球面

The formula can also be applied to computing convex polygon on ellipsoid.

因此，该公式的适用范围可由椭球面三角形推广至椭球面上任意凸多边形。

Now there is a hyperboloid, a concave ellipsoidal surface and a convex sphere surface need to be done.

现在是一个双曲面，一个凹椭球面，一个凸椭球面

The main purpose is to construct cubature formulae on an arbitrary spherical triangle. Firstly a method for accurately computing the definite integral of spherical polynomial functions on a spherical triangle is proposed.

本文主要研究定义在球面三角形上函数的数值积分，通过积分的插值多项式函数构造具有多项式精度的插值型求积公式，以及给出精确计算球面三角形上多项式函数方法。

The results show that as the distance of waveguide to mirror is short, the couple efficiencies for EH11 mode of the cylindrical mirror and the spherical mirror are similar but the cylindrical mirror has stronger restraining function on EH21 and EH12 modes, and as the distance of waveguide to mirror is long, the cylindrical mirror has more restraining function on EH21 mode and less restraining function on EH12 mode.

同时相对球面反射镜，柱面反射镜对EH21模和EH12模具有更强的抑制作用。在d较大时，相对球面反射镜柱面反射镜对EH21模的抑制作用将会变得更强，而对EH12模的抑制作用将会减弱。标签 laser technique reflection coupling diffraction waveguide laser square waveguide cylindrical mirror

Then we re-sampling all signals defined on the surface of the original triangle mesh at the vertices of the spherical subdivision mesh and get a set of discrete geometry signals with subdivision topology which can be compressed by using spherical wavelet.

于是，在参数域内位于细分网格顶点处对定义在参数网格表面上的各种几何信号进行重采样，可得到新的具有细分结构的几何信号近似表示原始几何信号，以此满足球面细分小波对处理对象的细分结构要求，从而使得用球面细分小波对几何信号进行压缩得以实现。

Namely, we discrete some function surfaces including sphere, elliptic paraboloid and hyperboloid paraboloid as samples, and give the error estimation in order to compare, analyze and explain results.

我们以离散型函数曲面（包括球面，椭球面，双曲抛物面）作为样本，对各种方法的实验结果进行误差统计和分析比较。

Two novel spherical helical antennas can be designed by projecting the planar equiangular spiral antenna onto the surfaces of hemisphere and partial sphere. Their radiation properties are analyzed by the moment method with curved basic and testing function, and the curves of the VSWR, gain, polarization and pattern vs.

将平面等角螺旋天线投影到半球面和部分球面上，可得到两种新型球面螺旋天线，采用基于曲线基函数的矩量法对其辐射特性进行了分析，给出了天线的驻波、增益、极化及方向图等随频率变化的曲线。

According to the theorem Euler characteristic is equal to 2 on the sphere, it is show that this maps has at least one fixed point,that is to say the vector field has at least one singular point.

在地壳的每一点，由于受力定义了整个地壳上的向量场，然后利用同胚，将其转化为球面上的自映射，并根据球面的欧拉示性数等于2，说明该自映射至少有一个不动点，即向量场至少有一个奇点。

The relation of the surface shape error to f-number and relevant spherical radius was achieved according to the reducing analysis model ignoring the local f-number. Two kinds of rhombic prism model are established by ZEMAX. According to the simulation results from ZEMAX, the correctness and limitation of the former methods are proved and analyzed. The results are used to analyze the effect of the surface shape error of the rhombic prism on parallelism of the emergent beam. The assignation plan of the surface shape error for each working surface is presented.

根据忽略局部光圈数的简化分析模型，获得面形误差对应光圈数与相关球面半径的关系，通过几何处理方法，求得一定面形误差对应的球面半径与平面倾角的关系，将斜方棱镜的工作面倾斜一定角度，运用折射定理，将具体面形误差转化为相应平面的倾斜角度，得到出射光相对于理想光轴的倾斜角度及其关系式，并在ZEMAX中建立斜方棱镜的两种模型。

Lastly,Using the extension theory of〓-algebras founded and developed by Brown-Douglas-Fillmore in 70s,inparticular,using the homotopy invariance of the extensions and the indexformule of Toeplitz operator matrices,the paper characterized the automorphismgroup of the continuous function symbol Toeplitz 〓-algebra in terms of thetopological degrees of the continuous mappings on the n-dimensional sphere.

最后，本文利用Brown-Douglas-Fillmore在七十年代建立并发展起来的C*-代数扩张理论，尤其是扩张的同伦不变性，以及Toeplitz算子矩阵的指标公式，通过球面上连续映射的拓扑度，刻划了高维球面Hardy空间上连续符号Toeplitz 〓代数的自同构群。

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。