The emphasis in intercultural communication studies is on cultural rules for regulationg communicative interaction. For instance, international students who attend public schools and universities in Canada and the United States often experience difficulties associated with communicative interaction in classroom.
I don't think I can help you much, Taka, but I think that if the writer meant that univirsities are public as well then it modifies them both and if it's only the schools that are public then it modifies "schools" only. I don't know if there's such thing "public unibersities" so I can't tell for sure
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This may turn out to be unanswerable grammatically.
From http://www.answers.com/topic/public-university :
A public university is an institution of higher education that is funded by public means through a national or regional government. In Australia, Canada, Germany, the United Kingdom and
Taka, perhaps you are asking more generally about adjectives that precede two nouns linked by 'and'. As a general rule, I feel the adjective would apply to both, unless the meaning and context made it apparent that it only applied to the first noun.
'in classroom' should be 'in class', or 'in classrooms'
The reason I quoted from the website is that Canada was mentioned.