The settling behaviors of a rectangular particle with different initial orientation angles and length-width ratios were simulated by using distributed Lagrange multiplier/fictitious domain method.

The distributed Lagrange multiplier/fictitious domain method was applied to do the direct numerical simulation.

Optimization of integral flange by Lagrangian method.;

In the new method,the Lagrangian method with inequality restriction is used to assign the load between the monoblock so as to increase the feasibility a.

The dynamic equations were derived applying the Lagrangian multiplier method.

In this paper,adopting the radar cross section as the constraint condition,a new conical aerodynamic configuration is presented using the Lagrange multiplier method,and the minimization problems are solved by the dynamic evolution method.

With Lagrange multiplier,Dirichlet boundary conditions are imposed along the essential boundaries.

With the loan s yield as the earning of financial asset and the volatility of loan as a criteria to reflect the risk of loan, a decision making model of loan risk portfolio s optimization was established through the solution of the problem of quadric program using the Lagrange multiplier with minimum risk in the feasible range.