Sentence examples for by using the multiplier from inspiring English sources

Furthermore, the conservation laws for the BKP equation are constructed by using the multiplier method.

Also, the conservation laws for the BKP equation were derived by using the multiplier method.

In 2008, Xu et al. [21] investigated the asymptotic behavior of solutions for (1.6) by using the multiplier method.

Furthermore, conservation laws for the system (1.1a) and (1.1b) were derived by using the multiplier method and the new conservation theorem.

And Park and Ha [20] studied the existence and uniqueness of solutions and uniform decay rates for the Klein-Gordon-type equation by using the multiplier technique.

By using the multiplier method and the integral estimate methods, we prove that the global strong solutions of the problem decay to zero exponentially as the time tends to infinity, under weaker conditions regarding the nonlinear term.

The restrictions on the zero dynamics are relaxed by using the Popov multiplier, which also reduces controller complexity.

The solution to the power allocation problem (P4) can be found by using the Lagrange multiplier technique.

We allowed for uncertainty in the copy number call when estimating individual odds ratios by using the ten multiply imputed datasets generated from the qPCR posterior probabilities [ 15], and averaging the estimates over those with the R mitools package [ 13].

The percentage of cells from each population was determined by flow cytometry (described below) and the absolute number of each cell population was calculated by using the percentage data multiplied by the isolated cells per gram of tissue.

Zn (II) concentrations in milk and yoghurt were determined by using the standard curves and multiplying the dilution factor.