"a certain event will occur by a" particular "period of time" means that said event can occur at any instant of time within said "period of time" [duplicate]

If something is supposed to happen by a certain day, it means it is supposed to happen not later than that, so it includes the day as well.

It means that at some point on May 30th, the entrants should have been notified.

Technically speaking, notifying them at 23:59:59 on May 30th will suffice to meet that criterion, although for business-related requests most people will operate on "standard working hours", so they probably expect you to notify them while they're at the office (e.g. before 5:00 p.m.) rather than hunting down their home address and waking them up after they've gone to bed.

It is decidedly ... ambiguous.

Return it to me by Mar 24th

can be interpreted as the deadline is before the 24th or _on the 24th. The nominal meaning of 'by' in this context is 'before' but pragmatically it means for the purposes of action on the 24th. From this one can infer that as long as, in this instance, the thing is returned sometime on the 24th and can be used on the 24th, then everything is OK. Returning it as 23:59, or really 5pm, is within the rules but might be considered rude.

In a business sense, the phrase "by May 30th" usually means "by close of business on May 30th" (i.e. the end of the business day, typically 5:00 PM in the English speaking world), while the same statement on a legal contract could have the meaning "by 11:59 PM on May 30th" (i.e. the end of the calendar day). So I would say there is an element on contextual interpretation.

This means there is no strict definition as there is some ambiguity, however I believe the term "by" in every case would include the day of the deadline.