论文标题
自由电位功能
Free potential functions
论文作者
论文摘要
本文建立了两个经典定理的免费版本：衍生物是无卷曲的，每个无卷曲的向量场（在简单连接的域上）都是衍生物。我们表明，非交通性的自由分析图的衍生物必须是自由滚动的 - 一个为零卷曲的类似物。此外，在自由域已连接的假设下，这种必要的条件就足够了。具体而言，如果$ t $是在连接的自由域上定义的无分析矢量字段，则$ dt（x，h）[k，0] = dt（x，k）[x，k）[h，0] $，并且仅当存在一个分析免费的地图$ f $时，因此$ df（x）[x）[h] = h] = t（x，x，x，x，x，h）$。
This article establishes free versions of two classical theorems: derivatives are curl-free and every curl-free vector field (on a simply connected domain) is a derivative. We show that the derivative of a noncommutative free analytic map must be free-curl free -- an analog of having zero curl. Moreover, under the assumption that the free domain is connected, this necessary condition is sufficient. Specifically, if $T$ is analytic free vector field defined on a connected free domain then $DT(X,H)[K,0] = DT(X,K)[H,0]$ if and only if there exists an analytic free map $f$ such that $Df(X)[H] = T(X,H)$.
