apologies

n. expression of regret or sorrow; defense, justification

Noun
1. an expression of regret at having caused trouble for someone; "he wrote a letter of apology to the hostess"
(hypernym) acknowledgment, acknowledgement
(derivation) apologize, apologise
2. a formal written defense of something you believe in strongly
(synonym) apologia
(hypernym) defense, defence, vindication
(derivation) apologize, apologise, excuse, justify, rationalize, rationalise
3. a poor example; "it was an apology for a meal"; "a poor excuse for an automobile"
(synonym) excuse
(hypernym) example, illustration, instance, representative

n. apologia, written defense of an opinion or stance

(pl. )
of Apology
  

fu4 jing1 qing3 zui4
Carrying a birch and asking for punishment.
Said of a person who admits his mistakes and offers apologies on his own initiative. To kiss the rod.