While reading the book, he nodded from time to time. (时间)

The teacher stood there surrounded by the students. (方式)

He sent me an e-mail, hoping to get further information.(伴随)

分词作时间状语，如果先与主动词的动作，且强调先后， 要用having done。如:

Having answered the letter, she went on to listen to the radio.

Having been criticized by the teacher, Li Ming gave up smoking.

注意:如果是否定句,not 一般放在句首,如:

Not having received his reply, he decided to write again.

分词做状语时有时可在其前面加上while、when 、if 、even if 、although 、once、 unless等连词,使用何种分词仍然取决于与主语的关系,主动关系用现在分词,被动关系用过去分词.如:

While staying in Beijing , I visited some of my friends.

Unless invited, I will not attend his party.

Although working very hard, he couldn't satisfy his boss.