In the meantime (idiom)

　　●While something else is being done or was being done.（与此同时，在这段时间裏）

　　Examples:　　

　　1.She spent four years studying for her law degree. In the meantime, she continued to work at the bank.　　

　　2.In the meantime, opposition to the regime was growing.

　　Beyond/without a shadow of a doubt (idiom)

　　●Without any doubt.（毫无疑问，不容置疑）

　　Examples:　　

　　1.This photo now proves, beyond a shadow of a doubt, that my client is innocent.　　

　　2. I knew beyond a shadow of a doubt that something bad had happened.

　　Take root (idiom)

　　●To become settled or established.（扎根，树立）

　　 Examples:　　

　　1.Compromise is essential if peace is to take root in this troubled area.　　

　　2.I'm afraid the cancer has taken root throughout his entire body.

　　Spare no expense (idiom)

　　●To spend as much money as necessary to make something good, without worrying about the cost.

　　 （不惜费用，不惜代价）

　　Examples:　　

　　1.No expense was spared in developing the necessary technology.　　

　　2.She spared no expense in getting the house to look just right.

　　Give the nod (idiom)

　　●To give approval; to give permission to do something.（批准，许可）

　　Examples:　　

　　1.I won't give the nod to treating conspiracy theories as facts.　　

　　2.Mom gave the nod to pizza for dinner!