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.

The proportional coefficient of the master and slave manipulators is an important parameter for an isomeric robotic system.

That is, the values of the proportional coefficient M of the horizontal resistance coefficient are listed according to the conditions and types of the foundation soil.

By using the characteristic that different form of feedback cam brought different non-linear flow rate to change the former flow rate of control valve,a soft measurement modeling and optimizing process of control valve curve function that is of linear character of flow rate was introduced combining with proportional coefficient.

Method of the fast PID control with changed scale coefficient;