御食い初め[okuizome] weaning ceremony
為初め[shisome] outset
為初める[shisomeru] to begin to do
仮初[karisome] temporary
業界初[gyoukaihatsu] the industry's first ...

月初め[tsukihajime] beginning of month
最初[saisho] beginning
初めに[hajimeni] to begin with (used as an introduction)
初めは[hajimeha] at first
手初めに[tehajimeni] at first

御誕生日おめでとうございます[otanjoubiomedetougozaimasu] Happy Birthday
また明日[mataashita] see you tomorrow
旭日[kyokujitsu] rising sun
旭日昇天[kyokujitsushouten] full of vigor and vitality (like the rising sun) (vigour)
或日[aruhi] one day (e.g. "one day while studying, ..")

一日の長[ichijitsunochou] superiority
一日一日[ichinichiichinichi] gradually
一日一夜[ichinichiichiya] all day and night
一日増しに[ichinichimashini] day by day
一日置き[ichinichioki] every other day