Sentence examples for solution to example from inspiring English sources

Following the vector partial order, it is obvious that the optimal solution ((x,y)= 0,0)) obtained here is a Pareto optimal solution to Example 1.

Figure 3 gives the plot of the numerical solution to Example 1. Figure 3 Numerical solutions of 2D convection diffusion equation at ( 0.5, 0.5 ).

It is noted that in [6], a Pareto optimal solution to Example 1 is ((x,y)= 0,0.5)^{T}), and the upper level objective value is (F x,y)=(1,-2)^{T}).

The MAE in u, u x and u y are listed in Table 3 for α = 1  and  2. Figure 5 gives the plots of the exact and numerical solutions to Example 3. Figure 5 Exact and numerical solutions of 2D Poisson's equation with cylindrical symmetry.

The maximum absolute errors (MAE) in u, u x and u y are listed in Table 2 for α = 1  and  2. Figure 4 gives the plots of the exact and numerical solutions to Example 2. Figure 4 Exact and numerical solutions of 2D Poisson's equation in polar coordinates.

The MAE for u, v and their first order normal derivatives are tabulated in Tables 8-10 for various values R e. Figures 7, 8, 9 give a comparison of the plots of the exact and the numerical solutions to Example 8(a), (b) and (c) respectively.

A sample solution is visualised in Figure 10(a) [38, 52]. Figure 10 Illustrations of solutions to examples with curved characterics.

The paper concludes with the evaluation results from applying our solution to two example workflows from this project.

The solution to an example shows that the maximum allowable temperature of the cooling water should be obtained as part of the optimal solution, which also helps to provide a suitable energy management for these systems.

A simple application of the solution to the example problem of a clamped strip subject to tension is calibrated and the results found used to infer the slip and separation lengths.

But there exists a -maximum solution to in Example 3.7.