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The derivatives are approximated using the central difference formula.

The displacement variables are approximated using the Ritz method.

The coefficients of the expansion are functions of (r, z), and they are approximated using the finite element method.

Two independent variables in the weak form, displacement and excess pore water pressure, are approximated using the same shape functions through PIM technique.

We consider an oracle model in which the values of the characteristic polynomials are approximated using the evaluations of the corresponding Boolean functions.

Also, the in-plane variations of the displacement components are approximated using the trigonometric series in the circumferential direction and the DQM in the axial direction.

The fractional time delay in the sensor to controller and controller to actuator channel is approximated using the Thiran approximation technique to design the sliding surface.

The integral can be approximated using the Laplace approximation, see (31– 31).

In addition, the P d for two-dimensional systems was approximated using the non-central/central approximation and provided in [18] following the results in [30].

which can be approximated using the simple absolute sum: (8).

The structural response is approximated using the same basis functions describing the geometry.