| 词汇 | cross-ratio |
| 释义 | BETA cross ratiocollocation in Englishmeanings of crossand ratioThese words are often used together. Click on the links below to explore the meanings. cross noun[ C ] uk /krɒs/ us /krɑːs/ UK a written mark (x or +) formed by two lines going across each other. The mark x is usually used to show where something is, or that something has not been ... See more at cross ratio noun[ C ] uk /ˈreɪ.ʃi.əʊ/ us /ˈreɪ.ʃi.oʊ/ the relationship between two groups or amounts that expresses how much bigger one is than ... See more at ratio Examples of cross ratiocross ratio In this paper, by the crossratio distortion we mean the distortion of the second crossratio. We will rather use the straightforward definition of the crossratio for the product of rank-one symmetric spaces. Then any crossratio preserving homeomorphism on the boundary can be extended isometrically into the space. But in our situation, it is not obvious to relate the marked length spectrum to this generalized crossratio. Then by the definition of the crossratio, the claim follows. Therefore, in every realization, there are four points having the same cross-ratio as the cross-ratio of the four collinear points in the realization derived from the regular pentagon. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The cross-ratio is preserved by the fractional linear transformations and it is essentially the only projective invariant of a quadruple of points, which underlies its importance for projective geometry. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It is also related to the cross-ratio. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The power of the method of cross-ratio, as an instrument of analysis, it is not easy to over-rate. Therefore, the cross-ratio is invariant under the affine transformations. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The computational aspect of this is the cross-ratio. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This can not be extended to 4-tuples of points, because the cross-ratio is invariant. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Using these symmetries, there can then be 6 possible values of the cross-ratio, depending on the order in which the points are given. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The interpretation in terms of the infinitesimal cross-ratio was given in [21]. The advantage of this representation is that the landmarks are more robust than the single cross-ratio. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. |
反思网英语在线翻译词典收录了377474条英语词汇在线翻译词条，基本涵盖了全部常用英语词汇的中英文双语翻译及用法，是英语学习的有利工具。