Sentence examples for by using this relation from inspiring English sources

By using this relation in inequality (26), we get the required result.

By using this relation, it is possible to predict the degree of surface modification.

By using this relation, we will give the explicit forms of the Green functions.

The 3k unidentified parameters are estimated by the grid search, i.e., all possible values of frequency and phase (amplitude can be estimated using the assumed frequency and phase by using this relation; a j ̂ = Σ t x ( t ) sin ( ω j ̂ t + ϕ ̂ ) Σ t ( x ( t ) sin ( ω j ̂ t + ϕ ̂ ) ) 2 [140] are tested and the one maximizing the likelihood function (66) is selected as the best estimate.

By using this relations, the phase is α t ( k ) = ± π / 2 + β r ( k ).

Using this relation, by means of successive action of the raising operator a 1 + we can construct Landau levels for electron [18] with energies E n L = s n 2 n v F l H (3). and wave functions ψ n k ( r ) = 2 δ n 0 - 1 s n ϕ n - 1, k ( r ) ϕ n k ( r ).

By using this formalism, most of the relations for the coupled stretching bending problems can be organized into the forms of Stroh formalism for two-dimensional anisotropic elasticity problems.

Levi and Scimiterna in [4] show that the complex Burgers and the Kundu-Eckhaus equations are related by a Miura transformation, and they use this relation to discretize the Kundu-Eckhaus equation.

Then variance can be obtained by using the relation ( {mu}_2=lambda;frac{d}{ dlambda};{mu}_1^ ).

The value of the activation energy of each trap is determined by using the relation given by [6].

By using the relation of Young, the minimum of E leads to the Cassie Baxter relation: (5).