Would you mind my sitting here? 这句话为什么不用me?

别听他们的，这个有逻辑在里头的。
smoking是分词，其实词性相当于一个名词。
既然是名词，那么前面自然要用my了

Would you mind意为“介意，反对吗”其后不能直接接宾语me .请看以下例句之区别：
Would you mind my smoking here?
你不反对我在这儿抽烟吧？
Would you mind looking over my essay?
我的这篇文章请你过目一下好吗？
Would you mind looking over my exercises?
你帮我把练习看一看好吗？
Would you mind my opening the window?
我打开窗子你反对吗？
Would you mind of I put my coat here?
我把大衣放在这儿你介意吗？
Would you mind taking your foot off my hand?
你踩著我的手了，请你把脚抬一下行吗？
Would you mind my pushing you out for a while?
请你出去一下您介意吗？
Would you mind helping me?
请帮帮我的忙好吗？
Would you mind translating for me?
请你帮我翻译一下好吗？
Would you mind explaining this to me?
请给我解释一下你不介意吧？
Would you mind giving me a light?
请你把火给我好吗？
Would you mind passing me the salt?
可否劳驾把盐递给我？
Would you mind showing me your showroom?
你可以带我去参观一下贵公司的展示间吗？
Would you mind buying some fruit for me?
帮我买点水果，你介意吗？
Would yo