Submersion (mathematics) - Wikipedia
In mathematics, a submersion is a differentiable map between differentiable manifolds whose differential is everywhere surjective. This is a basic concept in differential topology. The notion of a submersion is dual to the notion of an immersion.
SUBMERSION中文(简体)翻译：剑桥词典 - Cambridge Dictionary
noun [ U ] uk / səbˈmɜː.ʃ ə n / us / səbˈmɝː.ʒ ə n / Add to word list. the act of being, or putting something, under the surface of a liquid so that the liquid completely covers it. （使）潜入水 …
浸入 (微分几何) - 香蕉空间
在 微分几何 中, 浸入 是 光滑流形 间的一类 光滑映射. 与 嵌入 类似, 浸入也是将某个流形放入另一个流形中, 但浸入允许流形 “与自己相交”. 例如, 平面上与自身相交的曲线常常可以看成 R 到 R2 的浸入.
微分流形笔记：第三讲 - 知乎 - 知乎专栏
切向量： v\in T_p \mathcal M. 定义：. 方法一： v:C^\infty (p)/\sim\to \mathbb R. 方法二： 设 \alpha: (-\varepsilon,\varepsilon)\to\mathcal M 是光滑映射，且 \alpha (0)=p 、 \alpha' (0) (f):=\frac {d} {dt}f\circ \alpha (t)\bigg|_ {t=0}，则定义. v=\sum_ {i=1}^n a_i (\partial_ {x_i})
Submersion - Encyclopedia of Mathematics
2020年6月6日 · If $ M $ and $ N $ possess the structure of a piecewise-linear, -analytic or -differentiable (of class $ C ^ {k} $) manifold and the local coordinates can be chosen piecewise-linear, -analytic or -differentiable (of class $ C ^ {l} $, $ l \leq k $), then the submersion is said to be piecewise-linear, -analytic or -differentiable (of class $ C ...
SUBMERSION在剑桥英语词典中的解释及翻译 - Cambridge …
the act of being, or putting something, under the surface of a liquid so that the liquid completely covers it: The fruit was preserved by submersion in alcohol. Scuba diving is not without risk, and the longer the time of submersion, the greater the need for caution. 见.
SUBMERSION | English meaning - Cambridge Dictionary
the act of being, or putting something, under the surface of a liquid so that the liquid completely covers it: The fruit was preserved by submersion in alcohol. Scuba diving is not without risk, …
Submersion -- from Wolfram MathWorld
2024年11月7日 · A submersion is a smooth map f:M->N when dimM>=dimN, given that the differential, or Jacobian, is surjective at every x in M. The basic example of a submersion is the canonical submersion alpha of R^n onto R^k when n>=k, alpha(x_1,...,x_n)=(x_1,...,x_k).
Submersion vs. Immersion — What’s the Difference?
2024年3月8日 · Understanding the difference between submersion and immersion is crucial in contexts where the extent of interaction with a liquid or environment matters. While submersion emphasizes being completely under a liquid, immersion suggests a surrounding or involvement that may not require being fully covered by a fluid. 14. ADVERTISEMENT.
What is a submersion? - Mathematics Stack Exchange
2019年7月27日 · A proper submersion is a fiber bundle. So, basically, if you work in a compact domain (a closed manifold), then you can visualize submersions f: M → N f: M → N as maps which allow you to see the domain locally as a product of …