Sentence examples for by applying the linearization from inspiring English sources

The conditional linearization of third-order ordinary differential equations in each case from Table 1 is presented by applying the linearization theorem of Ibragimov and Meleshko [7], and then all of nonlinear ordinary differential equations are transformed to the linear equation (u"'=0).

Then coupling in the three-phase system can be calculated by applying the harmonic linearization method.

The gain of the observer is designed by applying the cone complementary linearization method to the matrix inequality.

The admissible state feedback controller can be found by solving a sequential minimization problem subject to LMI constraints by applying the cone complementary linearization method.

Then, the explicit characterizations of the observer/controller gains are obtained by means of certain nonlinear matrix inequalities that can be effectively solved by applying the cone complementary linearization algorithm.

The clustering effect was taken into account by applying the Taylor series linearization variance estimation for complex survey data using svy: commands in the STATA 11 software (STATA Corp ,College Station, TX).

SAS survey procedures were used (SAS Institute Inc., version 9.3) by applying the Taylor series linearization method to calculate SEs.

This is accomplished by introducing the notion of S-poles, which are the poles of the quasilinear system obtained by applying the method of stochastic linearization to the system with saturation.

By applying the stochastic central difference method and statistical linearization technique, a recursive relation for the variance of displacement of a Duffing oscillator excited by a class of non-stationary random disturbances is obtained and presented in this paper.

The linearization of the model response is given by applying the chain rule to Equation (2) (12) with response sensitivity matrix and state-sensitivity matrix, which can be obtained by solving (13) with initial condition along the systems dynamics, which is known as the forward-sensitivity matrix equation.

The construction of the linear system for the implicit scheme was performed by applying the backward Euler on the left-hand side of the conservation equation and Newton-type linearization on the right-hand side.