1.严格的说,应该叫动名词的复合结构.
2.该结构如下：one's/sb/sth doing sth,即：形容词性物主代词/名词所有格/人称代词宾格 + 动名词(短语).
它在句子充当名词性成分,即主语/宾语/表语,且其逻辑主语必须和句子主语不一致,否则就只需要直接用动名词(短语)了.
如：Do you mind waiting here?你介意在这儿等会儿吗?
wait的逻辑主语即句子主语you,所以直接用动名词短语.
再如：Do you mind my/me smoking here?你介意我在这儿抽烟吗?
smoke的逻辑主语是I,与句子主语you不同,所以必须使用动名词(短语)的复合结构.
3.其具体用法如下：
1）做句子主语时,只能是：形容词性物主代词/名词所有格 + 动名词(短语).
如：My being late made him angry.我的迟到使得他很生气.
Mary's marrying such an old man made us all surprised.玛丽嫁给那么老的男人让我们都很惊讶.
2）做句子宾语/表语时,只能是：形容词性物主代词/名词所有格/人称代词宾格 + 动名词(短语).
如：Would you mind my/me opeing the window?It's too hot inside.
你会介意我打开窗户吗?里面太热了.
The reason for the teacher's being angry was Tom's entering the classroom without permission.
老师生气的原因是汤姆未经许可就进入了教室.