流形 英语是什么意思 - 英语翻译

• manifold
• manifolds

在 中文 中使用 流形 的示例及其翻译为 英语

如果用正确的方式完成，结果也是流形。
If this is done the right way, the result is also a manifold.

流形将阻止工作表的移动(图3a.)。
The manifold will prevent the movement of the sheets(Figure 3a.).

他们的双封面是卡拉比-丘流形的两个定义（其实K3的表面）。
Their double covers are Calabi- Yau manifolds for both definitions(in fact, K3 surfaces).

流形不必连通（整个只有一片）；一对分离的圆可以是一个流形。
Manifolds need not be connected(all in"one piece"); an example is a pair of separate circles.

不像黎曼的情况，辛流形没有像曲率那样的局部不变量。
Unlike in the Riemannian case, symplectic manifolds have no local invariants such as curvature.

霍奇星号在流形上最重要的应用是用来定义餘微分δ。
The most important application of the Hodge star on manifolds is to define the codifferential δ on k-forms.

大多数定义断言，卡拉比-丘流形结构紧凑，但一些让他们成为非紧。
Most definitions assert that Calabi-Yau manifolds are compact, but some allow them to be non-compact.

特别地，任何施坦流形（嵌入Cn）或代数簇（嵌入CPn）是凯勒型的。
In particular, any Stein manifold(embedded in Cn) or algebraic variety(embedded in CPn) is of Kähler type.

图集不是唯一的，因为所有流形可以被不同的图的组合用很多方式覆盖。
An atlas is not unique as all manifolds can be covered multiple ways using different combinations of charts.

你不需要成为世界级的拓扑学家，也能理解特定类别的流形或决策边界。
You don't need to be a world class topologist to understand manifolds or decision boundaries of certain classes.

这个观念后来发展为G-结构的概念，其中G是流形"局部"对称性形成的李群。
This idea later led to the notion of a G-structure, where G is a Lie group of"local" symmetries of a manifold.

采样流形的设计，使测量周期可以完全从工厂本身分离。
The sampling manifolds have been designed so that the measurement cycle can be completely separated from the plant itself.

特别地，任何施坦流形（嵌入Cn）或代数簇（嵌入CPn）是凯勒型的。
In particular, any Stein manifold(embedded in Cn) or smooth projective algebraic variety(embedded in CPn) is Kähler.

对于某些流形，譬如球面，可以选取一些坐标图使得重叠区域在"手性"上一致；.
For some manifolds, like the sphere, charts can be chosen so that overlapping regions agree on their"handedness";

流形经常被定义为欧几里得空间Rn的子流形，所以这是一个非常重要的特例。
Manifolds are often defined as embedded submanifolds of Euclidean space Rn, so this forms a very important special case.

场论中，M是时空流形，而目标空间是场在任何给定可取的值的集合。
In field theory, M is the spacetime manifold and the target space is the set of values the fields can take at any given point.

第二，目标变量可能只依赖于数据流形中的少量可能的方向。
The second property is that target variables may have significant dependence on only a small number of possible directions within the data manifold.

任意洛伦兹流形（可能是弯曲的）的因果结构由于曲率的存在会较为复杂。
The causal structure of an arbitrary(possibly curved) Lorentzian manifold is made more complicated by the presence of curvature.

流形学习可以被认为是将线性框架（如PCA）推广到对数据中非线性结构敏感的一次尝试。
Manifold Learning can be thought of as an attempt to generalize linear frameworks like PCA to be sensitive to non-linear structure in data.

Bloomsbury群的流形置换，与情人，丈夫们，妻子的情人成为丈夫的情人，反之亦然；.
The manifold permutations of the Bloomsbury Group, with lovers, husbands, wives' lovers become husbands' lovers and vice-versa;

庞加莱提出，所有三维单连通闭流形--那些没有洞，范围有限的流形--都是球面。
Poincaré proposed that all closed, simply connected, three-dimensional manifolds- those which lack holes and are of finite extent- were spheres.

如果流形Q有一个黎曼或者伪黎曼度量g，那么相应的定义可以用广义坐标写出。
If the manifold Q has a Riemannian or pseudo-Riemannian metric g, then corresponding definitions can be made in terms of generalized coordinates.

最容易定义的流形是拓扑流形，它局部看起来象一些「普通」的欧几里得空间Rn。
The simplest kind of manifold to define is the topological manifold, which looks locally like some"ordinary" Euclidean space Rn.

流形的名字来自黎曼原来的德语术语Mannigfaltigkeit，WilliamKingdonClifford把它翻译为"manifoldness"（多层）。
The name manifold comes from Riemann's original German term, Mannigfaltigkeit, which William Kingdon Clifford translated as"manifoldness".

他们共同成为微分流形的几何理论-这个理论也可以从动力系统的角度加以研究。
Together they make up the geometric theory of differentiable manifolds- which can also be studied directly from the point of view of dynamical systems.

一个实二维流形可以变成为一个黎曼曲面（通常有几种不同的方式）当且仅当它是可定向的。
A two-dimensional real manifold can be turned into a Riemann surface(usually in several inequivalent ways) if and only if it is orientable and metrizable.

Thurston提出，每个三维流形可以被分为八种分支中的一块或多块，这八种分支中包括球面。
Thurston proposed that every three-dimensional manifold could be broken down into one or more of eight types of component, including a spherical type.

在数学中，一个殆複流形（almostcomplexmanifold）是在每个切空间上带有一个光滑线性複结构的光滑流形。
In mathematics, an almost complex manifold is a smooth manifold equipped with a smooth linear complex structure on each tangent space.

下面假设所有流形为Cr类微分流形，r≥1，并且所有映射为Cr类可微。
In the following we assume all manifolds are differentiable manifolds of class Cr for a fixed r≥ 1, and all morphisms are differentiable of class Cr.