can any body explain to me the definitions and the differences of and between SENTIMENT , MOMENTUM and TREND ?also what is the origin of each of these ? are they due to market inefficiencies or are they just an independent phenomenon ?also which are the mathematical models that are being used to model these ?

These are notions from the unscientific field of technical analysis, rather than quantitative finance.People who believe in Sentiment believe that asset prices, in addition to being based on available information (EMH hypothesis) are also affected by the excessive "moods" of investors. They seek indicators of these moods IN AN ATTEMPT TO TAKE THE OPPOSITE SIDE. For example some people believe that the VIX is a sentiment indicator; when the VIX is high it indicates that investors are unusually fearful of a stock decline, these people believe that such times would be a good time to BUY stocks, i.e. to do the opposite of what "the crowd" is doing.People who believe in MOMENTUM and TREND take the opposite view. They believe that when asset prices are going up they are likely to continue going up. Again this would mean that the market is not efficient; in an EM new information is incorporated instantly, while a trend would seem to be evidence of gradual, incomplete, adjustment to information. The exact definition of trend and momentum vary, but once they have determined that a stock is going up, these investors would TRY TO COME IN ON THE SAME SIDE as the market action indicates, i.e. to buy.