Sentence examples for by using the prolongation from inspiring English sources

By using the prolongation algebra method Hone and Wang [38] gave a matrix Lax pair and many conserved densities and a bi-Hamiltonian structure of the Novikov equation and showed how it was related by a reciprocal transformation to a negative flow in the Sawada-Kotera hierarchy.

By using the prolongation algebra method, Hone and Wang [3] gave a matrix Lax pair and many conserved densities and a bi-Hamiltonian structure of the Novikov equation, and they showed how it was related by a reciprocal transformation to a negative flow in the Sawada-Kotera hierarchy.

By using the standard linear prolongation and restriction operators, the Galerkin condition leads to inaccurate coarse grid discretizations.

The expansion of the form of (2.10) by using the definition of the first prolongation of the Noether operator and relations (3.6 - 3.10) is written as follows: (3.11).

Finally, we estimated the prolongation of ICU stay using the disability model approach [ 19].

Notably, a statistically significant prolongation in survival (P=0.022) was found, as calculated by the All Pairwise Multiple Comparison Procedures using the Holm Sidak method.

Length of stay prolongation was calculated with R software (R foundation, Vienna, Austria), using the change LOS library.

First, the global pressure problem is solved using the multiscale finite volume (MSFV) method in combination with the multiscale restricted-smoothed basis (MsRSB) prolongation operator.

Both methods use the criteria of principal angles between subspaces spanned between the previous and current prolongation operators.

The Quinlans and their priest had been guided by "The Prolongation of Life," a statement issued by Pope Pius XII in 1957; it obligated Catholics to use only ordinary means, rather than extraordinary means, to extend life.

Figure 9 also shows the image-source, obtained by mirroring over (the prolongation of).