Slope stability analysis based on arc height as control variable;

In the model, the melt flow index and melt density were taken as state functions and the feeding rate of hydrogen and comonomer, reaction temperature, discharge from system, feeding rate of catalyst and the fluidized bed level were set as control variables.

The paper took an example for the tremendous flood of Huolin River in 1998 and the six control variables——danger coefficient of flood produced, elevation, gradient of ground, rainfall, rate of alkalized soil and the reclaiming grassplot were classified as two main weight variables based influence on the water environment.

The state variables and the control variables for each branch room are given and the mathematical models for the branch rooms are also built.

The method employs a recently developed direct optimization technique that uses a piecewise polynomial representation for the state and control variables, thus converting the optimal control problem into a nonlinear programming problem, which can be solved numerically.

This article discusses the question concerning the limit of partial sum of the controlled sequence of independent random varialbes,and proves when controlled variable X conforms to the term: E|X|<+ ∞ and αη> 0,αnn-1↓b(b>0), aη2n-1↑∞, for some sequence {αn},then tim |∑xk| αn-1=0.