by
/from,considering,providing(如果，有的语法家看作是连词)，talking
of,generally
speakingprovided,supposed等。
分词或分词短语在句子中作状语时，其逻辑主语与句子的主语是一致的，如：Seeing these photos, I couldn’t help thinking of my childhood days. 如果分词的逻辑主语与句子的主语不一致，这时候我们应该把主语在分词前补充出来，如：All the money having been spent, we started to look for work.这就是分词的独立主格结构。 然而，当分词的主语既非句子的主语，也非独立主格结构，如：Going up thee hill, the city looked more beautiful. 这种分词就叫作垂悬分词。主要有下面几种：1．垂悬分词引出话题Talking of pop stars, students felt very happy. (谈到……)Getting back to our story, the tiger was killed finally. (回到……)Coming to this question, I say yes. (关于……)2．垂悬分词引出说话的方式Generally speaking, men can run faster than women. (总的来说)Broadly/Roughly speaking, dogs are more faithful to man than cats. (大体上说)Strictly speaking, you can’t do it like that. （严格地说）Putting it mildly, you have caused us some inconvenience. (说得客气点)Exactly speaking, it is two to two. (确切地说)Frankly/ honestly speaking, I don’t agree with you. (坦诚/坦白地说)Biologically speaking, the sentence structure is wrong. (从逻辑上讲)3．垂悬分词引出说话人的依据或视觉Judging from his expression, he is in a bad mood. (从….. 判断)Compared with your achievement, mine is nothing. (与….. 相比较)Personally speaking, what you said is right. (就我个人而言)Considering the low price, the car is well worth buying. (从……考虑)4．垂悬分词为说话人所说的话的成立提供条件，等于if 或withProviding (that) I am well enough, I will take part in the work. (如果)Supposing (that) it rained, what should we do? （如果、假如）Given better condition, the crops could have grown better. (等于with)5．垂悬分词表示转折，等于sinceGranting that you are right, you shouldn’t get angry.Seeing that he is young and inexperienced, he is not fit for the work.Admitting that he is drunk, that is no excuse.