查询词典 combinatorial sphere

The linear distance of any object space point in the sphere, from the center of the sphere, can be calculated by using the Pythagorean Theorem

在球上的从中心开始的空间点的线性距离，能通过勾股定理来计算

The evaluated distance of any point within the sphere must be between 0 and 1, but points that lie outside of the sphere will have values beyond that range and will cause the vCoordinate of the Ramp to wrap around, causing unrealistic illumination.

这个在球上的任何点的计算距离必定在0或1之间，但在球外上的点得到的数值一定超过这个范围将引起RAMP的 vCoordinate去环绕，产生一个不真实的照明。

When the sphere contacts 2-dimension world, it appears in the world just as growing bigger and shrinking to point. When the sphere goes through 2-dimension world, it disappears.

球体接触到二维平面，自然是慢慢变大再慢慢变小，当三维球体穿过二维平面，就消失了。

Applying a power of 0.5 to the input2 value of the Multiply Divide node calculates the square root of that input1 value, completing the calculation necessary to find the linear distance of any point within the sphere from the center of the sphere.

在Multiply Divide节点里赋予INPUT2数值一个幂值0.5去计算INPUT1值去平方根，完成的计算结果将得到在球上的任何点从球心到该点的线性距离。在图像上右侧上的在球上距离中心的边界点是通过执行下面计算过程来决定值的，它是1

It is found that energy density of static sphere symmetry of gravitational field is negative in the sphere coordinates and their energy density is positive definite in the Cartesian coordinates. This result shows that Einstien-Tolman expression of the energy-momentum pseudo tensor in the Cartesian coordinates have reasonable property.

在球坐标系和直角坐标系下我们用Einstien-Tolman表述计算球对称静态引力场的能量密度，发现在球坐标系下能量密度为负，而在直角坐标系下能量密度为正；这样的结果显示了Einstien-Tolman表述在直角坐标系下有其合理性。

Meanwhile, the reciprocity theorem is used to evaluate the composite scattering from plasma-coated sphere-sphere pair /cylinder-cylinder pair.

本文同时应用互易性原理计算了等离子体涂覆球-球，等离子体涂覆柱-柱复合目标的电磁散射特性。

On the other hand , illuminated by close relation between harmonic maps and sumanifold theory, we have also researched in-depth about some relative problems in submanifolds theory which include: the estimate of heat kernel and eigenvalue and it geometric application of submanifolds with or without boundary; many kinds of pinching problem of submanifolds which include the rigidity theorem, topological sphere theorem, differential sphere theorem and topological finite theorem.

另外，鉴于调和映照与子流形之间的密切关系，我们还要深入研究子流形几何中与之相关的一些问题，主要包括：带边与不带边子流形的热核与特征值估计及其几何应用；子流形的刚性定理、拓扑球定理、微分球面定理、拓扑有限性定理等各类Pinching问题。

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。

For the self-aligning outer ring and the seat rings between the holes, there is a sphere with the outer ring to match the outer surface of the inner surface of the sphere.

用于调心外圈与座孔间的套圈，有一个与外圈的球形外表面相配的球形内表面。

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。

More direct, directer ; most direct, directest

径直的，笔直的

Do you know how to use a chain saw?

你知道如何使用链锯吗？