When the covariance matrix used to measure the risk of investment is singular, by using the linear relationship of return rate, this paper deals with the mean-variance model of portfolio investment when short selling being allowed, and it gives calculating method for optimal investment coefficient of proportionality as well as efficient boundary.

When the definite matrix is non-positive,this paper studies the model of portfolio investment and it gives calculating method for optimal investment coefficient of proportionality,efficient boundary,unnecessary portfolio as well as arbitrage chance.

The paper studies the portfolio investment model on the condition of permitting shorting-selling and risk-free asset if the covariance of security investment portfolio is non-positive definite matrix and gives calculating methods for optimal investment coefficient of proportionality and its efficient frontier.

In particular,the investment ratio between diversion work and water retaining work of such station built on river with considerable runoff is getting even more unbalanced.

In order to give the best proportion of cement to fly-ash for coustructing cement-fly-ash stabilized crushed-stones pavement,through varying the proportion of cement to fly-ash while maintaining aggregate percentage and gradation,the variation law of mixture strength index with age is studied by experiment.