Sentence examples for exactly the same solution from inspiring English sources

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].

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.

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.

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

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.

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).

With both models, the sensitivity analysis did not converge exactly to the same solution; however, only three women at the most changed groups without noticeable changes in the log-likelihood values.

The advantages are the large volume of QC sample that can be prepared prior to this study, so that the same solution (at exactly the same concentration) could be used for comparison.