Sentence examples for by the corresponding linear from inspiring English sources

The increasing number of unknown coefficients when increasing the level approximation can be solved by the corresponding linear systems.

In the table, the nonlinear constraint in column 1 can be equivalently replaced by the corresponding linear constraints of column 3.

5, we show that, given any general initial perturbation, its nonlinear evolution is dominated by the corresponding linear dynamics along a fixed finite number of fastest growing modes.

The ion macroparticles (each representing a large number of real particles) are deposited on the grid by a cloud-in-cell method (linear weighting), and interpolation of the fields to the particle positions are done by the corresponding linear interpolation.

We address verification that, given any general perturbation of magnitude δ, its nonlinear evolution is dominated by the corresponding linear dynamics along a finite number of fixed fastest growing modes, over a time period of the order (ln(1/delta)).

To prevent the possible effect of unequal transfer on the results, the eccDNA signal was divided by the corresponding linear DNA signal.

As is shown in our theorem, they can be determined easily by solving the corresponding linear matrix inequalities.

By using Laplace transform methods, formula of solutions involving Mittag-Leffler functions (A_{alpha,beta}(w)), (alpha,betain(1,2)), (win R), and nonlocal terms of such equations are presented by studying the corresponding linear Langevin-type equations with two fractional derivatives.

∑ i = 1 p α i = 0 The b and α i, i=1,2⋯ p can be obtained by solving the corresponding linear system of the dual problem.

Under both models, parameters and hidden variables are estimated via maximum likelihood (ML) and BLUP of the unknowns is established by solving the corresponding linear kriging systems.

Percentages and means were compared using the likelihood ratio test and the F test, respectively, and homogeneity groups were determined when significant differences were found by using the corresponding linear contrasts.