Laguerre定理的推论求解出平面圆环点的共轭虚像，利用平行六面体照片存在的三对圆环点的虚像，构造对无穷远平面绝对二次曲线的像ω的约束，使用辗转相除法求解非线性问题。

The present thesis will adopt some of these methods to study on conjugation including the conjugate chord, Conjugate Direction and conjugate diameter of Conics as well as the Conjugate Direction, Conjugate net, Harmonic conjugate and Conjugate minimal surfaces of surfaces.

本文利用到了其中的某一些方法，讨论了这个问题，其中包括二次曲线的共轭弦、共轭方向，共轭直径。曲面上的共轭方向，共轭网，调和共轭，共轭极小曲面等。

Then, it made full use of the theory of harmonic conjugate in projective geometry to calculate the inner parameters of camera.

然后充分利用射影几何调和共轭的理论求取摄像机的内参数。

Two pairs of vanishing points of orthogonal directions from each image are obtained by using the concept of cross ratio and harmonic conjugate in projective geometry and the orthogonal property of the two diagonals on a square. All intrinsic parameters are calculated linearly after capturing the template from at least three shooting angles. Errors of edge detection and line fitting are avoided because the method does not require image matching.

充分利用了射影几何中交比和调和共轭的知识以及正方形模板对角线相互垂直的性质，根据一幅模板图像可以得到两组相互正交的消失点连线，在至少三个不同方向拍摄的图像上线性求解出摄像机的所有内部参数。

The main results are:(1) the L1 boundedness of the Cesaro means operator of the harmonic expansions on the unit sphere with reflection-invariant measures is proved, and the characterization of the convergence index is given; for the points not in the planes with singularities, the pointwise convergence is also proved; these results are the generalizations of those both for the classical spherical harmonic expansions and for the Jacobi expansions;(2) Using the differential-reflection operators of Dunkl type, the uncertainty principle of a class of Sturm-Liouville operators is established, and as consequences, the uncertainty principles of some well-known classical orthogonal expansions such as Jacobi, Hermite and Laguerre expansions are obtained;(3) by introducing the Cauchy-Riemann equations in terms of the differential-reflection operators of two variables, the harmonic analysis of the extended Jacobi expansions is studied; the results include the Lp boundedness and the weak-L1 boundedness of the conjugate extended Jacobi expansions; specially, for some indexes p smaller than 1, the basic theory of the related Hardy spaces is established.

主要成果有：（1）证明了带有反射不变测度的球面调和展开蔡沙罗平均算子的L1有界性，给出了收敛指标的特征刻划，对不在奇性平面上的点，还证明了点态收敛性，这些成果同时推广了经典球面调和展开和雅可比展开的结果；（2）利用Dunkl型的微分-反射算子建立了一类斯特姆-刘威尔算子的测不准原理，并由此得到一些著名的经典正交展开如雅克比展开、赫米特展开和拉盖尔展开的测不准原理；（3）利用由两个变量的微分-反射算子定义的柯西-黎曼方程组来研究扩展雅克比展开的调和分析，证明了共轭扩展雅克比展开的Lp有界性和弱L1有界性，特别是对小于1的一些指标p，建立了相应的哈代空间的基本理论。

Using the relations between harmonic conjugation elements,we can determine the relations between polar point and polar line more widely.

度量几何中圆的切割线之间所确定的数量关系，推广到射影几何里一般二次曲线中，利用调和共轭元素之间的关系，更广泛地确定了极与极线的相互关系，着重介绍了二次曲线的度量性质与射影性质的内在联系。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失