According to the following phrase,

"So, I think we have to take care after-the-fact policies, In my case, I always have more than ten expressions of apology in English."

some people are asking me to open them.

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Well,

(1)I am sorry.

(2)Excuse me.

(3)I'm awfully sorry

(4)It is my fault.

(5)I feel bad about it.

(6)I am sorry about the other day,

(7) Please forgive my rudeness.

(8)I don't know how to apologize to you.

(9)I am sorry to trouble you

(10)I am really sorry for troubling you.

In the case of E-mail, I remember having mainlined,

"Please accept our apologies for the trouble this matter has caused you."

and other similar phrases, especially.

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I be confident in myself that I had mislead some peple in an area in Colorado USA into believing,

"Anyway, when I can't understand the English conversation, APOLOGY is a easy way" , that is a kind of typical Japanese beatiful custom and tradition as "Ad hoc".