Sentence examples for exactly the same solution as 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.

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.

Mann-Whitney U test was used for statistical analysis Care was taken to stain control and β2−/−/γ3−/− cells in parallel using the same solutions as well as to acquire the confocal images with exactly the same settings of the microscope.

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.

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).

That is exactly the same result as last year.

This specific discretization is chosen because it has exactly the same stationary solution as the continuous-time version above (Haigh 1978).

Symmetry boundary conditions are given which allow to discretize and compute symmetric flows on the half model resulting in exactly the same flow solutions as if computed on the full model.

It is unnecessary to exactly reproduce the text of the example as long as your problem is solved with the same solution.