Sentence examples for by applying the generalized from inspiring English sources

Thirdly, by applying the generalized Taylor's formula, some error analysis is provided.

By applying the generalized path loss equation in (4), SINR at the receiver is given by: (25).

By applying the generalized Banach contraction principle, the monotone iterative method, and Krasnoselskii's fixed point theorem, some existence results of positive solutions are obtained.

In addition, we have listed the initial value problems, namely (3.1) and (3.2), and proved the uniqueness of solutions to these problems by applying the generalized Gronwall inequalities.

The effects of oil price shocks on the Pakistan Stock Exchange were explored by applying the generalized autoregressive conditional heteroskedasticity (GARCH) model.

By applying the generalized Halanay inequality, the stability results of nonlinear neutral functional differential equations (NFDEs) and nonlinear neutral delay integrodifferential equations (NDIDEs) are obtained.

The solution of this problem is obtained by applying the modified generalized Laguerre collocation method.

We further eliminate the cost and complexity associated with mesh generation by applying the interface-enriched generalized finite element method (IGFEM), which allows a non-conforming mesh to capture the discontinuous temperature gradient across the microchannels.

Comparison is made of the computed results applying the generalized ESCD method to those obtained by the Monte Carlo simulation (MCS).

By admitting the CM-II model, another important aspect before applying the generalized creep equation is how to vary the particle size experimentally.

An algorithm for approximating the analytic solution of Duffing type nonlinear integro-differential equation with integral boundary conditions is developed by applying the method of generalized quasilinearization.