admitdoing就是承認做了什麼

allowsbtodo/allowdoing允許做某事

acknowledge是大眾的承認（Itisgenerallyacknowledgedthat.......）

recognize是官方的承認而且有認出的意思

承認 [T]

例句：

I acknowledge that her criticism is just.

我承認她的批評是公正的。

例句：

He seemed by implication to acknowledge that fact.

他似乎含蓄地承認了那事實。

告知（信函等）的收到，確認…收悉 [T]

例句：

We acknowledge receipt of your letter of the 15th .

我們告知你方已收到你們15日的來信。