流形 in English translation

• manifold
• manifolds

Examples of using 流形 in Chinese and their translations into English

当外星种族为躲避跨星系恐怖袭击，而纷纷逃往地球时，宇宙队长和流形则必须跨上一趟穿越宇宙的旅程。
And when alien races fleeing an intergalactic terror crash to Earth, Captain Universe and Manifold must take a trip across the universe.

外爾（HermannWeyl）于1912年给出了微分流形的一个内在的定义。
Hermann Weyl gave an intrinsic definition for differentiable manifolds in 1912.

事实上，在分析中用到的很多空间，比如拓扑群和拓扑流形在其定义中明确的声明了豪斯多夫条件。
In fact, many spaces of use in analysis, such as topological groups and topological manifolds, have the Hausdorff condition explicitly stated in their definitions.

此外，我们同时考虑由以上的协边联系的四维、三维及二维流形，可以得到大量重要的实例。
Furthermore, we consider simultaneously 4-dimensional, 3-dimensional and 2-dimensional manifolds that are related by the above bordisms, then obtain ample and important examples.

这一基本的概念正当化了在欧氏空间和其他流形之间的微分。
This fundamental concept justifies a differential calculus between a Euclidean space and other manifolds.

光滑栈的概念非常广泛，显然所有光滑流形是光滑栈。
The notion of smooth stack is quite general, obviously all smooth manifolds are smooth stacks.

如果这个流形维数足够低，那么数据可以在低维空间中被可视化。
If the manifold is of low enough dimension, the data can be visualised in the low-dimensional space.

流形就是这样的几何空间，其上的每个小区域看起来都像普通的欧几里德空间。
A manifold is a type of geometrical space where each small region looks like normal Euclidean space.

流形中两点之间的因果关系可以用来描述时空中哪些事件可以影响到其他的哪些事件。
The causal relations between points in the manifold are interpreted as describing which events in spacetime can influence which other events.

流形在某一点的维数就是该点映射到的欧几里得空间图的维数（定义中的数字n）。
The dimension of the manifold at a certain point is the dimension of the Euclidean space that the charts at that point map to(number n in the definition).

这样，这个特殊的代表元素可以视为流形上所有上同调等价的形式中的一个极值(极小值)。
Thus, this particular representative element can be understood to be an extremum(a minimum) of all cohomologously equivalent forms on the manifold.

是灰质间的活动流形成了你熟悉的内在特性，动物本能的大脑和人类理性的大脑。
The flow of activity within the gray matter is what forms your familiar internal characters, the monkey brain and the rational human brain.

如果所有变换映射和这个结构相容，该结构就可以转到流形上。
If all the transition maps are compatible with this structure, the structure transfers to the manifold.

一个流形可以以不同方式构造，每个方式强调了流形的一个方面，因而导致了不同的观点。
A single manifold can be constructed in different ways, each stressing a different aspect of the manifold, thereby leading to a slightly different viewpoint.

在一个有越来越少的工作保障的世界里，这种现金流形式对他们而言有着更大的意义。
In a world with less and less job security, this cash flow pattern makes much more sense to me.

在宇宙学上，需要考虑"空间的曲率"，就是相应的伪黎曼流形的曲率，见黎曼流形的曲率。
In cosmology, the concept of"curvature of space" is considered, which is the curvature of corresponding pseudo-Riemannian manifolds, see Curvature of Riemannian manifolds.

因为拓扑空间极为多变且奇特，许多拓扑学的领域会专注于被称为流形的更为熟悉之空间。
While topological spaces can be extremely varied and exotic, many areas of topology focus on the more familiar class of spaces known as manifolds.

迪克写了两本书：歧管的几何形状（与克里滕登，1964年）和流形上的张量分析（与戈德堡，1968年）。
Dick wrote two books: Geometry of Manifolds(with Crittenden, 1964) and Tensor Analysis on Manifolds(with Goldberg, 1968).

根据莫尔斯的基本见解，一个流形上的一个可微函数在典型的情况下，很直接的反映了该流形的拓扑。
According to the basic insights of Marston Morse, a typical differentiable function on a manifold will reflect the topology quite directly.

这种方法的优点是形式不在是定义在流形自身上，而是在更大的主丛上。
The disadvantage to this approach is that the forms are no longer defined on the manifold itself, but rather on a larger principal bundle.