Sentence examples for of true solutions from inspiring English sources

A way to test this hypothesis is to make a direct comparison of an ensemble of solutions obtained by conventional methods with an ensemble of true solutions.

Figure 1 Graphs (a) and (b) exhibit the existence of true solutions from the monotone convergence of upper and lower solutions.

One way to test this hypothesis is to directly compare statistics obtained by conventional methods, with the statistics obtained from an ensemble of true solutions.

To enhance the capabilities of the Ritz method in dealing with cracked plates, new sets of admissible functions are proposed to represent the behaviors of true solutions along the crack.

In the analysis of relaxation oscillations,for example, singular solutions can be formed by concatenating slow trajectoriesassociated with silent and active phases and fast jumps between these phases, and thesecan guide the study of true solutions.

The underlying idea is that the statistics of an ensemble of N-body simulations are representative for the true statistics, obtained by an ensemble of true solutions, with the same set of initial conditions.

The theorem shows that the STM can reproduce the boundedness property of true solution (3.4).

This theorem shows that the STM can reproduce the upper bound of true solution (3.4) for the case of θ ∈ [ 0, 1 / 2 ).

Without the linear growth condition on the drift coefficient, this theorem shows that the STM can still reproduce the boundedness property of true solution (3.4).

Table 1 lists the comparison results of the relative errors of the true solutions and the approximate solutions yielded, respectively, by the mixed l 2/l q  method and the l q  method with active block number k varying in {4,12}, sample size r = M/k 0 in {3,4}, and the noise level σ in {0.02,0.05,0.10}.

The following two lemmas show the pth moment properties of the true solutions and numerical solutions.