球面

A standard accessorial reflecting mirror was incorporated into the beam path of an interferometer to build up a autocollimating system for measuring the aspheric wavefront aberration of paraboloidal, ellipsoidal and hyperbolic mirrors with the method of aberrationless point.

为了检测抛物面、椭球面和双曲面镜，在干涉仪工作光路中加入一个标准辅助反射镜，组成自准直系统，采用干涉法中的无像差点法实现对非球面波像差的检测。

Compilation of the plane trigonometry and spherical trigonometry book, spherical trigonometry to solve some problems in, and first proposed the introduction of auxiliary ...

编撰了有关平面三角学和球面三角学的著作，解决了球面三角学中的若干难题，并首先提出引进辅助。。。

The model for calculating the stability of the resonator containing a laser rod with curvature ends was developed,which was based on the transfer matrix theory of Gauss beam. The results from the numerical simulations on some typical resonators indicate that the laser rod with curvature ends can expand the stable region of plano-plano,plano-concave and plano-convex cavity notability;despite the laser rod with curvature ends can improve the stability of above mentioned cavities,it costs the effective mode volume.

计算结果表明，对于几类典型的谐振腔如平平腔、平凹腔，球面端面激光棒可以显著的扩展强热聚焦作用下的稳定工作范围；球面端面激光棒在提高约束稳定性和热稳定性的同时，通常是以牺牲有效模式体积为代价的。

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。

The experiment result shows that the system can realize high precision measurement for big curvature radii of optical spheres.

实验结果表明：设计的光学球面自动测量系统可以对大曲率半径光学球面实现高精度测量。

The paper analyzes theoretically the influence law of length distortion after the reductions from measured side length to reference ellipsoid surface and then from side length on the reference ellipsoid surface to gauss perspective plane. It also discusses theoretical methods to restrict and the projection distortion influence.

从理论上分析了将实测边长归算到参考椭球面上和将参考椭球面上的边长归算到高斯投影面上的长度变形影响规律，讨论限制和减小这种投影变形影响的理论方法。

Let x be an immersion of a compact Willmore surface M into the n-dimensional unit sphere Sn. In this thesis we first consider the Willmore surfaces in the unit 3-sphere, and establish an integral inequality for the square of the length of the trace free part of the second fundamental form and the mean curvature.

令x是一个从紧致威尔摩曲面M到n 维单位球面Sn的浸入，在本论文中我们首先考虑3维单位球面中的威尔摩曲面并建立一个包含第二基本型式迹为零部份的张量长度平方与平均曲率之积分不等式。

Based on the aspheric off-axis reflection projection system, the Zernike free form surface was adopted to replace the aspheric surface in order to further optimize the system structure. The relationship between Zernike polynomial and Seidel aberration was utilized to improve the system performance.

基于非球面离轴反射式投影系统，提出了采用Zernike自由曲面取代非球面进一步优化系统结构的设计方法，并利用Zernike多项式与Seidel像差之间的关系，优化系统的成像性能。

The traditional separation of variables method is used to get the solution of SEW electric-fields when the parameter of the media changes abruptly.On the basis of these,WKB method is used to get the solution of SEW electric-fields when the parameter of the media changes gradually.

运用传统的分离变量法得到了媒质参数突变情况下球面电磁波场强的分布，在此基础上，模仿WKB方法推导出了媒质参数渐变情况下球面电磁波的场强分布。

Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin).

大 约在一百年以前，庞加莱已经知道，二维球面本质上可由单连通性来刻画，他提出三维球面（四维空间中与原点有单位距离的点的全体）的对应问题。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。