So with apologies for being a bit more boring for twenty minutes, let's do something we'll call formal stuff.

抱歉接下来的二十多钟分可能有点枯燥,我们来做点正经事

耶鲁公开课 - 博弈论课程节选

So, assuming -- if anyone got it wrong because of that, that's my apologies, that's my fault.

如果有人是因为这个原因做错了，那我非常抱歉，这是我的错。

麻省理工公开课 - 化学原理课程节选

So with apologies to Strunk and White, this is in the passive form, that's dominated, passive voice.

斯特伦克和怀特很抱歉,我用了被动式,即劣势,被动语态

耶鲁公开课 - 博弈论课程节选