圆环面

The flexural vibration of a circular ring that is of axis symmetry is analyzed and calculated, the solid frequency expression of the flexural vibration is obtained.

对一类轴对称圆环的面内弯曲振动进行了分析计算，给出了圆环面内弯曲振动固有频率表达式。

Applying elliptic integral to calculate the electric potential due to uniformly charged ring, and then gets the general expression of the electric intensity by using gradient operation.

0引言对于均匀带电圆环电位和电场分布，在许多电磁学文献中仅仅只计算了与环面垂直的中心轴线和离圆环很远区域的电位和电场，而对其周围空间任意一点的值未作讨论。

The observations reveal warm (320 K) dust in a structure 2.1 parsec thick and 3.4 parsec in diameter, surrounding a smaller hot structure.

观测显示，在NGC 1068中心的尘埃圆环面原来是一个比较热的（320 K）的致密结构，直径约几个光年，它阻断了我们的视线，使我们无法看到该星系最里面的活动区域。

Next in section 2.3,usingthe finite isolated regular representations in SO(3)character varity of 〓,weobtained a computation formula of SO(3)Donaldson invariants with degree 1 of4—manifold 〓(Theorem 2.3.1).Finally in section 2.4 wediscussed the Donaldson invariants of 4—manifolds with smoothly embedded 2—torus 〓 whose selfintersection is +1,with the help of the single irreducibleSU(2)representation of the principal 〓—bundle over a 2—torus with Eulernumber—1,we got a gluing formula of the Donaldson invariant on the 2—homology represented by 2—torus 〓(Theorem 2.4.1),it is a supplement of P.

最后在§2.4我们讨论了具有自交数为+1的嵌入环面〓的4—流形的Donladson不变量，运用环面上欧拉数为-1的圆丛的单个不可约SU（2）表示给出了Donaldson不变量在环面表示的同调类上的一个粘合公式（定理2.4.1），这一结果补充了P。

The mathematical model of ruled helicoids on torus is constructed and two expression methods of ruled helicoids are discussed.

基于圆柱螺旋面和圆环螺旋线的形成原理，构建了圆环直纹螺旋面的数学模型，讨论了圆环直纹螺旋面的两种表示方法。

This paper proposes an algorithm of torus reconstruction based on feature recognition and semantics of engineering annotations.

机械零件中的管道和曲面过渡通常都由圆环面构成。

The constructed surface not only has the same structure to the bicubic Coons pacth, but also it can help us to obtain different surfaces by changing the values of the parameters. Furthermore, it can accurately represent torus、ellipsoid and so on.

所构造的曲面不仅具有双三次Coons曲面片的相似的结构，可以通过改变参数，得到不同的曲面片，而且还能精确地表示圆环面、球面、椭球面等二次曲面。

The paper discusses the position relationship between the litter circles of torus and the section circle of sphere figured out the intersection of torus and sphere when the central axis of torus and sphere center in XOZ coordinate plane through coordinate transformation.

利用坐标变换使圆环中心轴与球心同在XOZ平面内，讨论了在该平面内圆环截圆与球圆的位置不相交、相切和相交时圆环面和球面的相交情况，并给出了判别圆环面、球面相交情况的流程图以及圆环面和球面相交实例。

To overcome the drawbacks in the weight and cost of the antenna with the corrugated soft surface, a new patch antenna with patch rings is designed. Its weight is about 1/4 less than the antenna with the corrugated soft surface and it is inexpensive. Good experimental results are obtained. The radiation pattern of the antenna is more rotationally symmetric, and a more reduction on the sidelobe levels of the antenna is achieved as compared to the antenna with the corrugated soft surface. In conclusion, in the present thesis both theoretical and experimental research works have been carried out intensively on patch antennas based on photonic-bandgap structures.

为了克服皱褶软表面天线份量重，加工费用贵等缺点，我们对空气介质的皱褶圆环结构软表面天线进行了改进，将周期分布的皱褶圆环平面化，并保持结构的软表面特性，设计出了一种新的平面圆环结构的软表面天线并进行了实验研究，加工的平面圆环结构天线比皱褶圆环结构天线重量减轻了约1/4，加工费用大大降低，所取得的实验结果显示，该平面圆环结构软表面天线的方向图的轴对称性得到了改善，在俯仰角从0°～-90°的范围内天线H面的波束与E面重合，与皱褶圆环结构相比，天线的旁瓣和背瓣受到了更大的抑制，E面方向图上+120°方向的旁瓣被明显削弱。

The stable winding equations of the elbow torus and cylinder are established according to different geometry, and the winding pattern of the geodesics of torus and semi-geodesics of cylinder are also achieved.

根据微分几何建立弯管的圆环面及圆柱面稳定缠绕方程，给出了圆环面的测地线缠绕解及圆柱面的半测地线缠绕解，并提出了用OpenGL及VC++对所设计的线型进行仿真的具体实现办法。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。