We regret to inform you that you are being furloughed indefinitely.

我们遗憾地通知你：你被无限期地停职了。

We regret to inform you that your application has not been successful.

我们很遗憾地通知您，您的申请未通过。

I regret to advise you that the course is now full.

本课程已满额，特此通知。

I regret to have made your acquaintance so late.

识荆恨晚。

I regret to tell you a bad news.

我很遗憾地告诉你一个坏消息。