Sentence examples for exactly the same solutions from inspiring English sources

Algorithms for use in the finite element method are simplified since the adjoint system gives exactly the same solutions as those of the original system.

The results of the example showed from Tables 1-3 and Figures 1-6 that exactly the same solutions have been obtained with multivariate Padé approximation.

where d = b + ac and W = cU + V. Since (3) has been obtained by substituting (1) into (2), the system (1)–(2) has exactly the same solutions in X, Y, and Z as the system (1 - 3).

The approach leads to exactly the same solution as found through lifted ILC, but at a much smaller computational load (O(N) vs O N3)) for both linear time-invariant (LTI) and linear time-varying (LTV) systems.

Now we can apply series (4) to u ( x, t ) for 0 < α ≤ 1, and we have u ( x, t ) = x 2 + 2 k t α Γ ( α + 1 ), which is exactly the same solution as in [21].

We also examined two kinds of initial slip model: uniform slip model and vertical striped slip models in the same way as Yagi and Fukahata (2011a), and found that exactly the same solution was obtained for both of the initial slip models.

Consider now the self-mapping T ¯ : C → C which defines exactly the same solution as T : R p → R p for initial conditions in A 1 so that T ¯ is identified with the restricted self-mapping T : R p | C → C from a nonempty bounded, convex and closed set to itself.

Livingstone's solution on CNN was to offer Gaddafi a negotiated way out -- exactly the same solution he was suggesting behind the scenes to the Libyan ruler.

More recently, when the big banks nuked the economy, both parties had exactly the same solution: Give those same big banks trillions of dollars.

The synchronous algorithm does not modify the behaviour of the serial algorithm, and is deterministic in the sense that serial and parallel runs with the same set of random seeds will produce exactly the same solution.

Table 2 and Figure 1 illustrate the problem formulation where variables x ¯ 1 and x ¯ 2 represent two different inputs: only w ¯ 1 activates Y; only w ¯ 2 activates Y; w ¯ 1 and w ¯ 2 are required to activate Y. > -wrap-foot> When solutions are of a binary nature this formulation holds exactly the same solution as the previously shown for the mixed integer nonlinear case.