Sentence examples for been derived by using from inspiring English sources

In this section, we have presented only the final formulation of the gradient vector, which has been derived by using partial derivatives in analytical terms.

A procedure for choosing the safety factor for fatigue design has been derived by using first order approximation.

The equations of equilibrium of the nonlocal model have been derived by using the virtual displacement method.

However, coupling coefficient has been derived by using Henkel and Bessel function and assuming that cores of fibers are only touching each other.

The dynamic equations of this model have been derived by using the Hamilton method and considering the nonlinear inertia, curvature, piezoelectric and electrostatic terms.

The sine condition in the presence of spherical aberration has been derived by using this coordinate and its validity was later confirmed by practical lens designing.

The shape derivatives are derived by using a Lagrangian function and the adjoint method.

Here the results are derived by using augmented Lyapunov functionals.

Theoretical formulations are derived by using Hamilton's principle.

Governing equations are derived by using Hamilton's principle.

The dispersive equations are derived by using Bloch theorem.