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In this usage, I would say that state is the condition of a system. A related term is status, as in, "Status check" as a "Condition check."
The research/knowledge gap is a theroy: http://www.utwente.nl/cw/theorieenoverzicht/Theory%20clusters/Mass%20Media/knowledge_gap.doc/ Basically, know how there is the richest people that have the most money and the poorest that have the least and a huge gap? They are saying that there is something similar in education. It is generally accepted, but there are those that say it needs refinement or argue against parts of it or see it as being used improperly.
Lets break this down. State: the current situation. and knowledge: is pretty easy. The truth that you can back up with facts, something you learned in school, or something your are aware of. so, 'state of knowledge' i would think is what you know in that current situation. And for your 2nd question, "what does research/knowledge gap mean?" Well the gap in this situation would be missing information stuff you do not know yet. Think of it as a puzzle you have alot of parts put together just not sure where do they believe in the big picture of the puzzle. Lets make it into a math equation just because we can. 10*K=100 10 Times K, K is something we dont know what it is yet but what ever it is 10 times that = 100. So in knowledge it will kinda work the same way Lets i dont know make a biblical example, i dont know how much you know about the bible but according to the old testament in the bible some d00d named Moises was instructed by god to make a big boat for he was going to flood the earth and kill everyone but him and his wife and there kids. He told Moises to get 2 of every animal a male and a female so they can make more of that animal and repopulate the earth anyway we dont know how he got the animals we dont know how he found them and caught then lead them on the boat all we know is that he did according to the bible he did and that is the knowledge gap.
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Actually, because Knowledge Gap is used in conjunction with Research, it might be the other technical use of it. Fun when there is more than one technical term with the same words... This is a research theory that is widely practiced and poorly conceived. The idea is that there ate gaps in research and that when generating new research you must find something unique to make your research an improvement and not repeat old research. However, this is flawed thinking and contradicts the scientific method. See, in the scientific method the idea is to be repeatable so that others can confirm research until a theory is very strongly supported. Many times there have been small bit of research done and accepted as fact until someone repeated the experiment and found a flaw in the methodology. Those that strictly hold to the idea of new research only will miss out on this aspect of scientific development.